RESUMO
The ARX-Laguerre model is a very important reduced complexity representation of linear system. However a significant reduction of this model is subject to an optimal choice of both Laguerre poles. Therefore we propose in this paper two new methods to estimate, from input/output measurements, the optimal values of Laguerre poles of the ARX-Laguerre model. The first method is based on the Newton-Raphson's iterative technique where we prove that the gradient and the Hessian can be expressed analytically. The second method is based on Genetic Algorithms. Both proposed algorithms are tested on a numerical example and on a heating benchmark.
RESUMO
This paper proposes a method for synthesizing an adaptive predictive controller using a reduced complexity model. This latter is given by the projection of the ARX model on Laguerre bases. The resulting model is entitled MIMO ARX-Laguerre and it is characterized by an easy recursive representation. The adaptive predictive control law is computed based on multi-step-ahead finite-element predictors, identified directly from experimental input/output data. The model is tuned in each iteration by an online identification algorithms of both model parameters and Laguerre poles. The proposed approach avoids time consuming numerical optimization algorithms associated with most common linear predictive control strategies, which makes it suitable for real-time implementation. The method is used to synthesize and test in numerical simulations adaptive predictive controllers for the CSTR process benchmark.
