MIMO PID 调节示例--参考matlab 文档

MIMO PID 调节示例

参考：Tune MIMO Control System for Specified Bandwidth - MATLAB & Simulink (mathworks.com)

          Decoupling Controller for a Distillation Column - MATLAB & Simulink (mathworks.com)

程序

clc;clear; close all;

s = tf('s');
G = 1/(75*s+1)*[87.8 -86.4; 108.2 -109.6]
G.InputName = {'qL','qV'};
G.OutputName = 'y';
sys_ss = ss(G)；
[AS,BS,CS,DS] =ssdata(sys_ss)；

D = tunableGain('Decoupler',eye(2));
D.InputName = 'e';
D.OutputName = {'pL','pV'};

PI_L = tunablePID('PI_L','pi');
PI_L.InputName = 'pL';
PI_L.OutputName = 'qL';
  
PI_V = tunablePID('PI_V','pi'); 
PI_V.InputName = 'pV';
PI_V.OutputName = 'qV'; 

sum1 = sumblk('e = r - y',2);

C0 = connect(PI_L,PI_V,D,sum1,{'r','y'},{'qL','qV'});

wc = [0.1,1];
[G,C,gam,Info] = looptune(G,C0,wc);

showTunable(C)

T = connect(G,C,'r','y');
step(T)

 输出结果：

sys_ss =
 
  A = 
             x1        x2
   x1  -0.01333         0
   x2         0  -0.01333
 
  B = 
       qL  qV
   x1   2   0
   x2   0   2
 
  C = 
              x1       x2
   y(1)   0.5853   -0.576
   y(2)   0.7213  -0.7307
 
  D = 
         qL  qV
   y(1)   0   0
   y(2)   0   0
 
Continuous-time state-space model.


AS =

   -0.0133         0
         0   -0.0133


BS =

     2     0
     0     2


CS =

    0.5853   -0.5760
    0.7213   -0.7307


DS =

     0     0
     0     0

Final: Peak gain = 0.973, Iterations = 19
Achieved target gain value TargetGain=1.
Decoupler =
 
  D = 
           u1      u2
   y1   2.139  -1.303
   y2  -1.584   1.295
 
Name: Decoupler
Static gain.
-----------------------------------
PI_L =
 
             1 
  Kp + Ki * ---
             s 

  with Kp = 1.5, Ki = 0.0429
 
Name: PI_L
Continuous-time PI controller in parallel form.
-----------------------------------
PI_V =
 
             1 
  Kp + Ki * ---
             s 

  with Kp = -1.74, Ki = -0.0532
 
Name: PI_V
Continuous-time PI controller in parallel form.

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