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hw2 - ECEN 420 Linear Control Systems Homework 2 Due date...

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Unformatted text preview: ECEN 420 : Linear Control Systems Homework # 2 Due date: Feb 18, 2010 1.*1(30 points) Given the transfer function Y(s) 3+1 U(s) 52+55+6” realize it using summers nmltipliers and integrators. Use the realizations to obtain the controllable canonical state representatiom (a) (b) the observable canonical state representation and (c 2f“1 4 points) Given the matrix the modal(parallel) canonical state representation. calculate em (a) by evaluating £“1 [(81 — A)”1l and (b) by diagonalizing the matrix A. (c) Use the em obtained above to solve the equation . x [i2 34mg]. y I: [1 0p; 0. 0 (d) Compare the Mt) obtained in (0) above with the result that you would obtain using the transfer function approach. where $[0l 2:: l 1 and uh?) is unit step. 3.*1(22 points) Given _____ —1 0 ____ 1/2 -____ _ Aml 0 _31.Bml_1/2].$MA$+BU. find a state feedback u r: —F :1“: to place the closed loop eigenvalues at —4 and —5. ...
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