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Unformatted text preview: " x 1 x 2 # = A " x 1 x 2 # with initial condition x 1 (0) = . 5 ,x 2 (0) = 0 . 5 In each of the cases below, simulate the system for 5 seconds, and turn in plots of x 1 ( t ) versus x 2 ( t ). These are called phase portraits. On your plots, mark the initial condition by a hollow circle (a) A = " 11 0 # (b) A = "21 12 # (c) A = " 0 1 1 0 # (d) A = " 0 0 0 1 # (e) A = "1 0 1 # (f) A = " 11 # (g) A = "1 1 # (h) A = " 21 1 2 # 4 Controllable canonical form Consider the system x ( t ) = Ax ( t ) + Bu ( t ) where A = 6 13 7242243 , B = 3 1 1 (a) Transform this system into controllable canonical form. (b) Design a state feedback law u = Lx + r that places the closed loop eigenvalues at1 ,1 ,1. 2...
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 Fall '08
 Tomizuka

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