P5.11 A unity feedback control system has a process transfer function

Y(s) K =G(s): E(s) S The system input is a step function with an amplitude A. The initial condition of the system at time to is y(to) Q, where y(t) is the output of the system. The performance index is defined as 1 = e (1) dt. 0 (a) Show that I = (A-Q)/(2K). (b) Determine the gain K that will minimize the performance index I. Is this gain a practical value? (c) Select a practical value of gain and determine the resulting value of the per- formance index.