Consider the feedback control system in Figure DP6.7.The system has an inner loop and an outer loop. The inner loop must be stable and have a quick speed of response.
(a) Consider the inner loop first. Determine the range of K1 resulting in a stable inner loop. That is, the transfer function Y(s)/U(s) must be stable.
(b) Select the value of K1 in the stable range leading to the fastest step response.
(c) For the value of K1 selected in (b), determine the range of K2 such that the closed-loop system T(s) = Y(s)/R(s) is stable.
Figure DP6.7
Feedback system with inner and outer loop.

Process 20 s(s 10) U(s) Y(s) Ris) Controller KI Inner loop