System/Plant/Process(Transfer function)

OutputInput

)(

)()(

sU

sYsG

)(sU )(sY

The relationship between the input and output are mentioned in terms of transfer function, which is defined as the ratio between the Laplace transform of the output and the Laplace transform of the input. If the output is proportional to the input, the plant is called a linear system.

Controller Output

PLANT/PROCESS

InputOpen-loopController

Plant Output

(Setpoint or reference value)

An example of a block diagram of an open-loop control system. The term ‘open-loop’ comes from the fact that the output only depends on the inputs. This is a complete system by itself. The control system takes the input from the controller in order to produce output by the action of the plant.

)(1 sG )(2 sG

P l a n t - 1 P l a n t - 2

)()()( 21 sGsGsG

)(1 sG )(2 sG

P l a n t - 1 P l a n t - 2

)(1 sG )(2 sG

P l a n t - 1 P l a n t - 2

)()()( 21 sGsGsG )()()( 21 sGsGsG

The overall transfer function of the system is the product of individual transfer functions. In general, in open-loop configuration, mathematically, the overall transfer function of the composite system is given by the following formula.

)(.....).........()()()( 321 sGsGsGsGsG n

Field-controlled DC motor

Load Output speedDriving torqueDesired speed (set-point) Error

Sensor(Tachometer)

A closed-loop control system, on the other hand, uses input as well as some portion of the output to regulate the output. The closed-loop systems are also called feedback control systems. In feedback control the variable required to be controlled is measured. This measurement is compared with a given setpoint. If the error results, the controller takes this error and decides what action should be taken to compensate and hence to remove the error.

+

-

+

-

)(tc y)(ty

u )(te

PLANT

Load or disturbance

Error Amplifier

Control Systems

+

Controlled system

Setpoint

The closed-loop control schematic must have a plant which is to be controlled. The plant is referred to as the controlled system. The block that controls the plant (i.e., the controlled system) is called the controller. The controller is not a physical controller that you studied in the Chapter-8. It is a manipulation method that controls and regulates the output through feedback or closed-loop action. The algorithm of the manipulation can be implemented in a physical controller in order to achieve the objective, i.e., to regulate the output.

)(sG p

PLANT

)(sG f

Feedback loop

U(s)Y(s)

)()(1

)(

sGsG

sG

fp

p

U(s) Y(s)

(a) (b)

The equivalent transfer function of the feedback control system, shown in the figure- (b), is called closed-loop transfer function, which can be written as,

)()(1

)(

)(

)()(

sGsG

sG

sU

sYsG

fp

p

+

-

+

-

ON-OFF Controller

ONccy

yu )(te

OFFc

PLANT

From closed-loop control point of view there are commonly seven types of control actions which are considered as the most fundamental because the plant can adequately be controlled to attend the reachability point by designing appropriate controllers.

•On-off controller•Proportional controller•Integral controller•Derivative controller•PD controller •PI controller•PID controller

On-off controller

ON-OFF Controller

ONycy)(te

OFFy

Dead-band

On-off controller with hysteresis or dead-band

The turn-ON and turn-OFF in case of ON/OFF controller in many situation are deliberately made to differ by a small amount, known as the hysteresis or dead-band, to prevent noise from switching the controller unnecessarily when the output is nearly the setpoint. The sensitivity of the On-Off controller depends on the hysteresis.

Proportional controller

(Kp)

PlantOutput speedController

OutputDesired speed (set-point) Error

Measuredmanipulated

variable

U(s)

Y(s)

E(s)

Proportional Control means that the plant input is changed in direct proportion to the error, e(t). This controls the output so that the manipulated variable and the error has a proportional relation. The advantage of proportional controller is that it is relatively easy to implement. However, the disadvantage is that there always involves an offset in the output response causing difference between the set-point and the actual output.

Integral Controller Controller OutputDesired speed (set-point)

Error

s

K

sE

sCsG iy

IC )(

)()(

Feedback loop

When the controller controls the output by integrating the error signal, then it is called an integral control action. The offset in the output, and hence the steady-state performance of the system can be improved by employing integral control action. But the integral action may lead to oscillatory output resulting poor stability.

Controller output

Desired speed (set-point)Error

Feedback signal

+

++

sK d

s

K i

pK

The transfer function of the PID controller is

sKs

KK

sE

sCsG d

ip

yPID

)(

)()(

1x

2x

3x

4x

5x

ix

nx

iiwx

nw

iw5w

4w

3w

2w

1w

Output

INPUTS

Intelligent control incorporates biological information processing method and Fuzzy theory. Biological information processing method includes Neural Network, Genetic Algorithm and Immune Network.

At the core of the neural computation, there exist the concepts of distributed, adaptive, and nonlinear computing.

Input layer Hidden layerOutput layer

1x

2x

3x

4x

1y

2y

All ANNs have a similar structure as far as topology is concerned. Some of the neurons interface the real world to receive its inputs, and other neurons provide the real world with the network’s outputs. Besides input layer and output layer there may be many middle layers, with a variable number of nodes, depending upon the task at hand.

R

1x 2x

r

r

R

1x 2x

r

r

0

1

1

0.75

0.5

0.25

0

Degree Of Membership

0x

Uncertainties are of two types; stochastic uncertainty and fuzziness. Stochastic uncertainty has only two levels such as true or false. Where the event is not well defined, the outcome may be given by a quantity other than true or false, but rather fuzzy. There comes fuzzy logic. The outcome in presence of fuzziness is quantified by a degree

of belief. FL system is called soft linguistic system.

System study

Define the control functions

Classical plant modeling

Controller selection and Control algorithm

System study

Define the control functions

Implement using FL

Simulation, Testing, Refinement

Simulation, Testing, Refinement

(a)(b)

FL based strategy simplifies the design loop. This results in some significant benefits, such as reduced development time and simpler design.

Process

Faults

N

Y + dY

U

X + dX

P + dP

A schematic diagram of a process is shown. The mathematical description is expressed as,

)( PX,N,U,fY

Y = OutputU = inputN = Noise X = Process state variablesP = Process parameters

Detection IsolationDetection Isolation

Two main subtasks are involved within FDI techniques. Failure detection that indicates that something abnormal has happened in the system. Failure isolation is the ability to distinguish between specific faults and isolating the component that has failed.

Actuator ProcessDynamics Sensor

U Y

Model ofObserver System

Model of Nominal System

Model of Faulty System

State Estimation

parity space

observer methoddetection filter

Residual Generator

Parameter Estimation

Decision Makerdecision function generatorfault decision logic

Fault time, size, cause, location, type

Actuator FaultProcess Modelling Error + Noise

Sensor Fault

Implementation of FDI is achieved mainly through statistical and model-based approach. Method that relies on a quantitative mathematical relation between the I/O is called model-based

technique. Model-based fault detection depends only on the availability of a mathematical model of the plant.

1011

Slot-1 Slot-2 Slot-3 Slot-4

(Three pulses are generated in order to represent one pulse (Error correcting code)

(a)

(b)

(c)

Original digital Signal

Noise introduced during transmission

Distortioneliminator

Outputinput

Quantised level

Quantised level

The digital control technology to some extend is immune to noise. The effect of noise can be efficiently reduced using error correcting codes or distortion eliminator.

Power Power

converterPlant Load

Digital control

Mechanical variables •Position•Speed•Acceleration•Torque•Force, etc.

Sensor

Electrical variables•Voltage•Current

•Resistance•Flux, etc.

Sensor

From implementation schematic an advanced digital control system in its basic nature can be seen as shown in the figure. Digital control technology makes it easy to implement state feedback and adaptive control.

Diagnostics and

Prognostics

Monitoring and

Protection

StatusDisplay

Storage

Power circuitInterface

System logicRTOS

And Control

Communication

Data Acquisition

and Processing

Power converter drive signals

Sensor signals

Auxiliary functions

A full-fledged advanced control system has to incorporate auxiliary functions such as display, storage, monitoring, protection, diagnostics and prognostics as illustrated above. The blocks drawn inside the dotted box shows the schematic diagram of a typical control implementation scenario.