Please answer (a) and (c) only. (b) and (d) are not required.

Design of phase-lead 10-18. The block diagram of a type 2 control system with a series controller Gds is shown in controller Fig. 10P-18. that the following specifications are satisfied. The objective is to design a PD controller so Maximum overshoot 10 percent Rise time 0.5 sec (a) obtain the characteristic equation of the closed-loop system, and determine the ranges of the values of KP and KD for stability. Show the region of stability in the Ko-versus-Kr plane. (b) Construct the root loci of the characteristic equation with Ki 0 and 0 s K, x. Then construct the root contours for 0 s KD and several fixed values of KP ranging from 0.001 to 0.01. specifications given. Use the information (c) Design the PD controller to satisfy the performance on the root contours to help your design. Plot the step response of yn. the phase (d) Check the design results obtained in part (c in the frequency domain. Determine margin, gain margin, M, and BW of the designed system. U(s) R(s) G(s) Kip Kos s (s 10) Figure 10P-18