Generalized predictive control—Part I. The basic algorithm

• Published in: Automatica (Oxford) Vol. 23; no. 2; pp. 137 - 148
• Main Authors: Clarke, D.W., Mohtadi, C., Tuffs, P.S.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 1987
• Subjects: Adaptive control; LQ control; nonminimum-phase plant; predictive control; self-tuning control; self-tuning control; LQ control; nonminimum-phase plant; predictive control; Adaptive control
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/0005-1098(87)90087-2

Current self-tuning algorithms lack robustness to prior choices of either dead-time or model order. A novel method—generalized predictive control or GPC—is developed which is shown by simulation studies to be superior to accepted techniques such as generalized minimum-variance and pole-placement. This receding-horizon method depends on predicting the plant's output over several steps based on assumptions about future control actions. One assumption—that there is a “control horizon” beyond which all control increments become zero—is shown to be beneficial both in terms of robustness and for providing simplified calculations. Choosing particular values of the output and control horizons produces as subsets of the method various useful algorithms such as GMV, EPSAC, Peterka's predictive controller (1984, Automatica, 20, 39–50) and Ydstie's extended-horizon design (1984, IFAC 9th World Congress, Budapest, Hungary). Hence GPC can be used either to control a “simple” plant (e.g. open-loop stable) with little prior knowledge or a more complex plant such as nonminimum-phase, open-loop unstable and having variable dead-time. In particular GPC seems to be unaffected (unlike pole-placement strategies) if the plant model is overparameterized. Furthermore, as offsets are eliminated by the consequence of assuming a CARIMA plant model, GPC is a contender for general self-tuning applications. This is verified by a comparative simulation study.