Answer Happy

Question 1: A proportional-derivative (PD) controller (4 marks) For the control system in Figure 1: a) Find the closed-loop transfer function T(s) = C(s) R(S)' b) Find a value of Kp that will yield less than 10% overshoot for the closed-loop system. (Note: for your design calculations for Kp in this part, you may ignore the presence of the zero, which will alter the response compared to a canonical second order system). c) Using your K, from part b), write a MATLAB script that calculates the closed-loop transfer function, T(s) = CS and Simulate the unit step response of T'(s). R(S) d) Is the overshoot 10% as you designed? Explain (Hint: consider second order dominance and the effect of any zeros). R(s) Controller Plant 1 C(s) Motor 10 s +12 EH Kp (s +9) $2+ 6s + 15 Figure 1: Unity feedback with PD control