Problem 2: The block diagram for a system with state variable feedback is shown below. Note that the state variables x1 and x2 and the control u are identified on the diagram. The input is R. Q x2 1500 K (s+25) K S (a) (10 Points) Determine the transfer function relating Z(s) to R(s). The answer will be in terms of K and K2. (b) (5Points) Determine the values of Ki and K2 that give eigen values -2 j2 (c) (5 Points) From the block diagram, what is the equation for u in terms of K1, K2, x1, x2, and R? (d) (5 Points) Write the MATLAB commands for solving for the feedback gains to achieve the desired eigenvalues in part (b) using acker. The results of typing "help acker" are provided below. >> help acker ACKER Pole placement gain selection using Ackermann's formula. K-ACKER(A.B.P) calculates the feedback gain matrix K such that the single input system x-Ax+Bu with a feedback law of u=-Kx has closed loop poles at the values specified in vector P. i.e., P= cig(A-B*K).