IV.3 Stability of a closed loop process

The stability of a process is realized by the location of its poles. Existence of a positive pole leads to the instability of the process. One of the main purpose of the controller is to ensure stable closed loop process for the otherwise unstable open loop process.

IV.3.1 Stabilization of unstable system with a P controller

Consider an unstable process with transfer function

(IV.39)

Let us assume . The closed loop transfer function will be

(IV.40)

It is evident from the above equation that one needs to set in order to make the closed loop transfer function to be stable.

IV.3.2 Destabilization of a stable system with a PI controller

Consider a stable process with transfer function

(IV.41)