Int J Adv Manuf Technol (2002) 20:844–852 Ownership and Copyright  2002 Springer-Verlag London Limited Nonlinear Model-Based Predictive Control Using a Generalised Hammerstein Model and its Application to a Semi-Batch Reactor F. M’sahli 1 , R. B. Abdennour 2 and M. Ksouri 3 1 Institut Supe ´rieur des Etudes Technologiques de Ksar-Hellal, Ksar Hellal, Tunisia; 2 Ecole Nationale d’Inge ´nieurs de Gabes, Universite ´ de Sfax, Gabes, Tunisia; and 3 Institut National des Sciences Applique ´es et de Technologie, Tunis, Tunisia In recent years, much attention has been focused upon predic- tive control of nonlinear systems. The implementation of such a control strategy for real processes has greatly improved their performance. This paper deals with a model-based predic- tive control (MBPC) strategy using a generalised Hammerstein model and its application to the temperature control of a semi- batch reactor. Both unconstrained and constrained adaptive control problems are considered. A simple identification method based on the weighted recursive least squares method (WRLS) is used to estimate the model parameters on-line. An indirect adaptive nonlinear controller is designed by combining the predictive controller with an indirect parameter estimation algorithm. This adaptive scheme has been applied for the control of a semi-batch chemical reactor. Experimental results show that the performance of the generalised Hammerstein MBPC (NLMBPC) was significantly better than that of a linear model predictive controller (LMBPC). Keywords: Adaptive predictive control; Generalised Ham- merstein model; Nonlinear control; Reactor 1. Introduction Simple linear dynamic models are used extensively in standard process control practice, but they are limited in the type of process behaviour that they have represented. Model-based schemes that can exploit nonlinear dynamic models are becom- ing increasingly available [1–5]. Nonlinear model-based predic- tive control (NLMBPC) has emerged as the most widely studied design technique for many real process applications. The NLMBPC is an optimisation-based strategy in which a nonlinear process model is used to predict the effect of future manipulated input moves on future values of the controlled outputs. At each sampling time, a sequence of present and future input moves is calculated, by solving on-line, an open- Correspondence and offprint requests to: Dr F. M’sahli, Department of Electrical Engineering, ISETKH, Avenue Hadj Ali Soua, 5070, Ksar Hellal, Monastir, Tunisia. E-mail: msahli-fn@iyahoo.fr loop optimal control problem. A feedback controller is obtained by implementing only the first calculated input and resolving the optimisation problem at the next sampling time using new process measurements [6]. Because of the large number of different types of nonlin- earity that can occur in practice, it is unrealistic to extend a basic linear control scheme to account for all possibilities. A very interesting way of taking the general problem is to employ a framework, within which a large number of nonlinear processes can be adequately approximated. For adaptive con- trol, such a framework can be provided by the general Ham- merstein model [7]. Agarwal and Seborg [7] proposed two adaptive control strategies for nonlinear control problems using Volterra and Hammerstein model. Their approach is applicable to a broad class of nonlinear systems, which can include arbitrary nonlinear functions of the most recent input. In model-based predictive control (MBPC) literature, several methods have been employed to solve the constrained control problem for nonlinear systems. While for linear plants the MBPC problems are usually reduced to a standard quadratic program (QP) [8,9]. Application of the MBPC concept to nonlinear systems involves a high-order nonlinear program (NLP). However, this nonlinear program is much more difficult to solve than the QP problem. In order to reduce the complexity of NLP, alternative predictive control methods have been developed for the control of a class of nonlinear systems. The basic idea for these alternative methods is to combine two different control schemes: feedback linearisation and standard linear MBPC. The basic difficulty with this approach is caused by the fact that the original optimisation problem for the nonlinear system, subject to linear constraints on the input, has been transformed into an optimisation problem for a linear system subject to nonlinear constraints and is state dependent [10,11]. This second problem is not necessarily easier to solve. In this work, we consider the original nonlinear MBPC problem and we propose to solve it using an ellipsoidal cutting-plane algorithm [12,13]. The aim of this paper is to present an extension of the self- tuning control algorithms described in Agarwal and Seborg [7] to a constrained MBPC methodology based on the generalised Hammerstein model. When dealing with constraints, the control