一种线性化模糊内模自适应控制算法

针对非线性对象，提出一种线性化模糊内模自适应控制算法。该算法以一组模糊规则作为非线性对象内部模型，一条模糊规则表示一个局部线性系统；根据对象输入与输出测量值，利用TSK建模方法在线辨识局部模糊内部模型；同时依据辨识模型设计局部H2最优模糊控制规则，所有规则构成H2最优模糊控制器。仿真实验显示：该算法适用于非线性对象的控制，具有较好的鲁棒性和抗干扰能力。     

Design of Cascade Adaptive Fuzzy Sliding-Mode Control for Nonlinear Two-Axis Inverted-Pendulum Servomechanism

Because the dynamic characteristic of a two-axis inverted-pendulum servomechanism is a nonlinear underactuated system, it is difficult to design a suitable control scheme that realizes real-time stabilization and accurate tracking control simultaneously. In general, the techniques developed for fully actuated systems cannot be used directly in underactuated systems. In this study, a cascade adaptive fuzzy sliding-mode control (AFSMC) scheme including inner and outer control loops is investigated for the stabilizing and tracking control of a nonlinear two-axis inverted-pendulum servomechanism. The aim of the inner control loop is to design an AFSMC law with fuzzy estimators so that the stick-angle vector can fit the stick-angle command vector derived from the stick-angle reference model. In the outer loop, the reference signal vector is designed via a fuzzy path-planning scheme so that the cart position vector tracks the cart-position command vector and the stick-angle tracking-error vector converges to zero simultaneously. All adaptive algorithms in the cascade AFSMC system are derived in the sense of Lyapunov stability analysis, so that system stability can be guaranteed in the entire closed-loop system. The effectiveness of the proposed control strategy is verified by numerical simulations and experimental results, and the superiority of the cascade AFSMC system is indicated in comparison with a cascade sliding-mode control system.      

基于模糊T-S模型的批过程建模与最优控制

基于模糊T-S模型,提出一种具有自学习能力的模糊方法用于批过程建模和最优控制.通过引入与均方误差相关的动态误差传递因子,使用改进的梯度下降法,本方法能够辨识模糊T-S预测模型.对于批过程的受限非线性最优控制,基于所辨识的预测模型,运用庞特里亚金最小值原理和平行分布补偿算法,本方法能够把一个复杂非线性系统最优控制设计问题转化为一些基于复杂T-S预测模型的局部线性系统的最优问题,从而给出一种有效和简单的模糊最优控制策略.所提方法用于一个半连续式反应器的建模和最优控制,仿真结果表明新方法是有效和准确的.     

基于模糊模型的非线性内模控制策略研究

针对一类非线性动态过程提出了基于模糊模型的非线性内模控制算法(NFIMC)。NFIMC控制器包括逆模糊模型控制器和滤波器。过程的模糊模型和逆模糊模型均可由模糊辨识获得。CSTR的仿真结果表明:该算法可以对强非线性过程实现有效控制,并且具有结构简单、计算效率高等优点,有利于在线应用。     

非线性系统模糊神经网络变结构自适应控制

在非线性系统的模糊动力学模型基础上,提出一种模糊神经网络变结构自适应控制器;网络的结构根据非线性系统特性动态构成,基于该网络提出非线性预测器,基于梯度法提出了一种网络参数学习算法,并分析了收敛性及其性质。将网络预测器与参数学习算法相结合,构成自适应控制算法,证明了算法的收敛性。仿真结果证实了算法的有效性。     

利用模糊系统的自适应模糊控制器

针对非线性系统控制,设计了利用TSK(Takagi-Sugeno-Kang)模糊系统的自适应模糊控制器。所设计的自适应控制方法是参考模型自适应控制方法,而且利用Lyapunov函数保证了闭环系统的稳定性,同时推导了最优的自适应控制规律。首先,根据控制对象的输入输出数据建立TSK模糊模型,然后,由TSK模糊模型设计初期的TSK模糊控制器,并根据自适应规律随时调整模糊控制器参数。倒立摆系统的仿真实验验证了所设计的自适应模糊控制器的有效性。     

Controller design of uncertain nonlinear systems based on T-S fuzzy model

A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, the efficient maximal overlapped-rules group （EMORG） is presented, and a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires a local common positive definite matrix in each EMORG, can reduce the conservatism and difficulty in existing stability conditions. Finally, a simulation example shows the proposed approach is effective.     

Sugeno模糊模型的辨识与控制

提出了一种新的Sugeno模糊模型辨识算法和对非线性系统进行并行化设计的方法.在Sugeno模糊模型辨识中,应用模糊聚类方法可将其前提结构和结论参数的辨识分开进行,减少了计算量;对于非线性系统的控制,Sugeno模糊模型实际上是动态系统的局部线性化,可采用并行设计的方法设计控制器,然后通过模糊推理得到全局控制量.最后通过倒立摆系统的控制说明了本文算法的有效性.     

基于T-S模糊模型的转台鲁棒最优控制器设计

针对飞行器仿真转台系统的非线性以及不确定性问题,提出了基于T-S模糊模型的鲁棒最优控制器设计方法.首先,利用IF-THEN模糊规则将转台速度环系统的状态空间分成不同的区域,构建具有参数不确定性的T-S模糊模型;然后,根据给定的最优性能指标要求以及控制输入约束,通过求解一组线性矩阵不等式(LMIs)进行鲁棒最优控制嚣设计.仿真结果表明,该方法不仅具有比较好的控制效果,而且能有效地解决控制输入约束问题,并能很好地保证对参数变化的鲁棒稳定性.     

模糊聚类辨识算法

采用模糊输入聚类算法来辨识系统的模型,通过两个模糊聚类准则函数求得聚类中心和模糊规则数,然后求出各个子窨支态模型,再用隶属函数光滑地把他们连接成一个全局动态模糊模型,这种模型可以转化成状态空间模型,从而进行控制器的设计和稳定性分析。     

一种基于T-S模糊模型的混沌控制方法

用T-S模糊系统来逼近非线性系统,它的IF-THEN规则后件由线性状态空间子系统构成,进而可以应用模糊系统的控制理论求得模糊控制器,用此非线性控制器来控制非线性系统,以求良好的控制效果;将模糊控制技术应用于混沌控制中,可以克服反馈线性化等传统方法对参数完全精确已知的限制;模糊规则后件部分以局部线性方程形式给出的T-S模糊模型可以通过调整相关参数很好地逼近混沌系统,基于该模型采用平行分散补偿技术设计出具有相同规则数目的模糊控制器,控制器所有参数可以通过求解一组线性矩阵不等式一次性得到。仿真结果验证了该方法的有效性。     

基于模糊双线性模型的连续搅拌反应釜滑模控制

主要对连续搅拌反应釜系统(CSTR)的滑模控制问题进行研究;该系统的模型可由Takagi-Sugeno (T-S)模糊双线性模型进行描述,基于该模糊双线性模型,给出滑模控制方法;在之前学者的研究成果上对线性滑模面进行改进,构造积分滑模面,由此设计出的等效控制量与切换控制量,可以保证系统的控制精度;通过对其进行稳定性研究,得到全局稳定的充分条件,并求出滑模面的控制器参数;同时,构造7条模糊规则,采用模糊化方法对切换增益项进行模糊推理,使整体控制量平滑化,也避免系统状态出现抖振现象,实现实际可操作性;最后,连续搅拌反应釜的仿真验证了控制方法的有效性.     

基于T-S模型的自适应模糊广义预测控制

对一类非线性系统,利用一种基于模糊规则的快速模糊辨识方法建立起系统的T—S模型,并基于该模型应用局部递推最小二乘方法根据采样值对模型参数进行在线修正,根据系统动态线性化模型采取广义预测控制策略,从而实现了基于T—S模糊模型的非线性系统自适应模糊预潮控制。与以往的模糊广义预测控制算法相比,此方法简单,而且较大地减少计算量,适合于在线控制。通过仿真研究验证所提方法的有效性。     

具有模糊聚类功能的双向二维无监督特征提取方法

依据最大间距判别准则(Maximum margin criterion, MMC)的基本原理,并结合模糊技术和张量理论, 提出一种矩阵模式的模糊最大间距判别准则(Matrix model fuzzy maximum margin criterion, MFMMC),并在此基础上形成具有模糊聚类功能的双向二维无监督特征提取方法(Two-directional two-dimensional unsupervised feature extraction method with fuzzy clustering ability, (2D)2UFFCA). 该方法不但能直接实现矩阵模式数据的模糊聚类,而且还可以对矩阵模式数据进行双向二维特征提取,实现特征降维. 同时我们还从几何的直观含义出发,合理地设定矩阵模式的模糊最大间距判别准则中的调节参数γ并从理论上证明其合理性.为了提高特征提取的效率,还提出一种能有效计算矩阵模式数据的投影变换矩阵的方法.实验结果表明该方法具有上述优势.     

An Analytical Study on Structure, Stability and Design of General Nonlinear Takagi–Sugeno Fuzzy Control Systems

In this paper, we first study analytical structure of general nonlinear Takagi-Sugeno (TS, for short) fuzzy controllers, then establish a condition for analytically determining asymptotic stability of the fuzzy control systems at the equilibrium point, and finally use the stability condition in design of the control systems that are at least locally stable. The general TS fuzzy controllers use arbitrary input fuzzy sets, any types of fuzzy logic AND, TS fuzzy rules with linear consequent and the generalized defuzzifier which contains the popular centroid defuzzifier as a special case. We have mathematically proved that the general TS fuzzy controllers are nonlinear controllers with variable gains continuously changing with controllers’ input variables. Using Lyapunov’s linearization method, we have established a necessary and sufficient condition for analytically determining local asymptotic stability of TS fuzzy control systems, each of which is made up of a fuzzy controller of the general class and a nonlinear plant. We show that the condition can be used in practice even when the plant model is not explicitly known. We have utilized the stability condition to design, with or without plant model, general TS fuzzy control systems that are at least locally stable. Three numerical examples are given to illustrate in detail how to use our new results. Our results offer four important practical advantages: (1) our stability condition, being a necessary and sufficient one, is the tightest possible stability condition, (2) the condition is simple and easy to use partially because it only needs the fuzzy controller structure around the equilibrium point, (3) the condition can be used for determining system local stability and designing fuzzy control systems that are stable at least around the equilibrium point even when the explicit plant models are unavailable, and (4) the condition covers a very broad range of nonlinear TS fuzzy control systems, for which a meaningful global stability condition seems impossible to establish.     

模糊控制的系统化设计和稳定性分析

给出了一种模糊控制系统的系统化设计方法,它采用一组局部T-S模糊模型来表示模糊系统,对每个局部模型,利用状态反馈进行控制器设计,最后给出了全局模糊系统的稳定性分析.通过对一个典型的非线性球-棒控制系统的仿真研究,表明该方法是有效的,它的性能指标优于现有文献的结果.     

基于向量Lyapunov函数方法的模糊控制系统稳定性分析和设计

采用模糊动态模型对连续时间非线性系统进行模糊控制,对闭环模糊系统的稳定性进行分析,并给出系统化的控制器设计程序,在一系列局部模型通过模糊隶属函数连接得到的连续的全局模型中,全面考虑其它关联子系统对标称线性系统的摄动,并利用向量Lyapunov函数的概念和方法,得到了闭环模糊系统稳定的充分条件;仿真例子验证了该设计方法的正确性。     

Design of fuzzy sliding mode controller for SISO discrete-time systems

According to a class of nonlinear SISO discrete systems, the fuzzy sliding mode control problem is considered. Based on Takagi-Sugeno fuzzy model method, a fuzzy model is designed to describe the local dynamic performance of the given nonlinear systems. By using the sliding mode control approach, the global controller is constructed by integrating all the local state controllers and the global supervisory sliding mode controller. The tracking problem can be easily dealt with by taking advantage of the combined controller, and the robustness performance is improved finally. A simulation example is given to show the effectiveness and feasibility of the method proposed.     

非线性系统的鲁棒自适应模糊控制

针对反馈线性化后的不确定非线性对象,提出了一种鲁棒自适应控制方法.采用模糊模型逼近不确定项,用逐步后推技术构造出自适应律,在线调节模糊模型的参数,同时处理存在估计误差时的干扰抑制问题.该方法还用于感应电动机速度控制的仿真.用李亚普诺夫方法证明了整个系统的稳定性和鲁棒性.该方法适用于任意有界时变干扰,通过模糊模型还可以加入对干扰的经验知识.     

Fuzzy Modeling and Control for Conical Magnetic Bearings Using Linear Matrix Inequality

A general nonlinear model with six degree-of-freedom rotor dynamics and electromagnetic force equations for conical magnetic bearings is developed. For simplicity, a T–S (Takagi–Sugeno) fuzzy model for the nonlinear magnetic bearings assumed no rotor eccentricity is first derived, and a fuzzy control design based on the T–S fuzzy model is then proposed for the high speed and high accuracy control of the complex magnetic bearing systems. The suggested fuzzy control design approach for nonlinear magnetic bearings can be cast into a linear matrix inequality (LMI) problem via robust performance analysis, and the LMI problem can be solved efficiently using the convex optimization techniques. Computer simulations are presented for illustrating the performance of the control strategy considering simultaneous rotor rotation tracking and gap deviations regulation.