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PD control 1. The equation of motion for the DC motor are given by the equation: J ¨?m...

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Mechanical Engineering

PD control

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

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 achieveposition control of the motor shaft. Given a desired shaft position?r (the reference), the applied voltage is given by a proportionalcontroller:

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

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

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

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

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