Ch3 Feedback control system characteristics

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Ch3 Feedback control system characteristics
Main content

• Open- and closed-loop control systems
• Sensitivity to Parameter variations
• Transient response of control system
• Disturbance in feedback control system

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Main content

• Steady-state error
• The cost of feedback
• Examples and simulation

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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
Benefits

• Reduce error (eliminating the error)
• Reduce sensitivity or Enhance robustness
• Disturbance rejection or elimination
• Improve dynamic performance or adjust the
  transient response (such as reduce time constant)

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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 changing
environment , aging , and other factors that
affect a control process.All these uncertainties
in open-loop system will result in inaccurate
output 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
systems sensitivity to parameter
variation.Sensitivity analysis Robust
control
Continue
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Effect of parameter variations
If process is change as

• Open-loop system

• Closed-loop system

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In the limit, for small incremental changes, last
formula is
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Sensitivity comparison

• Open-loop system
• Closed-loop system

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Sensitivity to parameters
If system TF is
System sensitivity to is
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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 the most
  important characteristics of control system.
• If transient response is not satisfying, what
  shall we do?

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

• Cascade controller
• Feedback controller

Refer to P180 (Figure 4.6 and Figure 4.7)
Refer to P181 (Figure 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 systems 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 disturbancesNoise
• 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 sensitivity
System 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
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3.5 Steady-state error

• Steady-state error is the error after the
  transient response has decayed,leaving only the
  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

• Open-loop system

• Closed-loop system

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• Open-loop system under unit step input
• Closed-loop system under unit step input

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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
The fundamental reasons for using feedback are as
follows

• Decrease the sensitivity to parameter variation
• Improve transient or dynamic performance
• Enhance the robustness
• Reduce the steady-state error

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