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System Peak Time and Overshoot

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Please see the attached file for full problem description. I am not too sure how to go about solving this question. Any help would be appreciated.

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Please see the attached file.

We consider the controller:

Now the closed loop transfer function is:

Where

Then we will have:

Ok, what we want is:

This contains the dominant poles. Now we do this:

We want to find the unknown coefficients ...

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