A system has a plant Y(s) U(s) -G() 1 (s + 1)2 y = [1 0 2]x. (a) Find the matrix

Chapter 0, Problem P11.18

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A system has a plant Y(s) U(s) -G() 1 (s + 1)2 y = [1 0 2]x. (a) Find the matrix differential equation to represent this system. Identify the state variables on a block diagram model, (b) Select a state variable feedback structure using u(t), and select the feedback gains so that the response y(t) of the unforced system is critically damped when the initial condition is A'I(0) = 1 and A'2(0) = 0, where *, = y(t). The repeated roots are at 5 = - v2.

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