Analytical design of a generalised predictor-based control scheme for low-order integrating and unstable systems with long time delay

Abstract

In this study, the problem of controlling integrating and unstable systems with long time delay is analysed in the discrete-time domain for digital implementation. Based on a generalised predictor-based control structure, where the plant time delay can be taken out of the control loop for the nominal plant, an analytical controller design is proposed in terms of the delay-free part of the nominal plant model. Correspondingly, further improved control performance is obtained compared with recently developed predictor-based control methods relying on numerical computation for controller parameterisation. The load disturbance rejection controller is derived by proposing the desired closed-loop transfer function, and another one for set-point tracking is designed in terms of the H-2 optimal control performance specification. Both controllers can be tuned relatively independently in a monotonic manner, with a single adjustable parameter in each controller. By establishing the sufficient and necessary condition for holding robust stability of the closed-loop control system, tuning constraints are derived together with numerical tuning guidelines for the disturbance rejection controller. Illustrative examples taken from the literature along with temperature control tests for a crystallisation reactor are used to demonstrate the effectiveness and merit of the proposed method.