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Compute the gains

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Please see the attached file for the full problem description.

A plant has a transfer function

It is desired to use a negative unity feedback with a PID controller and a prefilter. The goal is to achieve a peak time of .75 second with ITAE-type performance. Compute the gains required to meet the design specification, , , .

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This solution is provided in 163 words in an attached .doc file. It uses a closed loop transfer function to find the answer to the problem step-by-step.

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Please see the attached file.

Well, we have:

and we want to use this controller:

In that case the closed loop transfer function (before applying the prefilter) would be:

Ok, we want two things:
The peak time and the ITAE ...

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