Development of a GPC-based PID controller for unstable systems with deadtime

Till now, traditional low-order control schemes have never been applicable to unstable systems with deadtime. In this paper, we present the first application of a PID controller with time-scheduled gains to unstable systems with deadtime, consisting of a single unstable pole. The control gains are designed based on a generalised predictive control (GPC) approach. The only user specifications required are simple and classical desired properties as in the natural frequency and the damping ratio of the closed-loop system. An approach is further developed to subsequent on-line self-tuning of control weights so that the overall control system remains applicable and effective in the face of disturbances and slowly varying dynamics. A detailed analysis of the closed-loop stability of the thus designed control system is further provided in the paper. Based on stability conditions developed, the prediction horizon for the GPC-based controller may be effectively computed. Finally, simulation examples illustrate the performance of the control system.