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Title: Identification and Control of Nonlinear Systems using Multiple Models
Keywords: Nonlinear Systems, Time-Varying Systems, Piecewise Affine Systems, Multiple Models Identification, Multiple Models Control, Reference Tracking
Issue Date: 29-Mar-2011
Citation: LAI CHOW YIN (2011-03-29). Identification and Control of Nonlinear Systems using Multiple Models. ScholarBank@NUS Repository.
Abstract: Most of the systems in our real life are inherently nonlinear. One simple way to control a nonlinear plant over a large operating region is by utilizing the ``divide and conquer" strategy. A few operating points which cover the whole range of system's operation are chosen, and a linear approximation is obtained at each of these operating points. The designer then designs one local controller for each local model, and activates one of these local controllers when the process is operating in the neighborhood of the corresponding linearization point. This is the basic idea behind the gain scheduling approach, supervisory control and multiple model control, which have found popularity in the industry as well as in flight control. The aim of our work is to design multiple model controllers for nonlinear systems for tracking purposes. To this aim, the nonlinear system is approximated as piecewise affine autoregressive system with exogenous inputs (PWARX). Firstly, we propose a general framework for the identification of discrete-time time-varying system, where both offline and online identification algorithms for linear as well as nonlinear systems can be derived. Built upon this work, we further propose a simple and efficient algorithm which can automatically provide accurate PWARX models of nonlinear systems based on measured input-output data. The proposed algorithm is shown to be robust against noise as well as uncertainties in the model order. Next, we move on to design the local controllers based on the obtained PWARX model, which are then patched together through switching to become a global controller for the nonlinear system. We provide a few solutions to deal with a causality issue whereby the determination of the active subsystem and the computation of control signal affect each other at the same time. The designed controllers show good performance both in simulation as well as in experimental studies. One issue related to the PWARX model identification is the number of subsystems to be used. We show that if the original piecewise affine system consists of $N$ state space subsystems, then we will need more than $N$ input-output subsystems to fully describe the system's behavior. We show via simulation studies that having the correct number of the input-output subsystems is crucial to obtain a good idenfication and control of piecewise affine system.
Appears in Collections:Ph.D Theses (Open)

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