Question

1. Given the following unity feedback system where s+z s2 (s + 10) and the controller is a proportional controller Ge = K, do the following: a. If z = 2, find K so that the damped frequency of the oscillation of the transient response is 5 rad/s. b. The system is to be redesigned by changing the values of z and K. If the new specifications are %OS = 4.32% and ts = 0.8, find the new values of z and K. 2. Consider a unity feedback system with plant transfer function к G,(s) = (5 + 1)2(s + 10) Design the controller Ge to be a Pl controller so that the closed-loop system has zero steady- state error and behaves like a second-order system with a damping ratio of ratio of = 0.6 3. Consider a unity feedback system with transfer function 1 Gp(S) s(s+20) (s +40) a. Design a proportional controller Ge = K so that the closed-loop response has 20% overshoot. What is the gain K and settling time ts (2% error bound) for this controller? b. Design a new controller that cuts the settling time in half while keeping the overshoot at 20%. Give the gain and location of any poles/zeros of this controller. C. Using Matlab, simulate the closed-loop step response for both the controller in (a) and in (b). See the "Matlab Primer" document on Canvas for a reminder on how to obtain closed- loop transfer functions and simulate step responses in Matlab. 4. Consider a unity feedback system with 1 Gp(s) Gp(S) = TS + 1)(8 + 3) Design a PID controller that will yield: • Peak time of tp =1.122 seconds • Damping ratio of = 0.707 • Zero steady-state error to a step input.

I have no more posting for this month, please solve these for me thanks