Feedback systems with memristors

2016

It is observed that the inductive and capacitive features of the memristor reflect (and are a quintessence of) such features of any resistor. The very presence of the voltage and current state variables, associated by their electrodynamics sense with electrical and magnetic fields, in the resistive characteristic v = f(i), forces any resister to accumulate some magnetic and electrostatic fields and energies around itself, i.e. L and C elements are always present. From the circuit-theoretic point of view, the role of the memristor is seen, first of all, in the elimination of the use of a unique v(i). This makes circuits with hysteresis characteristics relevant, and also suggests that the concept of memristor should influence the basic problem of definition of nonlinearity. Since the memristor mainly originates from the resistor, it was found necessary to overview some unusual cases of resistive circuits. The present opinion is that the framework of basic circuit theory and its connec...

2010

The conception of memristor as the fourth fundamental component in circuit theory, creates a new approach in nonlinear circuit design. In this paper the complex dynamics of Chua's canonical circuit implemented by using a memristor instead of the nonlinear resistor, was studied. The proposed memristor is a flux-controlled one, described by the function W(φ) = dq(φ) dφ , where q(φ) is a cubic function. Computer simulation of the dynamic behaviour of a Chua circuit incorporating a memristor, confirmed very important phenomena concerning Chaos Theory, such us, the great sensitivity of circuit behavior on initial conditions, the route to chaos through the mechanism of period doubling, as well as antimonotonicity.

research.ijcaonline.org

Memristive System is a class on non-linear systems with very interesting properties. It is considered to be the fourth basic circuit element like Resistors, Capacitors and Inductors. Till date most of the works on memristive systems concentrated on its applications in the field of designing super dense non volatile memory, crossbar latches, neural networks, modeling of neural synapses, nonlinear oscillators and filters. Much less work has been done in its use in the field of control theory. This paper presents groundwork in the field of using Memristive Systems for control purposes.

ArXiv, 2014

It is noticed that the inductive and capacitive features of the memristor reflect (and are a quintessence of) such features of any resistor. The very presence in the resistive characteristic v = f(i) of the voltage and current state variables, associated by their electrodynamics sense with electrical and magnetic fields, forces any resister to cause to accumulate some magnetic and electrostatic fields and energies around itself. The present version is strongly extended in the sense of the circuit theory discussion.

2021

In this paper we revisit the memristor concept within circuit theory. We start from the definition of the basic circuit elements, then we introduce the original formulation of the memristor concept and summarize some of the controversies on its nature. We also point out the ambiguities resulting from a non rigorous usage of the flux linkage concept. After concluding that the memristor is not a fourth basic circuit element, prompted by recent claims in the memristor literature, we look into the application of the memristor concept to electrophysiology, realizing that an approach suitable to explain the observed inductive behavior of the giant squid axon had already been developed in the 1960s, with the introduction of “time-variant resistors.” We also discuss a recent memristor implementation in which the magnetic flux plays a direct role, concluding that it cannot strictly qualify as a memristor, because its v − i curve cannot exactly pinch at the origin. Finally, we present numeric...

2010

Since the fourth fundamental element (Memristor) became a reality by HP labs, and due to its huge potential, its mathematical models became a necessity. In this paper, we provide a simple mathematical model of Memristors characterized by linear dopant drift for sinusoidal input voltage, showing a high matching with the nonlinear SPICE simulations. The frequency response of the Memristor's resistance and its bounding conditions are derived. The fundamentals of the pinched i-v hysteresis, such as the critical resistances, the hysteresis power and the maximum operating current, are derived for the first time.

DESCRIPTION Typically electronics has been defined in terms of three fundamental elements such as resistors, capacitors and inductors. These three elements are used to define the four fundamental circuit variables which are electric current, voltage, charge and magnetic flux. Resistors are used to relate current to voltage, capacitors to relate voltage to charge, and inductors to relate current to magnetic flux, but there was no element which could relate charge to magnetic flux. To overcome this missing link, scientists came up with a new element called Memristor. These Memristor has the properties of both a memory element and a resistor (hence wisely named as Memristor). Memristor is being called as the fourth fundamental component, hence increasing the importance of its innovation. Its innovators say ―memrisrors are so significant that it would be mandatory to re-write the existing electronics engineering textbooks.‖

2018

The memory resistor abbreviated memristor was a harmless postulate in 1971. In the decade since 2008, a device claiming to be the missing memristor is on the prowl, seeking recognition as a fundamental circuit element, sometimes wanting electronics textbooks to be rewritten, always promising remarkable digital, analog and neuromorphic computing possibilities. A systematic discussion about the fundamental nature of the device is almost universally absent. This report investigates the assertion that the memristor is a fundamental passive circuit element, from the perspective that electrical engineering is the science of charge management. With a periodic table of fundamental elements, we demonstrate that there can only be three fundamental passive circuit elements. The ideal memristor is shown to be an unphysical active device. A vacancy transport model further reveals that a physically realizable memristor is a nonlinear composition of two resistors with active hysteresis.

International journal of engineering research and technology, 2014

In this paper, for the first time, we propose a stability controller based on a new electrical element "Memristor" which will not only improve the system stability and performance, but also maintain that stability for a longer time, irrespective of different perturbation factors. Memristor changes its resistance on changing voltage or current through it which makes our proposed stability controller more flexible, compared to traditional stability controller. To illustrate this, a highly unstable Maglev train model is taken as an example which demands continuous stability for a long duration. The output results are demonstrated by simulation results and are verified by mathematical reasoning to support the unusual and unexpected characteristics.