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MEM355W07-08.HW6.soln_stud

# MEM355W07-08.HW6.soln_stud - MEM 355 Performance...

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MEM 355: Performance Enhancement of Dynamic Systems Winter 2007-08 Home work # 6 Relevance to a-k criteria: a, c, d, e, k

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solution I will present the solution with matlab code as an integral part of it, with comments as appropriate. Problem 1. ( variation of Problem 12.14) For a system with the transfer function ( ) 6 , ( ) ( 3)( 8)( 10) Y s s U s s s s + = + + + design a full state feedback controller to yield a closed-loop response of 10% overshoot with a settling time of 1 second. Follow these steps: a. Obtain its state space representation. Let x denote the states and set up the control law as u = -Gx + u ref , where the gain G is to be determined and u ref is a reference signal. Input the transfer function and convert the system representation to state space form. Let the state space representation be ; x Ax Bu y Cx Du = + = + & This need not be unique. num = [1 6]; den = conv([1 3],conv([1 8],[1 10])); [A,B,C,D] = tf2ss(num,den); [ ] 21 134 240 1 1 0 0 ; 0 ; 0 1 6 ; [0] 0 1 0 0 A B C D - - - �� �� = = = = �� �� �� b. Choose a set of eigenvalues to satisfy the given specifications.
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