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PI Controller tuning

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gary36

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I am trying to solve a problem , where I am using PI controller to compensate for integrator plant. The transfer function becomes, type 2 seconds order system, providing velocity tracking. I have issues with fixing the coefficients for critically damped response. With multiple trials, I am coming close, but I wanted a analytical method to fix the coeficients for acceleration constant ka, zeta and bandwidth. Can anybody guide how to do so?
 

Can anybody shed light on this problem
 

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