PI design from bode and root locus plot

[ashugtiwari]

Hello All,
Im designing a PI compensator for a 2-pole plant. I made polar/root locus and bode plot designs and designed an overall system, and after looking at step response, im satisfied with design. But, thr thing is i dont know how to derive Ki, Kp (also Kd for info) values from these plots and info like phase and gain margins.

If anyone knows, Please let me know how can i derive Ki and Kp values from these plots and the selected zero of PI compensator.

Thanks in advance
Ashutosh

 

[FvM]

What's the controller in your designed "overall system"? Either it's PI-like, then you know the parameters. Or it's different, e.g. higher order, then the results are void for a PI design. Instead you need to optimize the parameters of a PI controller according to a quality criterion.

 

[ashugtiwari]

here is the data: (cant show real values)
Plant=a/(s^2+b*s+c) , Compensator=(Kp*s+Ki)/s=Kp*((s+zero)/s) where zero=Ki/Kp

Feedback = Plant/(1+Plant*Compensator) ,(Something similar to feedback function in MATLAB) ----- 1
Kept Kp to 1 at first, then varying, zero value from root locus/polar plot from min pole value to max value and checking the step response with complete bode response and then finding out best output.

But in above method im fixing Kp to find Ki, i want a method where i can find both Kp and Ki.

After googling, i found this:
feedback sys=1/[(s^2+2*Wn*zeta*s+Wn^2)(s+a)] (in general)
So now, i can use equation 1 above to compare coefficients of denominator and find Ki and Kp, by altering Wn i.e. naturale frequency of system and zeta, the required damping factor. I know we can set requirement of system for damping factor and rising time, so zeta=damping_factor but im not sure how to find Wn. Any help is appreciated.

Also, if there is any other method, please let me know.

Thanks
Ashutosh

Edit: FYI, the system is a TF for DC motor which is a two pole system, the coefficients a, b, and c are constants, found after puuting different values like Kt, Ke, J, R, L etc.