Question

PD control

1. The equation of motion for the DC motor are given by the equation:

J ¨?m + (B + KbKT Ra ) ? ?m = KT Ra Va (2)

where: J = 0.01kg · m2 , B = 0.001N · m · s, KT = 0.02N · m/A, Kb = 0.02V /s and Ra = 10?.

(a) Suppose that feedback is added to the system to achieve position control of the motor shaft. Given a desired shaft position ?r (the reference), the applied voltage is given by a proportional controller:

Va = K(?r ? ?m) (3)

Where K is the feedback gain. Find the transfer function from ?r to ?m

(b) Can you find some value of K that provides a rise time of less than 4 seconds and keeps the system overshoot less than 20%? Why?

(c) If cannot (for question 2b), can you design a new controller that achieve all the requirements in question 2b? Write down your controller and show any work involved.

Answer 1