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Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method

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Chinese Physics B 2018年第4期27卷 551-558页

作者： Yao Xu Chun-Hui Zhang Ernst Niebur Jun-Song Wang School of Biomedical Engineering Tianjin Medical University Tianjin 300070 China Qingdao Stomatological Hospital Department of Medical Technology Equipment Qingdao 266001 China Zanvyl Krieger Mind/Brain Institute and Solomon Snyder Department of Neuroscience Johns Hopkins University Baltimore 21218 MD USA

Spontaneous alpha oscillations are a ubiquitous phenomenon in the brain and play a key role in neural information processing and various cognitive ***＇s neural mass model（NMM） was initially proposed to study the origin of alpha *** of previous studies of the spontaneous alpha oscillations in the NMM were conducted using numerical *** this study,we aim to propose an analytical approach using the describing function method to elucidate the spontaneous alpha oscillation mechanism in the ***,the sigmoid nonlinear function in the NMM is approximated by its describing function,allowing us to reformulate the NMM and derive its standard form composed of one nonlinear part and one linear ***,by conducting a theoretical analysis,we can assess whether or not the spontaneous alpha oscillation would occur in the NMM and,furthermore,accurately determine its amplitude and *** results reveal analytically that the interaction between linearity and nonlinearity of the NMM plays a key role in generating the spontaneous alpha ***,strong nonlinearity and large linear strength are required to generate the spontaneous alpha oscillations.

关键词： neural mass model spontaneous alpha oscillation describing function

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Analysis of Synchronization of n Metronomes on a Hanging Plate via describing function Method without Assumption on Amplitudes of Metronomes 36

Analysis of Synchronization of n Metronomes on a Hanging Pla...

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第36届中国控制会议

作者： Xin Xin Yoshinori Muraoka Shinsaku Izumi Taiga Yamasaki Faculty of Computer Science and Systems Engineering Okayama Prefectural University

ISBN: (纸本)9781538629185

This paper aims to analyze the synchronization phenomena in the system consisting of n identical metronomes on a hanging plate by using the describing function（DF） method, which deals with the driving torque as a discontinuous function of the angle and angular velocity of each metronome. Different from a previous study on the synchronization of the system with the first harmonic of the angle of each metronome having the same amplitude, this paper analyzes the synchronization without any assumption on the amplitudes of n metronomes. By investigating the relation between the motion of the hanging plate（common base） and n metronomes, this paper characterizes the synchronization phenomena by the following two types of synchronization:One is the inherent synchronization, whose frequency and amplitude of all synchronized metronomes are the same as those of a single metronome on a fixed base. The other is the non-inherent synchronization, which includes the in-phase synchronization with the same amplitude, and the synchronization with different amplitudes. The analytical results are validated by numerical simulation for three metronomes about the synchronization with the same or different amplitudes.

关键词： Synchronization metronomes pendulum clocks describing function phasor representation

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Dynamic model identification of a real-time simple level control system

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Journal of Control and Decision 2016年第4期3卷 248-266页

作者： Prasenjit Ghorai Somanath Majhi Saurabh Pandey Department of Electronics and Instrumentation Engineering National Institute of Technology AgartalaTripuraIndia Department of Electronics and Electrical Engineering Indian Institute of Technology GuwahatiAssamIndia

Using a relay feedback approach,mathematical expressions for identification of real-time level control system in transfer function form are proposed in this *** ideal relay with hysteresis is feedback to a simple level control system for the generation of sustained ***,limit cycle information is utilised in deduced expressions for the estimation of unknown system *** describing function analysis,the gain of an ideal relay with hysteresis is approximated to yield simple mathematical *** examples from literature are considered to show the effectiveness of the proposed identification *** distributed control system:CENTUM CS 3000 is considered as a platform for the realisation of both relay feedback and Ziegler-Nichols(ZN)*** accuracy of derived transfer function models is compared with a model derived from ZN method and thereafter demonstrated through frequency response plots which illustrate the experimental validation of the identified real-time process model.

关键词： describing function level control system limit cycle process identification and relay feedback

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Prevention of Limit Cycle for Nonlinear Control Systems with Parametric Uncertainties

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第二十六届中国控制会议

作者： Wang Yuan-Jay Hsi Shu-I Yen Ting-Ju Liang Chih-Chung Department of Electrical Engineering Tung Nan Institute of Technology

ISBN: (纸本)7900719229

A new method is proposed to synthesize robust stabilizing controllers for preventing the generation of limit cycle of control systems with parametric uncertainties both in the linear plant and *** for the generation of limit cycle and boundaries for asymptotic stability are *** region for prescribed limit cycle behavior and the region for asymptotic stability are *** overlapped region of the admissible parameter region for each Kharitonov polynomial is called the Kharitonov *** Kharitonov region constitutes all of the feasible controller gain sets to achieve robust prevention of limit ***,two illustrative examples are given.

关键词： Limit cycle describing function stability equation method Kharitonov theorem

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Exact Dynamic Modeling of PWM DC-to-DC Power Converters—Part I: Continuous Conduction Mode

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Journal of Power and Energy Engineering 2021年第5期9卷 26-47页

作者： Justin Simmons Richard Tymerski Maseeh College of Engineering and Computer Science Portland State University Portland USA

A general approach is presented by which the exact frequency response of any transfer function of switched linear networks can be determined. This is achieved with a describing function approach using a state space equation formulation. This work presents a somewhat simplified set of equations to one previously given by one of the authors. To demonstrate application of the general formulation, the frequency responses of switched networks used as PWM DC-to-DC converters operating in continuous conduction mode (CCM) under voltage mode control are derived. (The accompanying paper, Part II, will present results for converters operating in discontinuous conduction mode (DCM)). From the general sets of equations developed here, both the control to output and input source variation to output frequency responses are derived. The describing function approach enables exact frequency response determination, even at high frequencies where the accuracy using average models may be compromised. Confirmation of the accuracy of the derived models is provided by comparing the responses with those obtained using the commercial simulator PSIM on a PWM boost converter. The magnitude and phase responses are shown to match perfectly over the full range of frequencies up to close to half the switching frequency. Matlab code that implements the models is given such that the user can easily adapt for use with other PWM converter topologies.

关键词： describing function DC-to-DC Switching Power Converter Small-Signal Modeling Frequency Response

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Exact Dynamic Modeling of PWM DC-to-DC Power Converters—Part II: Discontinuous Conduction Mode

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Journal of Power and Energy Engineering 2021年第5期9卷 48-62页

作者： Justin Simmons Richard Tymerski Maseeh College of Engineering and Computer Science Portland State University Portland USA

This paper follows on from the first paper, Part I, where a general formulation of a describing function approach to frequency response determination of switched linear networks, such as PWM converters, was simplified and updated. The models assume a piecewise linear state space equation description of the system and results in a closed form solution for the sought after frequency response. In Part I, model derivation was demonstrated for the case of PWM converters operating in the continuous conduction mode (CCM). This operating mode does not feature any state dependent switching times. In this paper, Part II, frequency response models for any transfer function for PWM converters operating in discontinuous conduction mode (DCM) are derived based on the theory presented in Part I. This operating model features state dependent switching times. The describing function models developed are exact and therefore, in terms of accuracy, are to be preferred over averaged models which are widely used. The example of a boost dc-to-dc converter operating in DCM is simulated to obtain the control to output and input to output frequency responses and are compared with the models derived here. Excellent agreement between the simulated and model responses was found. Matlab code implementing the analytical models is also presented which the user can adapt for any other PWM converter topology. The models derived here may be used as a basis from which simplified models may be derived while still preserving required accuracy.

关键词： describing function DC-to-DC Switching Power Converter Small-Signal Modeling Frequency Response

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