Controller Process 1 R(S) K Y(S) S-a FIGURE CP4.6 A closed-loop control system with uncertain parameter a. = CP4.6 Consi

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Controller Process 1 R S K Y S S A Figure Cp4 6 A Closed Loop Control System With Uncertain Parameter A Cp4 6 Consi 1 (393.96 KiB) Viewed 47 times

Controller Process 1 R(S) K Y(S) S-a FIGURE CP4.6 A closed-loop control system with uncertain parameter a. = CP4.6 Consider the closed-loop control system shown in Figure CP4.6. The controller gain is K 2. The nomi- nal value of the plant parameter is a = 1. The nominal value is used for design purposes only, since in reality the value is not precisely known. The objective of our analysis is to investigate the sensitivity of the closed- loop system to the parameter a. (a) When a = 1, show analytically that the steady- state value of Y(s) is equal to 2 when R(s) is a unit step. Verify that the unit step response is within 2% of the final value after 4 seconds. (b) The sensitivity of the system to changes in the parameter a can be investigated by studying the effects of parameter changes on the transient re- sponse. Plot the unit step response for a = - 0.5, 2, and 5. Discuss the results.