[Solved] EE444/544 Homework #2

Problem. Consider the standard feedback control system with the plant

05] and define

• Find an uncertainty weight in the form

such that |W_a(j)| > |(j)| for all , and |W_a(j)| is as small as possible for each .

• Now consider the class of uncertain plants

P = {P = P + : P has one pole in C₊ , |(j)| < |W_a(j)| }

and find the allowable interval for > 0 so that the controller

is robustly stabilizing (C,P), for all P P.

• Now pick a value of in the interval determined above and verify that the feedback system formed by the controller C and the plant is stable.
• Let = 10; determine if there exists values in the interval determined in part (ii), satisfying the robust performance condition

where S = (1 + PC)¹.

What is the smallest value of _r > 0 such that there exists a feasible satisfying the robust performance condition? Find the corresponding optimal value of .