EEE444-Homework 1 Solved

Problem. Consider the standard feedback control system with an interval plant P ∈P,



where q0 ∈ [0.95 , 1], q1 ∈ [0.35 , 0.4], r0 ∈ [0.9 , 1], r1 ∈ [9 , 12], r2 ∈ [50 , 100], r3 ∈ [120 , 150], r4 ∈ [195 , 200], r5 ∈ [120 , 130], r6 ∈ [−δ , + δ].

(a)   By using the 16 plant theorem find the maximum value of δ such that there exists a robustly stabilizing controller of the form



for the family of plants P. Determine the corresponding optimal value of K.

(b)  Draw the root locus of this system with respect to K 0, by taking the nominal plant as



where δmax is as found in part (a), and show the location of the closed loop system poles for the optimal value of K determined above.

(c)   Find the gain, phase and delay margin of the nominal system defined in part (b). Also, draw themagnitude of the sensitivity function and compute its peak value.