A direct synthesis tuning method of unstable first-order-plus-time-delay processes

A direct synthesis tuning method is proposed for the PI controller settings of unstable ®rst-order-plus-time-delay processes. Unlike hitherto-known PI setting rules which often result in overshoots in time response or require the modi®cation of the feedback control structure, this method ensures the overdamped response as desired while retaining the conventional PI control structure. This enhanced performance is possible by introducing a ®rst-order set-point ®lter and applying simple rules for setting the values of the controller parameters without having any tuning parameters. The comparison with both conventional PI controllers and two-stage IMC method reveals that the proposed method produces not only smooth overdamped closed-loop response for set-point changes, but also fast regulatory control response for load changes. These responses are also shown to be quite robust against the uncer- tainties of the parameters as well as against the noise in the signal. The stability conditions for the processes having a large time delay or di€erent ratios of time delay/time constant have been investigated as well.