Piecewise affine approximation of nonlinear systems – a case study of a benchmark nonlinear boiler

This paper deals with piecewise affine (PWA) approximation of nonlinear systems. Its motivation is simple. If the controlled plant exhibits nonlinear behavior, linear controller based on linearized model may often be unable to achieve satisfactory performance. On the other hand, intrinsic complexity of the nonlinear controller based on full nonlinear model may prevent it from practical application. PWA model that uses a set of switched partial linear models can then represent the middle way between simplifications of the linearized model and complexity of the nonlinear model. The paper uses a case study of a nonlinear power plant boiler. It shows that its complex nonlinear dynamical behavior can well be approximated with a relatively simple PWA system. Unlike one linearized model, this PWA approximation fits boiler dynamic behavior very well. As the development of model predictive control of the PWA systems has already reached a substantial level of maturity, this PWA model can be used as a basis for the design of hybrid model predictive control for this boiler. Key-Words: Hybrid systems, piecewise affine systems, approximation of nonlinear systems