Parametric identification of nonlinear fractional Hammerstein models

In this paper, a system identification method for continuous fractional-order Hammerstein models is proposed. A block structured nonlinear system constituting a static nonlinear block followed by a fractional-order linear dynamic system is considered. The fractional differential operator is represented through the generalized operational matrix of block pulse functions to reduce computational complexity. A special test signal is developed to isolate the identification of the nonlinear static function from that of the fractional-order linear dynamic system. The merit of the proposed technique is indicated by concurrent identification of the fractional order with linear system coefficients, algebraic representation of the immeasurable nonlinear static function output, and permitting use of non-iterative procedures for identification of the nonlinearity. The efficacy of the proposed method is exhibited through simulation at various signal-to-noise ratios

Adaptive Observer for Nonlinearly Parameterised Hammerstein System with Sensor Delay – Applied to Ship Emissions Reduction

Taking offspring in a problem of ship emission reduction by exhaust gas recirculation control for large diesel engines, an underlying generic estimation challenge is formulated as a problem of joint state and parameter estimation for a class of multiple-input single-output Hammerstein systems with first order dynamics, sensor delay and a bounded time-varying parameter in the nonlinear part. The paper suggests a novel scheme for this estimation problem that guarantees exponential convergence to an interval that depends on the sensitivity of the system. The system is allowed to be nonlinear parameterized and time dependent, which are characteristics of the industrial problem we study. The approach requires the input nonlinearity to be a sector nonlinearity in the time-varying parameter. Salient features of the approach include simplicity of design and implementation. The efficacy of the adaptive observer is shown on simulated cases, on tests with a large diesel engine on test bed and on tests with a container vessel

Identification of nonlinear interconnected systems

This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.In this work we address the problem of identifying a discrete-time nonlinear system composed of a linear dynamical system connected to a static nonlinear component. We use linear fractional representation to provide a united framework for the identification of two classes of such systems. The first class consists of discrete-time systems consists of a linear time invariant system connected to a continuous nonlinear static component. The identification problem of estimating the unknown parameters of the linear system and simultaneously fitting a math order spline to the nonlinear data is addressed. A simple and tractable algorithm based on the separable least squares method is proposed for estimating the parameters of the linear and the nonlinear components. We also provide a sufficient condition on data for consistency of the identification algorithm. Numerical examples illustrate the performance of the algorithm. Further, we examine a second class of systems that may involve a nonlinear static element of a more complex structure. The nonlinearity may not be continuous and is approximated by piecewise a±ne maps defined on different convex polyhedra, which are defined by linear combinations of lagged inputs and outputs. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear subsystems. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine system identification techniques are employed for the estimation of the nonlinear component. Numerical examples show that the proposed procedure is able to successfully profit from the knowledge of the interconnection structure, in comparison with a direct black box identification of the piecewise a±ne system.Funding was obtained as a Marie Curie Early Stage Researcher Training fellowship, under the NET-ACE project (MEST-CT-2004-6724)

Reduced order modeling of infinite dimensional systems from frequency response data

Ankara : The Department of Electrical and Electronics Engineering and The Graduate School of Engineering and Science of Bilkent University, 2014.Thesis (Master's) -- Bilkent University, 2014.Includes bibliographical references leaves 55-58.In this thesis, a system identification method using frequency response data is studied. Identification method is applied to various types of distributed parameter systems, in particular flexible structures. One of the challenging tasks in the control of flexible structures is the estimation of the dominant modes (location of resonant frequencies and associated damping coefficients). In the literature, there are several studies where transfer functions of flexible structures are derived from PDEs (Partial Differential Equations); these are infinite dimensional models. In this study, a numerical method is proposed to identify the dominant flexible modes of a flexible structure with an input/output delay. The method uses a frequency domain approach (frequency response data) to estimate the resonating frequencies and damping coefficients of the flexible modes, as well as the amount of the time delay. A sequential NLLS (Non-Linear Least Squares) curve fitting procedure is adopted. Instead of optimizing over all available data collected on a frequency interval, a data selection scheme that increases the amount of data at each step is followed. Selecting relevant parts of data and optimizing sequentially increasing number of coefficients in every step is the essential part idea behind this approach. The optimization problem solved reduces to a curve fitting problem. It is illustrated that such a Newtonian optimization method has the capability of finding the parameters of a reduced order transfer function by minimizing a cost function involving nonlinearities such as exponential and rational terms. Further model reduction techniques can be applied by analyzing Hankel singular values of the resulting transfer function. Comparisons with other methods solving similar problems are illustrated with examples. Simulation results demonstrate efficiency of the proposed algorithm.Demir, OkanM.S

Uma nova abordagem para representações e identificações de classes de sistemas dinâmicos não-lineares

In the last few years, the growth of the academic production about non-linear dynamic systems was noticed. Although the researches evolved, there are still topics that deserve a close analysis. One of them includes the study of mathematical models which represents many non-linear systems and will be the focus of this study. The purpose is to propose a new representation for non-linear dynamics system classes. It will combine models of interconnected blocks related concepts and base function. The parameters estimation for this model is done through frequency response techniques, based on harmonic balance concepts. To show and test the proposed model, systems with variable parameterization related to input signal amplitude will be utilized with numeric examples. In this work, it will be also presented concepts related to the modeling and linear and non-linear dynamic systems identification and parameters estimation.Nos últimos anos, o interesse pelo estudo de sistemas dinâmicos não-lineares, incluindo sua modelagem e identificação, tem sido crescente. Embora as pesquisas nesse sentido tenham evoluído, existem tópicos relacionados aos sistemas não-lineares que merecem uma análise mais detalhada. Um deles inclui o estudo de modelos matemáticos que representem algumas classes de sistemas não-lineares, o que constitui um dos objetivos desta dissertação. Este trabalho propõe uma representação nova para algumas classes de sistemas dinâmicos não-lineares. Ela utiliza uma combinação dos conceitos relacionados a modelos de blocos interconectados e a funções de base. A estimação de parâmetros dessa representação é efetuada por técnicas de resposta em freqüência, baseando-se no conceito de balanço harmônico. Com o objetivo de ilustrar e testar a representação proposta, sistemas que possuem parâmetros variáveis em função da amplitude do sinal de entrada são utilizados como exemplos numéricos. Os resultados obtidos são comparados com dados resultantes de outras técnicas conhecidas. Neste trabalho, são apresentados também conceitos relacionados à modelagem e à identificação de sistemas dinâmicos lineares, não-lineares e estimação de parâmetros

Continuous-time block-oriented nonlinear modeling with complex input noise structure

The continuous-time closed-form algorithms to sinusoidal input changes are proposed and presented for single-input, single-output (SISO) Hammerstein and Wiener systems with the first-order, second-order, and second-order plus lead dynamics. By simulation on theoretical Hammerstein and Wiener systems, the predicted responses agree exactly with the true process values. They depend on only the most recent input change. The algorithms to SISO Hammerstein and Wiener systems can be conveniently extended to the multiple-input, multiple-output (MIMO) systems as shown by the two-input, two-output examples and demonstrated by the simulated seven-input, five-output continuous stirred tank reactor (CSTR). The predictions and the simulated theoretical responses agree exactly and the predicted multiple CSTR outputs are close to the true process outputs. The proposed algorithms can predict the responses closer to the true values when comparing with the piece-wise step input approximation of the sinusoidal input changes on a simulated MIMO CSTR. In addition, as the noisy process input could be decomposed as summation of sinusoidal signals imposed on a step input change; the proposed algorithms can be employed to predict outputs for the noisy process inputs once the decomposition is done and the predicted noisy process outputs are shown to be close to the true ones, and are much better than the predictions based on the perfect filtering of the input signals.;The estimating equations based on the moment method are proposed for the Wiener dynamic process with stochastically correlated process input disturbances or noises and they work well for the parameter estimation. No one has ever proposed such method before. This approach has led to stable and robust estimators that have reasonable estimation errors and there is no need to measure the input disturbances or noises, or to calculate the time derivative of the observed output variable. Only the original process output observations over time are needed. The original model can be shifted to an approximate model under some conditions. This approximation is acceptable based on some analysis and derivation. The estimating equation methodology was shown to work well for the approximate model, while other existing methods do not work at all