Question: Consider the closed-loop system in Figure AP6.5. Suppose that all gains are positive, that is, K1 > 0, K2 > 0, K3 > 0, K4

Consider the closed-loop system in Figure AP6.5. Suppose that all gains are positive, that is, K1 > 0, K2 > 0, K3 > 0, K4 > 0, and K5 > 0.
(a) Determine the closed-loop transfer function T(s) = Y(s)/R(s).
(b) Obtain the conditions on selecting the gains K1, K2, K3, X4, and K5, so that the closed-loop system is guaranteed to be stable.
(c) Using the results of part (b), select values of the five gains so that the closed-loop system is stable, and plot the unit step response.

t0 21-4 K2 RUs) -KA R(s) s + I s-10 K. K4 FIGURE AP6.5 Multiloop feedback control system. (a) Signal flow graph. (b) Block diagram.

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