Optimum tuning of PI-PD controllers for unstable sampled-data control systems

This paper discusses PI-PD tuning of open-loop unstable sampled-data control systems. The examples used in this paper include typical first and second order plants taken from the processes industry. We propose a class of tuning formulae based on minimization of integral square error and time-domain quality of fit indices to measure performance, that are used to obtain polynomial representation of the controller parameters. The results for the process control examples are indicative of vastly improved time-domain performance and reduction in controller variance in the case of PI-PD controller, when compared to the more traditional PID controller. The empirical formulae derived in this paper are shown to be valid for a wide range of process parameters.