MIT16_30F10_assn05

MIT16_30F10_assn05 - 16.30/31 Prof J P How and Prof E...

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Unformatted text preview: 16.30/31 October 22, 2010 Prof. J. P. How and Prof. E. Frazzoli Due: October 29, 2010 T.A. B. Luders 16.30/31 Homework Assignment #5 Goals: Controllability and observability (part 2), full-state feedback, LQR, system zeros 1. For each state-space model, identify whether the system is observable , controllable , detectable , and/or stabilizable . Conclude whether each model is a minimal realization. (a) A = − 1 3 , B = 1 1 , C = 2 − 1 , D = 1 1 6 ⎡ ⎤ ⎡ ⎤ 1 2 1 (b) A = ⎣ 1 − 3 ⎦ , B = ⎣ 1 ⎦ , C = 1 , D = − 1 − 1 − 3 1 2. Consider the state-space model x ˙ = − 5 1 x + 1 u, 14 1 y = 1 x . Suppose we want to apply full-state feedback to the system, of the form u = − K x . (a) Without computing the transfer function, identify the open-loop system poles and zeros. (b) Select K such that the closed-loop system poles are placed at the roots of s 2 + 2 ζω n s + ω n 2 = 0 ....
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MIT16_30F10_assn05 - 16.30/31 Prof J P How and Prof E...

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