Tuning of Fuzzy PID Controllers

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Tuning of Fuzzy PID Controllers

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• ????? ??
• ????? ??? 19953025

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• ????Tuned Nonlinear Fuzzy PID?Linear Fuzzy
  PID?PID ?????????????gain?Linear PID?Linear Fuzzy
  PID??Tuned Nonlinear Fuzzy PID,????????Rise
  time?Overshoot?Settling time ?Gain factor
  ???????,???Tuning of Fuzzy PID Controllers???????
  Auto-tuned Fuzzy PID Controllers ????? 2

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Tuned Nonlinear Fuzzy PID?????????

• 1.?Tune a PID Controller
• 2.??Equivalent Linear Fuzzy Controller
• 3.???Make the Fuzzy controller nonlinear
• 4.?? Fine tune it ?
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Figure Proportional controller with load
(L) and noise (n) 4
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1st step Tuning a PID controller

• U Kp (e l/ Ti?0t edt Td(de/dt))
  KpProportional gain, U controller output Ti
  integral time Td the derivative time , e error
  (ref-Y) y Process output Ts sampling period
• ?in discrete approximation???Un Kp (en l/ Ti
  SnJ1 ej Ts Td(en-en-1)/ Ts)
• n time instant tuning items Kp ?Ti ? Td
  ,??Propotional controller (P) ?
• Td0 ?1/ Ti0 ?Un Kp(en) 5

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?? proportional gain Kp ,process ?steady state
gain K,process output X

• X Kp K(Ref-n)/(1 Kp K) KL/(1 Kp K)
• ?n? L 0? ??Kp ?X??Ref ?L????????????L,?n ?????Kp
  ????????????????
• ???Process??,?Kp ????,??????,??Kp
  ???????????????????????????
  
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Hand-tuning PID???

• Action Rise time Overshoot Stability
• Kp ? ?? ?? ??
• Td ? ?? ?? ??
• 1/ Ti? ?? ?? ??
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Hand-tuning??

• 1.??Td 0,1/ Ti 0
• 2.??Kp ???????
• 3.???Kp??Td ?Overshoot ??
• 4.??1/ Ti ???????
• 5.?????Kp ????
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??PID

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• ?? ????????????
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2nd step ??Linear fuzzy controller

• ???PID????????Linear fuzzy controller????????????
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3rd step

• transfer gains from PID to fuzzy controller
• (1)Fuzzy proportional controller (FP)
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• ???FPD?EGEe
• controller output Unf(GEen)GU?
  (GEen)GUGEGU en ??GEGUkp
• ????-100, 100???input output universe ???????
• Max.en1 ( ?refstep 1 ) ?GE100 ???
• ?GUKp/100
• ??FPD(proportional and derivative control)?FPDI
  ??
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• FPD? Change in error
• Cen? (en-en-1)/Ts Unf(GEen,GCECen)GU?
  (GEenGCECen)GU
• GEGU(enGCEcen/GE)
• ??GEGUKp
• GCE/GETd
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• ?FInc???
• UnGCEGCU?GE/GCE Si1nei Tsen?
• ? GCEGCUKp GE/GCE1/Ti
• FPDI Un?GEGU?en(GCEcen/GE)ienGIE/GE?,????
  GEGUKp,GCE/GETd,GIE/GE1/Ti

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??

• Controller advantage disadvantage
• FP simple Maybe too simple
• FPD Less overshoot Noise sensitive,
• 
  derivative kick
• FInc removes steady slow
• state error
• smooth control signal
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• FPDI All in one Windup,derivative kick
• ??
• 1.?????????overshoot??????FPD
• 2.???????FInc ,FPDI ??????
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PID gain ?FUZZY ??

• Controller Kp 1/Ti
  Td
• FP GEGU
• FInc GCEGCU GE/GCE
• FPD GEGU GCE/GE
• FPDI GEGU GIE/GE GCE/GE
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4th-5th step

• 4th step ?????????????????????,???Rule base ? 3
  input terms 3 input terms9 Rules
• 5th step ?????(Fine-tuning the non-linear fuzzy
  controller),????GAIN????????,
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• 1.the sample period .the sample period ?????Cen
  ?????????,??sample period???gain
  factor??????????????
• 2.GEGE??????Ki integral gain ???FInc
  ?????FPD?,GE??proportional gain(Kp) ?derivative
  gain(Kd),???GE???????????????proportional
  gain(Kp)?FPDI??,???GE???????integral
  gain(Ki)?derivative gain(Kd)?????proportional
  gain(Kp) 22

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• 3.GCE???,???FPD?,GCE????derivative
  gain(Kd)???????proportional gain(Kp),?????GCE?????
  FInc?? GCE???proportional gain(Kp)?????integral
  gain(Ki),?????GCE?????????FPDI
  ??,GCE????derivative gain(Kd)??,?????GCE????
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• GCU?GU??????proportional gain(Kp),?????GCU?GU????
  ???overshoot??,????????????,???????????
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?????

• 1.Insert a crisp PID and tune it
• 2.Insert a linear FPDI
• 3.Transfer Kp?Td and l/Ti to GE?GCE?GIE and GU
• 4.Insert a nonlinear rule base
• 5.Fine-tune using hand-tuning use GE to improve
  the rise time ,GCE to dampen overshoot ,and GIE
  to remove any steady state error
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• ????
• ??
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