bolton mechatronics

61
Chapter one Introducing Mechatronics Objectives The objectives of this chapter are that, after studying it, the reader should be able to: Explain what is meant by mechatronics and appreciate its relevance in engineering design. Explain what is meant by a system and define the elements of measurement systems. Describe the various forms and elements of open-loop and closed-loop control systems. Recognise the need for models of systems in order to predict their behaviour. The term mechatronics was ‘invented’ by a Japanese engineer in 1969, as a combination of ‘mecha’ from mechanisms and ‘tronics’ from electronics. The word now has a wider meaning, being used to describe a philosophy in engineering technology in which there is a co-ordinated, and concurrently developed, integration of mechanical engineering with electronics and intel- ligent computer control in the design and manufacture of products and processes. As a result, mechatronic products have many mechanical func- tions replaced with electronic ones. This results in much greater flexibility, easy redesign and reprogramming, and the ability to carry out automated data collection and reporting. A mechatronic system is not just a marriage of electrical and mechanical systems and is more than just a control system; it is a complete integration of all of them in which there is a concurrent approach to the design. In the design of cars, robots, machine tools, washing machines, cameras, and very many other machines, such an integrated and interdisciplinary approach to engineering design is increasingly being adopted. The integration across the traditional boundaries of mechanical engineering, electrical engineering, electronics and control engineering has to occur at the earliest stages of the design process if cheaper, more reliable, more flexible systems are to be developed. Mechatronics has to involve a concurrent approach to these disci- plines rather than a sequential approach of developing, say, a mechanical system, then designing the electrical part and the microprocessor part. Thus mechatronics is a design philosophy, an integrating approach to engineering. Mechatronics brings together areas of technology involving sensors and measurement systems, drive and actuation systems, and microprocessor sys- tems (Figure 1.1), together with the analysis of the behaviour of systems and control systems. That essentially is a summary of this book. This chapter is an introduction to the topic, developing some of the basic concepts in order to give a framework for the rest of the book in which the details will be developed. What is mechatronics? 1.1

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Page 1: Bolton Mechatronics

Chapter one Introducing Mechatronics

Objectives

The objectives of this chapter are that, after studying it, the reader should be able to: ● Explain what is meant by mechatronics and appreciate its relevance in engineering design. ● Explain what is meant by a system and define the elements of measurement systems.● Describe the various forms and elements of open-loop and closed-loop control systems.● Recognise the need for models of systems in order to predict their behaviour.

The term mechatronics was ‘invented’ by a Japanese engineer in 1969, as acombination of ‘mecha’ from mechanisms and ‘tronics’ from electronics.The word now has a wider meaning, being used to describe a philosophy inengineering technology in which there is a co-ordinated, and concurrentlydeveloped, integration of mechanical engineering with electronics and intel-ligent computer control in the design and manufacture of products andprocesses. As a result, mechatronic products have many mechanical func-tions replaced with electronic ones. This results in much greater flexibility,easy redesign and reprogramming, and the ability to carry out automateddata collection and reporting.

A mechatronic system is not just a marriage of electrical and mechanicalsystems and is more than just a control system; it is a complete integration ofall of them in which there is a concurrent approach to the design. In thedesign of cars, robots, machine tools, washing machines, cameras, and verymany other machines, such an integrated and interdisciplinary approach toengineering design is increasingly being adopted. The integration across thetraditional boundaries of mechanical engineering, electrical engineering,electronics and control engineering has to occur at the earliest stages of thedesign process if cheaper, more reliable, more flexible systems are to bedeveloped. Mechatronics has to involve a concurrent approach to these disci-plines rather than a sequential approach of developing, say, a mechanicalsystem, then designing the electrical part and the microprocessor part. Thusmechatronics is a design philosophy, an integrating approach to engineering.

Mechatronics brings together areas of technology involving sensors andmeasurement systems, drive and actuation systems, and microprocessor sys-tems (Figure 1.1), together with the analysis of the behaviour of systems andcontrol systems. That essentially is a summary of this book. This chapter is anintroduction to the topic, developing some of the basic concepts in order togive a framework for the rest of the book in which the details will be developed.

What ismechatronics?

1.1

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1.1.1 Examples of mechatronic systems

Consider the modern autofocus, auto-exposure camera. To use the camera allyou need to do is point it at the subject and press the button to take the pic-ture. The camera can automatically adjust the focus so that the subject is infocus and automatically adjust the aperture and shutter speed so that thecorrect exposure is given. You do not have to manually adjust focusing andaperture or shutter speed controls. Consider a truck smart suspension. Sucha suspension adjusts to uneven loading to maintain a level platform, adjuststo cornering, moving across rough ground, etc., to maintain a smooth ride.Consider an automated production line. Such a line may involve a number ofproduction processes which are all automatically carried out in the correctsequence and in the correct way with a reporting of the outcomes at eachstage in the process. The automatic camera, the truck suspension and theautomatic production line are examples of a marriage between electronics,control systems and mechanical engineering.

1.1.2 Embedded systems

The term embedded system is used where microprocessors are embeddedinto systems and it is this type of system we are generally concerned with inmechatronics. A microprocessor may be considered as being essentially a col-lection of logic gates and memory elements that are not wired up as individ-ual components but whose logical functions are implemented by means ofsoftware. As an illustration of what is meant by a logic gate, we might wantan output if input A AND input B are both giving on signals. This could beimplemented by what is termed an AND logic gate. An OR logic gate wouldgive an output when either input A OR input B is on. A microprocessor isthus concerned with looking at inputs to see if they are on or off, processingthe results of such an interrogation according to how it is programmed, andthen giving outputs which are either on or off. See Chapter 15 for a moredetailed discussion of microprocessors.

For a microprocessor to be used in a control system, it needs additionalchips to give memory for data storage and for input/output ports to enable it toprocess signals from and to the outside world. Microcontrollers are micro-processors with these extra facilities all integrated together on a single chip.

An embedded system is a microprocessor-based system that is designedto control a range of functions and is not designed to be programmed by theend user in the same way that a computer is. Thus, with an embedded system,the user cannot change what the system does by adding or replacing software.

2 CHAPTER 1 INTRODUCING MECHATRONICS

Figure 1.1 The basic elements

of a mechatronic system.

Mechanicalsystem

Digitalsensors

Analoguesensors

Digitalactuators

Analogueactuators

Microprocessorsystem for control

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As an illustration of the use of microcontrollers in a control system, amodern washing machine will have a microprocessor-based control system tocontrol the washing cycle, pumps, motor and water temperature. A moderncar will have microprocessors controlling such functions as anti-lock brakesand engine management. Other examples of embedded systems are autofocus,auto-exposure cameras, camcorders, cell phones, DVD players, electroniccard readers, photocopiers, printers, scanners, televisions and temperaturecontrollers.

The design process for any system can be considered as involving a numberof stages:

1 The need

The design process begins with a need from, perhaps, a customer or

client. This may be identified by market research being used to establish

the needs of potential customers.

2 Analysis of the problemThe first stage in developing a design is to find out the true nature of theproblem, i.e. analysing it. This is an important stage in that not definingthe problem accurately can lead to wasted time on designs that will notfulfil the need.

3 Preparation of a specificationFollowing the analysis, a specification of the requirements can be pre-pared. This will state the problem, any constraints placed on the solution,and the criteria which may be used to judge the quality of the design. Instating the problem, all the functions required of the design, togetherwith any desirable features, should be specified. Thus there might be astatement of mass, dimensions, types and range of motion required, accu-racy, input and output requirements of elements, interfaces, powerrequirements, operating environment, relevant standards and codes ofpractice, etc.

4 Generation of possible solutionsThis is often termed the conceptual stage. Outline solutions are pre-pared which are worked out in sufficient detail to indicate the means ofobtaining each of the required functions, e.g. approximate sizes, shapes,materials and costs. It also means finding out what has been done beforefor similar problems; there is no sense in reinventing the wheel.

5 Selections of a suitable solution The various solutions are evaluated and the most suitable one selected.Evaluation will often involve the representation of a system by a modeland then simulation to establish how it might react to inputs.

6 Production of a detailed design The detail of the selected design has now to be worked out. This mightrequire the production of prototypes or mock-ups in order to determinethe optimum details of a design.

7 Production of working drawings The selected design is then translated into working drawings, circuitdiagrams, etc., so that the item can be made.

1.2 THE DESIGN PROCESS 3

The designprocess

1.2

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It should not be considered that each stage of the design process just flows onstage by stage. There will often be the need to return to an earlier stage andgive it further consideration. Thus when at the stage of generating possiblesolutions there might be a need to go back and reconsider the analysis of theproblem.

1.2.1 Traditional and mechatronics designs

Engineering design is a complex process involving interactions betweenmany skills and disciplines. With traditional design, the approach was for themechanical engineer to design the mechanical elements, then the controlengineer to come along and design the control system. This gives what mightbe termed a sequential approach to the design. However, the basis of themechatronics approach is considered to lie in the concurrent inclusion of thedisciplines of mechanical engineering, electronics, computer technology andcontrol engineering in the approach to design. The inherent concurrency ofthis approach depends very much on system modelling and then simulationof how the model reacts to inputs and hence how the actual system mightreact to inputs.

As an illustration of how a multidisciplinary approach can aid in the solu-tion of a problem, consider the design of bathroom scales. Such scales mightbe considered only in terms of the compression of springs and a mechanismused to convert the motion into rotation of a shaft and hence movement of apointer across a scale; a problem that has to be taken into account in thedesign is that the weight indicated should not depend on the person’s posi-tion on the scales. However, other possibilities can be considered if we lookbeyond a purely mechanical design. For example, the springs might bereplaced by load cells with strain gauges and the output from them used witha microprocessor to provide a digital readout of the weight on an LEDdisplay. The resulting scales might be mechanically simpler, involving fewercomponents and moving parts. The complexity has, however, been trans-ferred to the software.

As a further illustration, the traditional design of the temperature controlfor a domestic central heating system has been the bimetallic thermostat in aclosed-loop control system. The bending of the bimetallic strip changes asthe temperature changes and is used to operate an on/off switch for the heat-ing system. However, a multidisciplinary solution to the problem might be touse a microprocessor-controlled system employing perhaps a thermodiode asthe sensor. Such a system has many advantages over the bimetallic thermostatsystem. The bimetallic thermostat is comparatively crude and the tempera-ture is not accurately controlled; also devising a method for having differenttemperatures at different times of the day is complex and not easily achieved.The microprocessor-controlled system can, however, cope easily with givingprecision and programmed control. The system is much more flexible. Thisimprovement in flexibility is a common characteristic of mechatronics systemswhen compared with traditional systems.

In designing mechatronic systems, one of the steps involved is the creationof a model of the system so that predictions can be made regarding its behaviourwhen inputs occur. Such models involve drawing block diagrams to represent

4 CHAPTER 1 INTRODUCING MECHATRONICS

Systems1.3

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systems. A system can be thought of as a box or block diagram which has aninput and an output and where we are concerned not with what goes oninside the box but with only the relationship between the output and theinput. The term modelling is used when we represent the behaviour of a realsystem by mathematical equations, such equations representing the relation-ship between the inputs and outputs from the system. For example, a springcan be considered as a system to have an input of a force F and an output ofan extension x (Figure 1.2(a)). The equation used to model the relationshipbetween the input and output might be , where k is a constant. Asanother example, a motor may be thought of as a system which has as itsinput electric power and as output the rotation of a shaft (Figure 1.2(b)).

A measurement system can be thought of as a box which is used formaking measurements. It has as its input the quantity being measured and itsoutput the value of that quantity. For example, a temperature measurementsystem, i.e. a thermometer, has an input of temperature and an output of anumber on a scale (Figure 1.2(c)).

1.3.1 Modelling systems

The response of any system to an input is not instantaneous. For example, forthe spring system described by Figure 1.2(a), though the relationshipbetween the input, force F, and output, extension x, was given as ,this only describes the relationship when steady-state conditions occur.When the force is applied it is likely that oscillations will occur before thespring settles down to its steady-state extension value (Figure 1.3). Theresponses of systems are functions of time. Thus, in order to know how systemsbehave when there are inputs to them, we need to devise models for systemswhich relate the output to the input so that we can work out, for a giveninput, how the output will vary with time and what it will settle down to.

As another example, if you switch on a kettle it takes some time for the

water in the kettle to reach boiling point (Figure 1.4). Likewise, when a

microprocessor controller gives a signal to, say, move the lens for focusing in

F = kx

F = kx

1.3 SYSTEMS 5

Figure 1.2 Examples of

systems: (a) spring, (b) motor,

(c) thermometer.

Output:

extension

Input:

force

Output:

rotation

Input:

electricpower

(a) (b)

(c)

Output:Input:

temp. numberon a scale

Spring Motor

Thermometer

Figure 1.3 The response to

an input for a spring.

0

Ext

ensi

on

Final readingSpring

Input:

extensionwhich changeswith time

force attime 0

Output:

Time

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an automatic camera then it takes time before the lens reaches its position for

correct focusing.

Often the relationship between the input and output for a system is

described by a differential equation. Such equations and systems are

discussed in Chapter 10.

1.3.2 Connected systems

In other than the simplest system, it is generally useful to consider it as a

series of interconnected blocks, each such block having a specific function.

We then have the output from one block becoming the input to the next

block in the system. In drawing a system in this way, it is necessary to recog-

nise that lines drawn to connect boxes indicate a flow of information in the

direction indicated by an arrow and not necessarily physical connections. An

example of such a connected system is a CD player. We can think of there

being three interconnected blocks: the CD deck which has an input of a CD

and an output of electrical signals, an amplifier which has an input of these

electrical signals, and an output of bigger electrical signals, and a speaker

which has an input of the electrical signals and an output of sound (Figure 1.5).

Another example of such a set of connected blocks is given in the next

section on measurement systems.

Of particular importance in any discussion of mechatronics are measurement

systems. Measurement systems can, in general, be considered to be made

up of three basic elements (as illustrated in Figure 1.6):

1 A sensor which responds to the quantity being measured by giving as itsoutput a signal which is related to the quantity. For example, a thermo-couple is a temperature sensor. The input to the sensor is a temperatureand the output is an e.m.f. which is related to the temperature value.

2 A signal conditioner takes the signal from the sensor and manipulates itinto a condition which is suitable either for display, or, in the case of acontrol system, for use to exercise control. Thus, for example, the output

6 CHAPTER 1 INTRODUCING MECHATRONICS

Figure 1.4 The response to an

input for a kettle system.

KettleInput:

temperatureof water

electricity

100°C

20°C0 2 min

Time

Tem

pera

tureOutput:

Figure 1.5 A CD player.

Input:

CD

Electricalsignals

Biggerelectricalsignals Output:

soundLoudspeakerAmplifierCD deck

Measurementsystems

1.4

Page 7: Bolton Mechatronics

from a thermocouple is a rather small e.m.f. and might be fed through anamplifier to obtain a bigger signal. The amplifier is the signal conditioner.

3 A display system where the output from the signal conditioner is dis-played. This might, for example, be a pointer moving across a scale or adigital readout.

As an example, consider a digital thermometer (Figure 1.7). This has an

input of temperature to a sensor, probably a semiconductor diode. The

potential difference across the sensor is, at constant current, a measure of the

temperature. This potential difference is then amplified by an operational

amplifier to give a voltage which can directly drive a display. The sensor and

operational amplifier may be incorporated on the same silicon chip.

Sensors are discussed in Chapter 2 and signal conditioners in Chapter 3.

Measurement systems involving all elements are discussed in Chapter 6.

A control system can be thought of as a system which can be used to:

1 Control some variable to some particular value, e.g. a central heating

system where the temperature is controlled to a particular value.

2 Control the sequence of events, e.g. a washing machine where when the dials

are set to, say, ‘white’ and the machine is then controlled to a particular

washing cycle, i.e. sequence of events, appropriate to that type of clothing.

3 Control whether an event occurs or not, e.g. a safety lock on a machine

where it cannot be operated until a guard is in position.

1.5.1 Feedback

Consider an example of a control system with which we are all individuallyinvolved. Your body temperature, unless you are ill, remains almost constantregardless of whether you are in a cold or hot environment. To maintain thisconstancy your body has a temperature control system. If your temperaturebegins to increase above the normal you sweat, if it decreases you shiver. Boththese are mechanisms which are used to restore the body temperature backto its normal value. The control system is maintaining constancy of temper-ature. The system has an input from sensors which tell it what the temperatureis and then compare this data with what the temperature should be and pro-vide the appropriate response in order to obtain the required temperature.

1.5 CONTROL SYSTEMS 7

Figure 1.6 A measurement

system and its constituent

elements. SensorSignal

conditioner Display

Quantitybeingmeasured

Valueof thequantity

Signal relatedto quantitymeasured

Signal in suitableform fordisplay

Figure 1.7 A digital

thermometer system.

Sensor Amplifier Display

Quantitybeingmeasured:

Valueof thequantity

Signal relatedto quantitymeasured:

Signal in suitableform fordisplay:

temperature potentialdifference

biggervoltage

Control systems1.5

Page 8: Bolton Mechatronics

This is an example of feedback control: signals are fed back from the output,i.e. the actual temperature, in order to modify the reaction of the body toenable it to restore the temperature to the ‘normal’ value. Feedback controlis exercised by the control system comparing the fed-back actual outputof the system with what is required and adjusting its output accordingly.Figure 1.8(a) illustrates this feedback control system.

One way to control the temperature of a centrally heated house is for ahuman to stand near the furnace on/off switch with a thermometer and switchthe furnace on or off according to the thermometer reading. That is a crudeform of feedback control using a human as a control element. The termfeedback is used because signals are fed back from the output in order tomodify the input.The more usual feedback control system has a thermostat orcontroller which automatically switches the furnace on or off according tothe difference between the set temperature and the actual temperature(Figure 1.8(b)). This control system is maintaining constancy of temperature.

If you go to pick up a pencil from a bench there is a need for you to use a con-trol system to ensure that your hand actually ends up at the pencil.This is doneby your observing the position of your hand relative to the pencil and makingadjustments in its position as it moves towards the pencil. There is a feedbackof information about your actual hand position so that you can modify your re-actions to give the required hand position and movement (Figure 1.8(c)).Thiscontrol system is controlling the positioning and movement of your hand.

Feedback control systems are widespread, not only in nature and thehome but also in industry. There are many industrial processes and machineswhere control, whether by humans or automatically, is required. For example,there is process control where such things as temperature, liquid level, fluidflow, pressure, etc. are maintained constant. Thus in a chemical process theremay be a need to maintain the level of a liquid in a tank to a particular level orto a particular temperature. There are also control systems which involveconsistently and accurately positioning a moving part or maintaining aconstant speed. This might be, for example, a motor designed to run at a

8 CHAPTER 1 INTRODUCING MECHATRONICS

Figure 1.8 Feedback control:

(a) human body temperature,

(b) room temperature with

central heating, (c) picking up a

pencil.

Requiredtemperature

Feedback of dataabout actual temperature

Bodytemperature

control system

Bodytemperature

Requiredtemperature

Feedback of dataabout actual temperature

RoomtemperatureFurnace and

its controlsystem

(a) (b)

Feedback of dataabout actual position

Control systemfor hand positionand movement

Hand movingtowardsthe pencil

The requiredhand position

(c)

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constant speed or perhaps a machining operation in which the position,speed and operation of a tool are automatically controlled.

1.5.2 Open- and closed-loop systems

There are two basic forms of control system, one being called open loop andthe other closed loop. The difference between these can be illustrated by asimple example. Consider an electric fire which has a selection switch whichallows a 1 kW or a 2 kW heating element to be selected. If a person used theheating element to heat a room, he or she might just switch on the 1 kWelement if the room is not required to be at too high a temperature. The roomwill heat up and reach a temperature which is only determined by the fact thatthe 1 kW element was switched on and not the 2 kW element. If there arechanges in the conditions, perhaps someone opening a window, there is noway the heat output is adjusted to compensate. This is an example of open-loop control in that there is no information fed back to the element to adjustit and maintain a constant temperature. The heating system with the heatingelement could be made a closed-loop system if the person has a thermometerand switches the 1 kW and 2 kW elements on or off, according to the differ-ence between the actual temperature and the required temperature, to main-tain the temperature of the room constant. In this situation there is feedback,the input to the system being adjusted according to whether its output is therequired temperature. This means that the input to the switch depends on thedeviation of the actual temperature from the required temperature, the differ-ence between them being determined by a comparison element – the personin this case. Figure 1.9 illustrates these two types of system.

An example of an everyday open-loop control system is the domestictoaster. Control is exercised by setting a timer which determines the lengthof time for which the bread is toasted. The brownness of the resulting toast isdetermined solely by this preset time. There is no feedback to control thedegree of browning to a required brownness.

To illustrate further the differences between open- and closed-loop systems,consider a motor. With an open-loop system the speed of rotation of the shaftmight be determined solely by the initial setting of a knob which affects the

1.5 CONTROL SYSTEMS 9

(a)

(b)

Input:

decision toswitch onor off

SwitchElectricpower

Electricfire

Output:

a temperaturechange

Controller,i.e. person Hand

activated

SwitchElectric

fireOutput:

a constanttemperature

MeasuringdeviceFeedback of temperature-related signal

requiredtemperature

Comparisonelement

Deviationsignal

Electricpower

Input: Controller,i.e. person Hand

activated

Figure 1.9 Heating a room: (a) an open-loop system, (b) a closed-loop system.

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voltage applied to the motor. Any changes in the supply voltage, the charac-teristics of the motor as a result of temperature changes, or the shaft load willchange the shaft speed but not be compensated for. There is no feedbackloop. With a closed-loop system, however, the initial setting of the controlknob will be for a particular shaft speed and this will be maintained by feed-back, regardless of any changes in supply voltage, motor characteristics orload. In an open-loop control system the output from the system has noeffect on the input signal. In a closed-loop control system the output doeshave an effect on the input signal, modifying it to maintain an output signalat the required value.

Open-loop systems have the advantage of being relatively simple and conse-quently low cost with generally good reliability. However, they are often inaccu-rate since there is no correction for error. Closed-loop systems have theadvantage of being relatively accurate in matching the actual to the required val-ues. They are, however, more complex and so more costly with a greater chanceof breakdown as a consequence of the greater number of components.

1.5.3 Basic elements of a closed-loop system

Figure 1.10 shows the general form of a basic closed-loop system. It consists

of the following elements:

1 Comparison elementThis compares the required or reference value of the variable conditionbeing controlled with the measured value of what is being achieved and pro-duces an error signal. It can be regarded as adding the reference signal,which is positive, to the measured value signal, which is negative in this case:

error signal reference value signal measured value signal

The symbol used, in general, for an element at which signals are summedis a segmented circle, inputs going into segments. The inputs are alladded, hence the feedback input is marked as negative and the referencesignal positive so that the sum gives the difference between the signals. Afeedback loop is a means whereby a signal related to the actual conditionbeing achieved is fed back to modify the input signal to a process. Thefeedback is said to be negative feedback when the signal which is fedback subtracts from the input value. It is negative feedback that is re-quired to control a system. Positive feedback occurs when the signal fedback adds to the input signal.

2 Control elementThis decides what action to take when it receives an error signal. It maybe, for example, a signal to operate a switch or open a valve. The control

-=

10 CHAPTER 1 INTRODUCING MECHATRONICS

Measuringdevice

ProcessCorrection

unitControl

unitError signal

Measured value

Controlledvariable

Referencevalue

Comparisonelement

Figure 1.10 The elements of a closed-loop control system.

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plan being used by the element may be just to supply a signal whichswitches on or off when there is an error, as in a room thermostat, or per-haps a signal which proportionally opens or closes a valve according to thesize of the error. Control plans may be hard-wired systems in which thecontrol plan is permanently fixed by the way the elements are connectedtogether, or programmable systems where the control plan is storedwithin a memory unit and may be altered by reprogramming it.Controllers are discussed in Chapter 11.

3 Correction element

The correction element produces a change in the process to correct or

change the controlled condition. Thus it might be a switch which switches

on a heater and so increases the temperature of the process or a valve which

opens and allows more liquid to enter the process. The term actuator is

used for the element of a correction unit that provides the power to carry

out the control action. Correction units are discussed in Chapters 5 and 6.

4 Process element

The process is what is being controlled. It could be a room in a house with

its temperature being controlled or a tank of water with its level being

controlled.

5 Measurement element

The measurement element produces a signal related to the variable condition

of the process that is being controlled. It might be, for example, a switch

which is switched on when a particular position is reached or a thermo-

couple which gives an e.m.f. related to the temperature.

With the closed-loop system illustrated in Figure 1.10 for a person

controlling the temperature of a room, the various elements are:

Controlled variable – the room temperature Reference value – the required room temperature Comparison element – the person comparing the measured value

with the required value of temperature Error signal – the difference between the measured and

required temperatures Control unit – the person Correction unit – the switch on the fire Process – the heating by the fire Measuring device – a thermometer

An automatic control system for the control of the room temperature

could involve a thermostatic element which is sensitive to temperature and

switches on when the temperature falls below the set value and off when it

reaches it (Figure 1.11). This temperature-sensitive switch is then used to

switch on the heater. The thermostatic element has the combined functions

of comparing the required temperature value with that occurring and then

controlling the operation of a switch. It is often the case that elements in control

systems are able to combine a number of functions.

Figure 1.12 shows an example of a simple control system used to maintain

a constant water level in a tank. The reference value is the initial setting of

the lever arm arrangement so that it just cuts off the water supply at the

1.5 CONTROL SYSTEMS 11

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required level. When water is drawn from the tank the float moves down-

wards with the water level. This causes the lever arrangement to rotate and so

allows water to enter the tank. This flow continues until the ball has risen to

such a height that it has moved the lever arrangement to cut off the water

supply. It is a closed-loop control system with the elements being:

Controlled variable – water level in tankReference value – initial setting of the float and lever positionComparison element – the leverError signal – the difference between the actual and initial

settings of the lever positions Control unit – the pivoted lever Correction unit – the flap opening or closing the water supplyProcess – the water level in the tankMeasuring device – the floating ball and lever

The above is an example of a closed-loop control system involving just

mechanical elements. We could, however, have controlled the liquid level by

means of an electronic control system. We thus might have had a level sensor

12 CHAPTER 1 INTRODUCING MECHATRONICS

Switch HeaterOutput:

requiredtemperature

MeasuringdeviceFeedback of temperature-related signal

requiredtemperature

Comparisonelement

Deviationsignal

Electricpower

Input:Controller

Thermostatic element

Measuringdevice

ProcessCorrection

unitControl

unitError signal

Measured value

Controlledvariable:water level

Referencevalue: theinitial setting

Comparisonelement: the lever Pivoted lever The flap

The floating ball and lever

Water level in tank

Hollow ball

LeverWater input

Pivot

Figure 1.11 Heating a room: a closed-loop system.

Figure 1.12 The automatic control of water level.

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supplying an electrical signal which is used, after suitable signal condition-

ing, as an input to a computer where it is compared with a set value signal

and the difference between them, the error signal, then used to give an

appropriate response from the computer output. This is then, after suitable

signal conditioning, used to control the movement of an actuator in a flow

control valve and so determine the amount of water fed into the tank.

Figure 1.13 shows a simple automatic control system for the speed of

rotation of a shaft. A potentiometer is used to set the reference value, i.e.

what voltage is supplied to the differential amplifier as the reference value for

the required speed of rotation. The differential amplifier is used both to

compare and amplify the difference between the reference and feedback

values, i.e. it amplifies the error signal. The amplified error signal is then fed

to a motor which in turn adjusts the speed of the rotating shaft. The speed of

the rotating shaft is measured using a tachogenerator, connected to the rotating

shaft by means of a pair of bevel gears. The signal from the tachogenerator is

then fed back to the differential amplifier:

Controlled variable – speed of rotation of shaft Reference value – setting of slider on potentiometerComparison element – differential amplifierError signal – the difference between the output from

the potentiometer and that from thetachogenerator system

Control unit – the differential amplifierCorrection unit – the motorProcess – the rotating shaft Measuring device – the tachogenerator

1.5 CONTROL SYSTEMS 13

Differentialamplifier

Motor

Bevel gear

Rotatingshaft

TachogeneratorSpeed measurement

Potentiometerfor setting

reference value

Amplifies differencebetween reference

and feedback values

Measurementtachogenerator

Process,rotating shaftMotorAmplifier

Referencevalue

Output:

constantspeedshaft

Differential amplifier

D.C.supply

Figure 1.13 Shaft speed control.

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1.5.4 Analogue and digital control systems

Analogue systems are ones where all the signals are continuous functionsof time and it is the size of the signal which is a measure of the variable(Figure 1.14(a)). The examples so far discussed in this chapter are such sys-tems. Digital signals can be considered to be a sequence of on/off signals,the value of the variable being represented by the sequence of on/off pulses(Figure 1.14(b)).

Figure 1.15 shows the basic elements of a digital closed-loop controlsystem; compare it with the analogue closed-loop system in Figure 1.10.Analogue-to-digital converter (ADC) and digital-to-analogue converter(DAC) elements are included in the loop in order that the microprocessor sys-tem can be supplied with digital signals from analogue measurement systemsand its output of digital signals can be converted to analogue form to operatethe correction units. The microprocessor system combines the function ofcomparison and controller.

An example of such a system might be an automatic control system for thecontrol of the room temperature involving a temperature sensor giving ananalogue signal, which, after suitable signal conditioning to make it a digitalsignal, is inputted to the microprocessor system where it is compared withthe set value and an error signal generated. This is then acted on by themicroprocessor system to give at its output a digital signal, which, after suit-able signal conditioning to give an analogue equivalent, might be used tocontrol a heater and hence the room temperature. Such a system can readilybe programmed to give different temperatures at different times of the day.

As a further illustration of a digital control system, Figure 1.16 shows oneform a digital control system for the speed of a motor might take. Comparethis with the analogue system in Figure 1.13.

14 CHAPTER 1 INTRODUCING MECHATRONICS

Figure 1.14 Signals:

(a) analogue, (b) digital.

Time Time

Sign

al

Sign

al

0 0

(a) (b)

ProcessCorrection

unitControllerErrorsignal

Measured value

Controlledvariable

Referencevalue

Comparisonelement

Microprocessor system

DAC

ADCMeasuring

device

Figure 1.15 The elements of a digital closed-loop control system.

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1.5.5 Sequential controllers

There are many situations where control is exercised by items being switchedon or off at particular preset times or values in order to control processes andgive a step sequence of operations. For example, after step 1 is complete thenstep 2 starts. When step 2 is complete then step 3 starts, etc.

The term sequential control is used when control is such that actionsare strictly ordered in a time- or event-driven sequence. Such control couldbe obtained by an electric circuit with sets of relays or cam-operated switcheswhich are wired up in such a way as to give the required sequence.Such hard-wired circuits are now more likely to have been replaced by amicroprocessor-controlled system, with the sequencing being controlled bymeans of a software program.

As an illustration of sequential control, consider the domestic washingmachine. A number of operations have to be carried out in the correctsequence. These may involve a pre-wash cycle when the clothes in the drumare given a wash in cold water, followed by a main wash cycle when they arewashed in hot water, then a rinse cycle when they are rinsed with cold watera number of times, followed by spinning to remove water from the clothes.Each of these operations involves a number of steps. For example, a pre-washcycle involves opening a valve to fill the machine drum to the required level,closing the valve, switching on the drum motor to rotate the drum for aspecific time, and operating the pump to empty the water from the drum.The operating sequence is called a program, the sequence of instructions ineach program being predefined and ‘built’ into the controller used.

Figure 1.17 shows the basic washing machine system and gives a roughidea of its constituent elements. The system that used to be used for thewashing machine controller was a mechanical system which involved a set ofcam-operated switches, i.e. mechanical switches, a system which is readilyadjustable to give a greater variety of programs.

Figure 1.18 shows the basic principle of one such switch. When themachine is switched on, a small electric motor slowly rotates its shaft, givingan amount of rotation proportional to time. Its rotation turns the controllercams so that each in turn operates electrical switches and so switches oncircuits in the correct sequence. The contour of a cam determines the time atwhich it operates a switch. Thus the contours of the cams are the means bywhich the program is specified and stored in the machine. The sequence ofinstructions and the instructions used in a particular washing program aredetermined by the set of cams chosen. With modern washing machinesthe controller is a microprocessor and the program is not supplied bythe mechanical arrangement of cams but by a software program. The

1.5 CONTROL SYSTEMS 15

Measurementtachogenerator

Referencevalue

Output:constant speed

MotorAmplifierProcess,

rotating shaftMicro-

processor DACADC

Figure 1.16 Shaft speed control.

Page 16: Bolton Mechatronics

microprocessor-controlled washing machine can be considered an exampleof a mechatronics approach in that a mechanical system has become integratedwith electronic controls. As a consequence, a bulky mechanical system isreplaced by a much more compact microprocessor.

For the pre-wash cycle an electrically operated valve is opened when acurrent is supplied and switched off when it ceases. This valve allows coldwater into the drum for a period of time determined by the profile of the camor the output from the microprocessor used to operate its switch. However,since the requirement is a specific level of water in the washing machinedrum, there needs to be another mechanism which will stop the water goinginto the tank, during the permitted time, when it reaches the required level.A sensor is used to give a signal when the water level has reached the presetlevel and give an output from the microprocessor which is used to switch offthe current to the valve. In the case of a cam-controlled valve, the sensoractuates a switch which closes the valve admitting water to the washingmachine drum. When this event is completed the microprocessor, or therotation of the cams, initiates a pump to empty the drum.

16 CHAPTER 1 INTRODUCING MECHATRONICS

Waterlevel

Watertemperature

Drumspeed

Doorclosed

Feedback from outputs of water level, water temperature, drum speed and door closed

Outputs

Controlunit

Pump

Valve

Heater

Motor

Correction elements

Washingmachine

drum

ProcessProgram

Clock

InputsFigure 1.17 Washing machine

system.

Switchcontacts

Cam

Curved partgives switch

closed

A flat givesswitch open

Rotation of the cam closingthe switch contacts

Figure 1.18 Cam-operated

switch.

Page 17: Bolton Mechatronics

For the main wash cycle, the microprocessor gives an output which startswhen the pre-wash part of the program is completed; in the case of the cam-operated system the cam has a profile such that it starts in operation whenthe pre-wash cycle is completed. It switches a current into a circuit to open avalve to allow cold water into the drum. This level is sensed and the watershut off when the required level is reached. The microprocessor or cams thensupply a current to activate a switch which applies a larger current to anelectric heater to heat the water. A temperature sensor is used to switch offthe current when the water temperature reaches the preset value. The micro-processor or cams then switch on the drum motor to rotate the drum. Thiswill continue for the time determined by the microprocessor or cam profilebefore switching off. Then the microprocessor or a cam switches on thecurrent to a discharge pump to empty the water from the drum.

The rinse part of the operation is now switched as a sequence of signals toopen valves which allow cold water into the machine, switch it off, operatethe motor to rotate the drum, operate a pump to empty the water from thedrum, and repeat this sequence a number of times.

The final part of the operation is when the microprocessor or a cam switcheson just the motor, at a higher speed than for the rinsing, to spin the clothes.

In many simple systems there might be just an embedded microcontroller,this being a microprocessor with memory all integrated on one chip, which hasbeen specifically programmed for the task concerned. A more adaptable formis the programmable logic controller (PLC). This is a microprocessor-based controller which uses programmable memory to store instructions andto implement functions such as logic, sequence, timing counting and arith-metic to control events and can be readily reprogrammed for different tasks.Figure 1.19 shows the control action of a programmable logic controller, theinputs being signals from, say, switches being closed and the program usedto determine how the controller should respond to the inputs and the outputit should then give.

Programmable logic controllers are widely used in industry where on/offcontrol is required. For example, they might be used in process controlwhere a tank of liquid is to be filled and then heated to a specific temperaturebefore being emptied. The control sequence might thus be:

1 Switch on pump to move liquid into the tank.2 Switch off pump when a level detector gives the on signal, so indicating

that the liquid has reached the required level. 3 Switch on heater.4 Switch off heater when a temperature sensor gives the on signal to indicate

the required temperature has been reached.

1.6 PROGRAMMABLE LOGIC CONTROLLER 17

Control program

OutputsInputs

ABCD

PQR

S

Controller

Figure 1.19 Programmable

logic controller.

Programmablelogic controller

1.6

Page 18: Bolton Mechatronics

5 Switch on pump to empty the liquid from the container. 6 Switch off pump when a level detector gives an on signal to indicate that

the tank is empty.

See Chapter 21 for a more detailed discussion of programmable logiccontrollers and examples of their use.

Mechatronics brings together the technology of sensors and measurementssystems, embedded microprocessor systems, actuators and engineeringdesign. The following are examples of mechatronic systems and illustratehow microprocessor-based systems have been able not only to carry out tasksthat previously were done ‘mechanically’ but also to do tasks that were noteasily automated before.

1.7.1 The digital camera and autofocus

A digital camera is likely to have an autofocus control system. A basic system

used with less expensive cameras is an open-loop system (Figure 1.20(a)).

When the photographer presses the shutter button, a transducer on the front

of the camera sends pulses of infrared (IR) light towards the subject of the

photograph. The infrared pulses bounce off the subject and are reflected

back to the camera where the same transducer picks them up. For each metre

the subject is distant from the camera, the round-trip is about 6 ms. The time

difference between the output and return pulses is detected and fed to a

microprocessor. This has a set of values stored in its memory and so gives an

output which rotates the lens housing and moves the lens to a position where

the object is in focus. This type of autofocus can only be used for distances

up to about 10 m as the returning infrared pulses are too weak at greater

18 CHAPTER 1 INTRODUCING MECHATRONICS

IR pulsesent out

Return IRpulse

Micro-processor

Signalconditioning Motor

Lensposition

Shutterbutton pressed

IR pulses

(a)

(b)

MotorIR pulsesent out

Micro-processor

Signalconditioning

Masked IRdetector

Lensand mask

IR pulses

Figure 1.20 Autofocus.

Examples ofmechatronic

systems

1.7

Page 19: Bolton Mechatronics

distances. Thus for greater distances the microprocessor gives an output

which moves the lens to an infinity setting.A system used with more expensive cameras involves triangulation

(Figure 1.20(b)). Pulses of infrared radiation are sent out and the reflectedpulses are detected not by the same transducer that was responsible for thetransmission but by another transducer. However, initially this transducerhas a mask across it. The microprocessor thus gives an output which causesthe lens to move and simultaneously the mask to move across the trans-ducer. The mask contains a slot which is moved across the face of the trans-ducer. The movement of the lens and the slot continues until the returningpulses are able to pass through the slot and impact on the transducer. Thereis then an output from the transducer which leads the microprocessor to stopthe movement of the lens, and so give the in-focus position.

1.7.2 The engine management system

The engine management system of a car is responsible for managing the igni-tion and fuelling requirements of the engine. With a four-stroke internalcombustion engine there are several cylinders, each of which has a pistonconnected to a common crankshaft and each of which carries out a four-stroke sequence of operations (Figure 1.21).

When the piston moves down a valve opens and the air–fuel mixture isdrawn into the cylinder. When the piston moves up again the valve closes andthe air–fuel mixture is compressed. When the piston is near the top of thecylinder the spark plug ignites the mixture with a resulting expansion of thehot gases. This expansion causes the piston to move back down again andso the cycle is repeated. The pistons of each cylinder are connected to acommon crankshaft and their power strokes occur at different times so thatthere is continuous power for rotating the crankshaft.

The power and speed of the engine are controlled by varying the ignitiontiming and the air–fuel mixture. With modern car engines this is done by amicroprocessor. Figure 1.22 shows the basic elements of a microprocessor

1.7 EXAMPLES OF MECHATRONIC SYSTEMS 19

Valve opensfor air-fuel

intake

Intake stroke Compression stroke Power stroke

Spark for ignitionValve opensto ventexhaustgases

Exhaust stroke

Cam-shaft

Piston

Hot gasesexpand

Mixturecompressed

Air-fuelmixture

Figure 1.21 Four-stroke sequence.

Page 20: Bolton Mechatronics

control system. For ignition timing, the crankshaft drives a distributor whichmakes electrical contacts for each spark plug in turn and a timing wheel. Thistiming wheel generates pulses to indicate the crankshaft position. The micro-processor then adjusts the timing at which high-voltage pulses are sent to thedistributor so they occur at the ‘right’ moments of time. To control theamount of air–fuel mixture entering a cylinder during the intake strokes,the microprocessor varies the time for which a solenoid is activated toopen the intake valve on the basis of inputs received of the engine tempera-ture and the throttle position. The amount of fuel to be injected into the airstream can be determined by an input from a sensor of the mass rate of airflow, or computed from other measurements, and the microprocessor thengives an output to control a fuel injection valve. Note that the above is a verysimplistic indication of engine management.

Summary

Mechatronics is a co-ordinated, and concurrently developed, integration ofmechanical engineering with electronics and intelligent computer control inthe design and manufacture of products and processes. It involves the bring-ing together of a number of technologies: mechanical engineering, electronicengineering, electrical engineering, computer technology and control engi-neering. Mechatronics provides an opportunity to take a new look at problems,with engineers not just seeing a problem in terms of mechanical principles buthaving to see it in terms of a range of technologies. The electronics, etc.,should not be seen as a bolt-on item to existing mechanical hardware. Amechatronics approach needs to be adopted right from the design phase.

Microprocessors are generally involved in mechatronics systems andthese are embedded. An embedded system is one that is designed to controla range of functions and is not designed to be programmed by the end userin the same way that a computer is. Thus, with an embedded system, the usercannot change what the system does by adding or replacing software.

20 CHAPTER 1 INTRODUCING MECHATRONICS

Engine speed sensor

Crankshaft position sensor

Spark timing

Air–fuel mixture solenoid

Engine temperature sensor

Throttle position sensor

Microprocessor system

Spark timing feedback sensor

Mass air flow sensor

Fuel injection valve

Engine

Figure 1.22 Elements of an

engine management system.

Page 21: Bolton Mechatronics

A system can be thought of as a box or block diagram which has an inputand an output and where we are concerned not with what goes on inside thebox but with only the relationship between the output and the input.

In order to predict how systems behave when there are inputs to them, weneed to devise models which relate the output to the input so that we canwork out, for a given input, how the output will vary with time.

Measurement systems can, in general, be considered to be made up ofthree basic elements: sensor, signal conditioner and display.

There are two basic forms of control system: open loop and closedloop. With closed loop there is feedback, a system containing a comparisonelement, a control element, correction element, process element and thefeedback involving a measurement element.

Problems

1.1 Identify the sensor, signal conditioner and display elements in the measurementsystems of (a) a mercury-in-glass thermometer, (b) a Bourdon pressure gauge.

1.2 Explain the difference between open- and closed-loop control.

1.3 Identify the various elements that might be present in a control system involv-ing a thermostatically controlled electric heater.

1.4 The automatic control system for the temperature of a bath of liquid consistsof a reference voltage fed into a differential amplifier. This is connected to arelay which then switches on or off the electrical power to a heater in theliquid. Negative feedback is provided by a measurement system which feeds avoltage into the differential amplifier. Sketch a block diagram of the systemand explain how the error signal is produced.

1.5 Explain the function of a programmable logic controller.

1.6 Explain what is meant by sequential control and illustrate your answer by anexample.

1.7 State steps that might be present in the sequential control of a dishwasher.

1.8 Compare and contrast the traditional design of a watch with that of themechatronics-designed product involving a microprocessor.

1.9 Compare and contrast the control system for the domestic central heating sys-tem involving a bimetallic thermostat and that involving a microprocessor.

PROBLEMS 21

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Chapter two Sensors and Transducers

Objectives

The objectives of this chapter are that, after studying it, the reader should be able to: ● Describe the performance of commonly used sensors using terms such as range, span, error, accuracy,

sensitivity, hysteresis and non-linearity error, repeatability, stability, dead band, resolution, outputimpedance, response time, time constant, rise time and settling time.

● Evaluate sensors used in the measurement of displacement, position and proximity, velocity andmotion, force, fluid pressure, liquid flow, liquid level, temperature, and light intensity.

● Explain the problem of bouncing when mechanical switches are used for inputting data and how itmight be overcome.

The term sensor is used for an element which produces a signal relatingto the quantity being measured.Thus in the case of, say, an electrical resistancetemperature element, the quantity being measured is temperature and the sen-sor transforms an input of temperature into a change in resistance. The termtransducer is often used in place of the term sensor. Transducers are definedas elements that when subject to some physical change experience a relatedchange. Thus sensors are transducers. However, a measurement system mayuse transducers, in addition to the sensor, in other parts of the system to con-vert signals in one form to another form. A sensor/transducer is said to beanalogue if it gives an output which is analogue and so changes in a contin-uous way and typically has an output whose size is proportional to the size ofthe variable being measured. The term digital is used if the systems giveoutputs which are digital in nature, i.e. a sequence of essentially on/off signalswhich spell out a number whose value is related to the size of the variablebeing measured.

This chapter is about transducers and in particular those used as sensors.The terminology that is used to specify the performance characteristicsof transducers is defined and examples of transducers commonly used inengineering are discussed.

2.1.1 Smart sensors

Some sensors come combined with their signal conditioning all in the samepackage. Such an integrated sensor does still, however, require further dataprocessing. However, it is possible to have the sensor and signal conditioning

Sensors andtransducers

2.1

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2.2 PERFORMANCE TERMINOLOGY 23

combined with a microprocessor all in the same package. Such an arrangementis termed a smart sensor. A smart sensor is able to have such functions as theability to compensate for random errors, to adapt to changes in the environ-ment, give an automatic calculation of measurement accuracy, adjust fornon-linearities to give a linear output, self-calibrate and give self-diagnosis offaults.

Such sensors have their own standard, IEEE 1451, so that smart sensorsconforming to this standard can be used in a ‘plug-and-play’ manner, hold-ing and communicating data in a standard way. Information is stored in theform of a TEDS (Transducer Electronic Datasheet), generally in EEPROM,and identifies each device and gives calibration data.

The following terms are used to define the performance of transducers, andoften measurement systems as a whole.

1 Range and spanThe range of a transducer defines the limits between which the input canvary. The span is the maximum value of the input minus the minimumvalue. Thus, for example, a load cell for the measurement of forces mighthave a range of 0 to 50 kN and a span of 50 kN.

2 Error Error is the difference between the result of the measurement and thetrue value of the quantity being measured:

error measured value true value

Thus if a measurement system gives a temperature reading of 25 whenthe actual temperature is 24 , then the error is 1 . If the actual tem-perature had been 26 then the error would have been 1 . A sensormight give a resistance change of when the true change shouldhave been . The error is .

3 Accuracy Accuracy is the extent to which the value indicated by a measurement sys-tem might be wrong. It is thus the summation of all the possible errors thatare likely to occur, as well as the accuracy to which the transducer has beencalibrated. A temperature-measuring instrument might, for example, bespecified as having an accuracy of 2 . This would mean that the read-ing given by the instrument can be expected to lie within plus or minus2 of the true value. Accuracy is often expressed as a percentage of thefull range output or full-scale deflection. The percentage of full-scaledeflection term results from when the outputs of measuring systems weredisplayed almost exclusively on a circular or linear scale. A sensor might,for example, be specified as having an accuracy of 5% of full range out-put. Thus if the range of the sensor was, say, 0 to 200 , then the readinggiven can be expected to be within plus or minus 10 of the true reading.

4 Sensitivity The sensitivity is the relationship indicating how much output there is perunit input, i.e. output/input. For example, a resistance thermometermay have a sensitivity of / . This term is also frequently usedto indicate the sensitivity to inputs other than that being measured,

°C0.5 Æ

°C°C

;

°C

°C;

-0.3 Æ10.5 Æ10.2 Æ

°C-°C°C+°C

°C

-=

Performanceterminology

2.2

Page 24: Bolton Mechatronics

24 CHAPTER 2 SENSORS AND TRANSDUCERS

i.e. environmental changes. Thus there can be the sensitivity of thetransducer to temperature changes in the environment or perhaps fluctu-ations in the mains voltage supply. A transducer for the measurement ofpressure might be quoted as having a temperature sensitivity ofof the reading per change in temperature.

5 Hysteresis errorTransducers can give different outputs from the same value of quantitybeing measured according to whether that value has been reached by acontinuously increasing change or a continuously decreasing change. Thiseffect is called hysteresis. Figure 2.1 shows such an output with the hys-teresis error as the maximum difference in output for increasing anddecreasing values.

°C;0.1%

Figure 2.1 Hysteresis.

Decreasing

Increasing

Error

Value of measured quantity0

Out

put

6 Non-linearity error For many transducers a linear relationship between the input and outputis assumed over the working range, i.e. a graph of output plotted againstinput is assumed to give a straight line. Few transducers, however, have atruly linear relationship and thus errors occur as a result of the assump-tion of linearity. The error is defined as the maximum difference from thestraight line. Various methods are used for the numerical expression of thenon-linearity error. The differences occur in determining the straight linerelationship against which the error is specified. One method is to drawthe straight line joining the output values at the end points of the range;another is to find the straight line by using the method of least squares todetermine the best fit line when all data values are considered equallylikely to be in error; another is to find the straight line by using themethod of least squares to determine the best fit line which passesthrough the zero point. Figure 2.2 illustrates these three methods andhow they can affect the non-linearity error quoted. The error is generallyquoted as a percentage of the full range output. For example, a transducerfor the measurement of pressure might be quoted as having a non-linearityerror of 0.5% of the full range.

7 Repeatability/reproducibility The terms repeatability and reproducibility of a transducer are used todescribe its ability to give the same output for repeated applications of thesame input value. The error resulting from the same output not being

;

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2.2 PERFORMANCE TERMINOLOGY 25

given with repeated applications is usually expressed as a percentage ofthe full range output:

A transducer for the measurement of angular velocity typically might bequoted as having a repeatability of of the full range at a partic-ular angular velocity.

8 Stability The stability of a transducer is its ability to give the same output whenused to measure a constant input over a period of time. The term driftis often used to describe the change in output that occurs over time. Thedrift may be expressed as a percentage of the full range output. The termzero drift is used for the changes that occur in output when there iszero input.

9 Dead band/time The dead band or dead space of a transducer is the range of input val-ues for which there is no output. For example, bearing friction in aflowmeter using a rotor might mean that there is no output until theinput has reached a particular velocity threshold. The dead time is thelength of time from the application of an input until the output beginsto respond and change.

10 Resolution When the input varies continuously over the range, the output signals forsome sensors may change in small steps. A wire-wound potentiometer isan example of such a sensor, the output going up in steps as the poten-tiometer slider moves from one wire turn to the next. The resolution isthe smallest change in the input value that will produce an observablechange in the output. For a wire-wound potentiometer the resolutionmight be specified as, say, or perhaps a percentage of the full-scaledeflection. For a sensor giving a digital output the smallest change in out-put signal is 1 bit. Thus for a sensor giving a data word of N bits, i.e. atotal of bits, the resolution is generally expressed as .1>2N2N

0.5°

;0.01%

repeatability =max. - min. values given

full range* 100

Figure 2.2 Non-linearity error using: (a) end-range values, (b) best straight line for all values,

(c) best straight line through zero point.

ErrorError

Input %

(a)

0 100

100

Out

put %

of r

ange

Input %

(b)

0 100

100

Out

put %

of r

ange

Error

Input %

(c)

0 100

100

Out

put %

of r

ange

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26 CHAPTER 2 SENSORS AND TRANSDUCERS

11 Output impedance When a sensor giving an electrical output is interfaced with an elec-tronic circuit it is necessary to know the output impedance since thisimpedance is being connected in either series or parallel with that cir-cuit. The inclusion of the sensor can thus significantly modify thebehaviour of the system to which it is connected. See Section 6.1.1 fora discussion of loading.

To illustrate the above, consider the significance of the terms in the follow-ing specification of a strain gauge pressure transducer:

Ranges: 70 to 1000 kPa, 2000 to 70 000 kPaSupply voltage: 10 V d.c. or a.c. r.m.s.Full range output: 40 mVNon-linearity and hysteresis: full range outputTemperature range: to when operatingThermal zero shift: 0.030% full range output/

The range indicates that the transducer can be used to measure pressuresbetween 70 and 1000 kPa or 2000 and 70 000 kPa. It requires a supply of 10 Vd.c. or a.c. r.m.s. for its operation and will give an output of 40 mV when thepressure on the lower range is 1000 kPa and on the upper range 70 000 kPa.Non-linearity and hysteresis will lead to errors of of 1000, i.e.

kPa on the lower range and of 70 000, namely kPa, on theupper range. The transducer can be used between the temperatures ofand . When the temperature changes by 1°C the output of the trans-ducer for zero input will change by 0.030% of kPa on the lowerrange and 0.030% of kPa on the upper range.

2.2.1 Static and dynamic characteristics

The static characteristics are the values given when steady-state condi-tions occur, i.e. the values given when the transducer has settled down afterhaving received some input. The terminology defined above refers to such astate. The dynamic characteristics refer to the behaviour between thetime that the input value changes and the time that the value given by thetransducer settles down to the steady-state value. Dynamic characteristicsare stated in terms of the response of the transducer to inputs in particularforms. For example, this might be a step input when the input is suddenlychanged from zero to a constant value, or a ramp input when the input ischanged at a steady rate, or a sinusoidal input of a specified frequency. Thuswe might find the following terms (see Chapter 12 for a more detaileddiscussion of dynamic systems):

1 Response time This is the time which elapses after a constant input, a step input, isapplied to the transducer up to the point at which the transducer gives anoutput corresponding to some specified percentage, e.g. 95%, of the valueof the input (Figure 2.3). For example, if a mercury-in-glass thermometeris put into a hot liquid there can be quite an appreciable time lapse, per-haps as much as 100 s or more, before the thermometer indicates 95% ofthe actual temperature of the liquid.

70 000 = 211000 = 0.3

+120°C-54

;350;0.5%;5;0.5%

°C+120°C-54°C

;0.5%

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2.2 PERFORMANCE TERMINOLOGY 27

2 Time constant This is the 63.2% response time. A thermocouple in air might have a timeconstant of perhaps 40 to 100 s. The time constant is a measure of theinertia of the sensor and so how fast it will react to changes in its input:the bigger the time constant, the slower the reaction to a changing inputsignal. See Section 12.3.4 for a mathematical discussion of the time con-stant in terms of the behaviour of a system when subject to a step input.

3 Rise time This is the time taken for the output to rise to some specified percentageof the steady-state output. Often the rise time refers to the time taken forthe output to rise from 10% of the steady-state value to 90 or 95% of thesteady-state value.

4 Settling time This is the time taken for the output to settle to within some percentage,e.g. 2%, of the steady-state value.

To illustrate the above, consider the graph in Figure 2.4 which indicateshow an instrument reading changed with time, being obtained from a ther-mometer plunged into a liquid at time . The steady-state value is 55and so, since 95% of 55 is 52.25 , the 95% response time is about 228 s. °C

°Ct = 0

Steady-stateoutput

0

63.2

95100

Timeconstant

95%response time

Time

% s

tead

y-st

ate

outp

ut

Figure 2.3 Response to a

step input.

20

30

40

50

60

Tem

pera

ture

(°C

)

0 120 240 360

Time (s)

Steady-statevalue

Figure 2.4 Thermometer in

liquid.

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28 CHAPTER 2 SENSORS AND TRANSDUCERS

The following sections give examples of transducers grouped according towhat they are being used to measure. The measurements considered arethose frequently encountered in mechanical engineering, namely: displace-ment, proximity, velocity, force, pressure, fluid flow, liquid level, tempera-ture, and light intensity.

Displacement sensors are concerned with the measurement of the amountby which some object has been moved; position sensors are concerned withthe determination of the position of some object in relation to some referencepoint. Proximity sensors are a form of position sensor and are used to deter-mine when an object has moved to within some particular critical distance ofthe sensor. They are essentially devices which give on/off outputs.

Displacement and position sensors can be grouped into two basic types:contact sensors in which the measured object comes into mechanical contactwith the sensor, or non-contacting where there is no physical contact betweenthe measured object and the sensor. For those linear displacement methodsinvolving contact, there is usually a sensing shaft which is in direct contactwith the object being monitored. The displacement of this shaft is then mon-itored by a sensor. The movement of the shaft may be used to cause changesin electrical voltage, resistance, capacitance or mutual inductance. For angulardisplacement methods involving mechanical connection, the rotation of ashaft might directly drive, through gears, the rotation of the transducer ele-ment. Non-contacting sensors might involve the presence in the vicinity ofthe measured object causing a change in the air pressure in the sensor, or per-haps a change in inductance or capacitance. The following are examples ofcommonly used displacement sensors.

2.3.1 Potentiometer sensor

A potentiometer consists of a resistance element with a sliding contactwhich can be moved over the length of the element. Such elements can beused for linear or rotary displacements, the displacement being convertedinto a potential difference. The rotary potentiometer consists of a circularwire-wound track or a film of conductive plastic over which a rotatable slid-ing contact can be rotated (Figure 2.5). The track may be a single turn or hel-ical. With a constant input voltage , between terminals 1 and 3, the outputvoltage between terminals 2 and 3 is a fraction of the input voltage, theVo

Vs

1

2

3

A rotary potentiometer RLin parallel with xRp

The circuit as apotential divider

The circuit when connected to a load

1

3

2

3

Vs

Vout RL VL

SliderLoad

Slider

Rp(1 − x)

VL

Vs

Figure 2.5 Rotary potentiometer.

Displacement,position and

proximity

2.3

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2.3 DISPLACEMENT, POSITION AND PROXIMITY 29

fraction depending on the ratio of the resistance between terminals 2 and3 compared with the total resistance between terminals 1 and 3, i.e.

. If the track has a constant resistance per unit length, i.e.per unit angle, then the output is proportional to the angle through which theslider has rotated. Hence an angular displacement can be converted into apotential difference.

With a wire-wound track the slider in moving from one turn to the otherwill change the voltage output in steps, each step being a movement of oneturn. If the potentiometer has N turns then the resolution, as a percentage, is

Thus the resolution of a wire track is limited by the diameter of thewire used and typically ranges from about 1.5 mm for a coarsely wound trackto 0.5 mm for a finely wound one. Errors due to non-linearity of the tracktend to range from less than 0.1% to about 1%. The track resistance tends torange from about to Conductive plastic has ideally infinite res-olution, errors due to non-linearity of the track of the order of 0.05% andresistance values from about 500 to . The conductive plastic has ahigher temperature coefficient of resistance than the wire and so temperaturechanges have a greater effect on accuracy.

An important effect to be considered with a potentiometer is the effect ofa load connected across the output. The potential difference across theload is only directly proportional to if the load resistance is infinite.For finite loads, however, the effect of the load is to transform what was a lin-ear relationship between output voltage and angle into a non-linear relation-ship. The resistance is in parallel with the fraction x of the potentiometerresistance This combined resistance is The totalresistance across the source voltage is thus

The circuit is a potential divider circuit and thus the voltage across the loadis the fraction that the resistance across the load is of the total resistanceacross which the applied voltage is connected:

If the load is of infinite resistance then we have Thus the errorintroduced by the load having a finite resistance is

To illustrate the above, consider the non-linearity error with a poten-tiometer of resistance 500 , when at a displacement of half its maximumslider travel, which results from there being a load of resistance 10 k . Thesupply voltage is 4 V. Using the equation derived above

error = 4 *500

10 000(0.52 - 0.53) = 0.025 V

ÆÆ

= Vs Rp

RL

(x2 - x3)

error = xVs - VL = xVs -xVs

(Rp>RL)x(1 - x) + 1

VL = xVs.

=x

(Rp>RL)x(1 - x) + 1

VL

Vs

=xRLRp>(RL + xRp)

Rp(1 - x) + xRLRp>(RL + xRp)

total resistance = Rp(1 - x) + RLxRp>(RL + xRp)

RLxRp>(RL + xRp).Rp.RL

VoVL

RL

80 kÆ

200 kÆ.20 Æ

100>N.

Vo>Vs = R23>R13

R13

R23

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30 CHAPTER 2 SENSORS AND TRANSDUCERS

As a percentage of the full range reading, this is 0.625%. Potentiometers are used as sensors with the electronic systems in cars, being

used for such things as the accelerator pedal position and throttle position.

2.3.2 Strain-gauged element

The electrical resistance strain gauge (Figure 2.6) is a metal wire, metal foilstrip, or a strip of semiconductor material which is wafer-like and can bestuck onto surfaces like a postage stamp. When subject to strain, its resistanceR changes, the fractional change in resistance being proportional tothe strain , i.e.

where G, the constant of proportionality, is termed the gauge factor.

¢R

R= Ge

e¢R>R

Wire Metal foil Semiconductor

Connection leads Connection leadsConnection leads

(a) (b) (c)

Figure 2.6 Strain gauges:

(a) metal wire, (b) metal foil,

(c) semiconductor.

Since strain is the ratio (change in length/original length) then the resist-ance change of a strain gauge is a measurement of the change in length of theelement to which the strain gauge is attached. The gauge factor of metal wireor foil strain gauges with the metals generally used is about 2.0 and resistancesare generally of the order of about . Silicon p- and n-type semiconduc-tor strain gauges have gauge factors of about or more for p-type siliconand or more for n-type silicon and resistances of the order of 1000 to

The gauge factor is normally supplied by the manufacturer of thestrain gauges from a calibration made of a sample of strain gauges taken froma batch. The calibration involves subjecting the sample gauges to knownstrains and measuring their changes in resistance. A problem with all straingauges is that their resistance changes not only with strain but also with tem-perature. Ways of eliminating the temperature effect have to be used and arediscussed in Chapter 3. Semiconductor strain gauges have a much greatersensitivity to temperature than metal strain gauges.

To illustrate the above, consider an electrical resistance strain gauge witha resistance of 100 and a gauge factor of 2.0. What is the change in resist-ance of the gauge when it is subject to a strain of 0.001? The fractionalchange in resistance is equal to the gauge factor multiplied by the strain, thus

One form of displacement sensor has strain gauges attached to flexibleelements in the form of cantilevers (Figure 2.7(a)), rings (Figure 2.7(b)) or

change in resistance = 2.0 * 0.001 * 100 = 0.2 Æ

Æ

5000 Æ.-100

+100100 Æ

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2.3 DISPLACEMENT, POSITION AND PROXIMITY 31

U-shapes (Figure 2.7(c)). When the flexible element is bent or deformed asa result of forces being applied by a contact point being displaced, then theelectrical resistance strain gauges mounted on the element are strained andso give a resistance change which can be monitored. The change in resistanceis thus a measure of the displacement or deformation of the flexible element.Such arrangements are typically used for linear displacements of the order of1 to 30 mm and have a non-linearity error of about of full range.

2.3.3 Capacitive element

The capacitance C of a parallel plate capacitor is given by

where is the relative permittivity of the dielectric between the plates, aconstant called the permittivity of free space, A the area of overlap betweenthe two plates and d the plate separation. Capacitive sensors for the monitor-ing of linear displacements might thus take the forms shown in Figure 2.8.In (a) one of the plates is moved by the displacement so that the plate sepa-ration changes; in (b) the displacement causes the area of overlap to change;in (c) the displacement causes the dielectric between the plates to change.

For the displacement changing the plate separation (Figure 2.8(a)), if theseparation d is increased by a displacement x then the capacitance becomes

Hence the change in capacitance as a fraction of the initial capacitance isgiven by

¢C

C= -

d

d + x- 1 = -

x>d1 + (x>d)

¢C

C - ¢C =e0er

A

d + x

e0er

C =ere0A

d

;1%

Strain gauges

(a)

Straingauges

(b)

Strain gauges

(c)

Figure 2.7 Strain-gauged

element.

d

Plate movesand changes d

Plate movesand changes A

Overlap area

Dielectric moves

(a) (b) (c)

Figure 2.8 Forms of capacitive

sensing element.

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32 CHAPTER 2 SENSORS AND TRANSDUCERS

There is thus a non-linear relationship between the change in capacitanceand the displacement x. This non-linearity can be overcome by using

what is termed a push–pull displacement sensor (Figure 2.9). This hasthree plates with the upper pair forming one capacitor and the lower pairanother capacitor. The displacement moves the central plate between the twoother plates. The result of, for example, the central plate moving downwardsis to increase the plate separation of the upper capacitor and decrease theseparation of the lower capacitor. We thus have

When is in one arm of an a.c. bridge and in the other, then the result-ing out-of-balance voltage is proportional to x. Such a sensor is typicallyused for monitoring displacements from a few millimetres to hundreds ofmillimetres. Non-linearity and hysteresis are about of full range.

One form of capacitive proximity sensor consists of a single capacitorplate probe with the other plate being formed by the object, which has to bemetallic and earthed (Figure 2.10). As the object approaches so the ‘plateseparation’ of the capacitor changes, becoming significant and detectablewhen the object is close to the probe.

2.3.4 Differential transformers

The linear variable differential transformer, generally referred to by theabbreviation LVDT, consists of three coils symmetrically spaced along aninsulated tube (Figure 2.11). The central coil is the primary coil and theother two are identical secondary coils which are connected in series in sucha way that their outputs oppose each other. A magnetic core is movedthrough the central tube as a result of the displacement being monitored.

;0.01%

C2C1

C2 =e0er A

d - x

C1 =e0er A

d + x

¢CCapacitorC1

CapacitorC2

x

Figure 2.9 Push–pull sensor.

Coaxial cable

Guard ring

Object

Figure 2.10 Capacitive

proximity sensor.

Constant A.C. voltageinput to primary

Output voltage asdifference betweenthe two secondaryvoltages

Primary

Secondary 1

Secondary 2

Ferrous rodDisplacement movesrod from central position

Figure 2.11 LVDT.

When there is an alternating voltage input to the primary coil, alternatinge.m.f.s are induced in the secondary coils. With the magnetic core central,the amount of magnetic material in each of the secondary coils is the same.Thus the e.m.f.s induced in each coil are the same. Since they are so con-nected that their outputs oppose each other, the net result is zero output.

However, when the core is displaced from the central position there is agreater amount of magnetic core in one coil than the other, e.g. more in

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2.3 DISPLACEMENT, POSITION AND PROXIMITY 33

secondary coil 2 than coil 1. The result is that a greater e.m.f. is induced inone coil than the other. There is then a net output from the two coils. Sincea greater displacement means even more core in one coil than the other,the output, the difference between the two e.m.f.s increases the greater thedisplacement being monitored (Figure 2.12).

The e.m.f. induced in a secondary coil by a changing current i in theprimary coil is given by

where M is the mutual inductance, its value depending on the number ofturns on the coils and the ferromagnetic core. Thus, for a sinusoidal inputcurrent of sin to the primary coil, the e.m.f.s induced in the twosecondary coils 1 and 2 can be represented by

where the values of depend on the degree of coupling between theprimary and secondary coils for a particular core position. is the phase differ-ence between the primary alternating voltage and the secondary alternatingvoltages. Because the two outputs are in series, their difference is the output

When the core is equally in both coils, equals and so the output voltageis zero. When the core is more in 1 than in 2 we have and

When the core is more in 2 than in 1 we have A consequence ofbeing less than is that there is a phase change of 180° in the output whenthe core moves from more in 1 to more in 2. Thus

Figure 2.12 shows how the size and phase of the output change with thedisplacement of the core.

With this form of output, the same amplitude output voltage is producedfor two different displacements. To give an output voltage which is unique toeach value of displacement we need to distinguish between where the ampli-tudes are the same but there is a phase difference of 180°. A phase-sensitivedemodulator, with a low-pass filter, is used to convert the output into a d.c.voltage which gives a unique value for each displacement (Figure 2.13). Suchcircuits are available as integrated circuits.

= (k2 - k1) sin[vt + (p - f)]output voltage = - (k1 - k2) sin(vt - f)

k2

k1k1 6 k2.

output voltage = (k1 - k2) sin(vt - f)

k1 7 k2

k2k1

output voltage = v1 - v2 = (k1 - k2) sin(vt - f)

fk1, k2 and f

v1 = k1 sin(vt - f) and v2 = k2 sin(vt - f)

vti = I

e = Mdi

dt

Displacement

Out

put v

olta

ge

0

LVDTPhase-sensitive

demodulator Low-pass filter

Displacement A.C. D.C.

Figure 2.13 LVDT d.c. output.

0

+180°

−180°φ

Out

put v

olta

ge

0Displacement

Displacement

Core morein 1 than 2

Core morein 2 than 1

Corecentral

Figure 2.12 LVDT output.

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34 CHAPTER 2 SENSORS AND TRANSDUCERS

Typically, LVDTs have operating ranges from about mmwith non-linearity errors of about %. LVDTs are very widely used asprimary transducers for monitoring displacements. The free end of the coremay be spring loaded for contact with the surface being monitored, orthreaded for mechanical connection. They are also used as secondary trans-ducers in the measurement of force, weight and pressure; these variables aretransformed into displacements which can then be monitored by LVDTs.

A rotary variable differential transformer (RVDT) can be used for themeasurement of rotation (Figure 2.14); it operates on the same principle asthe LVDT. The core is a cardioid-shaped piece of magnetic material androtation causes more of it to pass into one secondary coil than the other. Therange of operation is typically with a linearity error of about ofthe range.

2.3.5 Eddy current proximity sensors

If a coil is supplied with an alternating current, an alternating magnetic fieldis produced. If there is a metal object in close proximity to this alternatingmagnetic field, then eddy currents are induced in it. The eddy currentsthemselves produce a magnetic field. This distorts the magnetic field respon-sible for their production. As a result, the impedance of the coil changes andso the amplitude of the alternating current. At some preset level, this changecan be used to trigger a switch. Figure 2.15 shows the basic form of such asensor; it is used for the detection of non-magnetic but conductive materials.They have the advantages of being relatively inexpensive, small in size, withhigh reliability, and can have high sensitivity to small displacements.

2.3.6 Inductive proximity switch

This consists of a coil wound round a core. When the end of the coil is closeto a metal object its inductance changes. This change can be monitored byits effect on a resonant circuit and the change used to trigger a switch. Itcan only be used for the detection of metal objects and is best with ferrousmetals.

2.3.7 Optical encoders

An encoder is a device that provides a digital output as a result of a linear orangular displacement. Position encoders can be grouped into two categories:incremental encoders that detect changes in rotation from some datumposition and absolute encoders which give the actual angular position.

Figure 2.16(a) shows the basic form of an incremental encoder for themeasurement of angular displacement. A beam of light passes through slotsin a disc and is detected by a suitable light sensor. When the disc is rotated,a pulsed output is produced by the sensor with the number of pulses beingproportional to the angle through which the disc rotates. Thus the angularposition of the disc, and hence the shaft rotating it, can be determined by thenumber of pulses produced since some datum position. In practice threeconcentric tracks with three sensors are used (Figure 2.16(b)). The inner

;0.5%;40°

;0.25;2 to ;400

PrimarySecondary 1 Secondary 2

Figure 2.14 RVDT.

Reference coil Sensor coil

Conductingobject

Figure 2.15 Eddy current

sensor.

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2.3 DISPLACEMENT, POSITION AND PROXIMITY 35

track has just one hole and is used to locate the ‘home’ position of the disc.The other two tracks have a series of equally spaced holes that go completelyround the disc but with the holes in the middle track offset from the holes inthe outer track by one-half the width of a hole. This offset enables the direc-tion of rotation to be determined. In a clockwise direction the pulses in theouter track lead those in the inner; in the anti-clockwise direction they lag.The resolution is determined by the number of slots on the disc. With60 slots in 1 revolution then, since 1 revolution is a rotation of , theresolution is

Figure 2.17 shows the basic form of an absolute encoder for the measure-ment of angular displacement. This gives an output in the form of a binarynumber of several digits, each such number representing a particular angularposition. The rotating disc has three concentric circles of slots and three sen-sors to detect the light pulses. The slots are arranged in such a way that thesequential output from the sensors is a number in the binary code. Typicalencoders tend to have up to 10 or 12 tracks. The number of bits in the binarynumber will be equal to the number of tracks. Thus with 10 tracks there willbe 10 bits and so the number of positions that can be detected is , i.e. 1024,a resolution of 360>1024 = 0.35°.

210

360>60 = 6°.360°

(a)

Outertrack

Middletrack

Innertrack

(b)

Light sensor

The disc with slots through whichthe light can pass

Disc

LEDFigure 2.16 Incremental

encoder: (a) the basic principle,

(b) concentric tracks.

LEDs 111

110

000

001

010

011 100

101

SensorsFigure 2.17 A 3-bit absolute

encoder.

The normal form of binary code is generally not used because changingfrom one binary number to the next can result in more than one bit chang-ing, e.g. in changing from 001 to 110 we have two bits changing, and if,through some misalignment, one of the bits changes fractionally before theothers then an intermediate binary number is momentarily indicated and socan lead to false counting. To overcome this the Gray code is generally used(see Appendix B). With this code only one bit changes in moving from one

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36 CHAPTER 2 SENSORS AND TRANSDUCERS

number to the next. Figure 2.18 shows the track arrangements with normalbinary code and the Gray code.

Optical encoders, e.g. HEDS-5000 from Hewlett Packard, are supplied

for mounting on shafts and contain an LED light source and a code wheel.

Interface integrated circuits are also available to decode the encoder and con-

vert from Gray code to give a binary output suitable for a microprocessor.

For an absolute encoder with seven tracks on its code disc, each track will

give one of the bits in the binary number and thus we have positions spec-

ified, i.e. 128. With eight tracks we have positions, i.e. 256.

2.3.8 Pneumatic sensors

Pneumatic sensors involve the use of compressed air, displacement or theproximity of an object being transformed into a change in air pressure.Figure 2.19 shows the basic form of such a sensor. Low-pressure air isallowed to escape through a port in the front of the sensor. This escaping air,in the absence of any close-by object, escapes and in doing so also reduces thepressure in the nearby sensor output port. However, if there is a close-byobject, the air cannot so readily escape and the result is that the pressureincreases in the sensor output port. The output pressure from the sensorthus depends on the proximity of objects.

2827

00000001

0010

0011

0100

0101

0110

0111

1000

1001

1010

00000001

0011

0010

0110

0111

0101

0100

1100

1101

1111

01

2

3

4

5

6

7

8

9

10

Normal binary Gray code

Figure 2.18 Binary and Gray

codes.

Low-pressureair inlet

Escapingair

Air dragged out of port and sodrop in system pressure

Low-pressureair inlet

Escapingair

Rise inpressure

Object blocking escaping air increasespressure in system

Figure 2.19 Pneumatic proximity sensor.

Such sensors are used for the measurement of displacements of fractionsof millimetres in ranges which typically are about 3 to 12 mm.

2.3.9 Proximity switches

There are a number of forms of switch which can be activated by the pres-ence of an object in order to give a proximity sensor with an output which iseither on or off.

The microswitch is a small electrical switch which requires physical con-tact and a small operating force to close the contacts. For example, in the case ofdetermining the presence of an item on a conveyor belt, this might be actuatedby the weight of the item on the belt depressing the belt and hence a spring-loaded platform under it, with the movement of this platform then closing theswitch. Figure 2.20 shows examples of ways such switches can be actuated.

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2.3 DISPLACEMENT, POSITION AND PROXIMITY 37

Figure 2.21 shows the basic form of a reed switch. It consists of twomagnetic switch contacts sealed in a glass tube. When a magnet is broughtclose to the switch, the magnetic reeds are attracted to each other and closethe switch contacts. It is a non-contact proximity switch. Such a switch isvery widely used for checking the closure of doors. It is also used with suchdevices as tachometers, which involve the rotation of a toothed wheel past thereed switch. If one of the teeth has a magnet attached to it, then every timeit passes the switch it will momentarily close the contacts and hence producea current/voltage pulse in the associated electrical circuit.

Photosensitive devices can be used to detect the presence of anopaque object by its breaking a beam of light, or infrared radiation, fallingon such a device or by detecting the light reflected back by the object(Figure 2.22).

Button to operateswitch

(a) (b) (c)

Switch contacts

Figure 2.20 (a) Lever-operated, (b) roller-operated, (c) cam-operated switches.

(a) (b)

PhotodetectorLight

Object breaksthe beam

LED LED

Photo-detector

Object reflectsthe light

Figure 2.22 Using

photoelectric sensors to detect

objects by (a) the object breaking

the beam, (b) the object reflecting

light.

Springy strips Electrical contacts

Magnet

Figure 2.21 Reed switch.

2.3.10 Hall effect sensors

When a beam of charged particles passes through a magnetic field, forcesact on the particles and the beam is deflected from its straight line path. Acurrent flowing in a conductor is like a beam of moving charges and thus canbe deflected by a magnetic field. This effect was discovered by E.R. Hall in1879 and is called the Hall effect. Consider electrons moving in a conduc-tive plate with a magnetic field applied at right angles to the plane of theplate (Figure 2.23). As a consequence of the magnetic field, the moving elec-trons are deflected to one side of the plate and thus that side becomes neg-atively charged, while the opposite side becomes positively charged sincethe electrons are directed away from it. This charge separation produces anelectric field in the material. The charge separation continues until the

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38 CHAPTER 2 SENSORS AND TRANSDUCERS

forces on the charged particles from the electric field just balance the forcesproduced by the magnetic field. The result is a transverse potential differ-ence V given by

where B is the magnetic flux density at right angles to the plate, I the currentthrough it, t the plate thickness and a constant called the Hall coefficient.Thus if a constant current source is used with a particular sensor, the Hallvoltage is a measure of the magnetic flux density.

Hall effect sensors are generally supplied as an integrated circuit withthe necessary signal processing circuitry. There are two basic forms of suchsensor: linear, where the output varies in a reasonably linear manner withthe magnetic flux density (Figure 2.24(a)); and threshold, where the outputshows a sharp drop at a particular magnetic flux density (Figure 2.24(b)).The linear output Hall effect sensor 634SS2 gives an output which is fairlylinear over the range to mT ( to 400 gauss) at about10 mV per mT (1 mV per gauss) when there is a supply voltage of 5 V. Thethreshold Hall effect sensor Allegro UGN3132U gives an output whichswitches from virtually zero to about 145 mV when the magnetic flux den-sity is about 3 mT (30 gauss). Hall effect sensors have the advantages ofbeing able to operate as switches which can operate up to 100 kHz repeti-tion rate, cost less than electromechanical switches and do not suffer fromthe problems associated with such switches of contact bounce occurring andhence a sequence of contacts rather than a single clear contact. The Halleffect sensor is immune to environmental contaminants and can be usedunder severe service conditions.

+-400+40-40

KH

V = KH

BI

t

Current

Potential differenceproduced by deflection

of electrons

Magnetic field

Current

Negativelycharged

Positivelycharged

Figure 2.23 Hall effect.

Out

put (

V)

Flux density0 0− +

(a)

Out

put (

V)

Flux density

(b)

Figure 2.24 Hall effect sensors:

(a) linear, (b) threshold.

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2.4 VELOCITY AND MOTION 39

Such sensors can be used as position, displacement and proximity sensorsif the object being sensed is fitted with a small permanent magnet. As anillustration, such a sensor can be used to determine the level of fuel in anautomobile fuel tank. A magnet is attached to a float and as the level of fuelchanges so the float distance from the Hall sensor changes (Figure 2.25). Theresult is a Hall voltage output which is a measure of the distance of the floatfrom the sensor and hence the level of fuel in the tank.

Another application of Hall effect sensors is in brushless d.c. motors.With such motors it is necessary to determine when the permanent magnetrotor is correctly aligned with the windings on the stator so that the currentthrough the windings can be switched on at the right instant to maintain therotor rotation. Hall effect sensors are used to detect when the alignment isright.

The following are examples of sensors that can be used to monitor linear andangular velocities and detect motion. The application of motion detectorsincludes security systems used to detect intruders and interactive toys andappliances, e.g. the cash machine screen which becomes active when you getnear to it.

2.4.1 Incremental encoder

The incremental encoder described in Section 2.3.7 can be used for themeasurement of angular velocity, the number of pulses produced per secondbeing determined.

2.4.2 Tachogenerator

The tachogenerator is used to measure angular velocity. One form, thevariable reluctance tachogenerator, consists of a toothed wheel of fer-romagnetic material which is attached to the rotating shaft (Figure 2.26). Apick-up coil is wound on a permanent magnet.As the wheel rotates, so the teethmove past the coil and the air gap between the coil and the ferromagnetic mate-rial changes. We have a magnetic circuit with an air gap which periodicallychanges. Thus the flux linked by a pick-up coil changes. The resulting cyclicchange in the flux linked produces an alternating e.m.f. in the coil.

Ground

OutputSupply

MagnetHallsensor

Float

Spring

Spring

Figure 2.25 Fluid-level

detector.

Velocity andmotion

2.4

Output

Pick-up coil

Toothed wheel

Figure 2.26 Variable reluctance

tachogenerator.

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40 CHAPTER 2 SENSORS AND TRANSDUCERS

If the wheel contains n teeth and rotates with an angular velocity thenthe flux change with time for the coil can be considered to be of the form

where is the mean value of the flux and the amplitude of the fluxvariation. The induced e.m.f. e in the N turns of the pick-up coil is

and thus

and so we can write

where the maximum value of the induced e.m.f. is and so is ameasure of the angular velocity.

Instead of using the maximum value of the e.m.f. as a measure of the angularvelocity, a pulse-shaping signal conditioner can be used to transform the outputintoasequenceof pulseswhichcanbecountedbyacounter, thenumbercountedin a particular time interval being a measure of the angular velocity.

Another form of tachogenerator is essentially an a.c. generator. It con-sists of a coil, termed the rotor, which rotates with the rotating shaft. Thiscoil rotates in the magnetic field produced by a stationary permanent magnetor electromagnet (Figure 2.27) and so an alternating e.m.f. is induced in it.The amplitude or frequency of this alternating e.m.f. can be used as a meas-ure of the angular velocity of the rotor. The output may be rectified to give ad.c. voltage with a size which is proportional to the angular velocity. Non-linearity for such sensors is typically of the order of % of the full rangeand the sensors are typically used for rotations up to about 10 000 rev/min.

;0.15

N£anvEmax

e = Emax sin vt

e = N£anv sin vt

-N d£>dt

£a£0

£ = £0 + £a cos nvt

v,

N S

Rotating coil

Figure 2.27 A.C. generator

form of tachogenerator.

2.4.3 Pyroelectric sensors

Pyroelectric materials, e.g. lithium tantalate, are crystalline materials whichgenerate charge in response to heat flow. When such a material is heated to atemperature just below the Curie temperature, this being about 610°C forlithium tantalate, in an electric field and the material cooled while remainingin the field, electric dipoles within the material line up and it becomespolarised (Figure 2.28, (a) leading to (b)). When the field is then removed, thematerial retains its polarisation; the effect is rather like magnetising a piece ofiron by exposing it to a magnetic field. When the pyroelectric material isexposed to infrared radiation, its temperature rises and this reduces theamount of polarisation in the material, the dipoles being shaken up more andlosing their alignment (Figure 2.28(c)).

A pyroelectric sensor consists of a polarised pyroelectric crystal with thinmetal film electrodes on opposite faces. Because the crystal is polarised withcharged surfaces, ions are drawn from the surrounding air and electrons fromany measurement circuit connected to the sensor to balance the surface charge

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2.4 VELOCITY AND MOTION 41

(Figure 2.29(a)). If infrared radiation is incident on the crystal and changes itstemperature, the polarisation in the crystal is reduced and consequently thatis a reduction in the charge at the surfaces of the crystal. There is then anexcess of charge on the metal electrodes over that needed to balance thecharge on the crystal surfaces (Figure 2.29(b)). This charge leaks awaythrough the measurement circuit until the charge on the crystal once again isbalanced by the charge on the electrodes. The pyroelectric sensor thusbehaves as a charge generator which generates charge when there is a changein its temperature as a result of the incidence of infrared radiation. For thelinear part of the graph in Figure 2.28(c), when there is a temperature changethe change in charge is proportional to the change in temperature

¢q = kp¢t

¢t:¢q

Excesscharge onelectrodes

Infraredradiation

(b)

+ + + + +

+ + + + +

− − − − −

− − − − −

Chargesbalanced

(a)

No incidentinfraredradiation

+ + + + +

+ + +

− − −

− − − − −

Figure 2.29 Pyroelectric sensor.

CRi

Figure 2.30 Equivalent

circuit.

(a)

++

++

−−

+

++

+ + +

++

+

+

−− −

−−

+ + +

− − −

− − −

− − −

+ + +

+ + +

(b)

Am

ount

of p

olar

isat

ion

or c

harg

e at

cry

stal

sur

face

s

Temperature

Curie temperature

(c)

Figure 2.28 (a), (b) Polarising a

pyroelectric material, (c) the

effect of temperature on the

amount of polarisation.

where is a sensitivity constant for the crystal. Figure 2.30 shows the equiv-alent circuit of a pyroelectric sensor, it effectively being a capacitor charged bythe excess charge with a resistance R to represent either internal leakageresistance or that combined with the input resistance of an external circuit.

To detect the motion of a human or other heat source, the sensing ele-ment has to distinguish between general background heat radiation and thatgiven by a moving heat source. A single pyroelectric sensor would not becapable of this and so a dual element is used (Figure 2.31). One form has thesensing element with a single front electrode but two, separated, back elec-trodes. The result is two sensors which can be connected so that when bothreceive the same heat signal their outputs cancel. When a heat source movesso that the heat radiation moves from one of the sensing elements to theother, then the resulting current through the resistor alternates from beingfirst in one direction and then reversed to the other direction. Typicallya moving human gives an alternating current of the order of A. Theresistance R has thus to be very high to give a significant voltage. For exam-ple, 50 G with such a current gives 50 mV. For this reason a transistor isincluded in the circuit as a voltage follower to bring the output impedancedown to a few kilo-ohms.

Æ

10-12

kp

OutputR

JFET V

Infrared

Figure 2.31 Dual pyroelectric

sensor.

Page 42: Bolton Mechatronics

42 CHAPTER 2 SENSORS AND TRANSDUCERS

A focusing device is needed to direct the infrared radiation onto thesensor. While parabolic mirrors can be used, a more commonly used methodis a Fresnel plastic lens. Such a lens also protects the front surface of thesensor and is the form commonly used for sensors to trigger intruder alarmsor switch on a light when someone approaches.

A spring balance is an example of a force sensor in which a force, a weight, isapplied to the scale pan and causes a displacement, i.e. the spring stretches.Thedisplacement is then a measure of the force. Forces are commonly measured bythe measurement of displacements, the following method illustrating this.

2.5.1 Strain gauge load cell

A very commonly used form of force-measuring transducer is based on theuse of electrical resistance strain gauges to monitor the strain produced insome member when stretched, compressed or bent by the application of theforce. The arrangement is generally referred to as a load cell. Figure 2.32shows an example of such a cell. This is a cylindrical tube to which straingauges have been attached. When forces are applied to the cylinder to com-press it, then the strain gauges give a resistance change which is a measure ofthe strain and hence the applied forces. Since temperature also produces aresistance change, the signal conditioning circuit used has to be able to elim-inate the effects due to temperature (see Section 3.5.1). Typically such loadcells are used for forces up to about 10 MN, the non-linearity error beingabout of full range, hysteresis error of full range andrepeatability error of full range. Strain gauge load cells based on thebending of a strain-gauged metal element tend to be used for smaller forces,e.g. with ranges varying from 0 to 5 N up to 0 to 50 kN. Errors are typicallya non-linearity error of about of full range, hysteresis error of full range and repeatability error of full range.

Many of the devices used to monitor fluid pressure in industrial processesinvolve the monitoring of the elastic deformation of diaphragms, capsules,bellows and tubes. The types of pressure measurements that can be requiredare: absolute pressure where the pressure is measured relative to zero pressure,i.e. a vacuum, differential pressure where a pressure difference is measuredand gauge pressure where the pressure is measured relative to the barometricpressure.

For a diaphragm (Figure 2.33(a) and (b)), when there is a difference in pres-sure between the two sides then the centre of the diaphragm becomes dis-placed. Corrugations in the diaphragm result in a greater sensitivity. Thismovement can be monitored by some form of displacement sensor, e.g. astrain gauge, as illustrated in Figure 2.34. A specially designed strain gauge

;0.02%;0.02%;0.03%

;0.02%;0.02%;0.03%

Force2.5

Figure 2.32 Strain gauge

load cell.

Strain gauges

Force

Figure 2.33 Diaphragms:

(a) flat, (b) corrugated.

(a) (b)

Pressure Pressure

Fluid pressure2.6

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2.6 FLUID PRESSURE 43

is often used, consisting of four strain gauges with two measuring the strainin a circumferential direction while two measure strain in a radial direction.The four strain gauges are then connected to form the arms of a Wheatstonebridge (see Chapter 3). While strain gauges can be stuck on a diaphragm, analternative is to create a silicon diaphragm with the strain gauges as speciallydoped areas of the diaphragm. Such an arrangement is used with the elec-tronic systems for cars to monitor the inlet manifold pressure.

With the Motorola MPX pressure sensors, the strain gauge element isintegrated, together with a resistive network, in a single silicon diaphragmchip. When a current is passed through the strain gauge element and pres-sure applied at right angles to it, a voltage is produced. This element,together with signal conditioning and temperature compensation circuitry, ispackaged as the MPX sensor. The output voltage is directly proportional tothe pressure. Such sensors are available for use for the measurement ofabsolute pressure (the MX numbering system ends with A, AP, AS or ASX),differential pressure (the MX numbering system ends with D or DP) andgauge pressure (the MX numbering system ends with GP, GVP, GS, GVS,GSV or GVSX). For example, the MPX2100 series has a pressure range of100 kPa and with a supply voltage of 16 V d.c. gives in the absolute pressureand differential pressure forms a voltage output over the full range of 40 mV.The response time, 10 to 90%, for a step change from 0 to 100 kPa is about1.0 ms and the output impedance is of the order of 1.4 to 3.0 k . Theabsolute pressure sensors are used for such applications as altimeters andbarometers, the differential pressure sensors for air flow measurements andthe gauge pressure sensors for engine pressure and tyre pressure.

Capsules (Figure 2.35(a)) can be considered to be just two corrugateddiaphragms combined and give even greater sensitivity. A stack of capsules isjust a bellows (Figure 2.35(b)) and even more sensitive. Figure 2.36 showshow a bellows can be combined with an LVDT to give a pressure sensor withan electrical output. Diaphragms, capsules and bellows are made from suchmaterials as stainless steel, phosphor bronze and nickel, with rubber andnylon also being used for some diaphragms. Pressures in the range of about

to Pa can be monitored with such sensors. 108103

Æ

Figure 2.34 Diaphragm

pressure gauge.

Diaphragm Strain gauge

Pressure

(a) (b)

Figure 2.35 (a) Capsule,

(b) bellows.

A different form of deformation is obtained using a tube with an ellipti-cal cross-section (Figure 2.37(a)). Increasing the pressure in such a tubecauses it to tend to a more circular cross-section. When such a tube is in theform of a C-shaped tube (Figure 2.37(b)), this being generally known as aBourdon tube, the C opens up to some extent when the pressure in the tubeincreases. A helical form of such a tube (Figure 2.37(c)) gives a greater sen-sitivity. The tubes are made from such materials as stainless steel and phos-phor bronze and are used for pressures in the range to Pa. 108103

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44 CHAPTER 2 SENSORS AND TRANSDUCERS

2.6.1 Piezoelectric sensors

Piezoelectric materials when stretched or compressed generate electriccharges with one face of the material becoming positively charged and theopposite face negatively charged (Figure 2.38(a)). As a result, a voltage isproduced. Piezoelectric materials are ionic crystals which when stretched orcompressed result in the charge distribution in the crystal changing so thatthere is a net displacement of charge with one face of the material becomingpositively charged and the other negatively charged. The net charge q on asurface is proportional to the amount x by which the charges have been dis-placed, and since the displacement is proportional to the applied force F:

q = kx = SF

Figure 2.37 Tube pressure

sensors.

(c)

Movement

(b)

Movement

Tube cross-section

(a)

Figure 2.38 (a) Piezoelectricity,

(b) piezoelectric capacitor.Surfacesbecomecharged

t

AreaForce

(a) (b)

+ + + + + +

− − − − − − −

Figure 2.36 LVDT with

bellows.

Primary coilSecondary coils

Iron rod

Bellows

Pressure

Page 45: Bolton Mechatronics

2.6 FLUID PRESSURE 45

where k is a constant and S a constant termed the charge sensitivity. Thecharge sensitivity depends on the material concerned and the orientation of itscrystals. Quartz has a charge sensitivity of 2.2 pC/N when the crystal is cutin one particular direction and the forces applied in a specific direction; bar-ium titanate has a much higher charge sensitivity of the order of 130 pC/Nand lead zirconate–titanate about 265 pC/N.

Metal electrodes are deposited on opposite faces of the piezoelectric crys-tal (Figure 2.38(b)). The capacitance C of the piezoelectric material betweenthe plates is

where is the relative permittivity of the material, A is area and t its thick-ness. Since the charge where v is the potential difference producedacross a capacitor, then

The force F is applied over an area A and so the applied pressure p is and if we write this being termed the voltage sensitivityfactor, then

The voltage is proportional to the applied pressure. The voltage sensitiv-ity for quartz is about 0.055 Pa. For barium titanate it is about0.011 Pa.

Piezoelectric sensors are used for the measurement of pressure, force andacceleration. The applications have, however, to be such that the charge pro-duced by the pressure does not have much time to leak off and thus tends tobe used mainly for transient rather than steady pressures.

The equivalent electric circuit for a piezoelectric sensor is a charge gen-erator in parallel with capacitance and in parallel with the resistance arising from leakage through the dielectric (Figure 2.39(a)). When the sen-sor is connected via a cable, of capacitance to an amplifier of input capac-itance and resistance we have effectively the circuit shown in Figure2.39(b) and a total circuit capacitance of in parallel with aresistance of When the sensor is subject to pressure itbecomes charged, but because of the resistance the capacitor will dischargewith time. The time taken for the discharge will depend on the time constantof the circuit.

RARs>(RA + Rs).Cs + Cc + CA

RA,CA

Cc,

RsCs

V/mV/m

v = Svtp

Sv = (S>e0er),F>A

v =St

e0 er

AF

q = Cv,er

C =e0er A

t

Figure 2.39 (a) Sensor

equivalent circuit, (b) sensor

connected to charge amplifier.

(a)

i

(b)

Sensor Cable Amplifier

Outputto display

RA

CACcCs

Rs

i

Page 46: Bolton Mechatronics

The traditional method of measuring the flow rate of liquids involves devicesbased on the measurement of the pressure drop occurring when the fluidflows through a constriction (Figure 2.41). For a horizontal tube, where isthe fluid velocity, the pressure and the cross-sectional area of the tubeprior to the constriction, the velocity, the pressure and the cross-sectional area at the constriction, with the fluid density, then Bernoulli’sequation gives

v21

2g+

P1

rg=

v22

2g+

P2

rg

rA2P2v2

A1P1

v1

Liquid flow2.7

46 CHAPTER 2 SENSORS AND TRANSDUCERS

2.6.2 Tactile sensor

A tactile sensor is a particular form of pressure sensor. Such a sensor is usedon the ‘fingertips’ of robotic ‘hands’ to determine when a ‘hand’ has come intocontact with an object. They are also used for ‘touch display’ screens where aphysical contact has to be sensed. One form of tactile sensor uses piezoelec-tric polyvinylidene fluoride (PVDF) film. Two layers of the film are used andare separated by a soft film which transmits vibrations (Figure 2.40). Thelower PVDF film has an alternating voltage applied to it and this results inmechanical oscillations of the film (the piezoelectric effect described above inreverse). The intermediate film transmits these vibrations to the upper PVDFfilm. As a consequence of the piezoelectric effect, these vibrations cause analternating voltage to be produced across the upper film. When pressure isapplied to the upper PVDF film its vibrations are affected and the outputalternating voltage is changed.

Figure 2.40 PVDF tactile

sensor.

PVDF

Soft film

A.C. inputOutput

PVDF

Figure 2.41 Fluid flow through

a constriction.

Flow of fluid

Cross-sectional area A1

Constriction

Cross-sectional area A2

Pressure p1

Pressure p2 Velocity v2

Velocity v1

Since the mass of liquid passing per second through the tube prior to theconstriction must equal that passing through the tube at the constriction, wehave But the quantity Q of liquid passing through the tubeper second is Hence

Q =A

21 - (A2>A1)2 A

2(P1 - P2)

r

A1v1 = A2v2.A1v1r = A2v2r.

Page 47: Bolton Mechatronics

2.8 LIQUID LEVEL 47

Thus the quantity of fluid flowing through the pipe per second is proportionalto (pressure difference). Measurements of the pressure difference can thusbe used to give a measure of the rate of flow. There are many devices based onthis principle, and the following example of the orifice plate is probably one ofthe commonest.

2.7.1 Orifice plate

The orifice plate (Figure 2.42) is simply a disc, with a central hole, which isplaced in the tube through which the fluid is flowing. The pressure differ-ence is measured between a point equal to the diameter of the tube upstreamand a point equal to half the diameter downstream. The orifice plate issimple, cheap, with no moving parts, and is widely used. It does not, how-ever, work well with slurries. The accuracy is typically about of fullrange, it is non-linear, and it does produce quite an appreciable pressure lossin the system to which it is connected.

2.7.2 Turbine meter

The turbine flowmeter (Figure 2.43) consists of a multi-bladed rotor that issupported centrally in the pipe along which the flow occurs. The fluid flowresults in rotation of the rotor, the angular velocity being approximately pro-portional to the flow rate. The rate of revolution of the rotor can be deter-mined using a magnetic pick-up. The pulses are counted and so the numberof revolutions of the rotor can be determined. The meter is expensive withan accuracy of typically about

The level of liquid in a vessel can be measured directly by monitoring theposition of the liquid surface or indirectly by measuring some variablerelated to the height. Direct methods can involve floats; indirect methodsinclude the monitoring of the weight of the vessel by, perhaps, load cells. Theweight of the liquid is Ah g, where A is the cross-sectional area of the ves-sel, h the height of liquid, its density and g the acceleration due to gravity.Thus changes in the height of liquid give weight changes. More commonly,indirect methods involve the measurement of the pressure at some point inthe liquid, the pressure due to a column of liquid of height h being h g,where is the liquid density.

2.8.1 Floats

A direct method of monitoring the level of liquid in a vessel is by monitoringthe movement of a float. Figure 2.44 illustrates this with a simple float system.The displacement of the float causes a lever arm to rotate and so move a slideracross a potentiometer. The result is an output of a voltage related to the heightof liquid. Other forms of this involve the lever causing the core in an LVDT tobecome displaced, or stretch or compress a strain-gauged element.

rr

rr

;0.3%.

;1.5%

1

Figure 2.42 Orifice plate.

Pressure difference

Orifice plate

Turbine

Magnetic pick-up coil

Liquid level2.8

Figure 2.43 Turbine

flowmeter.

Output

D.C.Potentiometer

Figure 2.44 Float system.

Page 48: Bolton Mechatronics

Changes that are commonly used to monitor temperature are the expansion orcontraction of solids, liquids or gases, the change in electrical resistance of con-ductors and semiconductors and thermoelectric e.m.f.s.The following are someof the methods that are commonly used with temperature control systems.

2.9.1 Bimetallic strips

This device consists of two different metal strips bonded together. The metalshave different coefficients of expansion and when the temperature changes thecomposite strip bends into a curved strip, with the higher coefficient metal onthe outside of the curve. This deformation may be used as a temperature-controlled switch, as in the simple thermostat which was commonly used withdomestic heating systems (Figure 2.46). The small magnet enables the sensor

48 CHAPTER 2 SENSORS AND TRANSDUCERS

Figure 2.46 Bimetallic

thermostat.

Bimetallicstrip

High-expansivity

material

Low-expansivity

material

Soft ironSmall magnet

Set temp.adjustment

Electricalconnections

2.8.2 Differential pressure

Figure 2.45 shows two forms of level measurement based on the measure-ment of differential pressure. In Figure 2.45(a), the differential pressure celldetermines the pressure difference between the liquid at the base of the ves-sel and atmospheric pressure, the vessel being open to atmospheric pressure.With a closed or open vessel the system illustrated in (b) can be used. Thedifferential pressure cell monitors the difference in pressure between thebase of the vessel and the air or gas above the surface of the liquid.

Figure 2.45 Using a differential

pressure sensor.

(a)

Differentialpressure cell

(b)

Differential pressure cellAtmosphere

Temperature2.9

Page 49: Bolton Mechatronics

2.9 TEMPERATURE 49

to exhibit hysteresis, meaning that the switch contacts close at a differenttemperature from that at which they open.

2.9.2 Resistance temperature detectors (RTDs)

The resistance of most metals increases, over a limited temperature range, ina reasonably linear way with temperature (Figure 2.47). For such a linearrelationship:

where is the resistance at a temperature the resistance at anda constant for the metal termed the temperature coefficient of resistance.

Resistance temperature detectors (RTDs) are simple resistive elements in theform of coils of wire of such metals as platinum, nickel or nickel–copper alloys;platinum is the most widely used. Thin-film platinum elements are often madeby depositing the metal on a suitable substrate, wire-wound elements involv-ing a platinum wire held by a high-temperature glass adhesive inside aceramic tube. Such detectors are highly stable and give reproducibleresponses over long periods of time. They tend to have response times of theorder of 0.5 to 5 s or more.

2.9.3 Thermistors

Thermistors are small pieces of material made from mixtures of metaloxides, such as those of chromium, cobalt, iron, manganese and nickel.These oxides are semiconductors. The material is formed into various formsof element, such as beads, discs and rods (Figure 2.48(a)).

a0°Ct(°C), R0Rt

Rt = R0(1 + at)

Figure 2.47 Variation of

resistance with temperature for

metals.

1

3

5

7

Rt

R0

0 400

Temperature (°C)

NickelCopper

Platinum

800

Figure 2.48 Thermistors:

(a) common forms, (b) typical

variation of resistance with

temperature.

0 40 80 120 160

Temperature (°C)

0

2

4

6

8

10

(b)(a)

Thermistor

Disc

Rod

Thermistor

Thermistor

Bead

Res

ista

nce

(kΩ

)

Page 50: Bolton Mechatronics

50 CHAPTER 2 SENSORS AND TRANSDUCERS

The resistance of conventional metal-oxide thermistors decreases in avery non-linear manner with an increase in temperature, as illustrated inFigure 2.48(b). Such thermistors have negative temperature coefficients(NTCs). Positive temperature coefficient (PTC) thermistors are, however,available. The change in resistance per degree change in temperature isconsiderably larger than that which occurs with metals. The resistance–temperature relationship for a thermistor can be described by an equation ofthe form

where is the resistance at temperature t, with K and being constants.Thermistors have many advantages when compared with other temperaturesensors. They are rugged and can be very small, so enabling temperaturesto be monitored at virtually a point. Because of their small size theyrespond very rapidly to changes in temperature. They give very largechanges in resistance per degree change in temperature. Their main disad-vantage is their non-linearity. Thermistors are used with the electronicsystems for cars to monitor such variables as air temperature and coolant airtemperature.

2.9.4 Thermodiodes and transistors

A junction semiconductor diode is widely used as a temperature sensor.When the temperature of doped semiconductors changes, the mobility oftheir charge carriers changes and this affects the rate at which electrons andholes can diffuse across a p–n junction. Thus when a p–n junction has apotential difference V across it, the current I through the junction is a functionof the temperature, being given by

where T is the temperature on the Kelvin scale, e the charge on an electron,and k and are constants. By taking logarithms we can write the equation interms of the voltage as

Thus, for a constant current, we have V proportional to the temperature onthe Kelvin scale and so a measurement of the potential difference across adiode at constant current can be used as a measure of the temperature. Sucha sensor is compact like a thermistor but has the great advantage of giving aresponse which is a linear function of temperature. Diodes for use as temper-ature sensors, together with the necessary signal conditioning, are suppliedas integrated circuits, e.g. LM3911, and give a very small compact sensor.The output voltage from LM3911 is proportional to the temperature at therate of

In a similar manner to the thermodiode, for a thermotransistor the volt-age across the junction between the base and the emitter depends on the tem-perature and can be used as a measure of temperature. A common method is

10 mV/°C.

V = a kT

eb lna I

I0

+ 1b

I0

I = I0 AeeV/kT - 1 B

bRt

Rt = Keb>t

Page 51: Bolton Mechatronics

2.9 TEMPERATURE 51

to use two transistors with different collector currents and determine thedifference in the base–emitter voltages between them, this difference beingdirectly proportional to the temperature on the Kelvin scale. Such transis-tors can be combined with other circuit components on a single chip to givea temperature sensor with its associated signal conditioning, e.g. LM35(Figure 2.49). This sensor can be used in the range to 110 and givesan output of

2.9.5 Thermocouples

If two different metals are joined together, a potential difference occursacross the junction. The potential difference depends on the metals used andthe temperature of the junction. A thermocouple is a complete circuit involv-ing two such junctions (Figure 2.50(a)).

10 mV/°C.°C-40

Figure 2.49 LM35.

Output

+5 V

LM35

Figure 2.50 (a) A thermocouple, (b) thermoelectric e.m.f.–temperature graphs.

0 200 400 600 800 1000 1200

E.M

.F. (

mV

)

SR

E J

T

K

Temperature (°C)

10

20

30

40

50

60

(b)

E.M.F. Metal AMetal A

Metal B

Hot junction

(a)

Reference junction

If both junctions are at the same temperature there is no net e.m.f. If,however, there is a difference in temperature between the two junctions,there is an e.m.f. The value of this e.m.f. E depends on the two metals con-cerned and the temperatures t of both junctions. Usually one junction isheld at 0 and then, to a reasonable extent, the following relationshipholds:

where a and b are constants for the metals concerned. Commonly used thermo-couples are shown in Table 2.1, with the temperature ranges over which theyare generally used and typical sensitivities. These commonly used thermo-couples are given reference letters. For example, the iron–constantan

E = at + bt2

°C

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52 CHAPTER 2 SENSORS AND TRANSDUCERS

thermocouple is called a type J thermocouple. Figure 2.50(b) shows how thee.m.f. varies with temperature for a number of commonly used pairs ofmetals.

A thermocouple circuit can have other metals in the circuit and theywill have no effect on the thermoelectric e.m.f. provided all their junctionsare at the same temperature. This is known as the law of intermediatemetals.

A thermocouple can be used with the reference junction at a temperatureother than 0 .The standard tables, however, assume a 0 junction and hencea correction has to be applied before the tables can be used. The correction isapplied using what is known as the law of intermediate temperatures,namely

The e.m.f. at temperature t when the cold junction is at 0 equals thee.m.f. at the intermediate temperature I plus the e.m.f. at tempera-ture I when the cold junction is at 0 . To illustrate this, consider a type Ethermocouple which is to be used for the measurement of temperature witha cold junction at 20 . What will be the thermoelectric e.m.f. at 200 ? Thefollowing is data from standard tables:

Temp. ( ) 0 20 200

E.M.F. (mV) 0 1.192 13.419

Using the law of intermediate temperatures

Note that this is not the e.m.f. given by the tables for a temperature of 180with a cold junction at 0 , namely 11.949 mV.

To maintain one junction of a thermocouple at 0 , i.e. have it immersedin a mixture of ice and water, is often not convenient. A compensation circuitcan, however, be used to provide an e.m.f. which varies with the temperatureof the cold junction in such a way that when it is added to the thermocouplee.m.f. it generates a combined e.m.f. which is the same as would have beengenerated if the cold junction had been at 0 (Figure 2.51). The compen-sating e.m.f. can be provided by the voltage drop across a resistancethermometer element.

°C

°C°C

°C

E200,0 = E200,20 + E20,0 = 13.419 - 1.192 = 12.227 mV

°C

°C°C

°CEI,0Et,I

°CEt,0

Et,0 = Et,I + EI,0

°C°C

Table 2.1 Thermocouples.Ref. Materials Range ( ) ( V/ )

B Platinum 30% 0 to 1800 3

rhodium/platinum 6% rhodium

E Chromel/constantan 200 to 1000 63

J Iron/constantan 200 to 900 53

K Chromel/alumel 200 to 1300 41

N Nirosil/nisil 200 to 1300 28

R Platinum/platinum 13% rhodium 0 to 1400 6

S Platinum/platinum 10% rhodium 0 to 1400 6

T Copper/constantan 200 to 400 43 -

----

°Cm°C

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2.10 LIGHT SENSORS 53

The base-metal thermocouples, E, J, K and T, are relatively cheap butdeteriorate with age. They have accuracies which are typically about to3%. Noble-metal thermocouples, e.g. R, are more expensive but are morestable with longer life. They have accuracies of the order of orbetter.

Thermocouples are generally mounted in a sheath to give them mechanicaland chemical protection.The type of sheath used depends on the temperaturesat which the thermocouple is to be used. In some cases the sheath is packedwith a mineral which is a good conductor of heat and a good electrical insula-tor. The response time of an unsheathed thermocouple is very fast. With asheath this may be increased to as much as a few seconds if a large sheath isused. In some instances a group of thermocouples are connected in series sothat there are perhaps 10 or more hot junctions sensing the temperature. Thee.m.f. produced by each is added together. Such an arrangement is known as athermopile.

Photodiodes are semiconductor junction diodes (see Section 9.3.1 for adiscussion of diodes) which are connected into a circuit in reverse bias, sogiving a very high resistance (Figure 2.52(a)). With no incident light, thereverse current is almost negligible and is termed the dark current. Whenlight falls on the junction, extra hole–electron pairs are produced andthere is an increase in the reverse current and the diode resistance drops

;1%

;1

Figure 2.51 Cold junction

compensation.Display

Compensation circuit

Resistanceelement

Block at constanttemperature

Hotjunction

MetalA

MetalB

Copper

Copper

Output ofcompensation p.d.

Light sensors2.10

Figure 2.52 Photodiode.Reverse bias

(a) (b)

+−

− +0

Dark current

Increasinglight intensity

Reversecurrent

Reverse bias voltage

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54 CHAPTER 2 SENSORS AND TRANSDUCERS

(Figure 2.52(b)). The reverse current is very nearly proportional tothe intensity of the light. For example, the current in the absence oflight with a reverse bias of 3 V might be 25 μA and when illuminatedby 25 000 lumens/ the current rises to 375 μA. The resistance of thedevice with no light is and with light is

A photodiode can thus be used as a variable resist-ance device controlled by the light incident on it. Photodiodes have a veryfast response to light.

The phototransistors (see Section 9.3.3 for a discussion of transistors)have a light-sensitive collector–base p–n junction. When there is no incidentlight there is a very small collector-to-emitter current. When light is inci-dent, a base current is produced that is directly proportional to the lightintensity. This leads to the production of a collector current which is then ameasure of the light intensity. Phototransistors are often available as inte-grated packages with the phototransistor connected in a Darlington arrange-ment with a conventional transistor (Figure 2.53). Because this arrangementgives a higher current gain, the device gives a much greater collector currentfor a given light intensity.

A photoresistor has a resistance which depends on the intensity of thelight falling on it, decreasing linearly as the intensity increases. The cadmiumsulphide photoresistor is most responsive to light having wavelengths shorterthan about 515 nm and the cadmium selinide photoresistor for wavelengthsless than about 700 nm.

An array of light sensors is often required in a small space in order todetermine the variations of light intensity across that space. An example ofthis is in the digital camera to capture the image being photographed andconvert it into a digital form. For this purpose a charge-coupled device(CCD) is often used. A CCD is a light-sensitive arrangement of many smalllight-sensitive cells termed pixels. These cells are basically a p-layer of silicon,separated by a depletion layer from an n-type silicon layer. When exposed tolight, a cell becomes electrically charged and this charge is then converted byelectronic circuitry into an 8-bit digital number. In taking a photograph thedigital camera electronic circuitry discharges the light-sensitive cells, activatesan electromechanical shutter to expose the cells to the image, then reads the8-bit charge value for each cell and so captures the image. Since the pn cellsare colour blind and we need colour photographs, the light passes through acolour filter matrix before striking the cells. This allows just green light tofall on some cells, blue on others and red light on others. Then, by latertaking account of the output from neighbouring cells, a colour image can becreated.

In selecting a sensor for a particular application there are a number of factorsthat need to be considered:

1 The nature of the measurement required, e.g. the variable to be measured,its nominal value, the range of values, the accuracy required, the requiredspeed of measurement, the reliability required, the environmental condi-tions under which the measurement is to be made.

8 kÆ.3>(375 * 10-6) =3>(25 * 10-6) = 120 kÆ

m2

Figure 2.53 Photo Darlington.

Selection ofsensors

2.11

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2.12 INPUTTING DATA BY SWITCHES 55

2 The nature of the output required from the sensor, this determining thesignal conditioning requirements in order to give suitable output signalsfrom the measurement.

3 Then possible sensors can be identified, taking into account such fac-tors as their range, accuracy, linearity, speed of response, reliability,maintainability, life, power supply requirements, ruggedness, availa-bility, cost.

The selection of sensors cannot be taken in isolation from a consideration ofthe form of output that is required from the system after signal conditioning,and thus there has to be a suitable marriage between sensor and signal con-ditioner.

To illustrate the above, consider the selection of a sensor for the measure-ment of the level of a corrosive acid in a vessel. The level can vary from 0 to2 m in a circular vessel which has a diameter of 1 m. The empty vessel has aweight of 100 kg. The minimum variation in level to be detected is 10 cm.The acid has a density of 1050 kg/ . The output from the sensor is to beelectrical.

Because of the corrosive nature of the acid an indirect method of deter-mining the level seems appropriate. Thus it is possible to use a load cell, orload cells, to monitor the weight of the vessel. Such cells would give an elec-trical output. The weight of the liquid changes from 0 when empty to, whenfull, Adding this to the weight ofthe empty vessel gives a weight that varies from about 1 to 17 kN. The reso-lution required is for a change of level of 10 cm, i.e. a change in weight of

If three load cells are used to sup-port the tank then each will require a range of about 0 to 6 kN with a reso-lution of 0.27 kN. Manufacturers’ catalogues can then be consulted to see ifsuch load cells can be obtained.

Mechanical switches consist of one or more pairs of contacts which can bemechanically closed or opened and in doing so make or break electrical cir-cuits. Thus 0 or 1 signals can be transmitted by the act of opening or closinga switch. The term limit switch is used when the switches are opened orclosed by the displacement of an object and used to indicate the limit of itsdisplacement before action has to be initiated.

Mechanical switches are specified in terms of their number of poles andthrows. Poles are the number of separate circuits that can be completed bythe same switching action and throws are the number of individual contactsfor each pole. Figure 2.54(a) shows a single pole–single throw (SPST)switch, Figure 2.54(b) a single pole–double throw (SPDT) switch andFigure 2.54(c) a double pole–double throw (DPDT) switch.

0.10 * 1050 * p(12>4) * 9.8 = 0.8 kN.

1050 * 2 * p(12>4) * 9.8 = 16.2 kN.

m3

Inputting databy switches

2.12

Figure 2.54 Switches:

(a) SPST, (b) SPDT, (c) DPDT.

(a) (b) (c)

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56 CHAPTER 2 SENSORS AND TRANSDUCERS

2.12.1 Debouncing

A problem that occurs with mechanical switches is switch bounce. When amechanical switch is switched to close the contacts, we have one contact beingmoved towards the other. It hits the other and, because the contacting ele-ments are elastic, bounces. It may bounce a number of times (Figure 2.55(a))before finally settling to its closed state after, typically, some 20 ms. Each ofthe contacts during this bouncing time can register as a separate contact.Thus, to a microprocessor, it might appear that perhaps two or more separateswitch actions have occurred. Similarly, when a mechanical switch is opened,bouncing can occur. To overcome this problem either hardware or softwarecan be used.

Initially,no connection

Connectionmade

Bounces

Finalclosed

contacts

(a)

+5 V

+5 V

(b)

Clocksignal input

(c)

S Q

R

D Q

CLK

Figure 2.55 (a) Switch bounce

on closing a switch,

(b) debouncing using an SR flip-

flop, (c) debouncing using a

D flip-flop.

With software, the microprocessor is programmed to detect if the switchis closed and then wait, say, 20 ms. After checking that bouncing has ceasedand the switch is in the same closed position, the next part of the programcan take place. The hardware solution to the bounce problem is based on theuse of a flip-flop. Figure 2.55(b) shows a circuit for debouncing an SPDTswitch which is based on the use of an SR flip-flop (see Section 5.4.1). Asshown, we have S at 0 and R at 1 with an output of 0. When the switch ismoved to its lower position, initially S becomes 1 and R becomes 0. Thisgives an output of 1. Bouncing in changing S from 1 to 0 to 1 to 0, etc. givesno change in the output. Such a flip-flop can be derived from two NOR ortwo NAND gates. An SPDT switch can be debounced by the use of a D flip-flop (see Section 5.4.4). Figure 2.55(c) shows the circuit. The output fromsuch a flip-flop only changes when the clock signal changes. Thus by choos-ing a clock period which is greater than the time for which the bounces last,say, 20 ms, the bounce signals will be ignored.

An alternative method of debouncing using hardware is to use a Schmitttrigger.This device has the ‘hysteresis’ characteristic shown in Figure 2.56(a).When the input voltage is beyond an upper switching threshold and giving alow output, then the input voltage needs to fall below the lower thresholdbefore the output can switch to high. Conversely, when the input voltage isbelow the lower switching threshold and giving a high, then the input needsto rise above the upper threshold before the output can switch to low. Sucha device can be used to sharpen slowly changing signals: when the signalpasses the switching threshold it becomes a sharply defined edge between

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2.12 INPUTTING DATA BY SWITCHES 57

two well-defined logic levels. The circuit shown in Figure 2.56(b) can be usedfor debouncing; note the circuit symbol for a Schmitt trigger. With theswitch open, the capacitor becomes charged and the voltage applied to theSchmitt trigger becomes high and so it gives a low output. When the switchis closed, the capacitor discharges very rapidly and so the first bounce dis-charges the capacitor; the Schmitt trigger thus switches to give a high out-put. Successive switch bounces do not have time to recharge the capacitor tothe required threshold value and so further bounces do not switch theSchmitt trigger.

2.12.2 Keypads

A keypad is an array of switches, perhaps the keyboard of a computer or thetouch input membrane pad for some device such as a microwave oven. Acontact-type key of the form generally used with a keyboard is shown inFigure 2.57(a). Depressing the key plunger forces the contacts together withthe spring returning the key to the off position when the key is released. A typ-ical membrane switch (Fig. 2.57(b)) is built up from two wafer-thin plastic

Out

put

High

Low

Lower threshold

Input

(a) (b)

Schmitt trigger

Switch

VCC

Debouncedoutput

Figure 2.56 Schmitt trigger:

(a) characteristic, (b) used for

debouncing a switch.

Figure 2.57 (a) Contact key,

(b) membrane key, (c) 16-way

keypad.

Key plunger

Switch contacts

(a)

+5 V

1

2

3

4

5

6

7

8

(c)(b)

Applied pressure

Conductive layers

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58 CHAPTER 2 SENSORS AND TRANSDUCERS

films on which conductive layers have been printed. These layers are sepa-rated by a spacer layer. When the switch area of the membrane is pressed, thetop contact layer closes with the bottom one to make the connection and thenopens when the pressure is released.

While each switch in such arrays could be connected individually to givesignals when closed, a more economical method is to connect them in anarray where an individual output is not needed for each key but each keygives a unique row–column combination. Figure 2.57(c) shows the connec-tions for a 16-way keypad.

Summary

A sensor is an element which produces a signal relating to the quantity beingmeasured. A transducer is an element that, when subject to some physicalchange, experiences a related change. Thus sensors are transducers.However, a measurement system may use transducers, in addition to the sen-sor, in other parts of the system to convert signals in one form to anotherform.

The range of a transducer defines the limits between which the inputcan vary. Span is the maximum value of the input minus the minimumvalue. The error is the difference between the result of a measurement andits true value. Accuracy is the extent to which the measured value might bewrong. Sensitivity indicates how much output there is per unit input.Hysteresis error is the difference between the values obtained whenreached by a continuously increasing and a continuously decreasing change.Non-linearity error is the error given by assuming a linear relationship.Repeatability/reproducibility is a measure of the ability to give the sameoutput for repeated applications of the same input. Stability is the abilityto give the same output for a constant input. Dead band is the range ofinput values for which there is no output. Resolution is the smallest changein input that will produce an observable change in output. Response timeis the time that elapses after a step input before the output reaches a speci-fied percentage, e.g. 95%, of the input. The time constant is 63.2% of theresponse time. Rise time is the time taken for the output to rise to somespecified percentage of its steady-state output. Settling time is the timetaken for the output to settle down to within some percentage, e.g. 2%, ofthe steady-state value.

Problems

2.1 Explain the significance of the following information given in the specifica-tion of transducers:

(a) A piezoelectric accelerometer. Non-linearity: of full range.

(b) A capacitive linear displacement transducer. Non-linearity and hysteresis: of full range. ;0.01%

;0.5%

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PROBLEMS 59

(c) A resistance strain gauge force measurement transducer. Temperature sensitivity: of full range over normal environmentaltemperatures.

(d) A capacitance fluid pressure transducer. Accuracy: of displayed reading.

(e) Thermocouple. Sensitivity: nickel chromium/nickel aluminium thermocouple: 0.039 mV/ when the cold junction is at 0 .

(f) Gyroscope for angular velocity measurement. Repeatability: of full range.

(g) Inductive displacement transducer. Linearity: of rated load.

(h) Load cell.Total error due to non-linearity, hysteresis and non-repeatability: .

2.2 A copper–constantan thermocouple is to be used to measure temperaturesbetween 0 and 200 . The e.m.f. at 0 is 0 mV, at 100 it is 4.277 mV andat 200 it is 9.286 mV. What will be the non-linearity error at 100 as apercentage of the full range output if a linear relationship is assumedbetween e.m.f. and temperature over the full range?

2.3 A thermocouple element when taken from a liquid at 50°C and plunged intoa liquid at 100 at time gave the following e.m.f. values. Determinethe 95% response time.

Time (s) 0 20 40 60 80 100 120

E.M.F. (mV) 2.5 3.8 4.5 4.8 4.9 5.0 5.0

2.4 What is the non-linearity error, as a percentage of full range, produced whena 1 k potentiometer has a load of 10 k and is at one-third of its maximumdisplacement?

2.5 What will be the change in resistance of an electrical resistance strain gaugewith a gauge factor of 2.1 and resistance 50 if it is subject to a strain of0.001?

2.6 You are offered a choice of an incremental shaft encoder or an absoluteshaft encoder for the measurement of an angular displacement. What is theprincipal difference between the results that can be obtained by thesemethods?

2.7 A shaft encoder is to be used with a 50 mm radius tracking wheel to mon-itor linear displacement. If the encoder produces 256 pulses per revolu-tion, what will be the number of pulses produced by a linear displacementof 200 mm?

2.8 A rotary variable differential transformer has a specification which includesthe following information:

Ranges: , linearity error full rangelinearity error full range

Sensitivity: 1.1 (mV/V input)/degreeImpedance: primary 750 , secondary 2000

What will be (a) the error in a reading of due to non-linearity when theRDVT is used on the range, and (b) the output voltage change thatoccurs per degree if there is an input voltage of 3 V?

;60°40°

ÆÆ

;2.0%;60°,;0.5%;30°

Æ

ÆÆ

t = 0°C

°C°C°C°C°C

;0.1%

;1%

;0.01%

°C°C

;1%

;1%

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60 CHAPTER 2 SENSORS AND TRANSDUCERS

2.9 What are the advantages and disadvantages of the plastic film type of poten-tiometer when compared with the wire-wound potentiometer?

2.10 A pressure sensor consisting of a diaphragm with strain gauges bonded to itssurface has the following information in its specification:

Ranges: 0 to 1400 kPa, 0 to 35 000 kPaNon-linearity error: of full rangeHysteresis error: of full range

What is the total error due to non-linearity and hysteresis for a reading of1000 kPa on the 0 to 1400 kPa range?

2.11 The water level in an open vessel is to be monitored by a differential pres-sure cell responding to the difference in pressure between that at the base ofthe vessel and the atmosphere. Determine the range of differential pressuresthe cell will have to respond to if the water level can vary between zero heightabove the cell measurement point and 2 m above it.

2.12 An iron–constantan thermocouple is to be used to measure temperaturesbetween 0 and 400 . What will be the non-linearity error as a percentage ofthe full-scale reading at 100 if a linear relationship is assumed betweene.m.f. and temperature?

2.13 A platinum resistance temperature detector has a resistance of 100.00 at0 , 138.50 at 100 and 175.83 at 200 . What will be the non-linear-ity error in at 100 if the detector is assumed to have a linear relation-ship between 0 and 200 ?

2.14 A strain gauge pressure sensor has the following specification. Will it be suit-able for the measurement of pressure of the order of 100 kPa to an accuracyof kPa in an environment where the temperature is reasonably constantat about 20 ?

Ranges: 2 to 70 MPa, 70 kPa to 1 MPaExcitation: 10 V d.c. or a.c. (r.m.s.)Full range output: 40 mVNon-linearity and hysteresis errors: Temperature range: to

Thermal shift zero: 0.030% full range output/Thermal shift sensitivity: 0.030% full range output/

2.15 A float sensor for the determination of the level of water in a vessel has acylindrical float of mass 2.0 kg, cross-sectional area 20 and a length of1.5 m. It floats vertically in the water and presses upwards against a beamattached to its upward end. What will be the minimum and maximumupthrust forces exerted by the float on the beam? Suggest a means by whichthe deformation of the beam under the action of the upthrust force could bemonitored.

2.16 Suggest a sensor that could be used as part of the control system for a fur-nace to monitor the rate at which the heating oil flows along a pipe. The out-put from the measurement system is to be an electrical signal which can beused to adjust the speed of the oil pump. The system must be capable of

cm2

°C°C

+120°C-54;0.5%

°C;5

°C°C°C

°CÆ°CÆ°CÆ

E.M.F. at 100°C = 5.268 mV; e.m.f. at 400°C = 21.846 mV

°C°C

;0.05%;0.15%

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PROBLEMS 61

operating continuously and automatically, without adjustment, for long periodsof time.

2.17 Suggest a sensor that could be used, as part of a control system, to determinethe difference in levels between liquids in two containers. The output is toprovide an electrical signal for the control system.

2.18 Suggest a sensor that could be used as part of a system to control the thick-ness of rolled sheet by monitoring its thickness as it emerges from rollers.The sheet metal is in continuous motion and the measurement needs to bemade quickly to enable corrective action to be taken quickly. The measure-ment system has to supply an electrical signal.