[Solved] EE444/544 Homework #1

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 [ , + ].

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

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

• Draw the root locus of this system with respect to K > 0, by taking the nominal plant as

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

• 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.