A system has a plant

(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 x1(0) = 1 and x2(0) = 0, where x1, = y(t). The repeated roots are at s = - ˆš2.

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U(s)