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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)).
This solution contains detailed explanations in finding the second order model, the bode magnitude, and time to peak. All workings and formulas are shown.
Control Systems Specifications
Given P = 1/(s/3+1), obtain a second order model for T(Y/Di) (transfer of input disturbance to plant output with feedback) to satisfy the following regulating requirements for a step input disturbance of height 15 units. Estimate lamba from the shape of the response.
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