Question

The transfer function of a process unit in a resource company is described by the first order plus delay model: G(s) = 0.5/s + 1 * e^-6s Design a PID controller to control this time delay system. Since there is an approximation used to approximate the time delay and there is a difference between the design model and the actual plant, we may need to adjust the desired closed-loop performance in order to obtain stable closed-loop control system. You may start with all desired closed-loop poles positioned at the plant pole −1, then simulate the closed-loop response with unit step set-point signal by suitably choosing the sampling interval and simulation time. If the closed-loop system is oscillatory or unstable, then you reduce the magnitude of the poles by half, and repeat the design and simulation, until you get the stable closed-loop system with fastest response possible yet without oscillation. You may use the pole-zero cancellation technique to simplify the computation.

Answer 1

Hello,
          Please find the answer attached as under. Please give a thumbs up rating if you find the answer useful! Have a rocking day ahead!

********** Matlab Code *********

%% transfer function
s = tf('s');
P = exp(-6*s)*0.5/(s+1);
C = 0.01*(1 + 10/s + 0.1*s);
%% feedback system and plot
T = feedback(P*C,1)
step(T)

Output:

You can see that the PID controller has stabilized the system and the step response has no oscialltions. The PID controller used is of the form:

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