Development of a stochastic predictive PID controller

A new stochastic, predictive proportional-integral-derivative (PID) controller is proposed which is mathematically equivalent to generalized predictive control (GPC) with steady state weighting. The main motivation of this paper is the extension of the classical PID algorithm on industrial computers to implement advanced control without employing specialized software. Predictive PID controller constants and the internal model are chosen by equating the discrete PID control law to a linear form of GPC. Predictive PID is stochastic because GPC is based on a model of both the plant and the disturbance/noise term. Performance of the predictive PID scheme is shown, via simulation, to be identical to GPC. An industrial application of predictive PID using an existing control computer shows a significant improvement in performance compared to the existing PID scheme.