ME661 - HOMEWORK SET NO. 4
Problem 1:
(a) For the project topic that you have selected, design a predictor and a minimum variance (or moving average) controller, and evaluate its performance through simulation studies.
(b) Design an adaptive version of the controller in part (a). Evaluate the controller using simulation studies.
Problem 2:
Consider the following discrete-time process:
(1 - 4q-1 + 3q-2)y(t) = (q-1 + 0.5q-2)u(t)
Assume that the computations for implementing an adaptive control require most of one sampling period, so that the system will effectively include a one step computational delay. Rewrite the above equations for this situation in both standard form and as a two step ahead predictor.
Problem 3:
Consider the following discrete-time process:
(1 - 1.2q-1)y(t) = q-1(1 - 3.1q-1 + 2.2q-2)u(t)
(a) Which adaptive control algorithm would you propose to use on this system, and why?
(b) Show that the controller must be unstable so that the closed-loop system is stable (hint: use root locus).
Problem 4:
(a) Show that G(s) = (3+2s)/(2+3s+s2) is strictly positive real.
(b) Find a coefficient c in G(s) = (1+cs)/(1+s)2 such that G(s) will be strictly positive real.
(c) Show that s/[s2+c2] is positive real, but that c/[s2+c2] is not.
Problem 5:
Problem 5.1 from your textbook.