P13.10 Consider a system as shown in Figure P13.10 with a zero-order hold, a process

Gp(s) = 1 s(s + 10)' and T = 0.1 s. Note that G(z) = Z{G(s)Gp(s)}. (a) Let D(z) = K and determine the transfer function G(z) D(z). (b) Determine the characteris- tic equation of the closed-loop system. (c) Calculate the maximum value of K for a stable system. (d) Determine K such that the percent overshoot is P.O. 30%. (e) Calculate the closed-loop trans- fer function T(z) for K of part (d) and plot the step response. (f) Determine the location of the closed- loop roots and the percent overshoot if K is one-half of the value determined in part (c). (g) Plot the step response for the K of part (f).