ee-474 feedback control system_2012

PRACTICAL WORK BOOKFor Academic Session 2012

FEEDBACK CONTROL SYSTEM (EE-474)For

BE (EE), BE (EL)

Name:Roll Number:Class:Batch: Semester/Term:Department :

Department of Electrical EngineeringNED University of Engineering & Technology

SAFETY RULES

1. Please don’t touch any live parts. 2. Never use an electrical tool in a damp place. 3. Don’t carry unnecessary belongings during performance of practicals (like

water bottle, bags etc). 4. Before connecting any leads/wires, make sure power is switched off. 5. In case of an emergency, push the nearby red color emergency switch of the

panel or immediately call for help. 6. In case of electric fire, never put water on it as it will further worsen the

condition; use the class C fire extinguisher. Fire is a chemical reaction involving rapid oxidation (combustion) of fuel. Three basic conditions when met, fire takes place. These are fuel, oxygen & heat, absence of any one of the component will extinguish the fire.

If there is a small electrical fire, be sure to use only a Class C or multipurpose (ABC) fire extinguisher, otherwise you might make the problem worsen. The letters and symbols are explained in left figure. Easy to remember words are also shown.

Don’t play with electricity, Treat electricity with respect, it deserves!

Figure: Fire Triangle

A(think ashes): paper, wood etc

B(think barrels): flammable liquids

C(think circuits): electrical fires

Feedback Control Systems ContentsNED University of Engineering and Technology Department of Electrical Engineering

Revised 2012 UP/ SAH

Lab Exercise Schedule

* Because of the excellent coverage of the subject, the experiments are taken from the Manual of Control Systems Lab, at the Lawrence

Technological university, By Professor B. D. Sweet.

DateSe

ssio

n N

o.

Exe

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e N

o.

Title of Experiments

Pa

ge

No

R e ma r ks

A - PID Control

1 1To Study the closed loop automatic control of level

2 2

To Study the effects of Proportional, Integrative and Derivative Components on the Automatic Level Control System

3EX 3: 3.1-3.2

PID control of Flow rate: Familiarization with the plant

4EX 3: 3.3-3.5

To Study the effects of Proportional, Integrative and Derivative Components on the Automatic Flow rate Control System

B - Analogue Servo Trainer

5 4 Familiarization with Analog Servo Trainer

6 5 Preliminary Procedures for Operation

7 6 Transient Response of the DC Motor

C - Modular Servo System

8* EX 7:7.0 To become familiar with the system

9*EX 7:7.5.1, 7.5.2

Parameter Determination of the Modular Servo System: VMAX, km, kt

10*EX 7:7.5.3, 7.5.4

Parameter Determination of the Modular Servo System: τm, kp

11*EX 7:7.5.5,

7.6

Parameter Determination of the Modular Servo System: Gain verification, τ1 and summarization

12* EX 8:8.5

Closed Loop Position Control System Design: Introduction and Pre-Lab

13* EX 8:8.6

Closed Loop Position Control System Design: Procedure

Feedback Control Systems Exercise 1 NED University of Engineering and Technology Department of Electrical Engineering

1

A – PID Control

Exercise 1 PID Control of Level

1.1 Object: To study the Close loop Automatic Control of level and the effect caused by the variation in the conditions.

1.2 Equipment: 1. Measurement Unit mod. IU9/EV. 2. Power Supply module PS1-PSU/EV. 3. Module holder. 4. Level, Pressure and Flow rate transducer kit G30A. 5. Level and Flow Control kit G30B. 6. Attachment unit TY30A/EV. 7. DIN cable. 8. Connecting wires.

1.3 Theory: MEASUREMENT OF LEVEL AND PRESSURE With pressure and level measurements, the pressure sensor set at the bottom of the vertical column of unit TY30A/EV is used see the figure bellow:


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DEFINITION OF AN ANALOG VARIABLE: An analog measurement ring permits the generation of a D.C. voltage which behavior follows the water level in the column; this means that each value of the column corresponds to only one value of the output voltage. So there is analogy between the level and the variable representing it (output voltage of the measurement system). We can say that a variable or information is analog when it varies in continuous, or when, it cannot be discontinuous by its own nature. This means that an analog variable (in our case, the water level of the column) can take infinite values.

THE PRESSURE SENSOR: Under static condition, the level of a liquid is linked to pressure, according to a law of proportionality. If "1" represents the level, which is the height, of a liquid in a tank, the pressure at the bottom will be given by:

p = 1.g.Ms where:

p = pressure (in Pa = Pascal = N.m2 = 10-5 bar) L = level (in m)

g = acceleration of gravity (g = 9.81 m.s-2) Ms = specific mass of the liquid (kg.m-3).

Consequently, it is sufficient to measure the pressure to obtain the level. Among the different available pressure transducers, the STRAIN GAUGE ones have become the mostly used.

The operating principle of these transducers is the piezo-resistivity (property of the materials which change their resistance as function of the deformation to which they are subjected). The four resistors connected at Wheatstone's bridge are taken from a silicon diaphragm (fig. bellow).


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The diaphragm is then welded on a glass ring which supports it. The bridge is powered on a diagonal by a constant voltage generator and a voltage variable with pressure which acts on the diaphragm is taken from the opposite diagonal. In this system, the sensor uses the pressure of the water on the column to generate an elementary deformation on the in-built strain gauges. The strain gauges are resistors, whose resistive value depends on the deformations they are subjected. In the sensor used, the resistors are connected with a Wheatstone's bridge, so the output voltage Vo varies proportionally with pressure. The sensor used in our system has an operation range ("pressure range") which varies from 0 to 0.07 bar. The dynamic of the output voltage of the last circuit is of 42 mV (which represents the Full Scale Output), when there is a power voltage of 10V. This device is available as differential sensor or, in this case, as absolute pressure sensor. In module G30A, the connection between level sensor and its signal conditioner is carried out via a cable to be inserted on the 8-pin DIN sockets marked as "TRANSDUCERS".

1.4 GENERAL NOTIONS: Before dealing with the control of level and flow, we will briefly survey the main concepts of automatic control which are necessary to understand the same process. This is not a treatment on the Theory of Automatic Controls, we just take the concepts of this theory which are necessary to explain the process controls. A "PHYSICAL PROCESS" or simply a "PROCESS" is a complex set of physical transformations and/or matter and/or energy transmissions. Examples of industrial processes can be: petrol refinery, metal lamination, vapour production, etc. These complex processes consist of more elementary processes.

The Theory of Automatic Controls, in fact, demonstrates that the knowledge of the single parts of the system gives the knowledge of the whole system. A "CONTROL" is the set of actions to be performed to condition a process until it takes the wished behavior. An "AUTOMATIC CONTROL" is the set of control actions made without the intervention of man. These actions can be made by the devices composing the "CONTROL SYSTEM. In a manual control, the action developed by man varies continuously according to the result coming from the comparison between the information related to the value of the controlled variable and the information related to the value prescribed for this variable. In automatic control, instead, the system alone can control the variables of the control action in order to zero the difference between the value taken by the controlled variable and the one


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prescribed for it. An "INPUT" or "SET-POINT" is the stimulus (or excitation) applied to the control system. It represents the ideal behavior of the output of the process. The "OUTPUT" of the process is the variable of the process which is wished to be controlled. A "SYSTEM" is the set composed by the process and by the control system.

DIVISION OF THE CONTROL SYSTEMS The control systems are classified into two general categories, precisely:

* Open-loop systems. * Feedback or Closed-loop Systems. An open-loop system is characterized by the fact that the control action is independent from the output. In closed-loop systems, instead, the control action depends in some way from the output. It is just the shift between the controlled action and the value of the reference variables which starts an action which last purpose is to zero this shift.

The block diagram of a generic control system with negative feedback is given bellow:

The meaning of the blocks and the signals is the following: Controller:

It consists by the set of devices required to generate a proper control signal to be applied to the amplifier and then to the process. Transducer and Signal Conditioner:

These are devices which convert the physical variable of the controlled output, into a variable homogeneous with the Set-Point.


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Error Signal: It is the signal obtained by the difference between the Set-Point and the feedback signal supplied by the Signal Conditioner.

Disturbance: It is an unwished (input) signal which changes the value of the output. The main advantages of the closed-loop control systems in respect to the open-loop ones and which justify the use of the closed-loop control can be synthesized in this way: Less sensitivity to parametric variations. Less effects on the disturbing actions.

The importance of these two advantages can be better explained by the fact that parametric variations and disturbances are generally aleatory, i.e. unpredictable if not in their statistic characteristics.

1.5 Procedure: 1. Connections between G30A and G30B:

• Connect jack 15 of G30B to input +12V DC/1.5A of G30A. • Connect jack 3 of G30B to jack 6 of G30A.

2. Connection between G30A and TY30A:

• Connect “+” and “-” present on G30A to corresponding terminals of TY30A. • With DIN cable connect G30A to TY30A.

3. Power supply for module G- 30A: connect power supplies ± 12 VDC/2A and 5VDC/1.5A 4. Power supply for module G- 30B: connect ± 12 VDC/2A & +12VDC/2A. 5. Inside module G30A, connect terminals 6 to 7,8 to 14 this will enable display to show level of liquid. 6. Make connections as per figure given bellow. 7. Put level switch to ON position on G30A. 8. Open valve V1 of Unit TY30A to half position and turn valve V2 ON. 9. Turn switch I1 to position LEVEL. 10. Set PID controller to half way position with the knobs PROPORTIONAL, INTEGRATIVE and DERIVATIVE. 11. From Set-point and Error Block of G30B apply a voltage of 0V at terminal 2 and note the display of G30A. 12. Fill the observation table taking corresponding readings. 13. Also note the effect of changing the flow of fluid by varying valve V1. 14. Draw graph taking Set-point values on x-axis and level in mm on y-axis.


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1.6 Observation:

S/No Set-point value (Volts)

Level in mm

1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7

1.7 Result: The Automatic Close Loop System of Level Control is studied and the effect of variations are observed.


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Exercise 2 The effects of PID parameters on control system performance

2.1 Object: The effect of PROPORTIONAL, INTEGRETIVE and DERIVATIVE Components of PID Controller on Closed Loop Automatic Control of level.

2.2 Equipment: 9. Measurement Unit mod. IU9/EV. 10. Power Supply module PS1-PSU/EV. 11. Module holder. 12. Level, Pressure and Flow rate transducer kit G30A. 13. Level and Flow Control kit G30B. 14. Attachment unit TY30A/EV. 15. DIN cable. 16. Connecting wires.

2.3 Theory: Proportional Action (P): It is the action introduced by the amplifier attenuator. The output, apart from the multiplicative coefficient, is a perfect copy of the input. The figure shows an amplifier attenuator which transfer function is equal to KP.

Integrative Action (I): This action is introduced by a pure integrator. The transfer function of the block bellow which carries out the integrative action is equal to:

W(s) = KI/s = 1/(τI.s)


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Where “τI” is called “Time constant of the Integrative Action". The output, related to a step input, has a delay of linear kind. After a time equal to the constant of the Integrative action, the output reaches the value of the input. Once the input value is reached, the output keeps on rising with the same slope, until the input is null.

Derivative Action (D): It is the action introduced by a pure derivator. The output, relative to a linear ramp input, has a value equal to the one the input will take after a time equal to the constant of the derivative action. The transfer function is equal to:

W(s) = s.KD = s.Τd Where τD is called "Time Constant of the Derivative Action" and which physical meaning is shown in fig. bellow.

The value of the output, equal to the value the input will take after a time τD, is kept until the input changes slope.

Regulation with (P) Controller: With this kind of regulator the output signal of the controller is proportional to its input signal: the variable which can be varied in this case is the constant of proportionality, i.e. the ratio between output and input. There is a value of the output signal for each value of the input signal, this value is determined by the constant of proportionality. The above said is true only if the controller is ideal; with a real controller, if the constant of proportionality is too big or if the constant of proportionality is too high, there is saturation and consequently a nonlinear behavior. It is obvious that the behavior is linear only for a limited band of input values (proportional band). Refer to fig. to see this fact better.


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The error signal, obtained by the comparison between the reference signal (wished value for the output) and the signal supplied by the signal conditioner of the transducer (value effectively obtained across the output), normally constitutes the input signal of the controller; this signal, on passing across the proportional controller, is amplified by the constant of proportionality (KP). Outside the proportional band (where the behavior is linear) the controller determines a production of ON/OFF power, i.e the actuator is applied all the power available or nothing, while inside it the power is modulated.

Once the transistors are modulated, the power supplied by the amplifier of the actuator, depends on the power supplied by the load and by the efficiency of the same actuator. The main characteristic of this controller is to have an error always different from zero; we can affirm that the error is proportional to the gain of the regulator and depends on the coefficient KP and by the value of the proportional band. We can also say that the error different from zero is necessary to obtain an output voltage different from zero. You must also note that, when the KP increases, if the error diminishes, the system gets toward unstable condition. According to the proportional band set there are different behaviors of the controlled variable (in this case level) as function of time.


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Fig. shows different behaviours of automatic control of level with:

a) Too large Bp b) Correct Bp c) Too narrow Bp

Regulation with (P I) and (P I D) Controller: In the integrative controller, the output voltage is the integral of the input voltage. The main disadvantage of the controller with proportional action is that it always needs an input voltage different from zero (and consequently an error different from zero in closed-loop control systems) to have an output voltage different from zero. With the integrative action, there can be an output different from zero with null output and then the error with at steady state can be reduced to zero. Then, the great advantage of the integrative controller is to reach a steady state with null error. Anyway, if the inertia of the system is high or if the time constant of. The integrative action is high, it may happen that the system is taken to unstable conditions (oscillations). To solve these problems, we can put together the proportional and the integrative actions, in order to exploit the advantages of both regulations and reduce the introduced problems. If the oscillations remain, you can add the derivative action, together with the proportional integrative one: the effectiveness of the derivative action depends largely on the controlled variable. In the derivative controller the output is the derivate of the input function and so it has a high influence on the signals which rapidly vary. As limit case with constant input voltage, its output is null. While the process evolves, the derivative action decades and the integrative one takes its .place to reduce the regulations error to zero in respect to the steady state value. We will see, that in case of level and position regulation, the Influence of the derivative action is very poor due to the fact that the variables under test vary very slowly.


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Effects of increasing a parameter independently

Parameter Rise time Overshoot Settling time

Steady-state error Stability

Kp Decrease Increase Small change Decrease Degrade

Ki Decrease Increase Increase Decrease significantly Degrade

Kd Minor decrease

Minor decrease

Minor decrease No effect in theory Improve if Kd

small

2.4 Procedure: 1. Connections between G30A and G30B:

• Connect jack 15 of G30B to input +12V DC/1.5A of G30A. • Connect jack 3 of G30B to jack 6 of G30A.

2. Connection between G30A and TY30A: • Connect “+” and “-” present on G30A to corresponding terminals of TY30A. • With DIN cable connect G30A to TY30A.

3. Power supply for module G- 30A: connect power supplies ± 12 VDC/2A and 5VDC/1.5A 4. Power supply for module G- 30B: connect ± 12 VDC/2A & +12VDC/2A. 5. Inside module G30A, connect terminals 6 to 7,8 to 14 this will enable display to show level of liquid. 6. Make connections as per figure given bellow. 7. Put level switch to ON position on G30A. 8. Open valve V1 of Unit TY30A to half position and turn valve V2 ON. 9. Turn switch I1 to position LEVEL. 10. Insert only PROPROTIONAL action of controller by connecting only the P knob and setting it to minimum value. 11. From Set-point and Error Block of G30B apply a voltage of 0V at terminal 2 and note the voltage level at terminal 4 of Set-point Block which is the Error signal. 12. Fill the observation table taking corresponding readings. 13. Measure for all values indicated in the observation column. 14. Now change the value of KP by P knob to maximum and repeat the same. 15. Draw the two graphs on single graph paper taking Set-point values on x-axis and Error output on y-axis and also give your conclusion on the space provided. 16. Now insert Integrative and Derivative control on PID and put them on half way positions and measure the Error signal. 17. Note how the Integrative action tends to zero the Error. 18. Turn I & P knobs to minimum and check the error again. 19. Give your observation stating why system is not stable at high P values.


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2.4 Observations:

2.5 Result: The effects of different components of PID on Automatic Close Loop System of Level Control are studied and the effects of variations in Proportional Band are observed.


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Exercise 3 PID Control of Flow rate

3.1 Object To Study the effects of Proportional, Integrative and Derivative Components on the Automatic Flow rate Control System 3.2 Apparatus The process control system consists of a structure including the equipment required for exercises. 3.2.1 Equipment of the Cycle

• AISI 304 stainless steel structure

• Feeding tank of stainless steel AISI 304 L, with capacity of 1001.

• 2 centrifugal pumps for feeding, with body and impeller of stainless steel, flow

rate of 10 m3 /h, discharge head of 14 m of H2O column

• Column of borosilicate glass, DN 100, height of 1000mm

• Pneumatic control valve of stainless steel AISI 316, DN 20, CV = 7

• Pneumatic control valve, DN 15, CV = 0.32

• Electronic transmitter of differential pressure with body of stainless steel AISI

316, scale of 0 to 10000 mm of H2 O, output signal of 4 to 20 mA, accuracy of

0.1 %

• Electronic pressure transmitter with body of stainless steel AISI316, scale of 0 to

3 bars, output signal of 4 to 20 mA, accuracy of 0.1%

• Microprocessor controller with four PID control loops: first loop, control of flow

rate; second loop, control of level; third loop, control of pressure; accuracy of

0.1%.

• 2 electropneumatic converters of 4 to 20 mA/0.2 to 1 bar

• Calibrated diaphragm of stainless steel AISI 316 for measuring the flow rate,

with scale of 0 to 10m3 /h, DN 40, d = 26.6mm

• 2Bourdon pressure gauges, with scale of 0 to 6 bars

• Flowmeter with scale of 0.4 to 4 m3 /h

• 2 valves of ½ “, in stainless steel AISI 316

• 7 valves 1”, in stainless steel AISI 316


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Loop

Ind

Esc /Menu

• Vales of 1”, in stainless steel AISI 316

• Connecting pipes of stainless steel AISI 304

• Switchboard IP 55, including synoptic of the plant

• Emergency button

• Safety valve calibrated at 2.7 bars

• Pressure reducer including pressure gauge

3.2.2 Brief description of the microprocessor controller DIGITRIC 500

This plant is equipped with a controller Digitric 500, multiloop PID type, programmed as

follow:

• First loop; is used

To control the flow rate, initials FICI, range 0 10m3 /h

• Second loop; is used:

To control the level, initials LIC1, range 0 1000mmH2O

• Third loop; is used:

To control the pressure, initials PICI, range 0 3 bar

Display indication

• 1st line: text line where the indications of menu and submenus appear

• 2nd line: process variable

• 3rd line: display of set-point (SP) value, error; out, %, bar. That can be selected

with the key

• 4th line: indication of the current loop

Description of frontal panel

• Key : it enables to select the desired loop

• Key : it enables to vary the parameter appearing in the third line of the

display, or to set the parameters as it will be explained in the next page

• Key : it enables to enter the menu or to exit from the menu and

submenus without storing the variations carried out

Ind


15

M/A/C

Enter

Esc /Menu

Enter

• Key : it enables to enter the menu and submenus and to confirm the

variations carried out.

• Key : it enables to switch from the automatic mode to the manual

mode

• Keys : they enable to increase or to reduce the set-point value, the

value of the parameter selected in the programming or to run the menu and

submenus

• Key : it enables to display the set-point value in the third line

Setting the parameters

The parameters are set in the submenu parameter that can be entered according to

the following procedure:

• Enter the main menu pressing the key ; position on the

submenu parameter running the list of submenus with the keys ; then

enter the submenu pressing the key

• Choose the parameter to be modified running the list with the keys and

press the key Enter to select

• Modify the value of the parameter pressing key Enter and then the keys

; press the key Ind and shift to the digits of the number to be modified;

pressing the key Ind for 3 s shifts the decimal point

• Exit without confirming by pressing the key Esc /Menu

• Confirm the variation pressing the key Enter

Example: modify the value of GAIN (proportional band), integral and derivative action

• Press the key Esc/Menu

• Run the list of submenus with the keys up to Parameter

• Press the key Enter

• Position on the digit to be varied pressing the key Ind

• Increase or reduce the value with the key

SP-w


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• Confirm the variation pressing the key Enter

• Vary the integral action (RESET TIME Tn) operating as in the case of

GAIN

• Vary the derivative action (RATE TIME Tv) operating as in the case of

GAIN

Example: setting the action of controller (P, I e D)

• Press the pushbutton Esc/Menu

• Select the list of submenu ‘Configuration’ pushbutton

• Press the pushbutton Enter

• Select the loop you want with the pushbutton

• Press the pushbutton Enter and select CONTR.PARAM. With the

pushbutton

• Press the pushbutton Enter

• Press again the push button Enter

• Select the action (for example P control, only proportional) with the

push button

• To confirm press the pushbutton Enter and the, with the pushbutton

Esc/Menu , return to the main window

For further information on the instrument DIGITRIC refer to the function modification

manual and to the service instructions manual.

3.3 Procedure for control of flow rate

• Close the draining valve V1 of the tank D1

• Fill the tank D1 with demineralized water, if possible

• Close the valves V2, V4, V5, V7, V8, V11, V12, V14 and V15

• Open the valves V3, V6, V9, V10 and V13

• Connect the switchboard with the single-phase power supply of 230V,

50Hz


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• Connect the system with the network of compressed air and set the

pressure reducer at 1.4 bar

• Press the starting button

• Turn the switch of Flow rate/Level to “Flow rate”

• Select the first loop (FIC1) with the pushbutton Loop

• Set the first loop (control of flow rate) to manual mode with the

pushbutton M/A/C (red led on)

• Open the control valve FV1 partially: select the out with the pushbutton

Ind and set the out (proportional to the opening of the valve FV1) for

example at 50% with the push button

• Start the pump G1; switch in position 1

• Fix the value of flow rate, operating the pneumatic valve FV1 with the

pushbutton

• Select the set point with the push button SP-W

• Set the value of set point with the pushbutton

• Set the controller FIC1 to the automatic mode with the pushbutton

M/A/C (green led on)

• Adjust, if necessary, the value of gain and integral time of controller

• Varying the set point of the controller will increase or reduce the values

of flow rate

• Operate the valve V3 to provoke some noise to the control.

• In any emergency press the emergency button

• For normal stops, turn the switch of the pump G1 to 0

• In case of long period of inactivity (4-7 weeks), drain the plant

completely.


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3.4 Observations

Write your observations against each of the following:

1- For each of the following set point values of flow rate, record the steady state

response of the plant, operating in Automatic Mode.

S. No. Set Point

(m3/h) Kp

KI

TI

KD

TD

Steady state response

(m3/h)

1

2

3

4

5

6

7

8

9

2- Effect of variation in the set point on the system response.

3- The time delay associated with the change in system response

4- Effect due to the change in proportionality gain and the steady state error in the

system response


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5- Effect due to the change in integrator and derivative control gain and the steady

state error in the system response

3.5 Result:

The effects of Proportional, Integrative and Derivative Components on the Automatic Flow

rate Control System have been studied.


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B – Analogue Servo Trainer Exercise 4

Familiarization with Analog Servo Trainer

OBJECT: Familiarization with Analog Servo-Trainer. INTRODUCTION The 33-002 Servo Fundamentals Trainer is intended to provide students with a sound introduction to the principles of analogue servomechanisms, and by extension to those of closed-loop systems more generally. The 33-002 consists of 2 units: • Mechanical Unit 33-100 • Analogue Unit 33-110 which are connected as in fig.4.1, where dotted boxes represent essential additional items.

Fig 4.1 - Principal System Interconnect ions


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Mechanical Unit 33-1 00 Contains a power amplifier to drive the motor from an analogue or switched input. The motor drives the output shaft through a 32:1 belt reduction. The motor shaft also carries a magnetic brake disc and an analogue speed transducer (tachogenerator). A two-phase pulse train for digital speed and direction sensing is also derived from tracks on the brake disc. The output shaft carries analogue (potentiometer) and digital (64 location Gray code) angle transducers. The unit contains a simple signal generator to provide low frequency test signals; sine, square and triangular waves, and requires an external power supply providing: +15V, 0, —15V at 1.5A +5V, 0, at 0.5A The Feedback PS446 or 01-100 are suitable. Analogue Unit 33-110 Connects to the Mechanical Unit through a 34-way ribbon cable wlich aries c power supplies and signals enabling the normal circuit interconnections to be made on the Analogue Unit using the 2mm patching leads provided. The unit enables a basic system as in fig 4.2 to be configured and contains facilities to introduce compensation to investigate improvement in overall system performance.

Fig 4.2 Analogue Control System


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Analogue Unit (33-110)

Fig 4.3 - The Analogue Unit Fig 4.3 shows the general arrangement of the panel, interconnections are made by 2mm plug leads and there are a few 4mm sockets for conversion or oscilloscope connections. These sockets give the voltage signals from the input and output shaft potentiometers. These are represented diagrammatically in the centre of the panel, the potentiometers themselves being in the Mechanical Unit.


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Mechanical Unit (33-100)

Fig 4 .4 shows the general arrangement of the panels. The unit is common to both Analogue and Digital systems. Since all signals, including supplies, for both units are available from the 34-way socket, the unit can be operated from any source of suitable signals connected to the 34-way socket. For full details refer to Appendix B. Power Supplies External supplies of +1 5V and —1 5V at 1 .5A and of +5V at O.5A are required. The input sockets (4mm) are protected against accidental misconnection of supplies, though misconnection may blow a fuse.

Fig 4.4 - Mechanical Unit


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THEORY What is an automatic control system? This is a system in which we are controlling the state of a Process; say the width and thickness of strip being rolled in a steel mill. In setting up the system we need to know what the required width and thickness are, and to set up reference or input signals to represent these values. We are able, by means of transducers, to generate similar signals to represent the actual values at the output of the process. We can then compare the actual width and thickness of the strip produced with those required. The system must be able, if there is a difference or error, to send modifying signals to an Actuator, in this case the motor and gearing controlling the roller setting. The closed-loop control system: The difference or error signal may be thought of as producing effects which move forward, from the point of comparison to the resulting action. The comparison itself depends on a signal which is fed back from the output of the process to be compared with the reference or input signal. The forward flow and feedback of signals form a loop around which information flows, fig 4.5. Such a system is therefore called a closed-loop system.

Fig 4.5 The Closed Control Loop.

Various names are given to the signals in different industrial or other contexts, but the meanings of words in any one of the columns below are much the same:

Where the system is electrical, the state will normally be represented by signals expressed in volts; in our example it might be, for the width, a signal representing ten inches per volt. In this manual, the difference in the comparison will be called the error signal and the part of the system that carries out the comparison is the error channel.


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There is usually a power amplifying device to drive the Actuator (which in fig 4.6 is the geared motor). It is usual for control engineers to describe their systems in a block diagram form. The block diagram below describes the type of system we shall be using in the assignments. Here there is a comparison by the error channel of the input and output, the error is then amplified to drive a motor and gearing in the forward path so that the speed or position of the output shaft can be modified.

Fig 4.6. Block Diagram of an Analogue Closed-Loop System.

Analogue & Digital Systems In the system of fig 4.6 it is assumed that the input and output are measured as voltages and lead to an error voltage which is amplified to operate the motor. This system has an analogue error channel since input and output are measured as continuous voltages. However it is common practice to use digital techniques to generate the error signal in digital form, either by digitizing the input and output by an analogue-to-digital (A/D) converter or by direct digital measurement techniques. The error signal is then processed in a computer to generate a digital signal to drive the motor. The motor may then be driven from a digital- to-analogue (D/A) converter or digitally by switching techniques.


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Thus the system may take the general form of fig 4.7

Fig 4.7. Block Diagram of a Digital Closed-Loop System.

The digitizing of inputs may be within the system or in an internal computer interface. The computer-generated motor command will be digital and may be converted to analogue form in the computer interface or within the system. Alternatively the command may be used to drive the motor by a switching technique. The Feedback Servo Fundamentals Trainer (33-002) provides facilities to investigate purely analogue systems as fig 4.6, or systems involving a range of digital techniques as fig 4.7. For the digital techniques it is necessary to use an IBM-compatible PC in which a Feedback interface unit has been installed, plus a Digital Board 33-1 20. The Assignments in this manual relate only to the analogue system. Assignments to investigate the digital system are provided as interactive Discovery software supplied with the 33-003 system.


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Exercise 5 Preliminary Procedures for Operation

OBJECT: (a) Initial Mechanical and Analog Unit Check.

(b) To Display the Waveforms. (c) To Display the speed response of Motor.

When you have completed this assignment you will:

• Realize that the 33-002 equipment comprises sub-systems which may be combined various ways to make control systems.

• Be familiar with two of the sub-systems, the Mechanical Unit and the Analogue Unit. KNOWLEDGE LEVEL

• Before you start this assignment you should: • Have some experience of using an electric motor. • Have some experience of handling electronic circuits. • Know how to use an oscilloscope

PRELIMINARY PROCEDURE The Power Supply should be connected by 4mm-plug leads to the ÷15V, +5V, OV and —15V sockets at the back of the Mechanical Unit.

Fig 5.1 - The Analogue Unit


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Fig 5.2 - The Mechanical Unit.

5(a) Initial Mechanical and Analogue Unit check With the power supply switched OFF, connect its outputs to the Mechanical Unit. Set the brake fully upwards. The Analogue Unit should not be connected. Switch the power supply ON. The motor should remain stationary — there may be a slight movement when the supply is actually switched. 5(b) To Display the Waveforms It is assumed that a suitable oscilloscope is available with: EITHER

• A single Y channel or preferably two Y channels when used in conjunction with a time base, with

• External sync input for the time base. OR

• A facility for X-Y operation with X and Y both able to operate with a d.c input.


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Test Waveforms Connect the oscilloscope to the test signals using either the 4mm sockets in the Mechanical Unit or the 2mm terminals in the Analogue Unit. Observe that the frequency may be varied between 0.1 and 1Hz or 1 and 10Hz. System Waveforms The system waveforms may be observed either from an externally triggered display against a timebase as shown in fig 5.3(a) or from an X-Y display as shown in fig 5.3(b). Signal source sockets are provided on the Mechanical Unit (4mm) and the Analogue Unit (2mm).

(a) (b)

Fig 5.3 - Oscilloscope Connections and Display


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The output shaft speed display should show: 0 . 0 0 This indicates that the 5V supply is operating. Hold the motor check switch to the right and the motor should run clockwise and the output speed display should indicate 15 to 25rpm. Hold the switch left and the motor should run anti-clockwise with approximately the same speed. This test indicates that the ±15V supplies are operating. Hold the check switch to one side and gradually lower the brake to maximum. The motor should slow down. These tests indicate that Power Supply and Mechanical Unit are operating correctly. Switch the power OFF. Connect the Analogue Unit to the Mechanical Unit by the 34-way cable. Raise the brake fully. Switch the power ON. Rotating the power amplifier zero adjustment should enable the motor to be driven in both directions up to about the same speed as before. Zero the amplifier to stop the motor. Overall the tests indicate that the system is working correctly. 5(c) To display the Speed Response of the Motor Set P3 to zero and make the connections on the panel shown in fig 5.4(a). Connect the oscilloscope to the system using the selected method of display. If the oscilloscope input has a 4mm plug use the transfer socket as shown dotted. This arrangement enables the square wave test signal to be applied to the power amplifier when P3 is adjusted. Set the test frequency to about 0.2Hz. Set P3 to about 30. The motor should rotate in both directions, giving speed displays as in fig 5.4 (b), using an X-Y connection; or against a time base as in (c). Note that the X-Y connection may give either of the two displays shown in fig 5.4(b) depending on the oscilloscope in use. Examine the effect of increasing or decreasing the test frequency between 0.1 and 1Hz. SUMMARY This assignment has provided a general look at the basic features of the Analogue and Mechanical Units of the 33-002 equipment. PRACTICAL ASPECTS The last practical shows that there is a delay in the motor response to an input, which is due to the mechanical inertia of the armature. All motors exhibit this general characteristic, which has very important consequences for control system design. Special armature design can reduce the inertia greatly for small motors.


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Fig 5.4 - Connections for Practical 5(c)


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Notes:


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Exercise 6 Transient Response of the DC Motor

OBJECT : (a) Transient Response of motor. (b) Investigate the Motor Time Constant.

Fig 6.1 - Connections for Exercise # 6


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6(a) Transient Response of Motor: The motor cannot change speed instantly due to the inertia of the armature and any additional rotating load (the brake disc in the 33-002). This effect was shown in the familiarization assignment, and has very important consequences for control system design.

(a) (b)

Fig 6.2- Transient Characteristics of Motor

If Va for an ideal motor has a step form as in fig 6.2(a), initially a large current will flow, limited only by the armature resistance. As the motor rotates and speeds up the back emf increases and the current is reduced to nearly zero in an ideal motor. This is shown in the left portion of fig 6.2(b). If Va is suddenly reduced to zero the back emf still exists, since the motor continues to rotate, and drives a current in the reverse direction dissipating energy and slowing the motor. This is illustrated in the right-hand portion of (b). The 33-001 motor shows a speed characteristic approximating to fig 6.2(b), but the power amplifier is arranged to limit the maximum armature current which does not show the ideal pulse characteristic. Connect the system as shown in fig 6.1 which enables the motor to be driven from the test square-wave, and allows the speed to be displayed on the Y axis of an oscilloscope; it is convenient to use an X-Y display. Set P3 to zero and the test signal frequency to 0.2Hz. Set the power amplifier zero adjustment to run the motor at maximum speed in one direction. Turn up P3 and the square-wave signal will speed up and slow down the motor. Adjust P3 until the motor is stationary for one half cycles. This corresponds with Va in fig 6.2(b). The oscilloscope will now display the speed corresponding with Va in 6.2(b).


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6(b) Motor Time Constant The delay in response of a motor is of great importance in control system design and is expressed as the time-constant. This is the time that would be required for the motor speed to change between any steady values if the initial rate of speed change was maintained. This is the dotted line in fig 4.3.8(a), while the actual speed response is shown as a solid line.

(a) (b)

Fig 6.3

It can be shown that the speed changes by 0.63 of the final change during the time constant. The time constant can be measured from a display of the speed against time. Jsr.g the sre1 distment of Practical 3.3 and square wave frequency of 0.2Hz, the time across the trace is 2.5s. Estimate the time constant by considering the initial slope and maximum speed. The value should be in the region of 0.5s. SUMMARY The motor, with no load, runs at a speed almost proportional to the applied voltage. The armature current increases with increasing load torque, causing a volt drop in the armature resistance. This effectively reduces the applied voltage, causing a drop in speed. The magnetic brake provides a torque proportional to speed and dependent also on the overlap between the magnet and the disc. If the applied voltage is suddenly changed, the motor does not respond instantly. Its time constant is defined as the time it would take to reach its final speed if the initial acceleration were maintained. PRACTICAL ASPECTS The slowing up process associated with reverse current, shown in fig 6.2(b), assumes that the reverse current can be returned through the source of Va. If this is not so the motor takes a much longer time to slow down. If the armature resistance is low, as for a normal motor, the initial armature current may be very large (dangerously so). Thus some starting equipment (a starter) is used to limit the current while the motor is being run up to speed. This applies especially with large motors.


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Notes:

Feedback Control Systems Modular Servo System NED University of Engineering and Technology Department of Electrical Engineering

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C - Modular Servo System 7.0 To become familiar with the system 7.0.1 System Description: The Feedback, Inc. servo motor system modular components are:

• Power Supply • Servo Amplifier • Motor • Tachometer/Generator (with Digital Volt Meter) • Position Indicator (1 Input/ 1 Output) • Pre-Amplifier • Operational Amplifier • Dual Attenuator • Function Generator

Elements can be switched between lab stations except for the Motor Generator. The same Motor Generator should be used for all lab exercises; otherwise the Km and τm parameters will be inconsistent, as motor properties are similar but not identical. Using the same motor will reduce experimental error. Certain “umbilical” connections are made between the Power Supply and Servo Amplifier in the rear of the boxes and from the Servo Amplifier to the Motor.

7.0.2 SERVO MOTOR SYSTEM Motor Linearization The motor is a DC constant field, armature current controlled motor. Its properties are not completely linear. To improve the linearity, the Pre-Amp, Servo-Amp, Motor, and Tachometer are used and modeled as ONE UNIT. This assembly forms the core of each subject system, and must be assembled at the beginning of each lab session. The connections are shown in Figure C-(i).

Figure C-(i) - Motor Linearization Connections


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The Pre-Amp has two controls on the faceplate: a three-position switch, which is set to defined τ, and a Zero Set dial. Also, at the top of both the Pre-Amp and Tachometer units are three power connections for +15V, −15V, and ground. This D.C. power can be provided either from the Servo-Amp or the Power Supply. (Note that the Servo-Amp and the Power Supply share the D.C. power sources by means of the rear “umbilical” connection between them.)

At the start of every lab session, the Balance Pre-Amp Output Procedure (refer to Appendix A, Procedure 1) must be performed to balance the differential output signal of the Pre-Amp unit.

7.0.3 TACHOMETER The Tachometer unit contains a tachometer/generator, a 1/30 gear reduction, a digital readout of RPM, and a digital volt meter read-out. The Tachometer unit requires +15V, -15V, and ground connections from either the Servo-Amp or the Power Supply.

The tachometer is a D.C. generator connected to the high RPM (motor) side of the gear. The negative potential (plug 1) is used as the velocity feedback to the system; the positive potential (plug 2) should be connected to ground.

The Tachometer unit contains two digital read-outs that share a common display; a twoposition switch selects which quantity is displayed.

• For a digital read-out (in RPM) of a frequency input on “tacho rpm” (plug 3), slide the two-way selector switch to the left (toward plug 3) and connect the signal to be measured to plug 3. Attaching plug 1 to plug 3 gives the motor speed in RPM.

• For a digital read-out of a D.C. Voltage (± 20V MAX) on “dc volts” (plug 4), slide the two-way selector switch to the right (toward plug 4) and connect the signal to be measured to plug 4.

7.0.4 DUAL ATTENUATOR The Dual Attenuator unit consists of two 10KΩ potentiometers.

The marks around the dials are only meant as a guide to the true setting. It is best to determine the actual voltage ratio by implementing a voltage divider with the potentiometer using the +15V and -15V sources and wiper.

For the dial marks to coordinate with the potentiometer wiper motion (i.e.: turning the dial toward increasing numbers results in smaller resistance between the higher potential terminal and the wiper, and therefore a higher voltage out of the voltage divider at the wiper terminal), ALWAYS connect the black plug to the lowest potential, ground or -15V, depending on the application.


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7.0.5 POSITION INDICATOR The Position Indicator unit consists of a 10KΩ potentiometer and a visual angular indicator on the front plate. The output Position Indicator is coupled directly to the Tachometer unit through a shaft. The top connection plate and the rotating front dial are shown in Figure C-(ii).

Figure C-(ii) - Output Position Indicator Faceplate and Front Dial

The faceplate shows the connections to the 10KΩ potentiometer. The faceplate will be used for determining the coefficients of the Position Indicator, and the non-dynamic coefficients of the motor and generator. The ends of the potentiometer are typically connected to +15V (plug 1) and -15V (plug 2). The potentiometer wiper (plug 3) is the output signal for indication of angular position, and is also used as a position feedback signal to the system. The front plate has three sets of marks. The outermost indicates angular rotation in 10° increments. The inner two are used to synchronize angular velocity to either 50Hz (Europe) or 60Hz (USA) lighting systems. The 60Hz ring has marks as seen on phonograph turntables. Room lighting provides an appropriate strobe effect, which is faster than the human eye can detect. The motor, by a gear reduction turns the output front plate. As the angular velocity is increased, the strobe effect is seen since the 60Hz portion of the plate appears to be stationary even though the plate is actually rotating. At the first appearance of this effect, the front plate is rotating at one revolution per second. Increasing the motor speed will bring a second strobe effect at two revolutions per second. The Tachometer unit has a built-in digital display on the high-speed shaft section; the shaft speed can be directly read from the Tachometer unit.

7.0.6 OPERATIONAL AMPLIFIER The operational amplifier is well known in Circuits courses and will only be briefly described here. The faceplate connections are shown in Figure C-(iii).

At the top of the Op-Amp unit are three power connections for +15V, -15V, and ground. This D.C. power can be provided either from the Servo-Amp or the Power Supply.

As with the Pre-Amp, the Op-Amp has a Zero set dial, which must separately adjusted from the Pre-Amp. At the start of every lab session that uses the Op-Amp unit, the Zero Op-Amp Output Procedure


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(refer to Appendix A, Procedure 4) must be performed to zero the output signal of the Op-Amp unit.

Figure 3 - Operational Amplifier Faceplate

The Feedback Network Selector is a three-position rotary switch to select the feedback circuit for the Op-Amp. The bottom (counter-clockwise) switch selection has a 100KΩ resistor so that the Op-Amp unit, as shown in Figure 3, is a signal summer with a unity gain. The middle switch selection turns the Op-Amp circuit into a first order lag with τ = RC = 100KΩ•1µF = 0.1 sec. The top (clockwise) switch selection allows for the insertion of any desired feedback network.


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7.0.7 Transient Response - Terminology Mp Percent Overshoot (also referred to as %OS) - The amount that the peak value of an under-

damped step response overshoots the final value, expressed as a percentage of the final value.

tp Peak-Time - The amount of time from the beginning of an under-damped step response to the response peak value.

tr Rise-Time - In an under-damped step response, the amount of time between the response first reaching 10% of the response final value and the response first reaching 90% of the final value.

ts Settling-Time - In an under-damped step response, the amount of time from the beginning of the step response until the response oscillation amplitude remains within a specified range of the response final value. The settling range (“band”) is typically expressed as a percentage of the final value. A 2% settling band has a range of ± 1% around the final value.

7.0.8 Error Analysis Accuracy, Precision & Resolution

Some values are exact: • 1000 meters in one kilometer • 60 seconds in one minute • 12 eggs in one dozen

Other values (such as measurements or estimations) have some degree of uncertainty.

Accuracy is the measure of how True or Correct the scale of a measurement is. Precision is the measure of Repeatability of a measurement (without the measurement necessarily


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being correct.) Precision could be evaluated for the same person taking the measurement several times, or for different people taking the same measurement. Resolution is the level of Fineness of a measurement, or the ability to distinguish between two measurement points. For example, which would be a “better” measurement for 1 centimeter?

• Using a meter-stick that is EXACTLY 1 meter long (Perfect Accuracy!) that has NO intermediate markings (Terrible Resolution!). How repeatable (Precise) would this measurement be?

• Using a ruler that was the prize from a box of cereal (Questionable Accuracy) that is marked off in centimeters (Perfect Resolution!). How repeatable (Precise) would this measurement be?

Digital meters are ASSUMED to be Accurate; regular calibrations help to assure this. Digital meters have a different number of digits after the decimal point (Resolution) based on the scale or range of the measurement (up to 1 Volt, up to 10 Volts, etc.) Evaluation of Measurement Error and Deviation

“The difference between theory and practice is that, in theory, there is no difference between theory and practice, and in practice there usually is.” - Author Unknown

When measurements are taken in the lab, the “actual” or “measured” values observed almost never equal the “expected” or “theoretical” values predicted from the calculations. This may be due to many factors:

• Tolerance in manufactured parts (5% resistors, etc.) • Unanticipated or un-accounted for resistance, inductance, and capacitance in wires and connectors • Resistance or “loading” from the measurement equipment • Errors in taking and/or reading the measurement (accuracy, precision, resolution) • “Round-Off” Error in the calculation of the theoretical value • Inaccuracies in the model used to derive the theoretical value (model simplifications, etc.) • etc., etc…

To quantify how closely reality (“measured”) comes to expectation (“theoretical”), a percent error analysis is performed:

It is necessary to divide the difference between the “theoretical” and “measured” values (the error) by the “theoretical” value to normalize the error. For example, if a theoretical value is 100V and the measured value is 90V, the error is 10V; if a theoretical value is 5V and the measured value is 4V, the error is 1V. Which error is “worse?” Certainly the 10V error has a larger magnitude, but it only deviates from the theoretical value by 10% while the 1V error deviates from its theoretical value by 20%. Therefore, one could say that the 1V error is more severe than the 10V error.

Deviation Analysis

In cases where a parameter is measured more than once or by more than one method, it is possible to analyze how closely the different measurements relate to one another. The term “error analysis” is not applicable since no single measurement can really be considered as the “True” value.


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Several different methods may be used to evaluate the deviation of the different measurements from one another:

• For two measurements - M1 & M2: Difference:

• For a set of measurements - M1 … Mn:

Deviation from the Mean for one of the measurements, Mi:

Range Deviation:


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Exercise 7

Parameter Determination for the Modular Servo System 7.1 Objective: In this lab exercise, the student will become familiar with the laboratory equipment and will also determine the various servo system parameters that will be used for the remainder of the lab exercises. Since the various components will be tested separately, the suggested order of investigation is not critical.

1. Motor Generator Assembly: a. Motor Linearity b. Motor Dynamics

2. Position Indicator 3. Operational Amplifier Performance

Figure 7.1 "Core" System Plant Block Diagram

Figure 7.2 “Core” System Plant Wiring Diagram

After completing this exercise, you will be able to: • Setup the “core” subject system plant: Pre-Amp, Servo-Amp, Motor, and Tachometer • Perform the Balance Pre-Amp Output Procedure • Measure RPM and D.C. voltages using the digital read-out on the Tachometer unit • Measure the Phase Delay Angle between two sinusoidal wave-forms • Measure the Time Constant of a first-order system step response


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Also, the following system parameters will be measured: • Maximum VMotor input for linear motor operation: VMAX

• Motor Gain Constant: Km (RPM/Volt) • Motor Time Constant: τm (seconds) • Tachometer Gain Constant: Kt (Volt/RPM) • Position Indicator Gain Constant: Kp (Volt/degree) • Op-Amp Lag Feedback Time Constant: τ1 (seconds)

7.2 Apparatus: The following pieces of lab equipment will be required to complete this exercise:

• Pre-Amp, Servo-Amp, Motor, and Tachometer “core” • Position Indicator • Dual Attenuator • Operational Amplifier • Signal Generator • Oscilloscope • Printer • Three coaxial cables with BNC to clip (alligator or microprobe) • Various interconnect wires

7.3 Theory: The “plant” (object of control system) to be used in the lab exercises is a D.C., constant field, armature-current controlled motor. A second order differential equation describes the motor dynamics relating applied voltage to angular velocity. One system dynamic is due to the electrical effects of the armature coil inductance and resistance. The other dynamic system is due to the mechanical effects of the armature and load inertia and the bearing friction. The electrical dynamics are much faster than mechanical dynamics. Thus, the motor can be modeled simply as a first order differential equation. The Servo-Amp and the Pre Amp are used to linearize the motor performance. The generator is physically much smaller than the motor and its dynamics do not influence the motor operation. The Motor Generator Assembly is represented by the block diagram in Figure 7.1, and its wiring diagram is shown in Figure 7.2. 7.4 Pre-Lab: There is no pre-lab for this exercise. 7.5 Procedure: Preliminary Preparation: Step 1 - Perform the Balance Pre-Amp Output Procedure (refer to Appendix A, Procedure 1) 7.5.1 Maximum VMotor Input: VMAX

Note that the change in motor speed due to changes in VMotor is not instantaneous. Therefore, allow several seconds between changing VMotor and observing the corresponding motor speed. Step 1 - Connect the Pre-Amp, Servo-Amp, Motor, and Tachometer as shown in Figure 7.2:

• The Dual-Attenuator provides a variable D.C. voltage, VMotor, to control motor speed. The motor speed should be zero near dial setting 5. The speed should increase in one direction as the dial is turned toward 10, and in the other direction as the dial is turned toward 0.

• On the Tachometer unit, connect the negative output from the Tachometer (plug 1) to the “tacho


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rpm” input (plug 3), and set the selector switch to read-out RPM. Step 2 - Find the saturation VMotor input - the point at which increasing VMotor input no longer results in increasing motor speed. (Note: saturation is one of the non-linear behaviors that our model for the D.C. motor is ignoring.)

• Increase the VMotor input by turning the dial from 5 toward 10 until the motor speed no longer increases (i.e.: the motor speed “saturates”).

• Slowly reduce VMotor until the motor speed begins to decrease; this is the threshold VMotor input for unsaturated motor operation - VSAT.

• Measure the voltage at the wiper of the Dual-Attenuator, VMotor, using the volt meter read-out on the Tachometer unit.

• Record this value in the table below. Step 3 - Compute the maximum VMotor input for linear motor operation, VMAX:

• Compute VMAX: round 90% of VSAT to the nearest 1/10 volt. • Record this value in the table below. • Note that ±VMAX should be the limits of VMotor inputs in this lab exercise to avoid the nonlinear effects

of motor speed saturation.

7.5.2 Motor Linearity: Km and Kt The coefficients Km and Kt will be determined by two methods. Method 1 - Steady-State Operation: Step 1 - With the Dual Attenuator providing the D.C. VMotor input as shown in Figure 7.2 (setup in the previous procedure), adjust VMotor to fill in the following data table-1 VMotor vs. VTach:

• Use the volt meter read-out on the Tachometer unit to measure both VMotor and VTach. • Use the RPM read-out on the Tachometer unit to measure the motor speed, ωHS.

Note: when setting inputs or other adjustable parameters to specified values, set the value as close as reasonably possible to the desired value (Input, [Approx.]), and then record the actual value (Set, [Actual]) rather than trying to get the adjustable value to be exact.

Table 1 - VMotor vs. VTach

Step 2 - Compute Km and Kt: Since the motor-tachometer assembly is assumed to be linear, the following ratios should be identical for all four table entries:

Note: The upper-case variable for motor speed, ΩHS, in the equations above indicates that the


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equations are Transfer Functions in the Laplace domain. This is further indicated by the Laplace variable, (s). The lower-case variable, ωHS, indicates a time-domain representation.

Table 2 - Km and Kt

Method 2 - Ramp Input Step 1 - Configure the system as shown in Figure 7.2 (setup in the previous procedure): • For the VMotor input to the Pre-Amp, replace the Dual Attenuator output with the function generator output. • Set the function generator for Triangle-wave, 0.01 Hz, and 3Vpp (limit to ±VMAX Vpp)

Step 2 - Oscilloscope setup: • Set the display mode to X-Y. • Ground both Channel 1 (CH1) and Channel 2 (CH2) inputs. • Center the beam dot vertically with the CH1 offset adjustment, and center it horizontally with

either the CH2 offset adjustment or the time base offset adjustment (depending on the oscilloscope).

• Connect the oscilloscope CH1 input to VMotor. Set CH1 (vertical displacement, Y-axis) scale to 0.5V/division.

• Connect the oscilloscope CH2 input to VTach. Set CH2 (horizontal displacement, X-axis) scale to 5V/division and Invert CH2.

• Set horizontal sweep to 10 seconds/div. • Activate the Store feature of the oscilloscope and/or adjust the display persistence.

The motor will turn; the speed will slowly increase, then slow, and reverse direction. This cycle will repeat due to the periodic Triangle-wave input. The trace on the scope will appear as a comet with an increasing tail. Eventually, the trace will look like a diagonal line on the screen.

Step 3 - Measure VMotor and VTach:

• Use the HOLD or RUN/STOP feature on the oscilloscope to capture the trace. • Use the Hard Copy feature on the oscilloscope to obtain a print-out of the trace. • Measure the vertical extent of the diagonal line; this is VMotor. Refer to CH1 setting for V/division

scale. • Measure the horizontal extent of the diagonal line; this is VTach. Refer to CH2 setting for V/division scale. • Record the values of VMotor and VTach in the table below. • Indicate these measured ranges of VMotor and VTach on the hard copy/print-out of the trace.

Step 4 - Compare VMotor and VTach with Km and Kt:

• The following ratio should hold:


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• On the hard copy/print-out of the trace, indicate the location of the four data points (VMotor, VTach) from Table 1.

7.5.3 Motor Dynamics: τm

To determine the motor time constant, τm, a faster time varying signal will be used as the input. Two methods will be used. The first method is a sinusoidal steady-state analysis, and the second method is a step-input response. Method 1 - Sinusoidal Steady-State Analysis Step 1 - Configure the system as shown in Figure 7.2, and with the function generator supplying the VMotor input to the Pre-Amp (setup in the previous procedure).

• Set the function generator for Sine-wave, 1 Hz, 2 Vpp (limit to ±VMAX Vpp) Step 2 - Oscilloscope setup: Change from previous procedure setup:

• Release the HOLD or RUN/STOP feature on the oscilloscope. • Deactivate the Store feature and/or reduce the display. • Set the display mode back to time-base (turn off X-Y display mode).

Step 3 - Measure Input/ Output Waveform Phase Delay Angle:

• Measure the Phase Delay Angle, Θ - Perform the Measure Sine-Waveform Phase Delay Angle Procedure (refer to Appendix A, Procedure 2).

Note: the value of Θ should be negative since the motor transfer function has only Poles and no Zeroes (i.e.: complex values only in the denominator) - and since the Output waveform (VTach) “Lags” the Input waveform (VMotor).

• Use the Hard Copy feature on the oscilloscope to obtain a print-out of the traces. • Record the values of t1, t2, and Θ in the table below. • On the hard copy/print-out of the traces, indicate t1 and t2.

t1 seconds

t2 seconds

Θ degrees

Step 4 - Compute τm: Discussion: In general, the phase delay (phase shift) angle of a complex function is: For complex functions with numerators and denominators, the overall phase delay is computed as:

Phase Delay = (Phase Delay of Numerator) − (Phase Delay of Denominator) degrees


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For the D.C. motor under investigation, the overall phase delay is computed as: • Compute the value of τm using the Phase Delay Angle, Θ, measured in Step 3, and the relationship given above:

Noting that1

12122tT

f ⋅⋅=⋅⋅=⋅⋅= πππω , the only unknown in the equation above is τm, which can be

solved for using algebraic manipulation. • Record the value of τm below:

τm seconds Method 2 - System Step-Input Response Step 1 - Configure the system as shown in Figure 7.2, and with the function generator supplying the VMotor input to the Pre-Amp (setup in the previous procedure):

• Set the function generator for Square-wave, 0.2 Hz, and 3Vpp (limit to ±VMAX Vpp). The input waveform period must be slow enough to allow the system response from each step-input (i.e.: each edge of the Square-wave) to achieve a steady-state angular velocity before the next step-input occurs.

Step 2 - Oscilloscope setup: Change from previous procedure setup:

• Release the HOLD or RUN/STOP feature on the oscilloscope. Step 3 - Measure the Time Constant of the Motor, τm:

• Perform the Measure Time Constant of a Step Response Procedure (refer to Appendix A, Procedure 3).

• Use the Hard Copy feature on the oscilloscope to obtain a print-out of the step response. • Record the measured value of τm below:

τm seconds • On the hard copy/print-out of step response, indicate τm.

Step 4 - Analyze/Compare the two values of τm from Method 1 - Sinusoidal Steady-State Analysis - and from Method 2 - System Step-Input Response:


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7.5.4 Position Indicator: Kp The Position Indicator is the potentiometer assembly that is connected to the motor via the gearbox. Its transfer function is described by a constant, Kp, that relates angular displacement to voltage. Step 1 - Disconnect the motor by removing the pair of connections between the Pre-Amp and the Servo-Amp (refer to Figure 7.2).

This will allow for free motion of the motor by hand. Step 2 - Setup for the Position Indicator:

• Connect +15V and −15V sources to the Position Indicator as shown in Figure 2, with +15V on plug 1 and −15V on plug 2.

• Connect the potentiometer wiper (plug 3), Vposition, to the digital volt meter read-out on the Tachometer unit.

Step 3 - Measure and record voltages, VPosition, at various angular positions:

• Manually rotate the motor high-speed shaft (ωHS in Figure 7.2) - do NOT rotate the potentiometer face-plate - and measure and record the values in Table 3. For a sign convention, consider Clockwise angles as positive and Counter-Clockwise angles as negative.

(The actual sign is not important; the overall change in voltage per change in angle is being measured.) • For each pair of angle and voltage measurements, compute the change in voltage with

respect to angular position, ∆Volts/∆degrees. (Consider only the absolute value; disregard any sign.)

• Compute the mean value of ∆Volts/∆degrees.

Table 3 - Position Indicator Angular Position and Voltage 7.5.5 Operational Amplifier Performance: Gain Verification and τ1 The Operational Amplifier (Op-Amp) unit will be used in later lab exercises as a summing junction, and to add dynamics (i.e.: poles) to the overall system.

Step 1 - Setup for the Op-Amp:

• Connect the three power connections (+15V, −15V, and ground) on the Op-Amp.


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• Connect one of the three Op-Amp input plugs (1, 2, or 3) to ground. • Set the three-position Feedback Network Selector rotary switch to the 100KΩ resistor. • Use the volt meter read-out on the Tachometer unit to measure the output voltage of the Op-Amp. • Adjust the Zero Set dial on the Op-Amp unit until the output voltage (plug 6) shows 0 Volts. • Remove the ground input to the Op-Amp.

Step 2 - Check the Op-Amp Gain and Summing function:

• Use both potentiometers on the Dual-Attenuator unit as voltage dividers. Set one of them to provide +3V at the wiper terminal, and set the other to provide -5V at the wiper terminal. (Get the values as close as reasonably possible and then record the actual values.)

• Connect the +3V source to one input of the Op-Amp (plug 1, 2, or 3), and the -5V source to one of the other inputs.

• The Op-Amp configuration is an inverting summer. Therefore, the output voltage should be: − (V1 + V2 ) = − (3V+ (−5V)) = 2V

Measure the actual Op-Amp output voltage and compare it with the expected value (using your measured input voltages to determine the expected value).

Step 3 - Measure the Op-Amp Resistor/Capacitor Feedback Network Time Constant, τ1: • Remove the +3V and -5V inputs to the Op-Amp. • Set the three-position Feedback Network Selector rotary switch to the 1 µF capacitor in parallel with

the 100KΩ resistor. • Set the function generator for Square-wave, 0.2 Hz, and 5Vpp. • Connect the output of the function generator to one of the Op-Amp inputs. • Connect the Op-Amp output to one of the oscilloscope input channels. • Perform the Measure Time Constant of a Step Response Procedure (refer to Appendix A, Procedure

3). Measure and record the time constant, τ1. • Use the Hard Copy feature on the oscilloscope to obtain a print-out of the step response. • On the hard copy/print-out of step response, indicate τ1. • In the Lab Report, derive the transfer function of the Op-Amp with the R-C feedback network, and

verify that the expected characteristic behavior is indeed a first-order exponential with a time constant of 0.1 seconds.


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7.6 Summary: Lab Exercise Checklist - Be sure that the following have been obtained in the Lab to complete the lab exercise:

Collected data supporting the measurements of VMAX, Km, τm, Kt, Kp, and τ1 Annotated hardcopies of traces from Motor Linearity, from both methods of

measuring τm, and from measuring τ1

Lab Report Checklist - The Lab Report should contain the following supporting documentation: All collected data and hardcopies of scope traces Parameter values (to be used in the remainder of lab exercises). [Where the value was measured by

more than one method, or was taken more than one time, use the mean value.] Error or appropriate deviation analysis of the measured data Derivation of Op-Amp transfer function with R-C feedback network

Summary of Measured Parameter Values - to be used in the remainder of the lab exercises:

The following should be considered as reference values of the system parameters for “sanity check” purposes only. They should NOT be considered as “correct” or “theoretical” values for error analysis.

• Motor Gain Constant - Km: 1800-2600 RPM/Volt • Motor Time Constant - τm: 0.20-0.26 seconds • Tachometer Gain Constant - Kt: 0.0023-0.0027 Volt/RPM • Position Indicator Gain Constant - Kp: 0.07-0.12 Volt/Degree • Op-Amp Lag Feedback Time Constant - τ1: 0.09-0.11 seconds

Review Questions - Answers must be included in the lab report: • Is it justifiable to model the motor as a first-order system, considering only the mechanical pole and ignoring the electrical pole from the inductance of the armature (as well as ignoring nonlinear effects of motor saturation and gear backlash, and armature resistance changes with temperature)? Why or why not? (Consider your deviation and difference analyses of the motor parameters Km and τm.).


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Exercise 8 Closed-Loop Position Control System Design

8.1 Purpose: The purpose of this lab exercise is to design and evaluate a closed-loop position control system, predict its behavior, and control its behavior. The component parameters measured in Lab Exercise #1 will be used to model the system components.

Figure 8.1 - Position Control Loop Block Diagram

Figure 8.2 - Position Control Loop Wiring Diagram

8.2 Objectives: After completing this exercise, you will be able to:

• Perform the Zero Op-Amp Output Procedure • Predict second-order system response to a step-input • Design basic second-order system step response by adjusting gain • Measure the Percent Overshoot, Peak-Time, and Settling-Time of an under damped second-order step

response

8.3 Equipment List: The following pieces of lab equipment will be required to complete this exercise:

• Pre-Amp, Servo-Amp, Motor, and Tachometer “core”


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• Position Indicator • Dual Attenuator • Operational Amplifier • Signal Generator • Oscilloscope • Printer • Three coaxial cables with BNC to clip (alligator or microprobe)

8.4 Theory: Lab Exercise #1 examined the open-loop motor. The transfer function for the motor that relates applied voltage to motor speed is a first-order function; the motor’s changes in speed due to a square-wave input exhibited the characteristic exponential step response of a first-order system. The new system transfer function introduces a 1/s term (discussed later), which results in an over-damped second-order system. However, as the system gain, Ka, is adjusted, the closed-loop system poles move from their open-loop positions; the system becomes critically-damped at some value of Ka, and is under-damped for Ka greater than that value. The objectives of this lab exercise include predicting the characteristics of the under-damped step response with a given value of Ka, and specifying the value of Ka to achieve the specified under-damped step response characteristics.

The Closed-Loop Position Control system is represented by the block diagram in Figure 8.1, and its wiring diagram is shown in Figure 8.2.

The new components that are introduced in the block diagram are the summing junction, the variable gain, Ka, the gear reduction factor, 1/30, the unit conversion factor, 6, and the integrator, 1/s. The summing junction is implemented with the Op-Amp using the resistor feedback network for a unity gain (gain factor of 1). (Note that the reversal of direction from the gear coupling provides the negative sign on the summing junction’s feedback input.) The variable gain, Ka, is implemented with one of the attenuators (potentiometers) configured as a voltage divider. Since the gain is implemented with an attenuator, the attainable gain is limited to values between zero and one. The gear reduction factor is just the transfer function of the gear-train:

Note that this transfer function ignores friction, the mass of the gears, gear backlash, etc. It would also be possible, if desired, to derive transfer functions for the gear-train that relate other input-output relationships such as input torque vs. output torque. The unit conversion factor, 6, appears in the block diagram but is not a physical element in the system. Since the digital read-out on the Tachometer unit displays motor angular speed as RPM (Revolutions-per-minute), and the position indicator produces a voltage relative to degrees (rather than revolutions), a conversion factor is necessary for consistency of units:


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The Integrator (1/s), like the unit conversion factor, is not a physical element in the system. Some transfer function derivations for the D.C. motor include the 1/s term, and relate applied voltage to angular position (recall that the motor transfer function used here relates applied voltage to angular velocity). By definition of the motor transfer function, the quantities on the High-Speed and Low-Speed shafts are velocities, ωHS and ωLS. Since the output of the Position Indicator is a voltage related to position, VPosition, then conceptually integration (1/s) is occurring based only on our definitions of the quantities, and not though a physical element performing an integration function. 8.5 Pre-Lab: Step 1 - Derive the Closed-Loop Transfer Function:

• Derive the closed-loop transfer function, T(s) = VP(s)/VIn(s), for the system shown in Figure 8.1. The transfer function should be derived with the symbols in the block diagram (Ka, Km, τm, Kp), and then the values measured in Lab Exercise #1 should be substituted in. Note that the gain, Ka, is still a variable.

Additionally, it may be convenient to algebraically manipulate the transfer function so that the coefficient of the s2 term in the denominator is 1. Step 2 - Predict Transient Response for Ka = 1:

• Predict the percent overshoot, Mp, peak time, tp, and settling time, ts, for the system when Ka = 1. Set Ka = 1 in the transfer function derived in Step 1 of the pre-lab, and use the second-order system design equations (from class lecture, the lab instructor, or from a control systems textbook - see references) to determine the expected Mp, tp, and ts for the system step-response.

Expected for

Ka = 1: tp seconds

ts seconds

Mp %

Step 3 - Compute Ka for Specified Transient Response: • Determine the value of Ka that will yield a 25% overshoot to a step input for the transfer

function derived in Step 1 of the pre-lab, and use the second-order system design equations as needed.

• Also, predict the peak time, tp, and settling time, ts, at this value of Ka. Expected for

Mp = 25%: Ka

tp seconds

ts seconds


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8.6 Procedure: 8.6.1 Preliminary Preparation Step 1 - Perform the Balance Pre-Amp Output Procedure (refer to Appendix A, Procedure 1) Step 2 - Perform the Zero Op-Amp Output Procedure (refer to Appendix A, Procedure 4) 8.6.2 Step Response for Ka = 1 Step 1 - Connect the system components as shown in Figure 8.2:

• Set the gain, Ka, to 1. The Dual-Attenuator provides the variable gain, Ka. With the black plug of the attenuator connected to ground, the gain will increase as the dial is turned toward 10 (voltage increases at the wiper terminal), and decrease as the dial is turned toward 0 (voltage decreases at the wiper terminal). Therefore, a gain of 1 should be observed with the dial turned all the way to 10. (This can be verified with the Set Gain using an Attenuator Procedure - Appendix A, Procedure 5.)

Step 2 - Function Generator setup:

• Set the function generator for Square-wave output, frequency low enough so that the step response has sufficient settling time before the next edge of the square-wave (use the settling time, ts, as a guide), amplitude for 50° peak-to-peak. Use Kp to convert from the angular specification to voltage.

Note that each edge of the square-wave represents half of the period of the overall waveform. • Connect the function generator output to the Op-Amp input, Vin, as shown in Figure 8.2. • Confirm that the VMotor input to the servo-amp is limited to ±VMAX Vpp; reduce Vin if necessary.

Step 3 - Oscilloscope setup:

• Connect the oscilloscope CH1 input to the Input Voltage, VIn. Adjust the vertical sensitivity (Volt/division) of CH1 so that the entire amplitude of the square-wave

input fits on the screen. • Connect the oscilloscope CH2 input to VPosition, the output of the Position Indicator (refer to Figure

8.2). Adjust the vertical sensitivity of CH2 so that the entire amplitude of the step response fits on

the screen. Invert CH2. • Adjust horizontal sweep (seconds/division) until a single step response (from the beginning of

the step until the final value is reached) is displayed on the screen. Step 4 - Measure and Record the Step Response characteristics:

• Perform the Measure Characteristics of an Under-Damped Step Response Procedure (refer to Appendix A, Procedure 6).

• Use the Hard Copy feature on the oscilloscope to obtain a print-out of the step response. • Record the measured values of tp, ts and Mp below and compare the measured values with the

expected values computed in the second part of the pre-lab:


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• On the hard copy/print-out of step response, indicate tp, ts and Mp.

8.6.3 Step Response for Mp = 25% Step 1 - With the same system component connections as shown in Figure 8.2:

• Use the Set Gain using an Attenuator Procedure (refer to Procedure section, page 44) to set the gain, Ka, to the value computed in the third part of the pre-lab to achieve a 25% overshoot.

Step 2 - Function Generator setup - setup in the previous procedure:

• Set the function generator for Square-wave output, frequency low enough so that the step response has sufficient settling time before the next edge of the square-wave (use the settling time, ts, as a guide), amplitude for 50° peak-to-peak.

Use Kp to convert from the angular specification to voltage. Note that each edge of the square-wave represents half of the period of the overall waveform. • Connect the function generator output to the Op-Amp input, Vin, as shown in Figure 8.2. • Confirm that the VMotor input to the servo-amp is limited to ±VMAX Vpp; reduce Vin if necessary.

Step 3 - Oscilloscope setup - setup in the previous procedure:

• Release the HOLD or RUN/STOP feature on the oscilloscope (from the previous procedure). • Connect the oscilloscope CH1 input to the Input Voltage, VIn. Adjust the vertical sensitivity (Volt/division) of CH1 so that the entire amplitude of the square-wave

input fits on the screen. • Connect the oscilloscope CH2 input to VPosition., the output of the Position Indicator (refer to Figure

8.2), adjust the vertical sensitivity of CH2 so that the entire amplitude of the step response fits on the screen. Invert CH2.

• Adjust horizontal sweep (seconds/division) until a single step response (from the beginning of the step until the final value is reached) is displayed on the screen.

Step 4 - Measure and Record the Step Response characteristics:

• Perform the Measure Characteristics of an Under-Damped Step Response Procedure (refer to Appendix A, Procedure 6).

• Use the Hard Copy feature on the oscilloscope to obtain a print-out of the step response. • Record the measured values of tp, ts and Mp below and compare the measured values with the

expected values computed in the third part of the pre-lab:

• On the hard copy/print-out of step response, indicate tp, ts and Mp.


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8.7 Summary: Lab Exercise Checklist - Be sure that the following have been obtained in the Lab to complete the lab exercise:

Collected data supporting the measurements of tp, ts and Mp for both Ka = 1 and Mp = 25% Annotated hardcopies of step response traces for both Ka = 1 and Mp = 25%

Lab Report Checklist - The Lab Report should contain the following supporting documentation:

All collected data and hardcopies of scope traces Derivation of closed-loop transfer function Pre-lab computations Error analysis of the measured vs. expected values

Review Questions - Answers must be included in the lab report: • Are the second-order system design equations adequate to predict and design the response of the under-damped step response? Why or why not? (Consider your error analyses of the measured vs. expected values of tp, ts and Mp.)

Feedback Control Systems Appendix A NED University of Engineering and Technology Department of Electrical Engineering

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Appendix A

Procedure 1: Balance Pre-Amp Output Purpose: This procedure must be performed before each lab exercise to balance the differential output signal of the Pre-Amp unit.

Figure A.1 - Pre-Amplifier Differential Output Balancing

Procedure: Step 1 - Connect the Pre-Amp, Servo-Amp, Motor, and Tachometer as shown in Figure A.1.

• Connect the three power connections (+15V, 15V, and ground) on both the Pre-Amp and Tachometer units from either the Servo-Amp or the Power Supply. • On the Pre-Amp unit, set the three-position switch to “defined τ.”

Step 2 - Ground the “V-Motor” input (plug 1) on the Pre-Amp unit. This provides a “command” input for Zero speed from the motor.

Step 3 - Adjust the Zero Set dial on the Pre-Amp unit until the motor does not turn.


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Procedure 2: Measure Sine-Waveform Phase Delay Angle Purpose: This procedure is used to measure the Phase Delay Angle (in degrees) between two sinusoidal wave-forms.

Figure A.2 - CH1 and CH2 Period and Phase Delay Time

Procedure: Step 1 - Oscilloscope setup:

• Connect the oscilloscope CH1 input to the system “input” signal (e.g.: VMotor). • Connect the oscilloscope CH2 input to system “output” signal (e.g.: VTach). Invert CH2. • Adjust the CH1 and CH2 vertical sensitivities (Volt/division) so that both Sine-waves

have about the same amplitude. • Adjust horizontal sweep (seconds/division) until a complete Sine-wave (from Peak to Peak) is

displayed on the screen from both CH1 and CH2. Step 2 - Measure Waveform Period and Phase Delay Time:

• Use the HOLD or RUN/STOP feature on the oscilloscope to capture the trace. • Use the Cursor or Measure feature on the oscilloscope to measure the Period of the CH1 signal - the

time between one peak and the next peak of the waveform; this is t1. (Refer to Figure A.2) • Use the Cursor or Measure feature on the oscilloscope to measure the Phase Delay Time between the

CH1 and CH2 signals - the time between the peak of the leading waveform and the corresponding peak of the lagging waveform; this is t2. (Refer to Figure A.2)

Step 3 - Compute the Waveform Phase Delay Angle:

• In general, the phase delay (phase shift) angle between two sinusoidal functions is the ratio of the time delay between the two functions (t2) and the period (t1) expressed as a fraction of one complete cycle (360°). This is computed as:

Phase Delay (degrees), Θ = °⋅⎟⎟⎠

⎞⎜⎜⎝

⎛360

1

2

tt

• For complex functions with complex numerators and denominators, the overall phase delay computed as:


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Phase Delay (degrees), Θ = (Phase Delay of Numerator) − (Phase Delay of Denominator) degrees

• The two phase delay calculations should be equal. Example: for the D.C. motor under investigation, the overall phase delay is computed as:


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Procedure 3: Measure Time Constant of a Step Response Purpose: This procedure is used to measure the Time Constant from a first-order exponential system step response.

Figure A.3 - Measuring the Time Constant from a First-Order Exponential Step Response


• Connect one oscilloscope input channel to the signal being evaluated (e.g.: VTach). • Adjust the vertical sensitivity (Volt/division) so that the entire amplitude of the step response fits on

the screen. • Adjust horizontal sweep (seconds/division) so that a single step response (from the beginning of the

step until the final value is reached) is displayed on the screen. Step 2 - Measure the Exponential Time Constant:

• Use the HOLD or RUN/STOP feature on the oscilloscope to capture a positive going step response. • Use the Cursor or Measure feature on the oscilloscope to measure the overall vertical displacement of

the step response (from the beginning of the step to the final value - Refer to Figure A.2.) Call this 100%.

The Time Constant of an exponential decay curve is the time required to reach 37% (e-1) of the initial value. The Time Constant of an exponential rise curve is the time required to reach 63% (1-e-1) of the final value.

• Compute 63% of the overall vertical displacement of the rising step response. The horizontal cursor will be used to measure the time from the beginning of the step response to the 63% point, however vertical cursor indicating the 63% vertical location will be lost when the cursor mode is switched from vertical to horizontal.

• Use the horizontal offset adjustment on the oscilloscope to align the intersection of the trace of the step response and the 63% cursor indication with one of the solid vertical lines on the oscilloscope display. (Refer to the “Triple Intersection” in Figure A.3.)

• Switch the cursor measurement mode from vertical to horizontal, and measure the time from the beginning of the step response to the 63% point (the intersection of the trace of the step response with the solid vertical line on the oscilloscope display).

• This time measurement is the time constant, τ, of the exponential curve.


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Procedure 4: Zero Op-Amp Output Purpose: This procedure must be performed before each lab exercise that uses the Op-Amp to zero the output signal of the Op-Amp unit. Note: This procedure must be performed AFTER performing the Balance Pre-Amp Output Procedure.

Figure A.4 - Op-Amp Zero Output Adjust

Procedure: Step 1 - Connect the Op-Amp, Pre-Amp, Servo-Amp, Motor, and Tachometer as shown in Figure A.4

• Connect the three power connections (+15V, 15V, and ground) on the Op-Amp, Pre-Amp, and Tachometer units from either the Servo-Amp or the Power Supply.

• On the Op-Amp unit, set the three-position selector to the single resistor feedback. • On the Pre-Amp unit, set the three-position switch to “defined τ.”

Step 2 - Ground the “V-In” input (plug 1) on the Op-Amp unit. This provides a “command” input for Zero speed from the motor. Step 3 - Adjust the Zero Set dial on the Op-Amp unit until the motor does not turn.


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Procedure 5: Set Gain using an Attenuator Purpose: This procedure describes how to set a specified gain value between the values of zero and one using an attenuator (potentiometer).

Figure A.5 - Setting Gain using an Attenuator

Procedure: Step 1 - Disconnect the Vout (wiper) terminal on the attenuator from other “downstream” connections. This will prevent the Vout voltage from driving the motor.

Step2 - Connect the +15V source voltage from either the Servo-Amp or the Power Supply as Vin, as shown in Figure A.5. Step 3 - Compute Vout.

• Measure and record Vin using the digital volt meter read-out on the Tachometer unit. Vin is supposed to be +15V; this is just for confirmation.

• Compute Vout as the product of the measured value of Vin and the desired gain value.

Step 4 - Set Vout. • Connect the Vout (wiper) terminal on the attenuator to the digital volt meter input on the Tachometer

unit (plug 4). • Adjust the potentiometer dial until Vout equals (reasonably closely; within a few tenths of one volt)

the computed Vout value from Step 3. Step 5 - Reconnect the attenuator Vin and Vout terminals to their original connections.


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Procedure 6: Measure Characteristics of an Under-Damped Step Response Purpose: This procedure is used to measure the Rise-Time, Peak-Time, Settling-Time, and Percent Overshoot of an under-damped second-order step response.

Figure A.6 - Measuring the Characteristics of an Under-Damped Second-Order Step Response


• Connect one oscilloscope input channel to the signal being evaluated (e.g.: VPosition). • Adjust the vertical sensitivity (Volt/division) so that the entire amplitude of the step response fits on

the screen (including the peak overshoot). • Adjust horizontal sweep (seconds/division) so that a single step response (from the beginning of

the step until the final value is reached) is displayed on the screen. • Use the HOLD or RUN/STOP feature on the oscilloscope to capture a positive going step

response. Step 2 - Measure the Final Value: • Use the Cursor or Measure feature on the oscilloscope to measure the overall vertical

displacement of the step response from the beginning of the step to the final value - Refer to Figure A.6. Call this 100%.

Note that due to disturbance inputs, system nonlinearities, etc., the oscillations may never decay to within the 2% (±1%) settling band. (This condition should be noted in your lab report.) If so,


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estimate and measure the value that the signal is oscillating around and use this as the final value.

If required: Step 3 - Measure the Rise-Time, tr:

• Use the Cursor or Measure feature on the oscilloscope to measure the time that it takes for the step response to transition from 10% to 90% or the final value. (Refer to Figure A.6.)

If required: Step 4 - Measure the Peak-Time, tp:

• Use the Cursor or Measure feature on the oscilloscope to measure the time that it takes for the step response to transition from the beginning of the step response to the first peak of the oscillation. (Refer to Figure A.6.)

If required: Step 5 - Measure the Settling-Time, ts:

• Use the Cursor or Measure feature on the oscilloscope to measure the time that it takes for the step response to transition from the beginning of the step response until the oscillation remains within 2% (±1%) of the final value (i.e.: the settling band). (Refer to Figure A.6.)

If the oscillations do not decay to within the 2% (±1%) settling band, this condition should be noted in your lab report. If required: Step 6 - Measure the Percent Overshoot, Mp:

• Use the Cursor or Measure feature on the oscilloscope to measure the amount of overshoot of the first peak of the oscillation above the final value. (Refer to Figure A.6.)

• Compute the percent overshoot as:

ee-474 feedback control system_2012

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