finding all possible Kp and Kd that makes the system stable?

G(s)=([1 2 10],[1 5 8 3 12]) for this transver function I need to find all possible Kp,Ki and Kd that makes the system stable? How can I do that? Thanks

Answer 1

[Birdman]

Define this transfer function in MATLAB command line:

 Gs=tf([1 2 10],[1 5 8 3 12]);

and then write

 pidTuner(Gs)

to enter PID Tuner app in MATLAB. Then, choose PID as the controller and adjust the controller parameters in order to obtain a stable closed loop response by dragging the ball in the bars above which makes your system robust or aggressive.

Or, you can use another app by typing

 sisotool(Gs)

and then you can design your controller by adding integrators, zeros, poles to the root locus. Choose whatever you want.