# ps9 - EE 428 PROBLEM SET 9 DUE 16 December 2007 Reading...

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EE 428 PROBLEM SET 9 DUE: 16 December 2007 Reading assignment: Ch 7, sections 7.1, 7.5, and 7.7.1 (we previously covered concepts in sections 7.2, 7.3, 7.4, and 7.6) Laboratory sections meet during the week of December 10. Problem 40: (25 points) Consider the closed-loop system in Figure 1 where G p ( s )= 1 s (10 s +1) . Figure 1: Feedback control system using cascade compensation. Design a phase-lead compensator G c ( s ) so that the steady-state error due to a ramp input r ( t t 1( t ) is less than 1/11, and the peak overshoot to unit-step input is less than 20%. Your solution must contain the following elements: 1. An analysis showing how the controller parameters are chosen, including appropriate Bode plots. 2. A Bode magnitude and phase plot of the compensated open-loop transfer function G c ( s ) G p ( s ). Indicate the gain-crossover frequency and phase margin on the Bode plot. 3. A plot of the unit-step response of the close-loop system. Use MATLAB to determine the peak overshoot. 4. If the peak overshoot is not within speci±cation, a brief description of what parameter(s) of the design you would change in the next iteration of the control design and the reason for doing so. Problem 41: (35 points) The concept of state feedback is an important topic in control systems engineering. Consider an n th

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ps9 - EE 428 PROBLEM SET 9 DUE 16 December 2007 Reading...

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