Washout Controller Research Articles

Dynamic response of the e-HR neuron model under electromagnetic induction

Due to the fluctuation of membrane potential of neuron, there are complex time-varying electromagnetic fields in nervous systems, and the exciting electromagnetic field will further regulate the discharge activities of neurons. In this paper, the coupling of magnetic flux variables to the membrane potential is realised by using a magnetron memristor, and then a 5D extended Hindmarsh–Rose (e-HR) neuron model is established. With the help of Matcont software, the distribution and bifurcation properties of the equilibrium point in the e-HR model is analysed. It is found that there are subcritical Hopf bifurcation, coexisting oscillation modes and hidden limit cycle attractors with period 1 and period 2. In addition, by applying the washout controller, the subcritical Hopf bifurcation point can be transformed into the supercritical Hopf bifurcation point. Thus, the hidden oscillation behaviour of the model can be effectively eliminated. In order to analyse the influence of various parameters on the bifurcation behaviour, numerical simulation of two-parameter bifurcation, single-parameter bifurcation, maximum Lyapunov exponential and time response are given. It is found that the e-HR neuron has a complex bifurcation structure, i.e., the bifurcation structure with period-doubling bifurcations, inverse period-doubling bifurcations, period-adding bifurcations with and without chaos. At the same time, the study also finds that the coexistence behaviour of the periodic cluster discharge and the mixed-mode oscillations (MMOs) can be observed from the bifurcation structure with unique ‘periodic dislocation layer’ on the two-parameter plane. Interestingly, the bursting mode of the system is converted into MMOs when the system parameters are randomly perturbed. The results of this study provide useful insights into the complex discharge patterns and hidden discharge behaviours of neurons under electromagnetic induction.

The hidden, period-adding, mixed-mode oscillations and control in a HR neuron under electromagnetic induction

Abstract Researching the discharge patterns of neurons under electromagnetic induction is of great practical significance for understanding the complex nervous system. In this paper, the discharge patterns of a HR neuron under electromagnetic induction(here called magnetic flux HR neuron system), including hidden, period-adding, mixed-mode oscillations and their control are researched by combining theoretical analysis and numerical simulations. Firstly, the distribution and stability of the equilibrium point in the magnetic flux HR neuron system is theoretical analyzed based on the Matcont software, and it is found that there are one supercritical and two subcritical Hopf bifurcation points. Through further analysis, the hidden limit cycle attractor and its existence range are shown near the subcritical Hopf bifurcation points. Then, the complex period-adding, mixed-mode and coexistence oscillations are simulated and analyzed in the two-parameter space. In the following, the stability control of subcritical Hopf bifurcation is realized by using the Washout controller, and the undesirable hidden discharge behavior is eliminated. At last, the Hamilton energy feedback controller is designed to control the mixed-mode oscillation of the membrane voltage to desired discharge states effectively, and the energy transform can also be detected in the control process. The results provide useful research for understanding the discharge pattern of the magnetic flux HR neuron and controlling membrane voltage transfer.

Dynamic expression of a HR neuron model under an electric field

The movement of large amounts of ions (e.g., potassium, sodium and calcium) in the nervous system triggers time-varying electromagnetic fields that further regulate the firing activity of neurons. Accordingly, the discharge states of a modified Hindmarsh–Rose (HR) neuron model under an electric field are studied by numerical simulation. By using the Matcont software package and its programming, the global basins of attraction for the model are analyzed, and it is found that the model has a coexistence oscillation pattern and hidden discharge behavior caused by subcritical Hopf bifurcation. Furthermore, the model’s unstable branches are effectively controlled based on the Washout controller and eliminating the hidden discharge states. Interestingly, by analyzing the two-parametric bifurcation analysis, we also find that the model generally has a comb-shaped chaotic structure and a periodic-adding bifurcation pattern. Additionally, considering that the electric field is inevitably disturbed periodically, the discharge states of this model are more complex and have abundant coexisting oscillation modes. The research results will provide a useful reference for understanding the complex dynamic characteristics of neurons under an electric field.

Dynamic response and control of neuros based on electromagnetic field theory

The time-varying electric fields generated by continuously pumping and transmitting calcium, potassium and sodium ions in cells not only affect the discharge activity of neurons, but also induce time-varying magnetic fields to further regulate the fluctuation of ions. According to the Maxwell's electromagnetic field theory, time-varying electric field and magnetic field can stimulate each other in the electrophysiological environment inside and outside the cells to produce electromagnetic field. In order to explore the discharge rhythm transition of neurons under the influence of electromagnetic fields, a five-dimensional (5D) HR neuron model (EMFN model for short) is established by introducing magnetic flux variable and electric field variable into a three-dimensional (3D) Hindmarsh-Rose (HR) neuron model. Firstly, the equilibrium distribution and global bifurcation properties of EMFN model are analyzed by Matcont software, then the existence of subcritical Hopf bifurcation, hidden discharge, coexistence of periodic discharge and resting state are found and analyzed. Secondly, by using the tools of two-parameter and one-parameter bifurcation, ISI bifurcation and the maximum Lyapunov exponent for numerical simulation, the period-adding bifurcation with and without chaos, mixed mode discharge and coexistence mode discharge in the EMFN model are analyzed in detail. At the same time, the transition law of discharge rhythm with the influence of electric field and magnetic field intensity is revealed. Finally, the Washout controller is used to convert the subcritical Hopf bifurcation into supercritical Hopf bifurcation, so the topological structure of EMFN model near the bifurcation point is changed for eliminating the hidden discharge. The research results of this paper confirm that the novel neuron model has rich discharge rhythm, which will affect the information transmission and coding, and provide some ideas for improving the neuron models, revealing the influence of electromagnetic field on biological nervous system, and exploring the pathogenic mechanism of some neurological diseases.

Control of Hopf Bifurcation in Autonomous System Based on Washout Filter

In order to further understand a Lorenz-like system, we study the stability of the equilibrium points and the existence of Hopf bifurcation by center manifold theorem and normal form theory. More precisely, we designed a washout controller such that the equilibriumE0undergoes a controllable Hopf bifurcation, and by adjusting the controller parameters, we delayed Hopf bifurcation phenomenon of the equilibriumE+. Besides, numerical simulation is given to illustrate the theoretical analysis. Finally, two possible electronic circuits are given to realize the uncontrolled and the controlled systems.

1P1-F06 センサドリフトの影響を受けない倒立振子型輸送ロボットの開発(車輪型/クローラ型移動ロボット(3))

We consider a stabilization problem of an inverted pendulum transport robot. The inverted pendulum robot can not balance for a long time when a sensor drift occurs. In previous research, it is investigated that steady-state blocking zeros of the stabilizing controller play an important role. Such a controller is called a washout controller. In this paper, we have illustrated the effectiveness of the proposed washout control method by the practical experiment which is the system of an inverted pendulum robot with a sensor drift in the output signals.

Washout Control for Manual Operations

It is known that limitations of human accuracy in manual manipulation hinder the quality of work performed by human operators of manual control systems. Indeed, movements of operators are apt to cause undesirable vibrations in manual control systems. In this paper, we propose a new operator-support control scheme for suppressing harmful oscillatory motions in such systems without disturbing human operator's manipulation. The proposed scheme is based on the fact that steady-state blocking zeros of a feedback controller do not affect the steady-state control input. A finite-dimensional feedback controller with steady-state blocking zeros, called a washout controller in this paper, plays the central role in support for operator's manipulation. However, the dynamics of a manual control system may become different significantly from its initial model used for the design of an initial washout controller when it is applied to the manual control system. Such difference can result in poor performance of operator-support control. In order to improve it, an iterative procedure is presented for redesign of washout controllers based on closed-loop subspace identification. Closed-loop identification is performed to refine the model for the control design, and then a more sophisticated washout controller is obtained using the identified model. The effectiveness of the proposed scheme is demonstrated by an experiment on manual control of an inverted pendulum.