2,022 research outputs found

    A new kernel-based approach for overparameterized Hammerstein system identification

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    In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of pp basis functions. We reconstruct the pp coefficients of the nonlinearity together with the first nn samples of the impulse response of the linear system by estimating an npnp-dimensional overparameterized vector, which contains all the combinations of the unknown variables. To avoid high variance in these estimates, we adopt a regularized kernel-based approach and, in particular, we introduce a new kernel tailored for Hammerstein system identification. We show that the resulting scheme provides an estimate of the overparameterized vector that can be uniquely decomposed as the combination of an impulse response and pp coefficients of the static nonlinearity. We also show, through several numerical experiments, that the proposed method compares very favorably with two standard methods for Hammerstein system identification.Comment: 17 pages, submitted to IEEE Conference on Decision and Control 201

    Identification of some nonlinear systems by using least-squares support vector machines

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    Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2010.Thesis (Master's) -- Bilkent University, 2010.Includes bibliographical references leaves 112-116.The well-known Wiener and Hammerstein type nonlinear systems and their various combinations are frequently used both in the modeling and the control of various electrical, physical, biological, chemical, etc... systems. In this thesis we will concentrate on the parametric identification and control of these type of systems. In literature, various identification methods are proposed for the identification of Hammerstein and Wiener type of systems. Recently, Least Squares-Support Vector Machines (LS-SVM) are also applied in the identification of Hammerstein type systems. In the majority of these works, the nonlinear part of Hammerstein system is assumed to be algebraic, i.e. memoryless. In this thesis, by using LS-SVM we propose a method to identify Hammerstein systems where the nonlinear part has a finite memory. For the identification of Wiener type systems, although various methods are also available in the literature, one approach which is proposed in some works would be to use a method for the identification of Hammerstein type systems by changing the roles of input and output. Through some simulations it was observed that this approach may yield poor estimation results. Instead, by using LS-SVM we proposed a novel methodology for the identification of Wiener type systems. We also proposed various modifications of this methodology and utilized it for some control problems associated with Wiener type systems. We also proposed a novel methodology for identification of NARX (Nonlinear Auto-Regressive with eXogenous inputs) systems. We utilize LS-SVM in our methodology and we presented some results which indicate that our methodology may yield better results as compared to the Neural Network approximators and the usual Support Vector Regression (SVR) formulations. We also extended our methodology to the identification of Wiener-Hammerstein type systems. In many applications the orders of the filter, which represents the linear part of the Wiener and Hammerstein systems, are assumed to be known. Based on LS-SVR, we proposed a methodology to estimate true ordersYavuzer, MahmutM.S

    A new toolbox for the identification of diagonal Volterra kernels allowing the emulation of nonlinear audio devices

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    Numerous audio systems are nonlinear. It is thus of great importance to study them and understand how they work. Volterra series model and its subclass (cascade Hammerstein-Wiener model) are usual ways to modelize nonlinear systems. However the identification methods of these models are still considered as an open topic. Therefore we have developed a new optimized identification tool ready for use and presented as a Matlab toolbox. This toolbox provides the parameters of the optimized sine sweep needed for the identification method, it is able to calculate the parameters of the Hammerstein model and to emulate the output signal of a nonlinear device for a given input signal. To evaluate the toolbox, we modelize a guitar distortion effect (the Tubescreamer) having a total harmonic distortion (THD) comprised in the range 10-23\%. We report a mean error of less than 0.7\% between the emulated signal and the signal coming from the distortion effect

    Nonlinear Model Predictive Controller Design for Identified Nonlinear Parameter Varying Model

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    In this paper, a novel nonlinear model predictive controller (MPC) is proposed based on an identified nonlinear parameter varying (NPV) model. First, an NPV model scheme is present for process identification, which is featured by its nonlinear hybrid Hammerstein model structure and varying model parameters. The hybrid Hammerstein model combines a normalized static artificial neural network with a linear transfer function to identify general nonlinear systems at each fixed working point. Meanwhile, a model interpolating philosophy is utilized to obtain the global model across the whole operation domain. The NPV model considers both the nonlinearity of transition dynamics due to the variation of the working-point and the nonlinear mapping from the input to the output at fixed working points. Moreover, under the new NPV framework, the control action is computed via a multistep linearization method aimed for nonlinear optimization problems. In the proposed scheme, only low cost tests are needed for system identification and the controller can achieve better output performance than MPC methods based on linear parameter varying (LPV) models. Numerical examples validate the effectiveness of the proposed approach

    From Nonlinear Identification to Linear Parameter Varying Models: Benchmark Examples

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    Linear parameter-varying (LPV) models form a powerful model class to analyze and control a (nonlinear) system of interest. Identifying a LPV model of a nonlinear system can be challenging due to the difficulty of selecting the scheduling variable(s) a priori, which is quite challenging in case a first principles based understanding of the system is unavailable. This paper presents a systematic LPV embedding approach starting from nonlinear fractional representation models. A nonlinear system is identified first using a nonlinear block-oriented linear fractional representation (LFR) model. This nonlinear LFR model class is embedded into the LPV model class by factorization of the static nonlinear block present in the model. As a result of the factorization a LPV-LFR or a LPV state-space model with an affine dependency results. This approach facilitates the selection of the scheduling variable from a data-driven perspective. Furthermore the estimation is not affected by measurement noise on the scheduling variables, which is often left untreated by LPV model identification methods. The proposed approach is illustrated on two well-established nonlinear modeling benchmark examples

    Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle

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    To restore functional use of paralyzed muscles by automatically controlled stimulation, an accurate quantitative model of the stimulated muscles is desirable. The most commonly used model for isometric muscle has had a Hammerstein structure, in which a linear dynamic block is preceded by a static nonlinear function, To investigate the accuracy of the Hammerstein model, the responses to a pseudo-random binary sequence (PRBS) excitation of normal human plantarflexors, stimulated with surface electrodes, were used to identify a Hammerstein model but also four local models which describe the responses to small signals at different mean levels of activation. Comparison of the local models with the Linearized Hammerstein model showed that the Hammerstein model concealed a fivefold variation in the speed of response. Also, the small-signal gain of the Hammerstein model was in error by factors up to three. We conclude that, despite the past widespread use of the Hammerstein model, it is not an accurate representation of isometric muscle. On the other hand, local models, which are more accurate predictors, can be identified from the responses to short PRBS sequences. The utility of local models for controller design is discussed
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