Behavioral Modeling of Memristor-Based Rectifier Bridge

Elena Solovyeva,Steffen Schulze,Hanna Harchuk

doi:10.3390/app11072908

Elena Solovyeva, Steffen Schulze + Show 1 more

Open Access

https://doi.org/10.3390/app11072908

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Abstract

In electrical engineering, radio engineering, robotics, computing, control systems, etc., a lot of nonlinear devices are synthesized on the basis of a nanoelement named memristor that possesses a number of useful properties, such as passivity, nonlinearity, high variability of parameters, nonvolatility, compactness. The efficiency of this electric element has led to the emergence of many memristor technologies based on different physical principles and, as a result, to the occurrence of different mathematical models describing these principles. A general approach to the modeling of memristive devices is represented. The essence is to construct a behavioral model that approximates nonlinear mapping of the input signal set into the output signal set. The polynomials of split signals, which are adaptive to the class of input signals, are used. This adaptation leads to the model’s simplification important in practice. Multi-dimensional polynomials of split signals are built for the rectifier bridge at harmonic input signals. The modeling error is estimated in the mean-square norm. It is shown that the accuracy of the modeling is increased in the case of using the piecewise polynomial with split signals.

Highlights

The element base for the designing of nonlinear dynamic devices is changed due to the emergence of elements with new properties and technologies for their creation.More and more devices are synthesized based on memristors or memristive structures [1,2,3,4].This process results from the effective characteristics of a memristor as a passive electrotechnical element
The way of overcoming the mentioned challenges is the modeling of memristors and memristor-based devices on the input/output approach, which proposes to build a behavioral model on using the assigned sets of the input and output signals of a device represented as a nonlinear dynamic system
As the analysis of expression (11) shows, the presented polynomial is two-dimensional for any degree, its basis functions are the samples of the input signal at the current and previous time instants

Summary

Introduction

The element base for the designing of nonlinear dynamic devices is changed due to the emergence of elements with new properties and technologies for their creation. The way of overcoming the mentioned challenges is the modeling of memristors and memristor-based devices on the input/output approach, which proposes to build a behavioral model on using the assigned sets of the input and output signals of a device represented as a nonlinear dynamic system According to this approach the device is considered to be a «black box» and we construct its general mathematical model without taking into account the internal parts of the device. This model obtains unique global optimum parameters resulting from approximating the operator of a nonlinear dynamic system in the mean-square norm that is superior to neural networks when we determine a lot of local optimum parameters. Multi-dimensional split polynomial has advantages over other mentioned models, which ensure its success in modeling of nonlinear dynamic systems including different memristor-based devices. Play an important role. based on physical considerations [48,49,50,51,52,53] play an important role

Multi-Dimensional Split Polynomial as a Behavioral Nonlinear Model

Forming the Sets of Input and Output Signals of the Memristor-Based

Smoothing Output Signals of the Memristor-Based Rectifier Bridge

Results of the Rectifier Modeling Based on Multi-Dimensional Polynomials

Conclusions