MODIFIED FUZZY GAIN SCHEDULING OF PID CONTROLLERS

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MODIFIED FUZZY GAIN SCHEDULING OF
PID CONTROLLERS
B.HEMAKUMAR
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OBJECTIVES

• To obtain responses for various SISO processes
  using fuzzy gain scheduling of PID
  controller and to compare this with conventional
  PID controller response.
• To implement fuzzy gain scheduled controller for
  four tank MIMO process.
• To perform real time implementation on SISO
  process using fuzzy gain scheduled PID controller
  and to compare it with conventional PID
  controller.

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DESIGN OF FUZZY GAIN
SCHEDULING OF

PID CONTROLLERS

• This scheme utilities fuzzy rules and
  reasoning to determine the controller parameters
  for PID controller to generate the control
  signals.
• WORKING RANGE FOR Kp AND Kd
• Kc,min 0.4Ku
  Kc,max 0.55Ku
• Kd,min 0.09KuTu
  Kd,max 0.16KuTu
• NORMALISATION

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• Ti a Td
• For fuzzy set small,
• µsmall (x) - ¼ ln(x) or xsmall (µ) e-4µ
• For fuzzy set big,
• µbig (x) - ¼ ln(1 - x) or xbig (µ) 1
  - e-4µ

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Fuzzy Tuning
Rules for Kc
?e(k) e(k) NB NM NS ZE PS PM PB
NB S S S B B B B
NM S S S B B S S
NS S S S B B S S
ZE S S S B S S S
PS S S B B B S S
PM S B B B S S S
PB B B B B S S S
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Fuzzy Tuning
Rules for Kd
?e(k) e(k) NB NM NS ZE PS PM PB
NB S B B S S S S
NM B B S S S B B
NS S S S B B S S
ZE B B B B B B B
PS B B B S B B B
PM B B S S S B B
PB S S S S B B S
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Fuzzy Tuning
Rules for a
?e(k) e(k) NB NM NS ZE PS PM PB
NB 5 5 5 2 2 2 2
NM 4 4 2 2 2 5 5
NS 4 3 3 2 3 3 4
ZE 5 4 3 3 3 4 5
PS 4 3 3 2 3 3 4
PM 3 3 2 2 2 3 3
PB 2 2 2 2 5 5 5
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• µi µAI e(k) µBI ?e(k)
• Based on µi, the values of Kc and Kd for
  each rule are determined from their corresponding
  membership functions.
• 
  

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CONCLUSION

• The proposed gain scheduling scheme uses fuzzy
  rules and reasoning to determine the PID
  controller parameters. The scheme had been tested
  on various SISO processes and MIMO process in
  simulation using C language and Matlab Software
  and satisfactory results were obtained.
• The responses obtained revealed that the proposed
  scheme i.e. the fuzzy gain scheduling yields
  reduced overshoot, settling time, rise time,
  delay time and peak time in comparison with the
  conventional PID controller. The real time
  implementation of a third order SISO process has
  been carried out and satisfactory response is
  obtained for fuzzy gain scheduled PID controller.

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REFERENCES

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