Parametric Identification of Parallel Hammerstein Systems (original) (raw)
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A Decoupling Derivative-Based Approach for Hammerstein System Identification
Proceedings of the 17th IFAC World Congress, 2008, 2008
This paper proposes a non iterative algorithm for the identification of Hammerstein model, using the sampled output data obtained from the step response, giving a continuoustime model for the linear part and a point-wise estimation of the nonlinear one. Key in the derivation of the results is the algebraic derivative method in the frequency domain yielding exact formula in terms of multiple integrals of the output signal, when placed in the time domain. By investigating the connection between such integrals and parameters to be estimated, a set of three linear regression equations is proposed. The first equation is used to estimate the structure of poles in the linear part, the second to estimate a point of the nonlinearity, the third to estimate the structure of zeros in the linear part. No a priori knowledge of the structure of the nonlinearity is required. The proposed algorithm is numerically robust, since it is based only on least squares estimation. Simulation results validate the proposed algorithm.
Identification of Hammerstein systems without explicit parameterisation of non-linearity
International Journal of Control, 2009
This article proposes a new approach to identification of Hammerstein systems, where a non-linearity precedes a linear dynamic system, driven by piece-wise constant inputs. The proposed approach does not require an explicit parameterisation of the non-linearity. Moreover, the non-linearity does not have to be static, but could be the one with finite memories like backlash. By exploiting input's piecewise constant property, the denominator of the linear system described by an ARX model is consistently identified from the information of the output only; next, a subspace direct equalisation method estimates the unmeasurable inner signal based on the resulted denominator estimate and output measurements. Contrary to the existing blind approaches, the numerator of the linear system is not required, which leads to a significant improvement of removing an error propagation. On the basis of the estimated inner signal, the measured input and output, the non-linearity and linear system are obtained separately. The proposed approach is validated and compared with two existing blind approaches through numerical and experimental examples.
Combined parametric-nonparametric identification of Hammerstein systems
Ieee Transactions on Automatic Control, 2004
A novel, parametric-nonparametric, methodology for Hammerstein system identification is proposed. Assuming random input and correlated output noise, the parameters of a nonlinear static characteristic and finite impulse-response system dynamics are estimated separately, each in two stages. First, the inner signal is recovered by a nonparametric regression function estimation method (Stage 1) and then system parameters are solved independently by the least squares (Stage 2). Convergence properties of the scheme are established and rates of convergence are given.
A New Identification Approach of MIMO Hammerstein Model with Separate Nonlinearities
Advances in Science, Technology and Engineering Systems Journal
A new coupled structure identification of Multi-Input Multi-Output (MIMO) Hammerstein models with separate nonlinearities is proposed. It is based on the use of the Recursive Least Squares (RLS) algorithm. A comparative study between a decoupled and coupled structures identification of MIMO Hammerstein models is discussed. A quadruple-tank process is used to illustrate the e ectiveness of the new structure.
New results for Hammerstein system identification
1995
Abstract A novel approach is presented for the analysis and design of identification algorithms for Hammerstein models, which consist of a static nonlinearity followed by an LTI system. The authors examine two identification problems. In the first problem, the system is excited with white noise and the LTI system is FIR, and they find a simple explicit solution for the optimal parameter estimate and show that for sufficiently large data lengths a standard iterative technique globally converges to this optimal value.
Hammerstein System Identification by a Semi-Parametric Method
2000
A semi-parametric algorithm for identification of Hammerstein systems in the presence of correlated noise is proposed. The procedure is based on the non-parametric kernel regression estimator and the standard least squares. The advantages of the method in comparison with the standard non-parametric approach are discussed. Limit properties of the proposed estimator are studied, and the simulation results are presented.
Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference, 2013
This paper describes a novel method for the identification of Hammerstein systems with time-varying (TV) static nonlinearities and time invariant (TI) linear elements. This paper develops a linear parameter varying (LPV) state-space representation for such systems and presents a subspace identification technique that gives individual estimates of the Hammerstein components. The identification method is validated using simulated data of a TV model of ankle joint reflex stiffness where the threshold and gain of the model change as nonlinear functions of an exogenous signal. Pilot experiment of TV reflex EMG response identification in normal ankle joint during an imposed walking task demonstrate systematic changes in the reflex nonlinearity with the trajectory of joint position.
2007
A combined, parametric-nonparametric routine for the identification of a static part of Hammerstein system is presented. Parameters of the input nonlinear characteristic of Hammerstein system are estimated for a wide range of random excitations and random noise, and without any knowledge of the parametric model of the output linear dynamics. The needed unmeasurable interaction inputs are estimated in a preliminary step by the nonparametric regression function estimation method. Next, they are used in the nonlinear optimization procedure for evaluating parameters of the static subsystem. Broad class of nonlinear characteristics including functions which are not linear in the parameters, as well as the infinite length impulse response of the linear dynamics are admitted. It is shown that the resulting parameter estimates are consistent for both white and colored noise. The analytical findings are validated using numerical simulation results.
Elektronika ir Elektrotechnika
Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents a linear dynamic component placed between the first two blocks. Some of the common linear model structures include a rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregressive with extra input (ARX), autoregressive moving average with exogenous inputs model (ARMAX), and output-error (O-E) model structure. This paper presents a new structure, and a new improvement is proposed, which is consisted of the basic structure of Hammerstein-Wiener models with an improved orthogonal function of Müntz-Legendre type. We present an extension of generalised Malmquist polynomials that represent Müntz polynomials. Also, a detailed mathematical background for performing improved almost orthogonal polynomials, in combination with Hammerstein-Wiener mo...
An adaptive approximation method for Hammerstein systems identification
2012 IEEE International Conference on Control Applications, 2012
This paper aims to describe a new identification method for Hammerstein systems relying on the framework of basis functions approximation in order to obtain an adequate model for the nonlinear static component. The specific coefficients of the basis functions approximation and also the parameters of the linear dynamic component are estimated using a nonlinear least squares method based on a modified version of Gauss-Newton algorithm. An algorithm is introduced based on wavelet multiresolution analysis that returns a low complexity approximation of the nonlinear component built on a grid hierarchy using adaptive bases. Such bases provides a powerful means to detect local singularities and often lead to quite simple refinement strategies. Finally, we present some numerical results for our method that show its efficiency.