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Control System with Tunable Components

This example shows how to create a tunable model of the control system in the following illustration.

The plant response G(s) = 1/(s + 1)2. The model of sensor dynamics is S(s) = 5/(s + 4). The controller C is a tunable PID controller, and the prefilter F = a/(s + a) is a low-pass filter with one tunable parameter, a.

Create models representing the plant and sensor dynamics.

Because the plant and sensor dynamics are fixed, represent them using numeric LTI models zpk and tf.

G = zpk([],[-1,-1],1);
S = tf(5,[1 4]);

Create a tunable representation of the controller C.

C = ltiblock.pid('C','PID');
C =

  Parametric continuous-time PID controller "C" with formula:

             1            s    
  Kp + Ki * --- + Kd * --------
             s          Tf*s+1 

  and tunable parameters Kp, Ki, Kd, Tf.

Type "pid(C)" to see the current value and "get(C)" to see all properties.

C is a ltiblock.pid object, which is a Control Design Block with a predefined proportional-integral-derivative (PID) structure.

Create a model of the filter F = a/(s + a) with one tunable parameter.

a = realp('a',10); 
F = tf(a,[1 a]);

a is a realp (real tunable parameter) object with initial value 10. Using a as a coefficient in tf creates the tunable genss model object F.

Connect the models together to construct a model of the closed-loop response from r to y.

T = feedback(G*C,S)*F

T is a genss model object. In contrast to an aggregate model formed by connecting only Numeric LTI models, T keeps track of the tunable elements of the control system. The tunable elements are stored in the Blocks property of the genss model object.

Display the tunable elements of T.

T.Blocks
ans = 

    C: [1x1 ltiblock.pid]
    a: [1x1 realp]

If you have Robust Control Toolbox™ software, you can use tuning commands such as systune to tune the free parameters of T to meet design requirements you specify.

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