Let us assume and let us take a PI controller with gain 50 and reset 0.2, then the closed loop transfer function will be

(IV.42)

The roots of the denominator of the closed loop transfer function are . The closed loop system has complex poles with positive real parts. Hence the open loop stable system becomes unstable due to inappropriate choice of controller parameters. On the other hand, if we choose a PI controller with gain 10 and reset 0.2, then the closed loop transfer function will be

(IV.43)

The roots of the denominator of the closed loop transfer function are . The closed loop system has complex poles with negative real parts. Hence the system remains stable.

Following observations are made from the above two exercises:

•  Stability characteristics are determined by the poles of

•  An otherwise stable system can be destabilized by wrong choice of controller parameters