please solve it carefully and detailed.Thank you!!

PROBLEM 1 Suppose that we have a unity feedback system as follows: T:(5) Controller Process R(.) Kp+ x + Kos Y) s(s + b)(s + 25W,) Figure 1: Closed loop control system with a PID controller. The process is given by G(S)= (1.1) s(s+b)(s+250) The parameters of the system are b=10, 5 = 0.707 and 0 =4. What is K and period P for sustained oscillations in this system? Find K,, K, and K, for settling time of T = 2.5 sec and maximum percent overshoot P.O=12.9% based on Root-Locus in MATLAB. PROBLEM 2 Consider the system in the previous problem with the designated parameters again. Find K,, K,, and K, based on Ziegler-Nichols technique. Plot the step response of this control system by MATLAB and obtain the maximum percent overshoot P.O and settling time T, from this plot. Compare these values to the results in previous