hmwk2 - University of California Santa Barbara Department...

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University of California, Santa Barbara Department of Electrical & Computer Engineering ECE 147b: Digital Control Winter 2009 Homework 1. Due 5.00pm Friday, 30th January, 2009 in the homework boxes on the 3rd floor of Harold Frank Hall. Problem 1. Consider x ( t ) to be a 5 Hz triangle wave with x (0) = 1 and x (0 . 1) = - 1. Find the lowest sampling frequency, f s , which ensures that at least 90% of the power in x ( k ) comes from frequencies which are not aliased. Problem 2. Calculate the zero-order hold equivalent of each of the following continuous-time systems. Assume that the sampling time is T = 1 second. a) P 1 ( s ) = s s + 1 b) P 2 ( s ) = e - 3 s s 2 + a 2 c) P 3 ( s ) = 10 e - 0 . 5 s s + 5 Problem 3. We are given a plant, P ( s ) = 2 s + 0 . 1 . for which we would like to design a discrete-time controller. a) Design a continuous-time PI controller that achieves the following: Gives zero steady-state error to a step. Gives a rise time which is approximately 1/10th of the rise-time of the open-loop plant.
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