Multi-Models Adaptive Control for Nonlinear Systems A. Nakrachi*, C. Lupu**, I. Matei** *LAGIS, University of Sciences and Technology of Lille **University Politehnica of Bucharest Splaiul Independetei, 313, Bucharest 060041 E-mail: Aziz.Nakrachi@polytech-lille.fr Abstract-A multiple models adaptive control system will be presented. The advantages of this control strategy with respect the classical control will be illustrated on a level control system with nonlinear model plant. A recent recursive identification method, in open and closed-loop, and a R-S-T control algorithm have been proposed to guarantee the desired performances in the adaptive control scheme. Experimental results obtained from using this procedure prove that the real time implementation of this control mechanism is suitable for nonlinear processes with typical large parameter variation. The experiment is also available as a virtual laboratory for remote control. I. INTRODUCTION Since the 90’s different approaches for the multimodel control strategy have been developed. The Balakrishnan’s and Narenda’s first papers which proposed several stability and robustness methods using classical switching and tuning algorithms have to be mentioned. Further research in this field determined the extension and improvement of the multi-model control concept. Magill and Lainiotis introduced the model representation through Kalman filters. In order to maintain the stability of minimum phase systems, Middelton improved the switching procedure using an algorithm with hysteresis. Petridis’, Kehagias’ and Toscano’s work focused on nonlinear systems with time variable. Landau and Karimi have important contributions regarding the use of several particular parameter adaptation procedures, namely CLOE (Closed Loop Output Error). The multi-model control version proposed by Narenda is based on neural networks. Finally, Dubois, Dieulot and Borne apply fuzzy procedures for switching and sliding mode control. In this paper a multi-model control procedure with closed loop identification for model parameter reestimation and with adaptive control (re-)design after each switching operation is proposed. This study emphasizes a new procedure for the multi-model control system design that assures improved performances for real time nonlinear control systems. We consider the next set of models: M ={ } 1 2 3 , , ... n M M M M and the class of the correspondent controllers: C ={ } 1 2 3 , , ... n C C C C , integrated in the closed-loop configuration, as presented in figure Fig. 1. Fig. 1 – Multi-Model Control Scheme The input and output of the process P are u and y respectively, and r is the set point of the system The Mi (i=1,2,… n) models are a priori evaluated. For each model Mi a controller Ci is designed in order to assure the nominal performances for the pair (Mi, Ci). The main idea of the multi-model adaptive control procedure is to chose the best model included in M that best approximates the process around a current operating point, to apply the correspondent controller and than to continue adaptively towards the current operating point of the process [Narenda and Balakrishnan, 1997],[ Zang et al., 1995]. In order to use this mechanism, the control problem is developed in two steps [ Narenda and Balakrishnan, 1997] and also [ Landau and Boumaiza, 1996] : a) The model with the smallest error with respect to a performance criterion is chosen: switching step. e1 e2 en y r u n 1 2 C1 u1 C2 u2 Cn un P M1 M2 Mn .....