Problem 3. (40 points) Consider a system given by the state-space form * = Ar + Bu y = Ca + Du where the state matrices are given by -5 A = [ 3 ] B-[H]. C = (1 1), D = 0. = 1) (8 points) Write the transfer function G(s) = Y(s)/U(s) for the system. 2) (8 points) Determine if it is possible to assign arbitrary pole locations for the system. 3) (12 points) Find the transformation T so that if z = Tr, the state matrices describing the dynamics of z are in controller canonical form (CCF). Compute the new matrices A, B, C, D. - 4) (12 points) Design a state feedback controller u = Kr that satisfies the following specifications: damping ratio = 0.707, and step-response peak time is under 3.14 sec. (Hint: If you do the control design in CCF, remember to convert the control law back to the original coordinates z.)