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Control System Specifications and Response

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I need some help with this question, look at attached files for better symbol representation and also diagrams:
For a system with P = (3e^-0.1x / 2s + 1), it is desired that a step input disturbance, di = 3 sigma (t), results in an output of not more than 0.1. (Note that the dead time gives a relatively small effect in the closed loop system bandwidth so a second order model is reasonable).
a. Find a second order model for Ty/di (s).C = 0.5 gives the appropriately shaped response.
b. Sketch the Bode magnitude plot of the specification. Show the low and high frequency asymptotes and mid frequency gain.
c. Calculate the time to peak. Sketch the expected output response and comment on this with respect to hte time constant of the plant (with corner frequency and damping factor of the plant P(s)).

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Solution Summary

This solution contains detailed explanations in finding the second order model, the bode magnitude, and time to peak. All workings and formulas are shown.

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Find a second order model to achieve the following response to a step output disturbance of height 0.5. Minimum value 0.05 after 0.1s. Make a rough sketch of the bode magnitude plot and the step response.

(Please see attachments for details.)

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