141_1_Final (2) 14-00-23

141_1_Final (2) 14-00-23 - EE 141 Final Duration 3 hours...

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EE 141 – Final 06/12/08 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. Problem 1: The linearized equations describing the vertical of motion of a hot-air balloon are given by: τ 1 ˙ T = - T + u τ 2 ¨ z + ˙ z = aT + w were T represents the deviation of the hot-air temperature from the equilibrium temperature, z represents the altitude of the balloon, u represents the deviation of the burner heating rate from the equilibrium rate, and w is the wind speed. In what follows we will assume that w = 0 and to simplify the computations the parameters τ 1 , τ 2 , and a will assume the following unrealistic values: τ 1 = 0 . 1 τ 2 = 0 . 2 a = 10 1. Compute the transfer function from the input u to the balloon’s altitude. 2. Design a compensator for a unity-feedback loop so that the steady-state error to a parabola is 0 . 2.
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