Application of orthonormal basis functions for identification of flexible-link manipulators

et al. 2012

IJMIC

This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalised orthonormal basis functions. The paper is separated in two parts. The first part of the paper approached issues related with linear models and models with uncertain parameters. Now, the mathematical foundations as well as their advantages and limitations are discussed within the contexts of non-linear system identification. The discussions comprise a broad bibliographical survey of the subject and a comparative analysis involving some specific model realisations, namely, Volterra, fuzzy, and neural models within the orthonormal basis functions framework. Theoretical and practical issues regarding the identification of these non-linear models are presented and illustrated by means of two case studies.

Section: Modelling a Magnetic Levitation Systemmentioning

confidence: 68%

An introduction to models based on Laguerre, Kautz and other related orthonormal functions Part II: non-linear models

Oliveira

Rosa

et al. 2012

IJMIC

“…In fact, inasmuch as equations (13)- (15) are satisfied, the orthonormal property of the basis is guaranteed [30].…”

Section: B Formulation Based On Gobfsmentioning

confidence: 96%

“…where β M ∈ C is the complex-valued pole included into the basis and λ ′ , γ ′ , λ ′′ , γ ′′ are real-valued parameters that relate to β M as follows [7], [30]:…”

Section: B Formulation Based On Gobfsmentioning

confidence: 99%

Optimization of Volterra models with asymmetrical kernels based on generalized orthonormal functions

Braga

Machado

2011 19th Mediterranean Conference on Control &Amp; Automation (MED)

et al. 2011

An improved approach to determine exact search directions for the optimization of Volterra models based on Generalized Orthonormal Bases of Functions (GOBF) is proposed. The proposed approach extends the work in [7], where a novel, exact technique for optimizing the GOBF parameters (poles) for Volterra models of any order was presented. The proposed extensions take place in two different ways: (i) the formulation here is derived in such a way that each multidimensional kernel of the model is decomposed into a set of independent orthonormal bases (rather than a single, common basis), each of which is parameterized by an individual set of poles intended for representing the dominant dynamic of the kernel along a particular dimension; and (ii) a novel, more computationally efficient method to analytically and recursively calculate the search directions (gradients) for the bases poles is derived. A simulated example is presented to illustrate the performance of the proposed approach. A comparison between the proposed method, which uses asymmetric kernels with multiple orthonormal bases, and the original method, which uses symmetric kernels with a single basis, is presented.

“…Other papers present experimental results regarding the use of orthonormal bases for the identification of real-world systems. In this context, one can cite Nalbantog˘lu et al (2003), which studied the pole location via frequency-domain techniques, and Ziaei and Wang (2006), where the system identification based on GOBFs with both real and complex poles is presented. In Patwardhan and Shah (2005), it is proposed a decomposed strategy to estimate only the GOBFs poles by nonlinear iterative search and the orthonormal expansion coefficients analytically.…”

Section: Introductionmentioning

confidence: 99%

An optimal expansion of Volterra models using independent Kautz bases for each kernel dimension

Rosa

International Journal of Control

Amaral

2008

A new solution for the problem of selecting poles of the two-parameter Kautz functions in Volterra models is proposed. In general, a large number of parameters are required to represent the Volterra kernels, although this difficulty can be overcome by describing each kernel using a basis of orthonormal functions, such as the Kautz basis. This representation has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a non-linear static mapping represented by the Volterra series. The resulting Wiener/Volterra model can be truncated into fewer terms if the Kautz functions are properly designed. The underlying problem is how to select the arbitrary complex poles that fully parametrize these functions. This problem has been approached in previous research by minimizing an upper bound for the error resulting from the truncation of the kernel expansion. The present paper goes even further in that each multidimensional kernel is decomposed into a set of independent Kautz bases, each of which is parametrized by an individual pair of conjugate Kautz poles intended to represent the dominant dynamic of the kernel along a particular dimension. An analytical solution for one of the Kautz parameters, valid for Volterra models of any order, is derived. A simulated example is presented to illustrate these theoretical results. The same approach is then used to model a real non-linear magnetic levitation system with oscillatory behaviour.