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Suppose the transfer function of a controlled system is given by
G(s)=(K)/(s(0.1s+1)(0.01s+1))
Design a controller to this system and choose the value of K so that the new open-loop transfer function of the system satisfies the following requirements:
1. The phase margin is at least 40 degrees
2. The velocity constant is at least 100s^-1.
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