Abstract
The main aim of the paper is to analyse effectiveness of the approximation method from the nonlinear discretised into discrete piece-wise affine model. Accuracy and numerical complexity of the piece-wise affine control system grow with the number of polyhedral partitions, that describe the system. The model with state dependent nonlinearity can be effectively approximated by proposed secant piece-wise linear approximation. The effectiveness of the proposed method is evaluated on the car on the nonlinear hill model. DOI: http://dx.doi.org/10.5755/j01.eee.20.10.4454
Highlights
In the last decade growing attention was paid to modelling and methods for piece-wise affine (PWA) systems [1]–[5]
Complexity of the PWA model is directly connected with the number of polyhedral partitions, describing the system
It may be expected that the more accurate is the PWA approximation; the better is the closed loop performance of the system with nonlinear plant and controller tuned for PWA model
Summary
In the last decade growing attention was paid to modelling and methods for piece-wise affine (PWA) systems [1]–[5]. From the practical point of view most of the PWA models are only approximation of the real nonlinear systems [5], [7]–[9]. Complexity of the PWA model is directly connected with the number of polyhedral partitions, describing the system. In general the more polyhedral partitions have the model; the more accurate is PWA approximation of the nonlinear system. Controller computed for the approximated model (e.g. PWA) operates on the nonlinear plant. It may be expected that the more accurate is the PWA approximation; the better is the closed loop performance of the system with nonlinear plant and controller tuned for PWA model. The paper is verification how the number of partitions in the approximated PWA model results in control performance for the nonlinear system. The investigation is made on the basis of the assumed model – car on the nonlinear hill, where the control objective is to drive the car from initial conditions to the origin, in minimum time, subject to limited force
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