现代应用数学理论在电力系统稳定分析中的应用

电力系统稳定分析是一项很重要的工作。目前电力系统稳定分析最常用的两种方法是基于采集的数据进行辨识分析和对系统进行建模分析。将分别研究现代应用数学的相关理论在这两种方法中的应用。采用辨识方法时,由于现场采集的数据噪声较多,往往得不到正确的结果,因此需要采用去噪技术对数据进行预处理,介绍了小波去噪在电力系统低频振荡辨识中的应用。采用数学建模方法时,由于电力系统属于非线性系统,当分析一些特定运行状态时(如电力系统受到大干扰后),要用非线性方法才能得出正确的结果,介绍了微分几何理论在电力系统非线性控制中的应用。     

多点正弦振动试验控制系统最优控制策略研究

针对传统多点正弦控制方法中,频响特性不更新和迭代步长不变导致控制系统潜在不稳定的缺点,提出采用最优控制策略进行系统控制。对多点正弦振动控制系统的稳定性进行研究,分析影响控制系统稳定性的因素,得出频响矩阵的估计误差是影响控制系统稳定性的根本原因。通过对建立的最优化模型进行理论分析,推导出系统解耦补偿矩阵实时更新迭代公式和控制系统迭代的最速收敛步长公式,归纳出多点正弦最优控制流程。仿真结果显示迭代步长选取是影响控制系统稳定性的重要因素,多点正弦最优控制策略收敛速度更快;试验结果表明采用最优控制策略的控制系统,其输出响应谱与参考谱的误差完全满足工程中常用的±3 dB控制要求,同时表现出良好的相位跟踪性能,具有实际工程应用价值。     

Identification of structural non-linearities using describing functions and the Sherman–Morrison method

In this study, a new method for type and parametric identification of a non-linear element in an otherwise linear structure is introduced. This work is an extension of a previous study in which a method was developed to localize non-linearity in multi-degree of freedom systems and to identify type and parameters of the non-linear element when it is located at a ground connection of the system. The method uses a describing function approach for representing the non-linearity in the structure. The describing function contains only the first harmonic terms. The Sherman–Morrison matrix inversion method is used in the present study to put the response expression in a form where the non-linearity term can be isolated. Using measured responses one can calculate the value of the describing function representation of the non-linear element and thus perform the identification. This new method can be used for type and parametric identification of a non-linear element between any two coordinates of the system. Case studies are given to demonstrate the applicability of the method.     

Application of memetic algorithm in modelling discrete-time multivariable dynamics systems

Evolutionary algorithm (EA) such as genetic algorithm (GA) has demonstrated to be an effective method for identification of single-input–single-output (SISO) system. However, for multivariable systems, increasing the orders and the non-linear degrees of the model will result in excessively complex model and the identification procedure for the systems is more often difficult because couplings between inputs and outputs. There are more possible structures to choose from and more parameters are required to obtain a good fit. In this work, a new model structure selection in system identification problems based on a modified GA with an element of local search known as memetic algorithm (MA) is adopted. This paper describes the procedure and investigates the performance and the effectiveness of MA based on a few case studies. The results indicate that the proposed algorithm is able to select the model structure of a system successfully. A comparison of MA with other algorithms such as GAs demonstrates that MA is capable of producing adequate and parsimonious models effectively.     

一种基于模型修改的结构多点损伤识别方法

可用于结构损伤识别的方法很多。一般来讲正向方法直接利用结构模态参数的变化，逆向方法则利用模态参数变化反演结构物理参数变化，还有些方法利用了神经网络和模式识别技术。文中利用模型修改的思想，通过逆向方法计算结构单元刚度变化系数来对结构的多点损伤进行识别。以一个七自由度弹簧阻尼质量系统作为研究对象，用数值模拟方法及特征系统实现算法计算系统的模态参数，并用这些模态参数验证所提出方法的可行性，结果表明该方法对多点损伤的识别是简单而可行的。     

利用Lyapunov指数分析机械手反馈控制中的混沌运动

给出了一种适用于一般混沌系统最大Lyapunov指数计算的数值算法，并应用于Duffing方程系统、Lorenz系统和Roessler系统．验证了该方法的有效性。分析了平面两自由度机械手基于多变量比例微分反馈控制中的混沌现象，在给定的几种特定参数条件下，计算了机械手混沌模型的最大Lyapunov指数，结果表明机械手在反馈控制下会出现混沌运动。     

NON-LINEAR CONTROL OF BUCKLED BEAMS UNDER STEP LOADING

The present paper studies a strategy for the active non-linear control of the oscillations of simply supported buckled beams, in order to mitigate the effects of dynamic loading on the vibration amplitudes and prevent dangerous instability phenomena. First, an analysis of the symmetric non-linear behaviour of the structure without any control system is carried out. In order to control the non-linear vibrations of the beam, an active tendon control system is adopted. A control method based on non-linear optimal control using state feedback is developed and the solution of the non-linear optimal control problem is obtained by representing system non-linearities and performance indices by power series with the help of algebraic tensor theory. In this work, general polynomial representations of the non-linear control law are obtained up to the fifth order. This solution procedure is employed to analyse the influence of the resulting non-linear control laws on the dynamic behaviour of a buckled beam under a lateral step load. This arch-like structural system is highly non-linear and under compressive lateral loading may suffer snap-through buckling. This may cause undesirable stresses and/or displacements, leading as a rule to a failure of the structural system. So, special attention is given to the determination of the potential of the present control methodology for efficiently limiting extreme state responses and preventing the snap-through buckling. Numerical results indicate that the control algorithm can effectively increase the load-carrying capacity of the buckled beam without demanding large control forces. Also, this study can be used as a basis for the non-linear control of more complex structures and for the design of control systems.     

APPLICATION OF THE CONDITIONED REVERSE PATH METHOD

Conventional frequency response estimations often give results contaminated by the presence of non-linearities and the extraction of underlying linear system properties is thus difficult. To overcome this problem, the implementation of the Conditioned Reverse Path spectral method to the identification of single- and multi-degree-of-freedom (sdof and mdof) non-linear systems is considered, showing that conventional methods such as ‘H₁’ and ‘H₂’ lead to estimated frequency response functions which are often completely inadequate, even in absence of measurement noise. This spectral method allows to estimate the coefficients of the non-linearities away from the location of the applied excitations and also to identify the linear dynamic compliance matrix when the number of excitations is smaller than the number of response locations. This paper presents some guidelines to successfully apply this method to real non-linear systems; furthermore, the results from an experimental test over a sdof suspension system are shown.     

Modeling of two-plate capacitive position sensing systems for high precision planar three DOF measurement

This paper investigates the issues associated with the use of two-plate capacitive sensors for the measurement of coupled linear and angular motions, particularly those of three planar degrees of freedom (DOF) micro/nano positioners. Commonly, such sensors are employed for the measurement of linear motions, and angular motion could introduce non-linearities in the capacitance response. An analytic model of a general three sensor system is developed, together with its linearization, which transform the position and orientation (pose) of the end effector of a planar positioner to the capacitance of each sensor. The sensitivities of pose estimations to capacitance non-linearity and parameter variation are analyzed, which further leads to the identification of optimized sensor positioning strategies. The response of a single sensor to tilt is investigated, and experimentation is performed to determine the magnitude of non-linear effects, and its subsequent impact on the three DOF position estimation.     

Convergence analysis of the alternating RGLS algorithm for the identification of the reduced complexity Volterra model

In this paper we provide a convergence analysis of the alternating RGLS (Recursive Generalized Least Square) algorithm used for the identification of the reduced complexity Volterra model describing stochastic non-linear systems. The reduced Volterra model used is the 3rd order SVD-PARAFC-Volterra model provided using the Singular Value Decomposition (SVD) and the Parallel Factor (PARAFAC) tensor decomposition of the quadratic and the cubic kernels respectively of the classical Volterra model. The Alternating RGLS (ARGLS) algorithm consists on the execution of the classical RGLS algorithm in alternating way. The ARGLS convergence was proved using the Ordinary Differential Equation (ODE) method. It is noted that the algorithm convergence canno׳t be ensured when the disturbance acting on the system to be identified has specific features. The ARGLS algorithm is tested in simulations on a numerical example by satisfying the determined convergence conditions. To raise the elegies of the proposed algorithm, we proceed to its comparison with the classical Alternating Recursive Least Squares (ARLS) presented in the literature. The comparison has been built on a non-linear satellite channel and a benchmark system CSTR (Continuous Stirred Tank Reactor). Moreover the efficiency of the proposed identification approach is proved on an experimental Communicating Two Tank system (CTTS).     

Adaptive identification of hysteresis and creep in piezoelectric stack actuators

The adaptive identification of the non-linear hysteresis and creep effects in a piezoelectric actuator is proposed in this paper. Model uncertainties related to the hysteresis and creep effects, most prominently in the high frequency zone (to 100 Hz), large operating amplitude and/long operating time, can make a piezoelectric actuator-driven micro-positioning system unstable in the closed loop. Furthermore, these uncertainties may lead to inaccurate open-loop control and frequently cause harmonic distortion when a piezoelectric actuator is driven with a sinusoidal input voltage signal. In order to solve the above issues, it is important to determine an accurate non-linear dynamic model of a piezoelectric actuator. An unscented Kalman filter-based adaptive identification algorithm is presented, which accurately determines the non-linear dynamics of a piezoelectric stack type actuator such that the non-linear hysteresis and creep effects can be accurately predicted. Since hysteresis and creep are dominant in open loop, the actuator is driven in an open-loop mode in this investigation.     

Parameter identification of Bouc-Wen model for MR fluid dampers using adaptive charged system search optimization

In this article, the charged system search (CSS) optimization method is improved to identify the parameters of a non-linear hysteretic Bouc-Wen differential model. The CSS is suitable for those optimization problems involving non-smooth or non-convex domains. Bouc-Wen is a well-established non-linear model which has been used to portray the hysteretic and high non-linear real behavior of numerous physical and mechanical systems. To improve the effectiveness and adaptability of the CSS algorithm, it is combined with sub-optimization mechanism. The obtained results show that the adaptive CSS embodies great robustness and accuracy to be successfully employed in such highly non-linear identification problems.     

A FREQUENCY DOMAIN METHOD FOR ESTIMATING THE PARAMETERS OF A NON-LINEAR STRUCTURAL DYNAMIC MODEL THROUGH FEEDBACK

A unifying perspective of non-linear structural dynamic systems as linear in the open loop with non-linear feedback in the closed loop has recently been revisited by the authors. The authors have previously used feedback to derive a new formulation of frequency response function matrices of non-linear systems, which are described as modulations of nominal linear systems. The modulation creates a pseudo-separation of the linear and non-linear dynamics of the system. The present article derives a new method for estimating parameters of non-linear parametric models that uses internal feedback to account for non-linearities. The main advantage of the new formulation of non-linear system identification is its simplicity. Moreover, the method estimates the linear frequency response matrix and non-linear system parameters at forced and unforced degrees of freedom of general multiple-degree-of-freedom non-linear systems simultaneously. This article demonstrates the implementation of this method on simulated data from single- and multiple-degree-of-freedom lumped parameter models.     

System identification of structural acoustic system using the scale correction

System identification can be a nice tool to make an accurate model of structural acoustic system that can describe the structure-borne noise in a car or an airplane. However, the implementation of the system identification technique to the structural acoustic system is difficult since the system is made of different physical systems. The responses from one system of the hybrid system show different characteristics from those of the others. If we try to identify the system from the responses of different physical systems, we meet a very embarrassing situation. The scales of those signals are so different that the system identification will concentrate on the modelling of the signals with large magnitude. Scale correction process is introduced to adjust the relative magnitude of those signals. When the scale correction is applied, the responses regenerated from the identified system model are similar with the original ones, which means the identified system is correct. This method will be useful for the other hybrid systems such as the structure–control system, structure–soil system and structure–fluid system.     

线性变参数振动系统的全局辨识

制造系统中存在大量振动特性随特定参数变化而变化的线性变参数振动系统。这类线性变参数振动系统的辨识目前主要通过局部辨识方法,为了准确辨识需要在不同调度变量下进行大量实验,往往效率很低。为了准确而高效地辨识线性变参数振动系统,提出一种全局辨识方法。对调度变量连续变化的线性变参数振动系统持续施加激励,将系统的振动微分方程进行时域离散,利用过完备字典函数库对离散模型进行表征,并利用稀疏回归进行求解,即可根据调度变量数据和系统的激励-响应数据一次辨识得到系统模型。以实际机床刀尖结构的模态参数数据,建立线性变参数振动系统代理模型进行验证。在单调度变量和多调度变量案例中,全局辨识得到的模态参数平均误差均在2.7%以下,充分显示了所提出全局辨识方法的有效性,也验证了线性变参数振动系统全局辨识的可行性。     

Friction-induced vibration for an aircraft brake system—Part 1: Experimental approach and stability analysis

Friction-induced vibrations are a major concern in a wide variety of mechanical systems. This is especially the case in aircraft braking systems where the problem of unstable vibrations in disk brakes has been studied by a number of researchers. Solving potential vibration problems requires experimental and theoretical approaches. A non-linear model for the analysis of mode aircraft brake whirl is presented and developed based on experimental observations. The non-linear contact between the rotors and the stators, and mechanisms between components of the brake system are considered.Stability is analyzed by determining the eigenvalues of the Jacobian matrix of the linearized system at the equilibrium point. Linear stability theory is applied in order to determine the effect of system parameters on stability.     

Semi-analytical derivation of approximate non-linear eigenvalues and eigenvectors for general non-linear MDOF systems

This work introduces a novel theoretical formulation for the evaluation of approximate eigenvalues and eigenvectors for general non-linear MDOF systems using the so-called “approximate non-linear mode evaluation” (ANME) method. The approach is based on analytically derived quasi-linear expressions which relate the change in modal parameters to physical non-linear elements that can be added anywhere in the system. Subject to assuming that the change in the mode shape is small, expressions for non-linear eigenvalues and eigenvectors become fully determined for a general MDOF system, even within typical experimental constraints. The errors arising from this assumption can be minimized via an iterative procedure. Preliminary results indicate that the rate of convergence is quite fast for systems with medium to high damping but more effort is required for lightly damped systems. The derived expressions provide a theoretical basis for observations made by previous researchers from an inspection of their experimental and/or numerical results: these indicate that an invariant relationship exists between a non-linear eigenvalue and its associated modal response.     

基于REFOR算法的多输出非线性系统动态参数化建模方法研究

针对多输出非线性系统动态模型的辨识问题,提出一种新的非线性系统动态参数化建模方法,即冗余向前延拓正交（Redundant extended forward orthogonal regression,REFOR）算法。该算法旨在消除传统向前延拓正交（Extended forward orthogonal regression,EFOR）算法因遗漏某些重要模型项而造成所建模型精度较低的问题。首先,基于系统在各工况下辨识所得非线性有源自回归（Non-linear autoregressive with exogenous inputs,NARX）模型,利用REFOR算法统一各模型结构得到模型系数与设计参数间的函数关系,进而建立多输出非线性系统的动态参数化模型。其次,以四自由度非线性系统为例,说明了REFOR算法的优势及其在系统建模中的应用。最后,利用REFOR算法建立悬臂梁的动态参数化模型,并将REFOR预测输出与试验测得输出进行对比,试验结果表明,基于REFOR算法建立的非线性系统动态参数化模型,能准确预测系统的输出响应,为非线性系统建模方法的优化设计提供了理论基础。     

Identification and control of dynamical systems using different architectures of recurrent fuzzy system

Fuzzy logic based systems are very widely used for modeling and control of complex non-linear, plants. Fuzzy systems require the knowledge about the structure of the dynamic plant in order to achieve fruitful results. Recurrent Fuzzy systems (RFS) are a variation of fuzzy systems and have the ability to model and control dynamic plants without using the information about the structure of the plant. This paper presents identification and control of non-linear dynamical systems using two different architectures of recurrent fuzzy system (RFS). It highlights the importance of RFS over the conventional type-1 fuzzy based system. The objective of system identification as well as control has been achieved using both the architectures of RFS and the simulation results clearly show their efficiency. This paper also highlights yet another advantage of RFS over the conventional type-1 fuzzy systems which comes into light when dealing with higher order systems. The paper explains how the computational complexity can be greatly reduced by using RFS for higher order dynamical systems. A comparative analysis between the conventional type-1 fuzzy system and the two recurrent fuzzy systems has also been performed.     

并联机构机电耦合动力学计算

并联机构动力学模型是一个多输入、多输出、非线性、强耦合的复杂机电系统,目前还没有一个成熟的并联机构动力学建模和仿真计算方法.针对三自由度并联机构,建立了包括机械机构、伺服电机一体化的动力学模型.最后在设计好的运动平台轨迹下,计算了移动腿的位移、驱动电机的负载转距;分析了移动腿的误差.计算机仿真结果展示了控制器对机构位移和伺服电机转距良好的控制.