Construct reference model for adaptive controller.

iam using model reference adaptive controller but i can not construct the reference model , i found there are method for constructing reference model :Zero-pole and frequency but i dont know how to use them or even apply them to my simulink model.

Answer 1

[Sam Chak]

Hi @Nour Akmal

Perhaps you can describe how the system state should behave according to the desired reference in your mind.

You can even sketch the desired state trajectory over the time interval from the initial value until the desired final value.

Else, you can try adjusting the parameter given in this code, until the desired settling time and overshoot are achieved.

param = sqrt(2);    % recommend to adjust between 0 to sqrt(2)
Gr    = tf([param 1], [1 2 1])

Gr =
 
   1.414 s + 1
  -------------
  s^2 + 2 s + 1
 
Continuous-time transfer function.

Gr = zpk(Gr)        % in Zero-pole-gain model

Gr =
 
  1.4142 (s+0.7071)
  -----------------
       (s+1)^2
 
Continuous-time zero/pole/gain model.

Rss = ss(Gr)        % in State-space model

Rss =
 
  A = 
           x1      x2
   x1      -1  0.5412
   x2       0      -1
 
  B = 
       u1
   x1   0
   x2   2
 
  C = 
            x1       x2
   y1  -0.3827   0.7071
 
  D = 
       u1
   y1   0
 
Continuous-time state-space model.

step(Gr, 10)

S = stepinfo(Gr)

S = struct with fields:
         RiseTime: 1.3435
    TransientTime: 2.0421
     SettlingTime: 2.0421
      SettlingMin: 0.9005
      SettlingMax: 1.0136
        Overshoot: 1.3628
       Undershoot: 0
             Peak: 1.0136
         PeakTime: 3.4100

[Nour Akmal]

Thanks alot sam , Can i use this code for refererence model of voltage source converter acting as A rectifier or inverter?

[Sam Chak]

You're welcome, @Nour Akmal. You can use one of the three types {transfer function (tf), zero-pole-gain (zpk), state-space (ss)} to describe the linear reference model. As long as the desired state trajectory looks logical for your Voltage Source Converter, you can use it.

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