Problem 4. Consider the control system shown below with plant G(s) that has time con- stants 72, 7210, and gain k = 0.1. T น C(s) k (871+1)(87₂+1) Y (1.) Sketch the pole-zero plot for G(s). Is one of the poles more dominant? Using MATLAB, simulate the step response of the plant itself, along with G₁(s) and G2(s) as defined by k G₁(s) = = 871+1 and k G2(s) = 872 +1 (2.) Design a proportional gain C(s) = K, so that the system has a steady state error of 5% for a step input. Simulate the resulting closed loop system's step response via MATLAB or Simulink. Compare the results. (3.) Now let the controller be given by the PI compensator (1. C(s) 50 (1+ 10s Determine the steady state error to a step input, as well as the steady state error to a ramp input. Simulate the step response of the system via MATLAB or Simulink. Examine the closed loop transfer function. Sketch the pole zero plot. What do you notice? Estimate the settling time and overshoot from the closed loop transfer function.