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Question 4 (30 marks) The block diagram of the control system for a second order mechanical positioning system is shown in Figure Q4. D(S) R(S) k(1++ s) Y() (52+45+1) s Figure Q4: Closed-loop System I where R(8) represents the desired position. D(s) represents the disturbance, Y (3) is the actual position and the gain k >0. a) Explain the purpose of each term in a typical PID controller. (5 marks) b) Assume the disturbance, D(s), is zero. Write down the transfer function relating Y(s) to R() and show the characteristic equation is given by 38 +(4+k)s? + (1 + 2) + 5= 0 (10 marks) c) Use the Routh-Hurwitz criteria to find the range of values of for which the closed-loop system is stable (10 marks) d) Compute the steady-state output response to a unit step input on R). (5 marks)