非线性系统的支持向量机逆模型辨识及控制

针对非线性系统逆模型建立难的问题,提出了基于回归型支持向量机(support vetor regression,SVR)的非线性系统逆模型辨识建模的方法,在此基础上,提出了基于SVR的非线性系统逆模型控制的方法.仿真试验结果表明:采用SVR建立的非线性系统逆模型具有很高的建模精度和较强的泛化能力,基于SVR的逆模型控制...     

基于正交匹配追踪算法的复杂系统动力学建模与分析

针对非线性系统模型的辨识问题,通过引入正交匹配追踪(Orthogonal matching pursuit,OMP)算法实现快速非线性系统建模。该方法旨在解决非线性有源自回归(Nonlinear autoregressive with exogenous inputs,NARX)模型针对大型数据建模时效性差的问题。首先,说明了正交最小二乘(Orthogonal least squares,OLS)算法存在正交次数多、耗时长的问题,采用OMP算法可有效解决,通过与OLS算法对比正交差异性证明了OMP算法计算效率提升的理论基础,采用模型预报方法验证OMP算法所得NARX模型的动力学特性。其次,以单自由度非线性系统为例,说明了OMP算法系统建模的有效性。最后,利用OMP算法建立悬臂梁NARX模型,并分别将NARX模型预报输出与试验实测输出,NARX模型固有频率与悬臂梁实际固有频率进行对比。结果表明,与OLS算法相比,所提方法的建模效率平均提升了10倍,且模型可有效反应系统动力学特性。     

串联式混合动力汽车辅助功率单元鲁棒辨识

串联式混合动力汽车柴油机辅助功率单元(APU)是一个多输入多输出的复杂非线性系统,为便于控制器的设计,提出一种简单的面向控制的APU模型鲁棒辨识方法。该方法基于非线性变增益控制的原理,把APU系统看成一个线性变参数系统,并将参数区域进行网格离散化,在每一工作点采用基于模型不确定性建模的方法进行模型辨识,其结果表示为名义模型及其不确定性区域。最后在APU试验台架上进行了辨识试验,试验结果表明该方法的可行性。     

一类迟滞非线性振动系统建模新方法

用理论和试验相结合的手段研究一类迟滞非线性振动系统的动力建模, 提出一种新的建模方法, 用此方法建立非线性模型用来描述这类系统的动态特性。该模型用非线性刚度和非线性阻尼机理构造, 刚度和阻尼机理由理论和试验推出, 模型中的参数由试验数据辨识。用所建模型重构恢复力——位移迟滞环, 结果表明, 该模型能很好描述这类非线性振动系统的特性, 模型中各参数的重要性得到展示, 提出的建模方法实用且有效。     

基于SVR的非线性系统故障诊断研究

针对非线性系统辨识建模和故障诊断难的问题,利用回归型支持向量机(support vector regression,SVR)分别设计了非线性系统的辨识建模系统和故障诊断系统,最后以某一非线性系统为例进行了仿真试验研究,建立了该非线性系统的SVR辨识模型,在此基础上进行了三种典型故障的诊断试验,仿真试验结果验证了该方法的有效性和先进性。     

基于DEAFCR算法的非线性系统模型参数辨识

针对非线性模型参数辨识困难和不准确的问题,提出一种基于改进的差分进化算法的辨识算法。通过建立寿命机制,根据寿命值,动态调整缩放因子和交叉率,在算法初期保持多样性来避免早熟收敛,在后期保留优质解,加快收敛速度。为验证改进算法的性能和实用性,用典型测试函数进行对比测试,并辨识非线性传递函数模型和Hammerstein模型,试验结果表明改进的算法收敛速度快,辨识精度高,对非线性系统参数辨识有效可行。     

时序数据的随机子空间模型辨识和一步预测

时序数据是指按先后顺序排列的一组随机数据。在系统辨识中,一组时序数据对应于随机子空间模型的输出响应。本文依照工程实际,用随机子空间辨识技术来解决时序数据的参数化建模和预测问题,提出了用改进的Positive算法进行参数识别和一步预测,来替代原有的AR参数化建模和预测技术。最后通过一组丝杆误差时序数据,对算法作了仿真和验证。     

多输入多输出Hammerstein Wiener交流电弧炉电极系统模型

在交流电弧炉中对于电极系统的描述,目前大都采用针对单相电极的单输入单输出的Hammerstein-Wiener(H-W)模型,这种模型过于简化真实电极系统结构,导致模型的预测精度较低。针对该问题,提出一种基于多输入多输出H-W模型的电极系统建模方法,该模型的结构与实际电极系统结构一致,有利于模型预测精度的提高,另外在多输入多输出的静态非线性块不可逆的条件下,提出可分非线性最小二乘算法对H-W模型参数进行辨识。最后采用实际数据验证,在预测精度上,多输入多输出H-W电极系统模型优于传统的单输入单输出H-W电极系统模型。     

基于混合算法的磁悬浮隔振器模型辨识与验证

针对磁悬浮隔振器动态电磁力模型存在非线性及磁滞且很难建立其精确模型的问题,提出了基于BP算法、改进遗传（MGA）算法的混合算法的BP神经网络的模型辨识方法,建立了磁悬浮隔振器动态电磁力气隙电流关系的模型。结果表明,基于混合训练算法辨识得到的模型具有更高的精度,能够满足磁悬浮隔振器动态电磁力模型辨识需求。最后,搭建了磁悬浮隔振实验平台,建立控制模型,并验证了辨识模型的有效性。     

基于最小二乘模型的Bayes参数辨识方法

现实中的系统都具有一定的非线性,并且这种非线性在非线性通道补偿和非线性系统故障诊断等领域是不可忽略的。针对有白噪声干扰的输出误差非线性系统,将数学模型与基于最小二乘的Bayes算法相结合,用数学模型参数代替辨识模型信息向量中的未知项,用基于白噪声的最小二乘模型进行不可预测辨识,从而提出了基于最小二乘模型的Bayes参数辨识方法。介绍了Bayes基本原理及2种常用的方法,经过理论分析和MATLAB仿真研究证明,该方法原理简单、计算量小、速度快、抗干扰能力强,可以对较高精度非线性系统进行参数估计和在线辨识。     

PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems

In response to the identification problem concerning multi-degree of freedom (MDOF) nonlinear systems, this study presents the extended forward orthogonal regression (EFOR) based on predicted residual sums of squares (PRESS) to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs (NARX) model and aims to explicitly reveal the physical design parameters of the system. The PRESS-based EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio (AERR)-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5-DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.     

Discrete state space modeling and control of nonlinear unknown systems

A novel procedure for integrating neural networks (NNs) with conventional techniques is proposed to design industrial modeling and control systems for nonlinear unknown systems. In the proposed approach, a new recurrent NN with a special architecture is constructed to obtain discrete-time state-space representations of nonlinear dynamical systems. It is referred as the discrete state-space neural network (DSSNN). In the DSSNN, the outputs of the hidden layer neurons of the DSSNN represent the system's (pseudo) state. The inputs are fed to output neurons and the delayed outputs of the hidden layer neurons are fed to their inputs via adjustable weights. The discrete state space model of the actual system is directly obtained by training the DSSNN with the input–output data. A training procedure based on the back-propagation through time (BPTT) algorithm is developed. The Levenberg–Marquardt (LM) method with a trust region approach is used to update the DSSNN weights. Linear state space models enable to use well developed conventional analysis and design techniques. Thus, building a linear model of a system has primary importance in industrial applications. Thus, a suitable linearization procedure is proposed to derive the linear state space model from the nonlinear DSSNN representation. The controllability, observability and stability properties are examined. The state feedback controllers are designed with both the linear quadratic regulator (LQR) and the pole placement techniques. The regulator and servo control problems are both addressed. A full order observer is also designed to estimate the state variables. The performance of the proposed procedure is demonstrated by applying for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) nonlinear control problems.     

Introducing an Evolving Local Neuro-Fuzzy Model – Application to modeling of car-following behavior

This paper proposes an Evolving Local Linear Neuro-Fuzzy Model for modeling and identification of nonlinear time-variant systems which change their nature and character over time. The proposed approach evolves through time to follow the structural changes in the time-variant dynamic systems. The evolution process is managed by a distance-based extended hierarchical binary tree algorithm, which decides whether the proposed evolving model should be adapted to the system variations or evolution is necessary. To represent an interesting but challenging example of the systems with changing dynamics, the proposed evolving model is applied to model car-following process in a traffic flow, as an online identification problem. Results of simulations demonstrate effectiveness of the proposed approach in modeling of the time-variant systems.     

非线性状态空间方法辨识电液伺服控制系统

针对回归神经网络辨识和建立非线性动态系统模型的问题,研究非线性状态空间描述的回归神经网络数学模型。讨论极小均方误差网络训练收敛准则,通过研究Kalman 滤波估计公式中的随机变量,提出一种参数增广的回归神经网络非线性状态方程,无导数的Kalman滤波器用于增广参数估计,人工白噪声强迫网络学习,更新网络权值,避免了扩展Kalman滤波器计算Jacobian信息和基于递度学习算法收敛慢的问题。在电液伺服系统辨识建模的应用中表明,回归神经网络较好地跟踪了液压油缸压力变化,与扩展Kalman滤波估计学习算法相比,新的算法具有较快的收敛和精度。     

基于UKF算法的汽车状态估计

准确实时获取行驶过程中的状态信息是汽车动态控制系统研究的关键问题。将unscented卡尔曼滤波(UKF)算法应用到汽车的状态估计之中,建立了包含时不变统计特性噪声和非线性轮胎的汽车动力学模型,采用具有对称采样策略和比例修正的UKF算法对汽车估计了多个关键状态量。将UKF估计器与常见的EKF估计器进行了比较分析,基于ADAMS/Car的虚拟试验和实车试验验证了UKF在汽车状态估计中的可行性。     

Kinematics and dynamic modeling for holonomic constrained multiple robot systems through principle of workspace orthogonalization

This paper deals with an efficient mathematical modeling for multiple robot manipulators (or multifingered robot hands) holding and transporting a rigid common object on the constraint surfaces, subject to a set of holonomic (integrable) constraints. First, the kinematics and dynamics of the multiple robot systems are formulated. After a series of model transformations, a combined dynamic model is derived from a unified viewpoint. Then the system dynamics can be decomposed into two orthogonal subsystems the (reduced-order) motion subsystem and the force subsystem. From a practical point of view, the new dynamic model presented in this paper is suitable form for dynamic analysis and hybrid (position/force) control synthesis.     

Stability analysis and dynamic regulation of multi-dimensional Taylor network controller for SISO nonlinear systems with time-varying delay

Though many studies are focused on the stabilization of nonlinear systems with time-varying delay, they fail to involve the dynamic regulation without on-line optimization commonly. For this sake, feedback linearization, Lyapunov-Razumikhin theorem and polynomial approximation theorem are employed here to verify that the multi-dimensional Taylor network (MTN) controller can stabilize the single input single output (SISO) nonlinear time-varying delay systems through dynamic regulation of the system output with no need for on-line optimization. Here, the design of the controller is transformed into a convex optimization problem, which is tackled by means of the appropriate optimization method. Like its PD-like controller peers, the MTN controller functions well in eliminating the dependence on the system model. The effectiveness of the proposed approach is demonstrated and confirmed via two examples.     

Spatial curvilinear path following control of underactuated AUV with multiple uncertainties

This paper investigates the problem of spatial curvilinear path following control of underactuated autonomous underwater vehicles (AUVs) with multiple uncertainties. Firstly, in order to design the appropriate controller, path following error dynamics model is constructed in a moving Serret–Frenet frame, and the five degrees of freedom (DOFs) dynamic model with multiple uncertainties is established. Secondly, the proposed control law is separated into kinematic controller and dynamic controller via back-stepping technique. In the case of kinematic controller, to overcome the drawback of dependence on the accurate vehicle model that are present in a number of path following control strategies described in the literature, the unknown side-slip angular velocity and attack angular velocity are treated as uncertainties. Whereas in the case of dynamic controller, the model parameters perturbations, unknown external environmental disturbances and the nonlinear hydrodynamic damping terms are treated as lumped uncertainties. Both kinematic and dynamic uncertainties are estimated and compensated by designed reduced-order linear extended state observes (LESOs). Thirdly, feedback linearization (FL) based control law is implemented for the control model using the estimates generated by reduced-order LESOs. For handling the problem of computational complexity inherent in the conventional back-stepping method, nonlinear tracking differentiators (NTDs) are applied to construct derivatives of the virtual control commands. Finally, the closed loop stability for the overall system is established. Simulation and comparative analysis demonstrate that the proposed controller exhibits enhanced performance in the presence of internal parameter variations, external unknown disturbances, unmodeled nonlinear damping terms, and measurement noises.     

滚动轴承-转子系统非线性参数、强迫联合振动

建立考虑非线性轴承力、径向游隙、变柔度等非线性因素和不平衡力的滚动轴承-转子系统动力学方程,并用自适应Runge-Kutta-Felhberg算法对其求解,利用分岔图、Poincaré映射图和频谱图,分析参数、强迫联合激励的滚动轴承-转子系统的响应、分岔和混沌等非线性动力特性.结果表明,滚动轴承-转子系统有多种周期和混沌响应形式,其振动频率不仅有参数振动频率成分和强迫振动频率成分,而且有二者的倍频成分和组合频率成分;随着径向游隙的增大,转子系统的非线性特性增强;不平衡力较小时,系统中参数振动占主导地位,增大不平衡力有利于抑制转子系统的不稳定振动.随不平衡力的增大,强迫振动逐渐增强,大的不平衡力会诱发系统产生混沌振动;转子系统进入混沌的主要途径是倍周期分岔.