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141_1_Final

# 141_1_Final - EE 141 Final Fall 2008 Duration 3 hours The...

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EE 141 – Final Fall 2008 12/09/08 Duration: 3 hours The final is closed book and closed lecture notes. No calculators. You can use a single page of handwritten notes. Please carefully justify all your answers. G(s) H(s) + - Figure 1: Feedback interconnection for Problem 1. Problem 1: Consider the following linear differential equation: d dt x 1 = - x 1 + 2 x 2 (1) d dt x 2 = x 2 + u (2) 1. Assuming that x 1 (0) = 0 and x 2 (0) = 0, what is the evolution of x 1 , in the time domain, when a step is applied as input at t = 0? 2. Assume that we place a controller with transfer function H ( s ) = K D s + K P in a feedback loop with the system defined by the differential equations (1) and (2), as depicted in Figure 1. Design K D and K P so that the rise time of the closed-loop system is 0 . 9 seconds and the damping ratio is 1. 3. For your design, compute the overshoot and the settling time. 1

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4. Sketch the step response. 5. Would the closed-loop system be able to track a ramp?
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141_1_Final - EE 141 Final Fall 2008 Duration 3 hours The...

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