多输入非线性数字模型的研究

以往使用的典型非线性数学模型为单变量模型，其存在着较大的局限性，如间隙非线性模型。本文提出了一种多输入的间隙非线性模型，它能较好地实现过去流行的单变量间隙模型无法进行的数字仿真。     

滚珠丝杠式电动舵机系统非线性特性分析

针对速度反馈控制的滚珠丝杠式电动舵机系统,建立更加完整的系统模型,模型中充分考虑间隙和摩擦等非线性因素的影响,并通过数值仿真,观察分析不等间隙和摩擦对系统输出的影响规律。采用LuGre模型和死区模型分别描述电动舵机运行时的摩擦和间隙行为,然后根据传动链结构特点提出非线性研究方案,并根据此方案将非线性环节加入所建立的电动舵机二阶模型中,分别对间隙和摩擦的影响进行仿真分析。仿真结果表明,间隙和摩擦会使伺服系统产生跟踪误差,影响定位精度,甚至影响系统稳定。     

一类非线性系统的多模型神经网络解耦控制器

针对多变量非线性离散时间系统设计多模型神经网络解耦控制器，在每个平衡点处用一神经网络离线辨识非线性系统的线性部分，利用另一神经网络在线辨识非线性部分，将非线性部分视为可测干扰并采用前馈的方法予以消除，所有平衡点处得到的系统模型汇集起来构成多模型集，在每一采样时刻基于切换指标选出最优模型作为当前模型，并据此设计解耦控制器实现控制，仿真结果表明系统在多个平衡点处仍然可以得到较好的控制效果。     

基于Preisach模型的迟滞系统建模与控制

针对一种复杂的非线性系统一迟滞系统，研究了基于KP算子Preisach模型对迟滞系统进行建模的方法。利用Preisach模型与其边界线之间的映射关系，建立了容易在线更新的迟滞模型。基于Preisach模型进行迟滞非线性系统的控制，采用PID方法来控制一类带有未知非线性特性迟滞的单输入单输出非线性系统。对迟滞非线性系统的建模与控制进行的数值仿真研究结果表明，该迟滞非线性系统的建模和控制方法具有理论意义和应用价值。     

基于Hammerstein模型的多变量动态矩阵解耦控制研究

许多工业过程都具有强耦合、非线性等复杂过程特性；针对具有变量间强耦合和执行机构非线性的一类典型过程对象，提出基于Hammerstein模型的多变量动态矩阵解耦控制算法；并针对实验室电加热锅炉与强制对流换热器组成的广义对象，采用s7—300可编程序控制器，将控制策略应用于该对象，实现了对锅炉内胆水温及强制对流换热器出口水温的控制；实验结果表明，采用基于Hammerstein模型的多变量动态矩阵解耦控制策略，在解耦效果、设定值跟踪及抗干扰响应等方面，都能取得满意的结果，能够解决一类多变量非线性系统的控制问题。     

基于规则的阀门非线性特性离散时间仿真模型

在控制阀非线性特性研究中,Choudhury模型得到了广泛应用。但在输入信号突变较大时,模型输出的阀位与实际阀位之间存在一定的偏差。此外,Choudhury模型只考虑了阀门非线性特性中的黏滞特性,而没有考虑间隙特性。在详细分析产生偏差原因的基础上,通过总结阀门输出特性的规律,增设多个描述阀门状态的变量,提出了一种新的基于规则的阀门非线性特性离散时间仿真模型。该模型对Choudhury模型进行了改进,同时包括了间隙特性。仿真表明在各种输入信号情况下,阀门非线性模型能够详细描述阀门的物理实际。同时,该模型能够用于计算机控制系统中阀门非线性特性的模拟。     

基于神经网络和多模型的非线性离散自适应控制

针对一类非线性离散时间单变量系统,提出了基于多模型切换策略的非线性自适应控制方法.首先将被控系统划分为多个工作区间,然后在每个工作区间内建立1个线性自适应控制器和1个非线性神经网络自适应控制器.线性控制器可以保证系统的稳定性,神经网络非线性控制器可以有效的改善系统的暂态性能,采用有效的切换策略可以在保证系统稳定的情况下很好的改善系统的性能.仿真结果验证了所提出方法的有效性.     

非线性系统控制的逆系统方法（Ⅰ）

介绍非线性系统控制的逆系统方法及相应的单一非线性系统的控制理论。包括：逆系统方法的基本概念和设计原理，单变量系统α阶积分逆的设计方法，连续单变量系统的系统的控制，逆系统在一类分布参数系统和离散时间系统上的推广示例。     

非线性零阶接近有界多模型神经网络自适应控制器

针对一类单变量非线性离散时间系统,提出一种零阶接近有界的多模型神经网络自适应控制器。该控制器包含一个非线性鲁棒自适应控制器和一个非线性神经网络自适应控制器。当系统非线性项放宽到零阶接近有界时,这两个控制器分别用于保证系统的稳定性和提高系统的性能,系统的控制输入由切换机构在两个控制器之间进行切换产生。最后给出了稳定性和收敛性证明,并通过仿真实验验证了该控制器的有效性。     

非线性系统的一种加权自适应控制方法

非线性系统的一种加权自适应控制方法１）许向阳祝和云（浙江大学工业控制研究所杭州３１００２７）关键词自适应控制，非线性系统，间隙非线性．１）国家级工业控制技术重点实验室资助课题．收稿日期１９９５－０３－０７１引言由于非线性系统的多样性，不能用统一的模型...     

Recursive identification for dynamic systems with backlash

A recursive algorithm for identification of nonlinear dynamic systems with backlash is proposed in this paper. In this method, the backlash, which is a non‐smooth function, is decomposed into a combination of a group of piecewise linearized models so that all the parameters of the backlash can be estimated separately. Moreover, the model of the backlash is embedded into a Hammerstein‐type model. Thus, a pseudo‐Hammerstein model with backlash is constructed. The estimation of the parameters for such a non‐smooth nonlinear system can be implemented through a so‐called recursive general identification algorithm (RGIA). Then, the corresponding convergence analysis of the RGIA for the model with backlash is also investigated. After that, two examples are presented to show the performance of the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

激光拾音头力矩器数学模型的研究

通过力矩器的结构分析，采用自动控制理论推导出一个动态数学模型。在此基础上。运用Matlab提出一种力矩器的非线性回复力模型实验仿真拟合的方法并对某种力矩器进行了实验仿真。这种方法可以方便和有效地使用于大部分光学头，但是由于非线性的存在。对大的动态范围仿真拟合的精度较差。     

齿隙非线性输入系统的迭代学习控制

针对一类具有输入齿隙特性的非线性系统, 提出一种实现有限作业区间轨迹跟踪的迭代学习控制方法. 在系统不确定项可参数化的情形下, 基于类Lyapunov方法设计迭代学习控制器, 回避了常规迭代学习控制中受控系统非线性特性需满足全局Lipschitz连续条件的要求. 对未知时变参数进行泰勒级数展开, 参数估计采用微分学习律, 并在控制器设计中, 采用双曲函数处理级数展开后的余项以及齿隙特性里的有界误差项, 以保证控制器可导, 且可抑制颤振. 引入一级数收敛序列确保系统输出完全跟踪期望轨迹, 且闭环系统所有信号有界.     

A convex approach for NMPC based on second order Volterra series models

In model predictive control (MPC), the input sequence is computed, minimizing a usually quadratic cost function based on the predicted evolution of the system output. In the case of nonlinear MPC (NMPC), the use of nonlinear prediction models frequently leads to non‐convex optimization problems with several minimums. This paper proposes a new NMPC strategy based on second order Volterra series models where the original performance index is approximated by quadratic functions, which represent a lower bound of the original performance index. Convexity of the approximating quadratic cost functions can be achieved easily by a suitable choice of the weighting of the control increments in the performance index. The approximating cost functions can be globally minimized by convex optimization techniques in order to compute the input sequence. The minimization of the performance index is carried out by an iterative optimization procedure, which guarantees convergence to the solution. Furthermore, for a nominal prediction model, asymptotic stability for the proposed NMPC strategy can be shown. In the case of considering an estimation error in the prediction model, input‐to‐state practical stability is assured. The control performance of the NMPC strategy is illustrated by experimental results. Copyright © 2014 John Wiley & Sons, Ltd.     

离散时间非线性系统线性化的泛模型方法

考虑离散时间非线性系统线性化问题，提出一种“泛模型”方法，泛模型是具有时变参数，形成为线性的模型族，证明了工程上能实现的非线性系统，在输入－输出等价的意义下可用泛模型来描述。     

A nonsmooth IMC method for mechanical systems with backlash

This paper proposes a discrete-time nonsmooth internal model control （NSIMC） approach for mechanical transmission systems described by so-called sandwich system with backlash. In this method, a dynamic compensator is introduced to compensate for the effect of the input linear subsystem. Thus, the sandwich systems with backlash can be simplified as a pseudo-Hammerstein system with backlash. The corresponding NSIMC strategy is designed to control this system. The design procedure of the controller is presented based on the analysis on the robust stability by considering the model errors involved with the effect of backlash as well as the compensated error of the input linear subsystem. Moreover, as the model is switched among the different operating zones, the robust filters are proposed to guarantee the robust stability and satisfactory control performance of the system.     

迟滞非线性动态系统神经网络自适应控制

为了减轻非线性动态系统中未知迟滞(Hysteresis)的不良影响，该文提出了一类Backlash型迟滞模型。将有限数量不同宽度的Backlash(Matlab／Simulink)算子进行叠加，来仿真执行器中的迟滞非线性动态。用此模型，提出了基于径向基函数神经网络的自适应控制方案，以控制伴有未知迟滞的非线性动态系统。该方案采用了动态逆的思想及伪控制的概念。利用Lyapunov稳定理论，设计了两个鲁棒控制项，保证动态系统的稳定性、系统中所有信号有界和误差收敛到起点的领域内。通过Matlab／Simulink仿真实验，证明了所提出方案的有效性。     

一类多变量非线性系统的特征模型及其在卫星姿态控制中的应用

本文对一类多输入-多输出高阶非线性系统从理论上详细推导出了其特征模型,并设计了基于特征模型的稳定的自适应模糊广义预测控制方案。由于控制结构中使用了分层模糊系统,因而极大地减少了模糊规则数目,提高了控制的实时性。此外,文中还将所设计的控制方案用于挠性卫星的姿态控制。仿真结果表明,该控制方法具有较强的鲁棒性,可实现高精度的卫星姿态控制。     

An iterative algorithm for simulation error based identification of polynomial input–output models using multi-step prediction

Effective identification of polynomial input–output models for applications requiring long-range prediction or simulation performance relies on both careful model selection and accurate parameter estimation. The simulation error minimisation (SEM) approach has been shown to provide significant advantages in the model selection phase by ruling out candidate models with good short-term prediction capabilities but unsuitable long-term dynamics. However, SEM-based parameter estimation has been generally avoided due to excessive computational effort. This article extends to the nonlinear case a computationally efficient approach for this task, that was previously developed for linear models, based on the iterative estimation of predictors with increasing prediction horizon. Conditions for the applicability of the approach to various model classes are also discussed. Finally, some examples are provided to show the effectiveness and computational convenience of the proposed algorithm for polynomial input–output identification, as well as the improvements achievable by enforcing SEM parameter estimation. A benchmark for nonlinear identification is also analysed, with encouraging results.     

Intelligent modeling and control for nonlinear systems with rate-dependent hysteresis

A new modeling approach for nonlinear systems with rate-dependent hysteresis is proposed. The approach is used for the modeling of the giant magnetostrictive actuator, which has the rate-dependent nonlinear property. The models built are simpler than the existed approaches. Compared with the experiment result, the model built can well describe the hysteresis nonlinear of the actuator for input signals with complex frequency. An adaptive direct inverse control approach is proposed based on the fuzzy tree model and inverse learning and special learning that are used in neural network broadly. In this approach, the inverse model of the plant is identified to be the initial controller firstly. Then, the inverse model is connected with the plant in series and the linear parameters of the controller are adjusted using the least mean square algorithm by on-line manner. The direct inverse control approach based on the fuzzy tree model is applied on the tracing control of the actuator by simulation. The simulation results show the correctness of the approach. Supported by the National Natural Science Foundation of China (Grant No. 60534020), the National Basic Research Program of China (Grant No. G2002cb312205-04), the Research Fund for the Doctoral Program of Higher Education (Grant No. 20070006060), and the Key Subject Foundation of Beijing (Grant Nos. XK100060526, XK100060422)