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PI controller design equation

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The plant is given as P(s)=(P/(0.3-s))*e^(-0.1s). The only uncertainty is in p E [0.2, 0.6].

Derive the fastest PI controller G9(s)=k(1+(1/T_i*S)) such that the closed-loop system is stable and |S| < 6dB for all w and p. Use frequencies between 0.01 and 100 rad/s and the nominal plant with p=0.6.

Indicate clearly both the (universal) sensitivity bound for the nominal design and the final nominal L(jw) on the logarithmic complex plane of the EdS Chart. Check stability by sketching the NYquist plot of the final design. Report the designed controller in the notes' space of the EdS Chart.

Please leave out the sensitivity part. Just help me design a PI controller. Forget about the fastest.

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Solution Summary

This solution offers explanations of how to derive the fastest PI controller.