ME661 - HOMEWORK SET NO

ME661 - HOMEWORK SET NO. 3

Problem 1:

(a) For your project topic, design a nonadaptive (e.g., pole placement or model following) controller, and evaluate its performance through simulation studies.

(b) Utilize the formulation in part (a) to design an adaptive version of this controller. Discuss, and compare, indirect and direct version of the adaptive controller. Evaluate the controller using simulation studies.

Problem 2:

Problem 3.1 from your textbook

Problem 3:

Consider the following discrete-time process:

(1 - 4q-1 + 3q-2)y(t) = (q-1 - 2q-2)u(t)

Use the polynomial controller design method presented in class (and in the Matlab function "polydesign") to design an error feedback (i.e., T(q) = S(q)) control system for this process, such that the closed-loop poles are placed at zero (deadbeat control).

Problem 4:

Consider the following discrete-time process:

(1 - 2q-1 + 1q-2)y(t) = (kh2/2)(q-1 + 1q-2)u(t)

where h is the sampling period, and k is a constant. This discrete-time system is obtained from a continuos-time system (d2y/dt2) = ku(t). The direct pole placement (i.e., model following) approach is used to control the process with a reference model of:

(1 - 0.9q-1)y(t) = 0.1 u_c(t)

where u_c(t) is the command or reference input.

(a) Explain, by reference to the process zeros, why the control signal can be expected to be oscillatory.

(b) What happens if the original continuos-time system is lightly damped (i.e., (d2y/dt2) + b(dy/dt) = ku(t), with b>0 but small)?

Problem 5:

Convince yourself that a sine wave of frequency r (i.e., y(t) = sin(rht) where h is the sampling period) can be modeled in discrete-time as:

(1 + a1q-1 + a2q-2)y(t) = 0

(a) What are the values of a1 and a2?

(b) Write a two step ahead predictor for y(t)