Generalized Hammerstein Model Research Articles

Measurements and Modeling of the Nonlinear Behavior of a Guitar Pickup at Low Frequencies †

Description of the physical behavior of electric guitars is still not very widespread in the scientific literature. In particular, the physical models describing a nonlinear behavior of pickups still requires some refinements. The study presented in this paper is focused on nonlinear modeling of the pickups. Two main issues are raised. First, is the currently most used nonlinear model (a Hammerstein model) sufficient for the complex nonlinear behavior of the pickup? In other words, would a more complex model, such as a Generalized Hammerstein that can deal better with the nonlinear memory, yield better results? The second troublesome issue is how to measure the nonlinear behavior of a pickup correctly. A specific experimental set-up allowing for driving the pickup in a controlled way (string displacement perpendicular to the pickup) and to separate the nonlinear model of the pickup from other nonlinearities in the measurement chain is proposed. Thanks to this experimental set-up, a Generalized Hammerstein model of the pickup is estimated for frequency range 15–500 Hz and the results are compared with a simple Hammerstein model. A comparison with experimental results shows that both models succeed in describing the pickup when used in realistic conditions.

Nonparametric Identification of Nonlinear Systems in Series

In this paper, a method allowing the identification of two nonlinear systems in series is presented. More precisely, the identification of the second nonlinear subsystem under test is achieved by taking into account the effects of the nonlinearities of the first subsystem. The method is based on the estimation of the Higher Harmonic Frequency Responses (HHFRs) from the measurement of distorted input and output signals. The second nonlinear system is then modeled by non-parametric generalized Hammerstein model made up of power series associated with linear filters. The method is experimentally validated in the well-known framework of nonlinear propagation of acoustic waves.

Constrained Model Algorithmic Control for the Generalized Hammerstein Model with Impulse Response

A Generalized Hammerstein Model with Impulse Response for symmetric nonlinear systems was presented in this paper. A hyper-quadratic object function was developed by adding highest order control input term with a symbolic function into the object function, and a constrained multi-step model algorithmic control for the non-minimum phase systems with open-loop stable characterization was established by forcing the control input with saturated limitation. The algorithm with one control policy can guarantee the simulative results without steady state deviation and the control input being converged to a varying region centered in the zero-point. Simulated results validated the constrained model algorithmic control for Generalized Hammerstein Model with impulse response is reasonable and applicable.

Identification of an additive nonlinear system and its applications in generalized Hammerstein models

An identification algorithm is developed for a class of nonlinear systems that are multi-input and multi-output in an additive form. The convergence results are achieved and its applications to identification of a generalized Hammerstein system is also discussed.

Modelling and Control of Multivariable Processes Using Generalized Hammerstein Model

In this paper, a generalized Hammerstein model consisting of a static polynomial function in series with time-varying linear model is proposed in order to model the Hammerstein-like multivariable processes whose linear dynamics vary over the operating space. An iteration procedure is proposed to identify the generalized Hammerstein model by using the just-in-time learning (JITL) technique. Unlike the conventional Hammerstein model, only the static nonlinear part of generalized Hammerstein model, thus identified is retained in its subsequent application in controller design. Consequently, the on-line use of proposed model requires the identification of linear model by using the JITL technique and current process data. An adaptive decentralized PID control strategy based on the proposed model is also developed. The controller parameters are adjusted on-line by using the gradient descent algorithm and information provided by the JITL. Simulation results show that the proposed methods have better prediction accuracy and control performance than those achieved by the conventional Hammerstein model and its associated adaptive decentralized PID controller design, respectively.

Non-parametric identification of generalized Hammerstein models

The Hammerstein model is considered in a generalized form, where its nonlinear element can have multi-inputs and a finite memory. The identification of the multi-input finite memory nonimearity and the impulse response sequence of the model is treated using a non-parametric approach. A numerical example is given. The identification results of the example illustrate the effectiveness of the developed technique.

A Self-tuning Extremal Controller for the Generalized Hammerstein Model

A self-tuning extremal controller is presented which provides to find the extremum and to maintain it with minimum variance using the generalized Hammerstein model as the approximate description of a nonlinear dynamic process. A simulation example is given to illustrate the work of the new regulator.