P11.18 A system has a plant

Y(s) G(s) = _ U(s) 1 (s+2)21 (a) Find the matrix differential equation to represent this system. Identify the state variables on a block dia- gram model. (b) Select a state variable feedback struc- ture 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 x (0) = 1 and x2 (0) = 0, where xy(t). The repeated roots are at s = -3.