Use the MATLAB pidtool to design a PID controller for the system of Problem 8.6-2. Start with these parameters, then try to improve the design \(\left(G_{p}=1 /\left(s^{2}+sight), T=0.2, H=1, P_{m}=45, \omega_{w 1}=3.0ight)\).

Problem 8.6-2

Repeat Problem 8.4-2 using a phase-lead controller. In part (c), the overshoot is approximately 26 percent.

Problem 8.4-2. 

To satisfy the steady-state constraints for the system of Problem 8.2-3, the de gain of the digital controller must be equal 4.

(a) Design a phase-lag controller with this de gain that will result in a \(45^{\circ}\) phase margin.

(b) Estimate the percentage of overshoot in the step response of the compensated system.

(c) Verify the step-response results in part (b) using MATLAB. The step response will show an overshoot in the step response of approximately 24 percent.