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Principles of Control Systems

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CHAPTER 1: INTRODUCTION TO CONTROL SYSTEMS

1.1 Introduction

In recent years, control systems have assumed an increasingly important role in the

development and advancement of modern civilisation and technology. Practically, every

aspect of our day-to-day activities is affected by some type of control systems. For

instance, automatic control air-conditioner controlled the temperature and the humidity in

house and building to give comfortable life to the users.

Control systems play very important role in many modern manufacturing industries such

as automatic assembly system, computer control, machine-tool control, transportationsystems, robotics and many others.

1.1.1 Definition of control system

A control system is an interconnection of components forming a system configuration

that would provide a desired output in response to input signals.

Figure 1.1

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1.1.2 History of control systems

The selected historical developments of control systems are listed below:

1769: James Watts steam engine and governor development. The Watt steam engine

is often used to mark the beginning of the Industrial Revolution in Great Britain.

During the Industrial Revolution, Great Britain strides were made in the

development of mechanisation, a technology preceding automation.

1800: Eli Whitneys a concept of interchangeable parts manufacturing demonstrated in

the production of muskets. Whitneys development is often considered as the

beginning of mass production.

1868: J. C. Maxwell formulates a mathematical model for a governor control of a steam

engine.

1913: Henry Fords mechanised assembly machine introduced to automobile production.

1927: H. W. Bode analyses feedback amplifiers.

1932: H. Nyquist develops method for analysing the stability of systems

1.2 Control Terminology

It is very important to know the basic terminologies before discussing further on control

systems. The common terminologies are listed below:

a) Controlled variable: The controlled variable is the quantity or condition that is

measured and controlled

b) Manipulated variable: The manipulated variable is the quantity or condition that is

varied by the controller so as to affect variable value of the controlled variable.

c) Plants: A plant is a piece of equipment perhaps just a set of machine parts

functioning together, to perform a particular operation.

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d) Process: A process is to be a natural, progressively continuing operation or

development marked by a series of gradual changes that succeed one another in

relatively fixed way and lead toward a particular result

e) System: A system is combination of components that act together and perform a

certain objective. A system is not limited to physical ones. The concept of the

system can be applied to abstract, dynamic phenomena such as those encountered

in economics. The word system should be therefore, be interpreted to imply

physical, biological, and economic.

f) Disturbance: A disturbance is a signal that tends to adversely affect the value of

the out signal. If the disturbance is generated within the system is called internal,

while an external disturbance is generated outside the system and is an input to the

systems.

g) Open-loop(Non-feedback) system: An open-loop system utilises an actuating

device to control the process directly without using feedback

h) Feedback control/closed-loop system: A closed-loop system uses a measurement

of the output and feedback of this signal to compare it with the desired output

(reference or command).

1.3 Basic components of a control system

The basic ingredients of a control system can be described by:

a) Objectives of control (Input)

b) Control system components(plant/process)

c) Results (outputs)

The basic relationship between these three components is illustrated in block diagram

shown in figure 1.2.

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CONTROL SYSTEM

RESULTSOUTPUT, Y

OBJECTIVESINPUT, R

Figure 1.2: Basic components of a control system

In more technical terms, the objectives can be identified with inputs, or actuating signals,

R orU, and the results are called outputs, or the controlled variables, Y. In general the

objectives of control system can be to:

a) Control/regulate the output from some process to be constant at the

required/desired value.

b) Make the process output follow a particular changing form

c) Make events in a particular sequence. This might be the sequence which is time

driven with events occurring at particular times or event driven so that events

occur when certain conditions are realised.

Figure 1.3 shows the examples of control systems

(a)

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(b)

(c)

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(d)

Figure 1.3 (a): Traffic light system (sequence time/event)

(b): Washing Machine (sequence time/event)

(c): Turntable speed control

(d): Steering a car on a curve road

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1.4 Closed-loop Control Versus Open-loop Control

An open-loop system is a system where the input has no effect on the control action. In

other words, in an open-loop control system the output is neither measured nor feedback

for comparison with the input. The elements of an open-loop control system can usually

be divided into two parts that are the controller and the process as shown in figure 1.4

CONTROLLER

Controlled variable,

output, YReference input, R

PLANT

Actuating

signal, U

Figure 1.4: Block diagram of an open-loop control system

Examples in figure 1.3 (a), traffic light system and (b), washing machine are the examples

of open-loop control systems. In any open system the output is not compared with the

reference input. Thus, to each reference input there correspond a fixed operating

condition; as a result, the accuracy of the system depends on calibration. In practice, onlyif the relationship between input and output is known and if there are neither internal nor

external disturbances.

What is missing in the open-loop control system for more accurate and more adaptive

control is link or feedback from the output to the input of the system. To obtain more

accurate control, the controlled signal (output), Y should fed back and compared with the

reference input and actuating signal proportional to the difference(error) of the input andthe output must be sent through the system to correct the error and this system is called

closed-loop system. The basic components of a closed-loop control system are shown in

figure 1.5.

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CONTROLLER

C

output, YReference

input, R PLANT

G

Error

signal, E

SENSOR

H

-

+

Feedback

Figure 1.5: The basic components of a closed-loop control system

Table 1 shows the advantages and disadvantages of an open-loop and closed-loop control

systems.

Type of system Advantages Disadvantages

1. Open-loop control

system

1. Simple construction and

ease of maintenance.

2. Less expensive than a

corresponding closed-

loop control system

3. There is no stability

problem

4. Convenient when output

is hard to measure or

measuring the output

precisely is

economically not

feasible.

1. The system response very

sensitive to external

disturbance and internal

variations in system

parameters.

2. Recalibration is necessary

from time to time in order

to maintain the required

quality in the output

2. Closed-loop control

system

1. Makes the

system response

relatively insensitive to

external disturbance and

internal variations in

system parameters.2. Possible to

use relatively inaccurate

and inexpensive

components to obtain

the accurate control of a

given plant.

3. Better control of

transient & steady-state

response

4. Increased accuracy

-Increased ability toreproduce output with

1. Risk instability

2. Complexity in analysis and

implementation and

expensive

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varied input.

1.5 Principle of feedback and its effects

The feedback is used for reducing the error between the reference input and the system

output. However the significance of the effects of control systems is more complex than

is demonstrated by the previous examples. Applying the feedback to the system causes

effects on system performance such as stability, bandwidth, overall gain, disturbance and

sensitivity. By simple algebraic manipulations, it is simple to show the relationship

between input and output is given by:

GH

G

R

YM

+

==

1(1.1)

1.5.1 Effect of Feedback on Overall Gain

A seen from eq. (1.1), feedback affects the gain G of the non-feedback system by a factor

1 + GH (for negative feedback). General effect of feedback is that it increase or decrease

the gain G. In a practical control system G and H are functions of frequency, so the

magnitude of 1 + GH may greater than 1 in one frequency range but less than 1 in

another. Therefore, feedback could increase or decrease the system gain in one frequencyrange but decrease it in another.

1.5.2 Effect of Feedback on Stability

Stability is a notion that describes whether the system will be able to follow the input

command. In a non-rigorous manner, a system is said to be unstable if its output is out of

control. To investigate the effect of feedback on stability, again refer to eq. (1.1).If GH =

-1, the output of the system is infinite for any finite input, and the system is said to be

unstable. Therefore we can state that feedback can cause a system that is originally stable

to become unstable.

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1.5.3 Effect of Feedback on Sensitivity

Sensitivity considerations often are important in the design of control systems. In general,

a good control system should be very insensitive to parameter variations but sensitive to

input commands. The sensitivity of the gain of the overall system, M to the variation in G

is defined as:

=M

GS M/M = Percentage change in M (1.2)

G/G Percentage change in G

Where M denotes the incremental change in M due to the incremental change in G, G.

Using eq. (1.1), the sensitivity function is written:

(1.3)

This relationship shows that if GH is a positive constant, the magnitude of the sensitivity

function can be made arbitrarily small by increasing GH, provided that the system remain

stable. In general feedback can increase or decrease the sensitivity of the system.

1.5.4 Effect of Feedback on External Disturbance or Noise

All physical systems are subject to some types of extraneous signals or noise during

operation. Examples of these signals are thermal-noise voltage in electronic circuit and

brush or commutator noise in electric motors. External disturbance, such as wind acting

on antenna, is also quite common in control systems. Therefore in the design of a control

system, considerations should be given so that the system is insensitive to noise and

disturbance and sensitive to input command.

The effect of feedback on noise and disturbance depends greatly on where these

extraneous signals occur. No general conclusion can be made, but in many situations,

feedback can reduce the effect of noise and disturbance on system performance.

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GHM

G

G

MSM

G

+=

=

1

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