Identification scheme for fractional Hammerstein models with the delayed Haar wavelet

Abstract

The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identification strategy for a block-oriented Hammerstein process is proposed using the Haar wavelet operational matrix (HWOM). To determine all the parameters in the Hammerstein model, a special input excitation is utilized to separate the identification problem of the linear subsystem from the complete nonlinear process. During the first test period, a simple step response data is utilized to estimate the linear subsystem dynamics. Then, the overall system response to sinusoidal input is used to estimate nonlinearity in the process. A single-pole fractional order transfer function with time delay is used to model the linear subsystem. In order to reduce the mathematical complexity resulting from the fractional derivatives of signals, a HWOM based algebraic approach is developed. The proposed method is proven to be simple and robust in the presence of measurement noises. The numerical study illustrates the efficiency of the proposed modeling technique through four different nonlinear processes and results are compared with existing methods.

Parameter learning for the nonlinear system described by Hammerstein model with output disturbance

“…There are a number of parameter estimation methods for the Hammerstein model. Generally, they are mainly divided into two categories, that is, synchronous parameter estimation method [9][10][11][12][13][14] and asynchronous parameter estimation method [15][16][17][18][19][20][21][22][23][24]. The synchronous parameter estimation methods do not need to estimate the intermediate unmeasurable variables of the model, and the parameter estimation values are calculated directly by using mixed parameters model of the nonlinear block and the linear block, for instance, subspace method [9][10][11], direct identification algorithm [12], and over-parameter method [13,14].…”

“…The synchronous parameter estimation methods do not need to estimate the intermediate unmeasurable variables of the model, and the parameter estimation values are calculated directly by using mixed parameters model of the nonlinear block and the linear block, for instance, subspace method [9][10][11], direct identification algorithm [12], and over-parameter method [13,14]. In contrast, asynchronous parameter estimation methods are carried out for estimating separately the nonlinear block parameters and the linear block parameters through reconstructing unmeasurable variables, such as special signal methods [15,16], iterative methods [18,19], frequency domain methods [20][21][22], random algorithms [23], and separable least square methods [24].…”

Modeling and parametric identification of Hammerstein systems with time delay and asymmetric dead-zones using fractional differential equations

“…Furthermore, most approaches require the order to be commensurate which is not ideal and is practically infeasible. These limitations for FO Hammerstein model identification were overcome in [28] and [29] as low-order modeling techniques were proposed and the fractional operator represented with a generalized operational matrix through orthogonal basis functions, such as the block pulse (BPF) and Haar wavelets respectively. The fractional integral operation is converted into an algebraic expression which significantly reduces mathematical complexity.…”

An H∞ approach to data‐driven fault estimation, and isolation for Hammerstein‐Wiener systems

“…22,23 General Hammerstein-Wiener structure consists of a linear dynamic block embedded between two nonlinear blocks. 24 It effectively used to approximate most nonlinear systems such as deadzone nonlinearity, 25 backlash input nonlinearity, 26 DC/DC boost converters, 27 biological process, 28 fuel cells 29 and so forth. In this article, a new approach for fault detection and isolation for Hammerstein-Wiener systems has been developed based on subspace predictor.…”