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1
Introduction Introduction to Control to Control
SystemSystem
CHAPTER 1CHAPTER 1
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Basic terminologies. Open-loop and closed-loop. Block diagrams. Control structure. Advantages and Disadvantages of closed-loop..
Chapter Objective.Chapter Objective.
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Definition of a control system;
The control system consists of subsystems and process (or plant) assembled for the purpose of controlling the output with desired performance, given a specified input.
1.1 Introduction.1.1 Introduction.
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Cont’d…Cont’d…Advantages of control systems; Can move large objects with precision; for
example (i) elevator, (ii) radar antenna to pickup strong radio signal and (iii) robot to operate in the dangerous environment.
Example:(i) Elevator
When pressed fourth-floor from first floor, the elevator rises to the fourth floor with a speed and floor-leveling accuracy design for passenger comfort.
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(a) Sub-system and Systemsubsystem subsystem subsystem
Subsystem is part of the system that is grouped for a certain function
System is a combination of physical and non-physical components that are configured to serve certain tasks to maintain the output
(b) Plant subsysteminput output
Plant is a subsystem where an output signal is derived from the input signal
blower room thermostat
plant
1.2 Basic Terminologies.1.2 Basic Terminologies.
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(c) Input and Output
Input = Stimulus Output = Response
Cont’d…Cont’d…
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Cont’d…Cont’d…
(d) System Response Ability of system to achieve desired result is measured in terms
of system response: comparison of output versus input.
Transient response. Steady State Response. Steady State Error.
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Disturbance is the unwanted signal that may sway the output .
Controller is a subsystem that is used to ensure the output signal follows the input signal.
The Open-Loop System cannot compensate for any disturbance that add to the system.
Example; bread toaster.
1.3 Open Loop System.1.3 Open Loop System.
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The Close-Loop (feedback control) System can overcome the problem of the Open Loop System in term of sensitivity to disturbance and inability to correct the disturbance.
1.4 Close-Loop System.1.4 Close-Loop System.
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The design of a control system follows these steps;Step 1: Transform Requirement into a Physical System.Step 2: Draw the Functional Block Diagram.Step 3: Create the Schematic.Step 4: Develop the Mathematical Model or Block
Diagram.Step 5: Reduce the Block Diagram.Step 6: Analyze and Design.
1.5 The Design Process.1.5 The Design Process.
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Transfer function is the ratio of the output over the input variables.
The output signal can then be derived as; C = GR
(a) Multi-variables.
1.7 Block Diagram.1.7 Block Diagram.
)(
)()(
sR
sCsG
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(b) Block Diagram Summing point.Cont’d…Cont’d…
Figure 1.7: Block Diagram of Summing Point.
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(c) Linear Time Invariant System.Cont’d…Cont’d…
Figure 1.8: Components of a Block Diagram for a Linear, Time-Invariant System.
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Cont’d…Cont’d…
Figure 1.10: Parallel System and the Equivalent Transfer Function.
Figure 1.9: Cascade System and the Equivalent Transfer Function.
(d) Cascade System.
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(e) Summing Junction.
(f) Pickoff Points.
Cont’d…Cont’d…
Figure 1.12: Block diagram algebra for pickoff points—
equivalent forms for moving a block (a) to the left past a
pickoff point; (b) to the right past a pickoff point.
Figure 1.11: Block diagram algebra for summing
junctions: equivalent forms for moving a block (a) to the left past a summing junction; (b) to the right past a summing
junction.
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Cont’d…Cont’d…
Figure 1.13: Block diagram reduction Example 1. (a) collapse summing junctions; (b) form equivalent
cascaded system in the forward path and equivalent parallel system in the feedback path; © form equivalent
feedback system and multiply by cascaded G1(s)
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E(s) error signal R(s) reference signal Y(s) output signal
C(s) output signalB(s) output signal from feedback
Feed forward transfer function,
Feedback transfer function,
Open-loop transfer function,
1.8 Control Signal.1.8 Control Signal.
)(
)()(
sR
sCsG
)(
)()(
sC
sBsH
)()()(
)(sHsG
sE
sB
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Close-Loop transfer function, Assume give
Variable difference,
Characteristic equation,
)()()( sBsRsE
)()()()( sYsHsRsE
)()()()(
)(sYsHsR
sG
sY
)()(1
)(
)(
)(
sHsG
sG
sR
sY
Cont’d…Cont’d…
1)( sH )()( sBsY
.
)()(1)( sHsGsT
0)()(1 sHsG
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Physical model. Graphical model. Mathematical model.(a) Current-voltage relationship v = ir.
v – voltage in Volt (V).i – current in Ampere (A).r – resistance in Ohm.
(b) Force-deflection relationship f – force in Newton (N).k – spring constantx – displacement in meter (m).
(c) Mass-spring model fo - applied forcex - displacement fs - reaction force
1.9 Model.1.9 Model.
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Transient state A state whereby the system response after a perturbation
before the response approach to a steady conditionSteady state A state whereby the system response becomes steady after a
transient state.Stability The condition of the steady state. If the response converges
to a finite value then it is said to be in a stable condition and if the response diverges, it is known to be unstable.
A system must be stable in order to produce the proper transient and steady state response.
Transient response is important because it effects the speed of the system and influence human patience and comfort.
1.10 Design Analysis.1.10 Design Analysis.
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1.11 Design.1.11 Design.Analogue controller A controller that used analogue subsystem.
Digital Controller A controller that used computer as its
subsystem.
Figure 1.14: Controller in Computer Subsystem.
computer drive plant
sensor
_
+ Referene
input
Actual output
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0 2 4 6 8 10 12 14 160
500
1000
1500
Time [s e conds ]
Sp
ee
d [r
pm
]
S ine Wa ve Re fe re nce a nd S pe e d Re s pons e of Dire ct Inve rs e C ontrol S che me .
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0 2 4 6 8 10 12 14 160
200
400
600
800
1000
1200
1400
1600
Time [s e conds ]
Sp
ee
d [r
pm
]
Ra mp Wa ve Re fe re nce a nd S pe e d Re s pons e of Dire ct Inve rs e C ontrol S che me .
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0 1 2 3 4 5 6 7 8 9 100
200
400
600
800
1000
1200
1400
1600
1800
Time [s e conds ]
Sp
ee
d [r
pm
]
Unit S te p Re s pons e with Dire ct Inve rs e C ontrol.
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0 2 4 6 8 10 12 14 160
200
400
600
800
1000
1200
1400
1600
1800
Time [s e conds ]
Sp
ee
d [r
pm
]
S qua re Wa ve Re fe re nce a nd S pe e d Re s pons e of Dire ct Inve rs e C ontrol S che me .
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