Use the MATLAB pidtool to design a PID controller for the system of Problem 8.6-1. Start with these parameters, then try to improve the design \(\left(G_{p}=1 /\left(s^{2}+sight), T=1, H=1, P_{m}=45, \omega_{w 1}=1.0ight)\).

Problem 8.6-1

Consider the system of Problem 8.4-1.

(a) Design a unity-dc-gain phase-lead compensator that yields a phase margin of approximately \(45^{\circ}\).

(b) Obtain the system step response of part (a) using MATLAB, and find the rise time \(t_{r}\) and the percent overshoot.

(c) Compare the step-response parameters of part (b) with Problem 8-2 (c) and (e).