Control-system synthesis for open-loop unstable process with time delay

To avoid performance limitations caused by an open-loop unstable pole, a three-element structure, which is equivalent to a two-degrees-of-freedom control design, is proposed to synthesise a control system for an open-loop unstable process with time delay. Through this proposed approach, control problems such as stabilising an unstable pole, servo-tracking and disturbance rejection can be treated independently. The resulting three-element structure can then be used to derive conventional two-degrees-of-freedom elements or conventional PID systems. Tuning rules for a PID controller are also provided. Examples are presented to illustrate the proposed method.