Tuning Of Model Predictive Controllers Using Fuzzy Logic

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					 Tuning of Model Predictive
Controllers Using Fuzzy Logic

            Emad Ali
       King Saud University
          Saudi Arabia
  Presentation Outline

Objectives
MPC Control Law
Time-domain Performance
Tuning procedure
Simulation Example
Conclusion
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            Objectives


To achieve good MPC performance

To simplify the MPC tuning procedure



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                MPC Control Law
                                                      2                   2
   min        (YP (k  1)  R(k  1))                        U (k )
  U ( k )

                 T
Subject to:     A U(k)  b

                                              m
where:               YP (k  1)  MY (k )  S P U (k )
                                                                   T
                  . U(k) = [u(k+1)  u(k+m-1)]

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 Time Domain Specification

         Set Point                                 Disturbance
Output




                                          Output
                     Time                                        Time



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    General Tuning Guidelines
Tuning action Effect (set point)                         Effect (disturbance)
parameter
         increase Slower response                       Slower response
                   variable overshoot                    Higher overshoot
                   Less aggressive                       Less aggressive

         increase More weight for the                   More weight for the
                   corresponding output                  corresponding output

P         increase Slightly faster response Slightly faster response
                   More stable              More stable
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Specification violation measure

                                         y j (k  m)  y u (k  m)
                                                         j
Upper bound violation:             A
                                                    y u (k  m)
                                                      j


                                        y lj (k  m)  y j (k  m)
Lower bound violation:            B
                                                y lj (k  m)


                                         y j (k  m)  y j (k  m  1)
Bound violation rate:              C
                                                     y j (k  m)


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Fuzzification of the bound violation
           G                                          H
                                    1.0




                   -1      0      1
               Universe of Discourse, A , B

          N                    Z                      P
                                    1.0




               -0.5   -0.1      0         0.1   0.5
                  Universe of Discourse, C
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             Inference Rules
no Rule                        Result          Result     Result
                               for            for       for P
1   If A is H and B is G        is SN         is SP   P is SP
2   If A is G and B is H        is LN         is SP   P is SP
3   If A is G and B is G        is ZE         is ZE   P is ZE
4   If A is H and C is P        is LN         is SP   P is SP
5   If A is H and C is Z        is SP         is SN   P is SN
6   If A is H and C is N        is ZE         is ZE   P is ZE
7   If B is H and C is P        is SN         is SP   P is SP
8   If B is H and C is Z        is SP         is SN   P is SN
9   If B is H and C is N        is ZE         is ZE   P is ZE

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                  Defuzzification
                 LN                 SN        ZE          SP            LP
                                                    1.0




                        -2           -1         0          1        2
                        Output Universe of Discourse

           nR n f
              j , i ( z )i A j , i                             nR n f
           j 1 i 1                                      w( P )     j ,i ( P )i
w( z ) 
             nR n f                                                j 1 i 1
               j ,i ( z ) A j ,i
            j 1 i 1
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Tuning Parameter Adaptation
Each sampling instant, set:

     =  + w()

     =  + w()

    P = P + w(P)P

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Evaporator example
                                      F4
                                                     F200
                                                     T200
                                       L2

Steam                                           F5
                                    Separator
 P100                    P2
 F100
 T100




                    F3


          F1
          C1               Pump-1               F2
          T1             Product                C2
        Feed                                    T2
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    A series of set point changes
C2         0.20


           0.17


           0.14
           36.0                            fixed
                                           adapted
P2 (Kpa)




                                           bounds
           34.0


           32.0
                  0    40            80              120   160
                                  Time (min)
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            Conclusions
Tuning of MPC parameters is simplified
 using Fuzzy logic
General well-known tuning guidelines are
 easily incorporated
Improved feedback performances are
 obtained
Computational load is kept at minimum

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