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hw10 - MEEN 651 Control System Design Homework 10 State...

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MEEN 651 Control System Design Homework 10: State Feedback and Observers Assigned: Tuesday, 4 Nov. 2008 Due: Tuesday, 11 Nov. 2008, 5:00 pm Do the following problem: Problem 1) For the following problems do the following (by hand): a) determine stability (eigenvalues) b) determine controllability using the controllability matrix c) determine controllability using the Hautus-Rosenbrock test d) if appropriate, determine controllability using the grammian; if this is not appropriate, explain why. = = 1 1 4 0 1 5 B A , and = = 1 0 0 0 0 0 1 0 0 0 1 0 B A Do the following problem from “ Feedback Control of Dynamic Systems ” 5 th ed., Franklin and Powell. Problem 2) Problem 7.20 Problem 3) Problem 7.22 Problem 4) Problem 7.44 Problem 5) Problem 7.45 Do the following design problem: Use of Controllability/Observability in Model Reduction In real problems, states are rarely uncontrollable or unobservable. More commonly, we find that some dynamic modes are “weakly” controllable or observable.
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