# hmwk4 - 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 4. Due 5.00pm Friday, 6th March, 2009 in the homework boxes on the 3rd. floor of Harold Frank Hall. If you use Matlab to solve any part of the homework, you must attach a copy of the Matlab script to your homework to get any credit for the problem. Problem 1. We want to control the continuous-time plant, P ( s ) = s - β s + α , α, β > 0 , using the configuration shown here. Note that the controller has access to a delayed sample of the output. z - 1 P ( s ) ZOH C ( z ) a109 + - a116 a27 a27 a27 a27 a64 a64 a27 a45 a54 y ( k ) T y ( t ) u ( t ) u ( k ) e ( k ) r ( k ) w ( k ) a) Derive a state-space representation for P ( s ). Choose your representation so that the B matrix does not contain either α or β . b) Using your representation in part a) as a starting point, derive a state-space representation for zero- order hold equivalent of P ( s ). Express this as function of the sampling time, T .

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• Winter '08
• Staff
• Santa Barbara, Department of Electrical & Computer Engineering, state-space representation, closed-loop poles, Harold Frank Hall

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