Suppose that dc motor can be modelled by a transfer function Gp(s) = Y(s)/X(s) = a/[s(s+b)] 1) Assume that you may apply a step type input to the motor, and that position and velocity can be measured directly. Outline an experiment how you may determine the plant. 2) Suppose that you want the motor to rotate to a fixed angle or rotate at a constant speed. Explain why you may need a feedback control system to achieve these tasks. 3) Consider the following parameters for the DC motor in the sequel: a = 2, b = 2.25. Suppose that we choose the sampling time to be T = 0.02sec. Explain why this choice of T is reasonable. The control objective is to track the reference signal r(t) = 90., t >= 0 with zero steady state error, a settling time of less than 2 seconds, and a maximum overshoot of 10%. Design a digital PID controller with unity feedback to achieve this task. Do you need the I and D components to meet these control specifications? What do you expect if you were to increase the value of T? Explain your reasoning