Volterra-Laguerre modeling for NMPC

Abstract

Volterra series are perhaps the best understood nonlinear system representations in signal processing. They can be used to model a wide class of nonlinear systems. However, since these models are non-parsimonious in parameters, the symmetric kernel parameters are used. This model is used to evaluate identification of a pH-neutralization process. The aim is to use this model in nonlinear model predictive control framework. For this purpose various orders of the Laguerre filters and also Volterra kernels are tested and the results are compared in terms of the validation of these models. The results show that to have a good trade off between simplicity of the model and its corresponding fitness, the selected nonlinear Volterra model has the memory of 3 while the number of its kennel is 4. The VAF of this model is 99.63% which is completely acceptable for nonlinear model predictive control applications.

Generalized Laguerre Reduction of the Volterra Kernel for Practical Identification of Nonlinear Dynamic Systems

“…The Laguerre Polynomials are a series of orthogonal polynomials that can be used to reduce the number of coefficients required to describe a Volterra kernel. The application of orthogonal functions to identification and control is not new, see (Schetzen, 1980), (Dumont et al, 1991), Zafiriou, 1994), (Mäkila, 1990), (Clement, 1982), (Mahmoodi et al, 2007), (Zheng and Zafiriou, 1995),and (Lee, 1960). A mathematical review of orthogonal and orthonormal fucntions can be found in Appendix 6.…”

Parallel Based Support Vector Regression for Empirical Modeling of Nonlinear Chemical Process Systems

“…Over the years, numerous nonlinear empirical models have been reported in literature, e.g. Volterra models (Ljung 2010;Mahmoodi 2007), artificial neural networks (Norgaard 2000), fuzzy-logic based models (Beyhan & Alci 2010), nonlinear auto regressive with exogenous input (NARX) models (Nelles 2001), some combinations of them like neuro-fuzzy models (Babuška & Verbruggen 2003), support vector machine and kernel methods of modeling (Tötterman & Toivonen 2009) and wavelet decomposition based methods (Billings 2005). One modeling technique that has been gaining popularity in the recent past is the support vector machine (SVM) (Suganyadevi & Babulal 2014;Tötterman & Toivonen 2009).…”

Development of dynamic model of a 7DOF hydraulically actuated tele-operated robot for decommissioning applications

“…More specifically, task patterns in nuclear reactor operational environment requires reliable control algorithms which will be able to provide an estimation that maintains predictive power both in mild, high speed and difficult tasks carried out by the manipulator. This necessitates development of more sophisticated and high performance identification [7,15,16,22,23,24] and model-based control algorithms working based on a reliable dynamic model of the manipulator. Therefore, developing a more general nonlinear dynamic model of the bespoke robot which has the potential to be utilized for design and development of such a model-based nonlinear control strategies determines the major motivation of this paper.…”