Question: A control system, as shown in Figure E7.17, has a process G(s) = 1 / s(s - 1). (a) When Gc(s) = K, show that

A control system, as shown in Figure E7.17, has a process
G(s) = 1 / s(s - 1).

(a) When Gc(s) = K, show that the system is always unstable by sketching the root locus.
(b) When
Gc(s) K(s + 2) / s + 20,
sketch the root locus and determine the range of K for which the system is stable. Determine the value of K and the complex roots when two roots lie on the jÏ‰-axis.

FIGURE E7.17 Feedback system.

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