Impulsive control of permanent magnet synchronous motors with parameters uncertainties

The permanent magnet synchronous motors (PMSMs) may have chaotic behaviours for the uncertain values of parameters or under certain working conditions, which threatens the secure and stable operation of motor-driven. It is important to study methods of controlling or suppressing chaos in PMSMs. In this paper, robust stabilities of PMSM with parameter uncertainties are investigated. After the uncertain matrices which represent the variable system parameters are formulated through matrix analysis, a novel asymptotical stability criterion is established. Some illustrated examples are also given to show the effectiveness of the obtained results.     

参数不确定永磁同步电机混沌的模糊控制

通过Takagi-Sugen控制技术,建立了参数不确定永磁同步电机的Takagi-Sugen模糊控制模型,然后利用矩阵分析和Lyapunov稳定性理论,得到了参数不确定永磁同步电机渐进稳定的充分条件,最后通过实例证实了结果的正确性,相比传统的模糊控制方法,基于Takagi-Sugen模型的模糊控制方法具有一定的优越性. 关键词： 混沌控制 Takagi-Sugen模型 模糊控制 永磁同步电机     

Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory

This paper reports that the performance of permanent magnet synchronous motor (PMSM) degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system's security operation.     

Robust exponential stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters

This Letter is concerned with delay-dependent robust exponential mean square stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters. Time delays here are discrete and distributed time-varying delays. Based on Lyapunov-Krasovskii stability theory, delay-dependent stability conditions are derived in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

Adaptive synchronization of Rossler and Chen chaotic systems

A novel adaptive synchronization method is proposed for two identical Rossler and Chen systems with uncertain parameters. Based on Lyapunov stability theory, we derive an adaptive controller without the knowledge of the system parameters, which can make the states of two identical Rossler and Chen systems globally asymptotically synchronized. Especially, when some unknown uncertain parameters are positive, we can make the controller more simple and, besides, the controller is independent of those positive uncertain parameters. All results are proved using a well-known Lyapunov stability theorem. Numerical simulations are given to validate the proposed synchronization approach.     

Chaos in complex motor networks induced by Newmanben Watts small-world connections

We investigate how dynamical behaviours of complex motor networks depend on the Newman-Watts small-world (NWSW) connections. Network elements are described by the permanent magnet synchronous motor (PMSM) with the values of parameters at which each individual PMSM is stable. It is found that with the increase of connection probability p, the motor in networks becomes periodic and falls into chaotic motion as p further increases. These phenomena imply that NWSW connections can induce and enhance chaos in motor networks. The possible mechanism behind the action of NWSW connections is addressed based on stability theory.     

Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems

We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional(2D) systems.The mathematical model of the discrete-time 2D system is established upon the well-known Roesser model,and the uncertainty phenomenon,which appears typically in practical environments,is modeled by a convex bounded(polytope type) uncertain domain.The stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the Lyapunov stability theory.In the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques.Moreover,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,numerical examples are given to demonstrate the effectiveness of the obtained results.     

Brake squeal reduction of vehicle disc brake system with interval parameters by uncertain optimization

An uncertain optimization method for brake squeal reduction of vehicle disc brake system with interval parameters is presented in this paper. In the proposed method, the parameters of frictional coefficient, material properties and the thicknesses of wearing components are treated as uncertain parameters, which are described as interval variables. Attention is focused on the stability analysis of a brake system in squeal, and the stability of brake system is investigated via the complex eigenvalue analysis (CEA) method. The dominant unstable mode is extracted by performing CEA based on a linear finite element (FE) model, and the negative damping ratio corresponding to the dominant unstable mode is selected as the indicator of instability. The response surface method (RSM) is applied to approximate the implicit relationship between the unstable mode and the system parameters. A reliability-based optimization model for improving the stability of the vehicle disc brake system with interval parameters is constructed based on RSM, interval analysis and reliability analysis. The Genetic Algorithm is used to get the optimal values of design parameters from the optimization model. The stability analysis and optimization of a disc brake system are carried out, and the results show that brake squeal propensity can be reduced by using stiffer back plates. The proposed approach can be used to improve the stability of the vehicle disc brake system with uncertain parameters effectively.     

Fractional-order permanent magnet synchronous motor and its adaptive chaotic control

In this paper we investigate the chaotic behaviors of the fractional-order permanent magnet synchronous motor(PMSM).The necessary condition for the existence of chaos in the fractional-order PMSM is deduced.And an adaptivefeedback controller is developed based on the stability theory for fractional systems.The presented control scheme,which contains only one single state variable,is simple and flexible,and it is suitable both for design and for implementation in practice.Simulation is carried out to verify that the obtained scheme is efficient and robust against external interference for controlling the fractional-order PMSM system.     

基于线性反馈控制的不确定混沌系统的参数辨识

基于线性反馈控制方法和Lyapunov稳定性理论,研究了参数不确定系统的混沌同步和参数辨识,设计了普遍适用的参数自适应控制律,理论证明设计的控制器可使得两个结构相同但参数不同的混沌系统渐近地达到同步,并且可以辨识出响应系统的未知参数. Lorenz系统和蔡氏电路的数值仿真进一步表明了该方法的有效性. 关键词： 不确定混沌系统 同步 参数辨识 Lyapunov函数     

Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays

This Letter is concerned with stability analysis problem for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov-Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI) and by introducing some free-weighting matrices. Finally, two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.     

Robust H_∞ control for uncertain Markovian jump systems with mixed delays

We scrutinize the problem of robust H∞control for a class of Markovian jump uncertain systems with interval timevarying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H∞control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov–Krasovskii functional(LKF), sufficient conditions for delay-dependent robust H∞control criteria are obtained in terms of linear matrix inequalities(LMIs). The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.     

Interval analysis of transient temperature field with uncertain-but-bounded parameters

Based on the traditional finite volume method, a new numerical technique is presented for the transient temperature field prediction with interval uncertainties in both the physical parameters and initial/boundary conditions. New stability theory applicable to interval discrete schemes is developed. Interval ranges of the uncertain temperature field can be approximately yielded by two kinds of parameter perturbation methods. Different order Neumann series are adopted to approximate the interval matrix inverse. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed model and methods.     

Mean square exponential stability of uncertain stochastic delayed neural networks

This Letter concerns with the mean square exponential stability of uncertain stochastic delayed neural networks. By applying Lyapunov functional method, new delay-dependent/independent mean square exponential stability criteria are derived in terms of linear matrix inequalities. Two examples are presented which show our result are less conservative than the existing stability criteria.     

基于微分几何方法的永磁同步电动机的混沌运动的控制

永磁同步电动机(PMSM)在某些参数及工作条件下会出现混沌运动，这将危及电机传动系统的稳定运行，因此如何抑制或消除PMSM中的混沌成为保持其稳定性的关键问题.利用微分几何控制理论，首先从解析上推导出PMSM混沌运动控制律的表达式，然后对控制过程进行仿真.理论分析及数值仿真结果表明：该控制策略不仅行之有效，而且相对其他控制方法具有一定的优越性.研究结果对保证电机传动系统的稳定运行具有较好的参考价值. 关键词： 混沌控制 微分几何 准确线性化 永磁同步电动机     

不确定Chua’s电路的参数辨识与自适应同步

针对含有不确定参数的Chua’s电路,提出一种仅需传递单路信号实现混沌自适应同步的方法. 基于Lyapunov稳定性理论证明了该方法可使得两个Chua系统——驱动系统和未知参数的响应系统渐近地达到同步,并且可以辨识出响应系统的未知参数. 数值计算结果表明了该方法的有效性. 关键词： 不确定Chua’s电路 混沌同步 参数辨识 Lyapunov函数     

参数不确定量子细胞神经网络与Lorenz超混沌系统的函数投影同步研究

研究了具有不确定参数的量子细胞神经网络系统与Lorenz超混沌系统的函数投影同步.设计了自适应追踪控制器来实现两个不同系统渐进同步到已知的比例函数,并运用Lyapunov稳定性方法进行了证明.理论分析了量子细胞神经网络系统不确定参数的系数向量线性无关性,实现了不确定参数的识别和估计.数值仿真结果验证了函数投影同步和参数估计的有效性.     

Nonlinear Dynamics of Permanent-magnet Synchronous Motor with v/f Control

The nonlinear dynamics of permanent-magnet synchronous motor(PMSM) with v/f control signals is investigated intensively.First,the equilibria and steady-state characteristics of the system are formulated by analytical analysis.Then,some of its basic dynamical properties,such as characteristic eigenvalues,Lyapunov exponents and phase trajectories are studied by varying the values of system parameters.It is found that when the values of the system parameters are smaller,the PMSM operates in stable domains,no matter what the values of control gains are.With the values of parameters increasing,the unstability appears and PMSM falls into chaotic operation.Furthermore,the complex dynamic behaviors are verified by means of simulation.     

带有未知非对称控制增益的不确定分数阶混沌系统自适应模糊同步控制

针对带有非对称控制增益的不确定分数阶混沌系统的同步问题设计了模糊自适应控制器. 模糊逻辑系统用来逼近未知的非线性函数, 非对称的控制增益矩阵被分解为一个未知的正定矩阵、一个对角线上元素为+1或-1的已知对角矩阵和 一个未知的上三角矩阵的乘积. 基于分数阶Lyapunov稳定性理论构造了模糊控制器以及分数阶的参数自适应律, 在保证所有变量有界的情况下实现驱动系统和响应系统的同步. 在分数阶系统稳定性分析中给出了一种平方Lyapunov函数的使用方法, 根据此方法很多针对整数阶系统的控制方法可以推广到分数阶系统中. 最后数值仿真结果验证了所提控制方法的可行性.     

复Ginzburg-Landau方程时空混沌的网络同步与参量辨识

研究了参量未知的时空混沌系统构成复杂网络的同步与参量辨识问题. 设计的参量辨识律可以有效地辨识复杂网络中所有节点时空混沌系统中的未知参量. 基于稳定性定理, 通过构造适当的Lyapunov函数, 确定了网络完全同步的条件. 以参量未知的一维复Ginzburg-Landau方程作为网络节点为例, 通过仿真模拟检验了参量辨识律以及同步方法的有效性.