Solutions for a three-dimensional non-linear stabilized oscillator

A system of coupled non-linear equations, describing a three-phase stabilized oscillator, is analysed by introducing ‘cyclotomic’ co-ordinates. We show that this system, under certain conditions, approaches asymptotically non-conservative linear systems; and yet it does have stabilized solutions (limit cycles). The non-linear system is solved analytically for an important class of stabilizing functions. We show that the frequency ω of our oscillator responds instantaneously to changes of certain parameters. This result has useful applications in building quickly responding novel electronic voltage-controlled oscillators.     

A method for the investigation of high-order two-frequency asynchronous oscillators

A general method for analysing asynchronous high-order two-frequency oscillators is presented. the oscillator model is made up of a GC non-linear parallel group embedded in a linear lumped time-invariant network of any order. the approach devised rests on the identification of a pair of narrow-band impedance operators which permit one to derive first-approximation steady state and dynamic equations in the phasor domain—as well as stability criteria—in a simple and expressive manner. Previous results from averaging and perturbation treatments on fourth-order asynchronous oscillators are shown to be obtainable from this theory as particular cases. the sixth-order oscillator chosen as an application example shows that computational efficiency and accuracy are among the features of the method.     

A study of amplitude‐to‐phase noise conversion in planar oscillators

This paper explores the many interesting implications for oscillator design, with optimized phase‐noise performance, deriving from a newly proposed model based on the concept of oscillator conjugacy. For the case of 2‐D (planar) oscillators, the model prominently predicts that only circuits producing a perfectly symmetric steady‐state can have zero amplitude‐to‐phase (AM‐PM) noise conversion, a so‐called zero‐state. Simulations on standard industry oscillator circuits verify all model predictions and, however, also show that these circuit classes cannot attain zero‐states except in special limit‐cases which are not practically relevant. Guided by the newly acquired design rules, we describe the synthesis of a novel 2‐D reduced‐order LC oscillator circuit which achieves several zero‐states while operating at realistic output power levels. The potential future application of this developed theoretical framework for implementation of numerical algorithms aimed at optimizing oscillator phase‐noise performance is briefly discussed.     

Development of a symmetrically stabilized four-phase oscillator and some implications

This paper treats the development of a non-linearly stabilized oscillator model which generates four sine waves in quadrature. This system is dealt with in spite of the fact that quadrature signals can be generated by a simple two-phase oscillator. the latter generates only two of the signals needed in a four-phase system. the rest of the phases signals could nevertheless be obtained by inventing the originally existing signals. It appears, however, that for certain applications the generation of all four signals in a completely cyclic and symmetrical manner (the one described here) is preferable. It is envisaged that one such application is related to recent methods of actively feeding phased array antennas, where each element in the array is connected to an appropriate oscillator phase stage. Most of the paper deals with the development of an appropriate generator model. the non-linear oscillator dynamics is treated comprehensively. the peculiar behaviour associated with the limit cycle dynamics and with other manifestations of the system dynamics is investigated. It appears from the detailed simulation work that there exist regions of initial conditions where the system solutions are expected to be relatively sensitive to initial conditions. As a result, it is believed that the system with certain additions may reveal chaotic dynamic behaviour. the realization of the system in electronic hardware is also discussed.     

Using modal series to analyze the transient response of oscillators

In this paper, a new form of Modal series is used to obtain the transient time‐domain response of oscillators. It is applicable to n‐dimensional systems and is not dependent on the existence of a small parameter in circuit's model. In addition, it provides an approximate analytical expression for the transient response instead of numerical solutions. It is valuable since the transient response of oscillators is not frequency stationary and therefore the FFT of numerical methods may not be so useful. The Colpitts oscillator is selected as a case study and a closed‐form expression for its transient response is derived which approximates the real response up to the steady state. Copyright © 2009 John Wiley & Sons, Ltd.     

Fully nonlinear oscillator noise analysis: an oscillator with no asymptotic phase

Oscillators exist in many systems. Detailed and correct characterization and comprehension of noise in autonomous systems such as oscillators is of utmost importance. Previous approaches to oscillator noise analysis are based on some kind of perturbation analysis, some linear and some nonlinear. However, the derivations of the equations for perturbation analysis are all based on information that is produced by a linearization of the oscillator equations around the periodic steady‐state solution, where it is assumed that the oscillator is orbitally stable and it has the so‐called asymptotic phase property. In this paper, we first discuss these notions from a qualitative perspective, and demonstrate that the asymptotic phase property is crucial in validating all of the previous approaches. We then present the case of a simple oscillator that is orbitally stable but without asymptotic phase, for which previous approaches fail. We then present a fully nonlinear noise analysis of this oscillator. We derive and compute nonlinear, non‐stationary and non‐Gaussian stochastic characterizations for both amplitude and phase noise. We arrive at results that are distinctly different when compared with the ones obtained previously for oscillators with asymptotic phase. We compare and verify our analytical results against extensive Monte Carlo simulations. Copyright © 2006 John Wiley & Sons, Ltd.     

基于SVPWM五相感应电机直接转矩控制研究

针对感应电机直接转矩控制(DTC)采用开关表的滞环方法时,存在电流和转矩脉动等问题,提出在DTC中应用空间矢量脉宽调制(SVPWM)的方法。根据五相感应电机模型和DTC基本原理,推导出参考电压矢量。分析了五相逆变器的空间电压矢量,并从中选取出22个有效电压矢量,根据最近四矢量SVPWM算法,计算出第k扇区中工作电压矢量的作用时间。建立了基于双DSP控制的实验系统,实验结果表明,该方法减小了电流和转矩脉动,具有良好的稳态和动态性能。     

New structures of four‐phase oscillators obtained by strongly interweaving mono‐phase limit‐cycle oscillators

The present work is a part of our effort of developing multiphase oscillators. The particular system dealt with here is that of strongly nonlinearly coupled four oscillators that form a multiphase source. Such sources possess potential applications in power electronics, in phased‐array antennas, and in modern methods of modulation and especially in demodulating multi‐phased modulated signals. The present system can be interpreted as embracing four two‐phase oscillators. Nevertheless, as a result of the strong coupling, the second state equation of each oscillator merges with the first equation of the following oscillator. The resulted four‐phase source is, therefore, represented by merely four state equations. The applications related to communications (especially those related to receivers) may be susceptible to the noise performance of the source. We believe that the presently suggested system, which relies on strong coupling of oscillators, is advantageous in its noise performance in comparison to more straightforward recently described multiphase sources, which incorporate loosely coupled oscillators. Copyright © 2007 John Wiley & Sons, Ltd.     

采用混沌振子和新相态判别法的局部放电检测

为了降低信号检测的信噪比,利用新型混沌振子作为检测工具,采用Lyapunov指数法分析动力学特性,通过提升临界混沌阈值精度减少在覆盖初始相位差方面混沌振子的使用数量。针对各主要相态判别方法的局限性,利用系统周期特点提出新相态判别法并设计仿真电路,实现相态的自动识别并记录间歇混沌状态周期。最后对单指数衰减振荡型局部放电信号进行检测。仿真结果表明,新型混沌振子动力学特性丰富,抗噪性能优越,能够实现更低的信噪比检测,新相态判别法不受过渡过程的影响,适用于任何混沌振子且具备电路实现的可行性,配合超高频传感器可以检测超高频毫伏级的变压器局部放电信号。     

Canonic coupling of oscillators in a ring

The paper deals with the phenomenon of coupling of several sinusoidal oscillators. The oscillators are arranged in a ring, and each oscillator affects its next neighbour in the ring. The coupling is unilateral and its main effect is due to variations in phase differences between neighbouring oscillators. The simple approach to the treatment of the behaviour of the coupling and the relative simplicity of the models of oscillators participating in the system enable an analytical solution of the problem to be found without a need to resort to complicated approximate methods. The results are supported by computer simulations. Several modes of dynamic behaviour of the system are identified. The number of possible modes increases with the number of oscillators in the ring. The paper concludes by demonstrating that the present results possess a potential of being useful in analysing some technological and natural systems.     

Extension of the variational equation to analog/digital circuits: numerical and experimental validation

Conventional shooting methods cannot be used to determine the steady‐state solution of circuits whose model is characterised by a vector field exhibiting zero order discontinuities. In the analysis of circuits working on a stable limit cycle, this limitation prevents the use of methods that exploit Floquet theory to compute the variational model and thus the properties of the fundamental matrix and, for example, phase noise in oscillators. In this paper, we use an improved shooting method that solves this drawback by resorting to saltation matrices and show how this method makes possible the correct computation of the first left eigenfunction (known as ppv ) of the fundamental matrix. ppv s are a key aspect in determining phase noise. The results obtained through numerical simulations are compared with measurements on a relaxation oscillator serving as a simple but significant comparison vehicle. Copyright © 2012 John Wiley & Sons, Ltd.     

Switching‐mode counterparts of the Rayleigh and Van‐der‐Pol oscillators

The present work deals with two fundamental oscillator models. One of them can be regarded as a switching‐mode counterpart of the Rayleigh oscillator, while the other can be regarded as a switching‐mode counterpart of the Van‐der‐Pol oscillator. The models are investigated by several means. Their structure is discussed by treating their circuit models. It is also shown that the related differential equations can be solved analytically and explicit forms of exact solutions are attained by employing recursive algebraic processes. The latter solutions are successfully compared to comprehensive direct simulations based on the original differential equations. Furthermore, the exhibited solutions of the switching‐mode counterparts for small and moderate values of ϵ are shown to be closely similar to the solutions of their parent oscillators. Possible applications of the present oscillatory models are discussed. It is argued that the models can favourably serve for simply representing biological and other systems that rely on oscillatory processes. Copyright © 2000 John Wiley & Sons, Ltd.     

五相集中整距绕组感应电机缺相容错控制

定子绕组开路是多相电机调速系统中的常见故障。建立了五相集中整距绕组感应电机绕组开路后的方程,计算了电机绕组开路后的稳态输出电磁转矩,分析了减小转矩脉动的条件,提出了五相电机缺相容错控制方法。此方法在无需额外增加硬件的前提下,可以保证电机继续平稳地运行。对于电机定子绕组多相同时开路,建立相应的变换矩阵、重新计算电感参数后,也可以采用提出的控制方法。对电机定子绕组一相开路进行的仿真和实验结果表明,该容错控制方法可以大大减小电机缺相运行时的转矩脉动。     

基于稳定性和电压精度协调控制的新型模糊励磁调节器

在保持比例积分微分(PID)励磁调节器优良电压调节特性的基础上,部分采取线性最优控制理论设计附加励磁调节通道,并通过一模糊控制器动态协调电压调节通道和附加调节通道的作用权重,设计了一种新型模糊励磁调节器。分析了电力系统各种典型运行状态及其对励磁调节的要求,总结了不同状态下电压和稳定的协调控制策略,以期对电压调节和增强阻尼进行动态协调。数值仿真结果表明,该新型励磁调节器在稳态时具有同PID一样高的电压调节精度,动态过程中则能明显提高系统阻尼特性,具有满意的控制效果,并对系统工况变化具有一定适应性。     

Five-Phase Interior Permanent-Magnet Motors With Low Torque Pulsation

High torque pulsation is a major disadvantage of most interior permanent-magnet (IPM) motor configurations. Choosing the proper number of stator slots and winding distribution as well as increasing number of phases are among the possible solutions for reducing torque pulsation. In this paper, five-phase IPM motor with fractional-slot stator is studied. It is shown that despite other IPM motors, the new five-phase IPM motor with fractional slot has a very low torque pulsation. For comparison purposes, a five-phase IPM motor with common configuration is also considered. It is shown that the torque pulsation of the proposed fractional-slot five-phase IPM motor is much lower than the conventional five-phase IPM motor. Nonlinear finite-element method is used to analyze different machine configurations. A prototype four-pole five-phase IPM motor with 15 stator slots has been built and is used for experimental verification     

APF中一种改进的变步长LMS自适应谐波检测算法

在有源电力滤波器(Active Power Filter, APF)的低信噪比(Signal Noise Ratio, SNR)环境下,为了提高变步长最小均方(Least Mean Square, LMS)自适应算法对谐波电流检测的跟踪速度及精度,提出改进的变步长LMS算法。该算法在MVSS-LMS算法的基础上,增加历史误差的遗忘加权和估计并控制步长更新,动态控制步长更新范围,采用滑动窗遗忘加权减小了计算复杂度。同时,对改进算法性能进行稳定性分析。实验结果表明,该算法不仅具有较快的动态响应速度,而且在APF的低信噪比情况下,稳态误差有所减小,具有较高的抗干扰能力,谐波电流检测效果较好。     

The averaging perturbation method for the dominant behaviour analysis of adiabatic single-controlled oscillators

Electrical oscillators are called single-controlled when their non-linear elements depend on a unique variable, while they are termed adiabatic when their transient operation signal can be represented as a narrowband-modulated Fourier series with only a finite number of dominant components, including the DC one. the novel method presented here allows one to analyse the dominant dynamics, steady state and dynamical stability of such oscillators. the approach devised is perturbative and is termed averaging, since it moves from the differential equation in the oscillator signal to provide a set of simultaneous differential equations in the complex envelopes of the dominant components of that variable. Owing to the treatment generality, investigable circuit topologies comprise a linear lumped time-invariant network of any order with bias sources, and any number of non-linear elements, with or without memory, with a common control variable. to illustrate the use of the method, formulae concerning a seventh-order oscillator are derived.     

State-Variable Steady State Analysis of a Phase-Controlled Cycloconverter-Induction Motor Drive

An attempt to obtain directly the steady state performance of a phase-controlled cycloconverter-induction motor system by using state-variable techniques is presented. State-variable approach is used to generate without iteration, the unique set of initial conditions which will yield the steady state solutions instead of going through the transient state as by the step-by-step method. The induction motor is represented as a two-axes model, and the cycloconverter model used is as developed in an earlier paper by the authors. A suitable digital program is evolved making simplifying assumptions, and in one approximate method of analysis suggested, initial currents are obtained without matrix inversion, thus saving computer time. Computer results of the performance of the system are presented and typical results are compared with experimental results as well as with the results obtained by other methods.     

无刷电磁弹射器中电磁力的仿真计算

设计了一个基于无刷直流直线电机的电磁弹射器模型，采用二维场仿真方法计算了模型的电磁力静态特性曲线，分析了结构参数如气隙长度，磁钢厚度，铁磁材料特性等对电磁力特性的影响，该分析对模型的设计具有重要的指导意义。     

Improved switching mode oscillators employing generalized switching lines

The present work proposes an unusual method for controlling the activation of the switches of switching mode oscillators. The proposed method is in fact a tool for developing switching mode oscillators that are controlled by full variable feedback. The methods developed in the present article rely on characterizing the switching procedure by intentionally moulding the related switching line (the switching line is the line in the state space, where the switches change polarity). The switching line in most of the switching mode oscillators is relatively simple. For example, in many cases the switch changes state in accordance with the output current sign. Hence, the line ‘output current’ is zero, is the switching line in this case. Relatively many advantages are attained by the present moulding of the switching line. For example, oscillators that oscillate even with very low‐quality factor (large load) are obtainable. The proposed method enables a simple way for controlling the output voltage and the frequency of the switching mode oscillator. Furthermore, current limiter property of the oscillator output can be obtained by the method, even in cases where the original oscillator is inherently a voltage source. The output impedance is also made controllable by the method. The successfully improved characteristics are demonstrated by investigating a particular structure, namely, a switching mode series resonant oscillator. Copyright © 2000 John Wiley & Sons, Ltd.