Direct design of a U-model-based generalized predictive controller for a class of non-linear (polynomial) dynamic plants

Abstract

Facing the big challenge of directly designing a generalized predictive controller (GPC) for a class of smooth non-linear dynamic plants described with polynomial models, this study reformulates the classical GPC into a U-model-based implementation. Mathematically, the final solution of the controller output is converted into resolving a polynomial equation in terms of current controller output u( k), which dramatically reduces the difficulties and complexity encountered in non-linear control system synthesis, algorithm development, and online implementation. It is believed that the integrated procedure provides a straightforward methodology to apply linear control system design techniques to design non-linear control systems without any enforced linearization of plant models. For a demonstration of the feasibility and effectiveness of the designed procedure, a continuously stirred tank reactor, and the other simulated example to represent chemical kinetics, are selected for the initial bench tests. The key contribution of the study is to derive and demonstrate feasibility and effectiveness of the U-model approach to GPC of non-linear systems. This is further evidence to support the author’s insight on the U-model approach that was previously used to design pole placement controller (PPC).