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Compensation for Single Integration Plant

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garimella

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Experimenting in matlab to improve the response of a single integrator plant(1/s) using PI controller.
The closed loop TF resembles that of second order system. But there is a numerator term in the TF. I would like to understand how the numerator term influences the dynamics of the system. What is the optimal method to tune PI to meet the required time domain specifications?

The closed loop T.F is (Kp*s+Ki)/s^2+Kp*Ki*s+Ki
 
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Dynamics are ruled by the characteristic polynomial. Adjust the characteristic polynomial to meet your time domain characteristics from the usual 2nd order Transfer Function relationships.

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I would like to understand how the numerator term influences the dynamics of the system
Sum of two responses, in your case.
 

Thanks, I designed a PI compensator for integrator plant , which works well in continuous and discrete domain with a step input. I have used the same design with the inputs changed(Sinusoidal). But this time my continuous model works , while discrete domain fails to get me results. Advice will be highly appreciated.
 

Pure integral plant without additional poles or dead time is a somehow unrealistic assumption, it could be perfectly compensated by a P controller with arbitrary kp achieving 90 degree phase margin. Infinity kp gives infinite bandwidth.

I can't reproduce by the way your closed loop characteristic. I would expect

(kp*s + ki) / (s^2 + kp*s + ki)

PI transfer function is (kp*s + ki)/s
open loop gain -(kp*s + ki)/s^2
 

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