Poles and Stability of a Feedback Control System
Snapshot of the front panel of the simulator:
Description of the simulated system
In this simulator a feedback system, namely a control system, is simulated. The controller is a P controller. The front panel of the simulator shows a block diagram of the control system.
It can be shown that the transfer funcion from setpoint ymSP to process measurement ym is
ym(s)/ymSP(s) = [Hc(s)Hp(s)]/[1 + Hc(s)Hp(s)]
= Kp/(s3+2s2 + s + Kp)
where a(s) is the characteristic polynomial.
The stability property of the feedback system can be determined from the poles, which are the roots of the characteristic equation:
a(s) = s3+2s2 + s + Kp = 0
In the simulator the controller gain Kp can be adjusted in real time, and the response in the process measurement and the poles are shown.
The aim of this simulator is to observe the connection between stability and pole placement.