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Ch3 Feedback control system

characteristics

Open- and closed-loop control systems

Sensitivity to Parameter variations

Transient response of control system Disturbance in feedback control system

 Main content:

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continue

Steady-state error 

The cost of feedback 

Examples and simulation

 Main content:

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3.1 Open-loop and closed-loop

control systems

Review the concepts and structure

Refer to P174-175

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The roles of feedback 

Reduce error (eliminating the error)

Reduce sensitivity or Enhance robustness

Disturbance rejection or elimination

Improve dynamic performance or adjust thetransient response (such as reduce time

constant)

 Benefits:

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3.2 Sensitivity of system to

 parameter variations

System are time-varying in its nature because

of inevitable uncertainties such as changingenvironment , aging , and other factors that

affect a control process.All these uncertainties

in open-loop system will result in inaccurateoutput or low performance. However, a closed-

loop system can overcome this disadvantage.

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A primary advantage of a closed-loop

feedback control system is its ability to

reduce the system¶s sensitivity to

 parameter variation.

Sensitivity analysis Robust control

C ontinue

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Effect of parameter variations

If process is change as)( sG )()( sG sG (

Open-loop system

)()()( s R sG sY  (!(

Closed-loop system

)(

)1(

)(

)()1)(1(

)()(

2s R

GH 

 sG

 s RGH GH GH 

 sG sY 

(!

(

(

!(

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continueIn the limit, for small incremental changes, last

formula is

 InG

 InT 

 sG sG

 sT  sT S 

x

x!

x

x!

)(/)(

)(/)(

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Sensitivity comparison Open-loop system

Closed-loop system

1!T 

GS 

)()(1

1

 s H  sGS T 

G

!

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Sensitivity to parametersIf system TF is

),(

),(),( E

E

E  s D

 s N  sT  !

System sensitivity to is

 D N T S S 

 In

 InD

 In

 InN 

 In

 InT S 

EEE

EEE!

x

x

x

x!

x

x!

E

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Example of sensitivity Feedback amplifier 

Goal: Reduce the sensitivity to parameters

variation, that is enhance the robustness to

change in amplifier gain.

Refer to 178-179

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3.3 Transient response of system

Transient response is the response of a

system as a function of time. It is one of themost important characteristics of control

system.

If transient response is not satisfying, whatshall we do?

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Control of transient response(Take speed control system as example)

Cascade controller 

Feedback controller 

Refer to P180 ( F igure 4.6 and  F igure 4.7)

Refer to P181 ( F igure 4.8)

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3.4 Disturbance in a feedback 

control system

Disturbance signal is an unwanted extraneous

input signal that affects the system¶s output

signal, such as noise for amplifier,wind gusts

for radar antennas,etc.

Feedback control can completely or partially

eliminate the effect of disturbance signal.

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Example of steel rolling mill Refer to P183-187

Load changes or d isturbances+ Noise

Feedback can alleviate the effects of 

disturbances and noise signal occurring

within the feedback loop.

If system exists noise at the input point, we

can design a low-pass filter to improve SNR

(signal-noise ratio)

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System sensitivitySystem sensitivity is defined as the ratio of the

 percentage change in the system transfer function

to the percentage change of the process transfer function. It is defined as

)(/)()(/)(

 sG sG sT  sT S 

(

(!

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3.5 Steady-state error  Steady-state error is the error after the

transient response has decayed,leaving onlythe continuous response.

Feedback can reduce the steady-state error 

of control system

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How to define the error ? From input point:

From output point:

 E  a(s)=R(s)-H(s)Y(s)

 E (s)=R(s)-Y(s)

Only for unit feedback H(s)=1,We have

 E  a (s)=  E  (s)

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Comparison of error 

)())(1()()()( s R sG sY  s R s E o !!

1)(,)()(1

1)( !

! s H  for  s R

 sG s E 

o

Open-loop system

C losed -loop system

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continue Open-loop system under unit step input

Closed-loop system under unit step input

)0(11))(1(lim)(lim)(00

G s

 sG s s s E e s

o s

o !!!gpp

)0(111)

)(11(lim)(lim)(

00 G s sG s s s E e

 sc

 sc

!

!!g

pp

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Example illustration Refer to P189-190

An example of first-order system

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3.6 The cost of feedback 

Increase of complexity

Loss of gain

Instability

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An unrealistic dream

Why not simply set G(s)=Y(s)/R(s)=1?

Transfer function represent the physical

system or process, Therefore G(s)=1 is

unrealizable.

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3.7 Design examples English channel boring machines

Mars rover vehicle

PD controller, and how to select  K ?

To compare the sensitivity and steady-state error  between open-loop and closed-loop system

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3.8 Simulation using MATLAB Refer to P196-202

Self-learning after class

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Summary

Decrease the sensitivity to parameter variation

Improve transient or dynamic performance

Enhance the robustness

Reduce the steady-state error 

The fundamental reasons for using feedback are as

follows:

Refer to P205-207

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Assignment E4.1

E4.3

E4.4

E4.6

E4.8 P4.2 , P4.5, P4.7