7) For assignment only. P+l control is difficult to tune in practice especially

Question

7) For assignment only. P+l control is difficult to tune in practice especially with actuator saturation. Sometimes saturation helps, other times it makes things worse. Keeping a consistent response is difficult in the presence of integral action A direct state-space method is to use an inverse dynamics controll law using full state feedback given by: u(t)(CB) (r(t)-y)) (CB)- CAx(t) This control law can be derived by assuming that the inductance of the motor armature windings to be small such that L 0 so that the state-space equations reduce to (t) and y(t)=10 1] le(t) and by using an extra measurement such that (t) = y(t) + mu(t) Having derived your control law build a Simulink Model using this control law by replacing the P+l controller and save your model as "motorid.sk Hint: In the Simulink model you do not have access to the state-vector ait), so change Cto give the output from the state-space model to be C 1001 so the output isu(t) not But then you can construct 6jt) in Simulink using a transfer function block such that (s) =- (s) By setting 5, manually tune m (note m cannot = Og to give a satisfactory response. Present and comment on the results. What could be the benefits and practical drawbacks of using this controller when compared with a P+l controllier

Explanation / Answer

The above state space equation is for PID controller

Benefits of PID controller:

      (i) It operates in 3 modes like propotional,integral & derivative

        propotional controller stabilizes gain,integral controller reduces steadystate error which produced by propotional and derivative controller reduces change of error.

(ii)it is easy to implement

(iii)accurate

so it is peferable compare to pi controller.

practical drawback of PID controller is

(i) cost is high

(ii)more no PID controllers make large time delay

(iii)at disturbances it provide low robustness.

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