1. Design a phase-lead cascade compensator for the system: Let the lead compensa

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1. Design a phase-lead cascade compensator for the system: Let the lead compensator be Gc= k s+z/s+p Using Bode plot method, design the compensator to meet the following specification: (1) Settling time (within 2% criterion) to a unit step less than 2 seconds. (2) Percentage overshoot less than 10% and the = 0.01 Phim. (3) Simulate the closed-loop system with a step input, and show the time history of output. Suggestion: (1) get the damping ratio from percentage overshoot, thus obtain the desired phase margin (2) assume k = 1 first and raise the gain later to meet the settling time requirement (3) design the compensator to get the desired phase margin (4) try several K for the settling time.

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