Digital Control

With reference to Figure 1 and using the last 2 digits of your student ID for
the plant model, G(s), determine the discrete-time equivalent model, G(z), via
ZOH for a sampling period of T = 0.1 seconds. Write a short Matlab script to
validate your derivation.
2. Determine the poles and zeros of the plant model, G(z). Show how the poles
and zeros may be determined using Matlab. Is the plant model stable? Justify
your answer.
3. Derive the general closed-loop transfer function, Gcl(z), for the feedback configuration in Figure 1. For K(z) = 1.xx, where xx are the last 2 digits of your
student ID, determine the characteristic equation for the closed-loop system. Is
the closed-loop system stable? Justify your answer. Show how the closed-loop
transfer function may be determined using Matlab.
4. Derive the respective plant model and closed-loop system difference equations
where for the latter use K(z) = Kp for 0 < Kp ∈ R. Briefly comment on
the influence (or weighting) of the digital controller, Kp, on closed-loop system
response.
5. Using the Matlab filter function, plot on one graph the plant model (G(z)) and
closed-loop system (Gcl(z)) impulse responses and on a separate graph plot the
respective unit step responses. In terms of system response, briefly comment
on any observations you may have in each case.