hw1soln_f09

hw1soln_f09 - β 1 β 2 β N(1 − β α =(1 β 1 β...

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ME 132 Fall 2009 Solutions to Homework 1 1. There are several examples from each Feld that are valid descriptions of feedback sys- tems. As long as you showed the dependence of the control signal on some measured variable, your example should be su±cient. 2. Problem 1.3.1 in the class notes. (a) ²or β = 1, α = N s k =0 β k = N s k =0 1 k = 1 0 + 1 1 + 1 2 + · · · + 1 N = N + 1 (b) ²or β n = 1, α = N s k =0 β k = 1 +
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Unformatted text preview: β 1 + β 2 + · · · + β N (1 − β ) α = (1 + β 1 + β 2 + · · · + β N ) − ( β 1 + β 2 + · · · + β N + β N +1 ) = 1 − β N +1 ⇒ α = 1 − β N +1 1 − β (c) If | β | < 1, then lim n →∞ β n = 0 So α ∞ := lim n →∞ α = ∞ s k =0 β k = lim n →∞ 1 − β n +1 1 − β = 1 1 − β 1...
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This note was uploaded on 10/20/2010 for the course ME 132 taught by Professor Tomizuka during the Spring '08 term at Berkeley.

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