Local Model Networks For Modelling And Predictive Control Of Nonlinear Systems

The paper deals with the problem of modelling and control using the Local Model Network (LMN). The idea is based on development of multiple local models for the whole operating range of the controlled process. The local models are then smoothly connected using the validity or weighting functions to provide a nonlinear global model of the plant. For saving the computational load, linear model is obtained by interpolating the parameters of local models at each sample instant and then used in Model Predictive Control (MPC) framework to calculate the future behaviour of the process. The supervisory program, based on a nonlinear global model, computes desired values of manipulated variables leading to minimum utility consumption. The approach is verified in a control of model of a heat exchanger. INTRODUCTION Many of the processes in the chemical industry exhibit nonlinear behaviour. Their nonlinearities arise from the dynamics in chemical reactions, thermodynamic relationships, etc. Such processes are difficult to model and control. For such problems, there is a strong intuitive appeal in building systems which operate over a wide range of operating conditions by decomposing them into a number of simpler linear modelling or control problems. Multiple-model approaches for the modelling and control of nonlinear systems were proposed in the last decade (Murray-Smith and Johansen, 1997). Here local models are identified over the operating range of the process and form a global nonlinear model process by incorporating the validity function for each of these models (Johansen and Foss 1995). The basic principles of this modelling approach have been more or less independently developed in different disciplines like neural networks, fuzzy logic, statistics and artificial intelligence with different names such as local model networks (Johansen and Foss 1993), Takagi–Sugeno fuzzy model (Takagi and Sugeno 1985) or neuro-fuzzy model ( Narendra and Parthasarathy 1990; Zhang and Morris 2002). Similarities and differences between the LMN, radial basis function network (RBFN), fuzzy and Gaussian process model can be found in (Gregorcic and Lightbody 2008). Model Based Predictive Control (MBPC) or only Predictive Control is one of the control methods which have developed considerably over a few past years. The main advantage of this methodology is that it enables a simple treatment of input and output constraints (Maciejowski 2002), and copes in a natural way with multivariable systems. There are two ways to design controllers for local model structures, the linearization based and the local model-based approach. For linearization-based approach the local model network is linearized at the current operating point and linear controller is designed. The linearization of the LM network is very simple due to the structure of the model. In the second realisation a local controller is designed for each local model and the control output is then calculated as an interpolation of the local controller according to the current operating point. Both realisations have been widely used in the literature for control of nonlinear systems (Johansen et al., 2000;Mollov et all. 1999). In this paper the operating regions are distributed in the operating space using the steady-state characteristic of the process. The data for identification of the local models were created by application perturbations around the chosen operating points. The local models were identified using the least-squared method. The parameters of the validity functions were then optimized by minimizing the output error. Thus a nonlinear global model of the process was obtained. Predictive control strategy that uses parameters obtained from linearization of the global model was then applied to provide set point tracking of the output of the plant. The paper is organized as follows: Section II presents an overview of the local model network approach. The basics of Model Predictive Control are outlined in Section III. In Section IV, the heat-exchanger process is described. Section V describes the modelling of a heatexchanger using the LMN approach. In Sections VI a VII results of predictive control with and without the utility costs taken into consideration are presented. Proceedings 23rd European Conference on Modelling and Simulation ©ECMS Javier Otamendi, Andrzej Bargiela, Jose Luis Montes, Luis Miguel Doncel Pedrera (Editors) ISBN: 978-0-9553018-8-9 / ISBN: 978-0-9553018-9-6 (CD) LOCAL MODEL NETWORKS The basics of Local Model Networks approach are to decompose the operating space into zones where linear models are adequate approximations of dynamic behaviour within that regime, with a trade-off between the number of regimes and the accuracy of the global model. The architecture of LMN benefits from being able to incorporate the a priori knowledge about the system and conventional system identification methodology. The LMN structure also gives transparent and simple representation of the nonlinear system. In the LMN representation, each model is a local approximation of the modelling surface over a subspace of the operating space, which can be seen as an operating regime (Figure 1). Figure 1: The nonlinear input/output approximation (c) is obtained by combining three linear models (a) with validity functions (b) If linear local models are assumed, the structure of the ith submodel can be defined as follows: