problemset6

# problemset6 - The University of Texas at Austin Department...

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The University of Texas at Austin Department of Electrical and Computer Engineering EE362K: Introduction to Automatic Control—Fall 2009 Problem Set Six C. Caramanis Due: Friday, October 30, 2009. This problem set focuses on the new concepts introduced in the last three classes: reachability and state feedback, and integral action, and also observability and state estimation. As usual, we also work in some exercise with important concepts from linear algebra. 1. Integral Action: (a) Consider the system: A = ± 1 - 6 40 ² ,B = ³ 0 1 ´ , C =[10 ] Compute a feedback control policy, u = - Kx , so that the closed loop eigenvalues are both at - 1. (b) Let the reference signal r be equal to 1. Compute the feedforward term so that the steady state output is equal to the reference signal, r . (c) Plot the trajectory of the output (i.e., plot y ( t )) to verify that you have chosen K and k r appropriately so that the system is stable, and so that the steady state output is equal to r .

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## This note was uploaded on 10/26/2009 for the course EE 362K taught by Professor Friedrich during the Fall '08 term at University of Texas.

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problemset6 - The University of Texas at Austin Department...

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