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Unformatted text preview: University of Maryland at College Park Dept. of Aerospace Engineering ENAE 432: Aerospace Control Systems Problem Set #4 Issued: 19 Feb. 2011 Due By: 25 Feb. 2011 Suggested Reading: Nise, 4.1-4.6. Question 1: Consider an arbitrary linear system with all initial conditions zero. We know that Y ( s ) = G ( s ) U ( s ), where G ( s ) is the system transfer function and and U ( s ) is the Laplace transform of the system input u ( t ). Prove that the dynamics of the system can be equivalently modeled using y ( t ) = c u ( t ) + n X k =1 c k z k ( t ) where each ˙ z k ( t ) = p k z k ( t ) + u ( t ) and p k are the poles of G ( s ). a.) Under what conditions will c 6 = 0? Explain how c is calculated. Explain how the remaining c k are calculated. b.) Express in the form above the dynamics of a system governed by the transfer function G 1 ( s ) = 2 s 2 + 8 s + 2 s 2 + 3 s + 2 c.) Express in the form above the dynamics of a system governed by the transfer function G 2 ( s ) = 2 s 2 + 5 s + 6 s 3 + 5 s 2 + 6 s Question 2: Suppose f ( t ) = e- t for t ≥ 0 and f ( t ) = 0 otherwise....
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