Copyright © IFAC Advanced Control of Chemical Processes Hong Kong, China, 2003 ELSEVIER PUBLICATIONS www.elseyier.comllocalclifac EXPERIMENTAL VERIFICATION OF GAP METRIC AS A TOOL FOR MODEL SELECTION IN MULTI-LINEAR MODEL-BASED CONTROL Omar Galan!, Jose A. Romagnoli 2 , Ahmet Palazoglu 3 , Yam an Arkun 4 1 ABB Australia Limited Pty, VPP9 Project, 436 Gadara Road, Tumut NSW 2720 AUSTRALIA, 2Dept. of Chemical Engineering, The University of Sydney, Sydney, NSW, 2006, AUSTRALIA, 3Dep t. of Chemical Engineering and Materials Science, University ofCalifomia, Davis, CA 95616 USA, 4College of Engineering, KoC; University, Rumelifeneri, Sanyer, istanbul, 80910 TURKEY Abstract: A nonlinear system can be modeled using a set of linear models that cover the range of operation. A model-based control strategy then can be employed that uses the local models in a cooperative manner to control the nonlinear system. The decision of how many models are sufficient for effective control can be tackled by the use of the gap metric that quantifies the distance between two linear operators. A pH control experiment is used to demonstrate the effectiveness of gap metric as a tool for model selection. Copyright © 2003 IFAC Keywords: model-based control, nonlinear systems I. INTRODUCTION Classical linear design tools have matured to a point where one can incorporate robustness and perfonnance requirements in a natural fashion. However for nonlinear processes strictly linear designs may not provide satisfactory perfonnance unless they are suitably modified. One approach which tries to keep the features of linear design and at the same time account for nonlinearities is the multi-model approach for controller design (Yu et al., 1992; Murray-Smith and Johansen, 1997; Ozkan et al., 2003). The key concept is to represent the nonlinear system as a combination of linear systems where classical control design techniques can be applied. The controller design based on the multi- model approach requires either simultaneous plants stabilization using a single controller, subject to perfonnance and stability constrains (Schoming et ai, 1995; Gabin et ai, 2000), or interpolation using model validity functions, where local controllers are selected as a function of the current state of the process (Foss et ai, 1995; Banerjee et ai, 1997). However, in all these approaches the question of how many and which models are required remains largely unanswered. Although it is common to use a large number of local models to improve the piece-wise linear approximation of the nonlinear system (Narendra et ai, 1995), the optimization problem to 257 solve the design problem becomes fonnidable when the number of local models is large. We shall fonnulate the multi-model control problem by assuming a set of local plants and controllers that stabilize these plants and by asking the question, "Is there a reduced set of controllers, which are based on models that are 'close' in some sense?" To detennine when two systems are close to one other is a nontrivial task, and furthennore, what is meant by "close" is not entirely obvious. Since systems can be visualized as input-output operators, a natural distance concept would be the induced operator nonn. Yet, the nonn cannot be generalized as a distance measure (Vidyasagar, 1985). The aim of this paper is to discuss the application of a distance measure between systems, the so-called Gap Metric, to select a reduced set of models that contain non-redundant process infonnation for robust stabilization of feedback systems based on multi- model controller design 2. GAP METRIC The concept of the gap between the graphs of two linear systems goes back to Hausdorf (1935). Later the gap and other metrics were used to study how close different operators are (e.g. Newburgh (1951),