??? ???? ?????? ?????? Advanced Control Lecture three

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??? ???? ?????? ??????Advanced ControlLecture
three

• Mohammad Ali Fanaei
• Dept. of Chemical Engineering
• Ferdowsi University of Mashhad

Reference C. C. Yu, Autotuning of PID
Controllers, 2nd ed., Springer, 2006
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Off-Line Tuning of PID Controllers
About 250 tuning rules are exist for PI and PID
Controllers What is the suitable tuning rule?
It really depends on your process (Type, Order,
Parameters, Nonlinearity, Uncertainty, etc)

1. Ziegler-Nichols(1942) Recommended for 0.2lt D/t
   lt2 ( )

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Off-Line Tuning of PID Controllers

1. Tyreus-Luyben(1992) Recommended for
   time-constant dominant processes

• Ciancone-Marlin(1992) Recommended for dead-time
  dominant processes

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Off-Line Tuning of PID Controllers

1. PID tuning based on IMC (Rivera et al., 1986)

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On-Line Tuning of PID Controllers

• Ziegler-Nichols Test (1942)

1. Set the controller gain Kc at a low value,
   perhaps 0.2.
2. Put the controller in the automatic mode.
3. Make a small change in the set point or load
   variable and observe the response. If the gain
   is low, then the response will be sluggish.
4. Increase the gain by a factor of two and make
   another set point or load change.
5. Repeat step 4 until the loop becomes oscillatory
   and continuous cycling is observed. The gain at
   which this occurs is the ultimate gain Ku , and
   the period of oscillation is the ultimate period
   Pu.

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On-Line Tuning of PID Controllers

• Relay Feedback Test (Astrom Hagglund, 1984)

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On-Line Tuning of PID Controllers

• Relay Feedback Test

1. Bring the system to steady state.
2. Make a small (e.g. 5) increase in the
   manipulated input. The magnitude of change
   depends on the process sensitivities and
   allowable deviations in the controlled output.
   Typical values are between 3 and 10.

• As soon as the output crosses the SP, the
  manipulated input is switched to the opposite
  position (e.g. 5 change from the original
  value).
• Repeat step 2 until sustained oscillation is
  observed .
• Read off ultimate period Pu from the cycling and
  compute Ku from the following Equation Ku
  4h/(pa)

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On-Line Tuning of PID Controllers

• Advantages of Relay Feedback Test

• It identifies process information around the
  important frequency, the ultimate frequency.
• It is a closed-loop test therefore, the process
  will not drift away from the nominal operating
  point.
• The amplitude of oscillation is under control (by
  adjusting h ).
• For processes with a long time constant, it is a
  more time-efficient method than conventional step
  or pulse testing. The experimental time is
  roughly equal to two to four times the ultimate
  period.
• If the normalized dead time D /t is less than
  0.28, the ultimate period is smaller than the
  process time constant. Therefore the relay
  feedback test is more time efficient than the
  step test.

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On-Line Tuning of PID Controllers

• Advantages of Relay Feedback Test

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On-Line Tuning of PID Controllers

• Process model identification from a
• Relay Feedback Test

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Recommended Tuning Formulas
The following formulas are recommended by Luyben
and Yu for tuning The PI controllers
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Example 3 Using relay Feedback
In this example for the system that described in
example 2 a relay feedback test is used for
on-line tuning of a PI controller