Analytical structures and analysis of the simplest fuzzy PDcontrollers

This paper deals with simplest fuzzy PD controllers which employ only two fuzzy sets on the universe of discourse of each input variable, and three fuzzy sets on the universe of discourse of output variable. First, analytical structures of the simplest fuzzy PD controllers are derived via triangular membership functions for fuzzification, intersection T-norm, Lukasiewicz OR and Zadeh (1965) OR T-conorms, Mamdani's minimum, Larsen's product and drastic product inference methods, and center of area method for defuzzification. Properties of such fuzzy PD controllers are investigated. Based on these properties a comparative study is made on fuzzy controllers derived, and also on the fuzzy controllers and their counterpart-conventional linear PD controller. Finally, sufficient conditions for bounded-input bounded-output stability of fuzzy PD control systems are established using the well known small gain theorem.     

Vague controller: A generalization of fuzzy logic controller

In this research, a vague controller (VC) is synthesized by using the notion of vague sets, which are a generalization of fuzzy sets and characterized by a truth-membership function and a falsity-membership function. The vague sets follow the basic set operations and logic operations defined for fuzzy sets, and are superior to fuzzy sets in that they could deal with the uncertainty encountered in real-world applications in a more natural way. Depending on the vague sets, the VC is developed as a generalization of fuzzy logic controller (FLC). The design procedures of the VC, which allow an arbitrary number of input variables, and each variable could have a distinct number of linguistic values, are outlined in this paper. In order to compensate the effort in constructing two series of membership functions for vague sets and to ease the difficulties in designing VCs, a new means of designating membership functions for VCs is also presented in this article. This method constructs a set of membership functions systematically by using only two parameters: number of linguistic values of a linguistic variable and shrinking factor. The membership functions generated by this method, shrinking-span membership functions (SSMFs), have different spans over the universe of discourse and, therefore, are more rational and more practical from the human expert's point of view.     

Multiple Fuzzy Relation and Its Application to Coupled Fuzzy Control

Using semi‐tensor product (STP) of matrix, this paper investigates the fuzzy relation of multiple fuzzy and uses this to design coupled fuzzy control is designed. First of all, under the assumption that the universe of discourse is finite, a fuzzy logical variable can be expressed as a vector, which unifies the expression of elements, subsets, and fuzzy subsets of a universe of discourse. Then, the matrix expression of set mappings is naturally extended to fuzzy sets. Second, based on STP, logic‐based matrix addition and product are proposed. These are particulary useful for the calculation of compounded fuzzy relations. Third, a dual fuzzy structure is introduced, which assures the finiteness of the universe of discourse, and is used for fuzzification and defuzzification. Finally, using the results obtained, a new technique is developed to design a coupled fuzzy controller for multi‐input multi‐output (MIMO) systems with coupled multiple fuzzy relations.     

一种可变论域模糊控制器的设计及仿真

根据模糊控制器的特点,提出一种可变论域模糊控制器,即二级可变论域模糊控制器。首先介绍了可变论域模糊控制器的工作原理,然后阐述了二级可变论域模糊控制器的设计原理。第二级模糊控制器的论域由第一级模糊控制器动态改变。然后给出了二级可变论域模糊控制器的结构设计及参数确定方法,最后通过仿真与常规模糊控制对比。结果表明了二级模糊控制器能够在控制过程中能有效地减小系统稳态误差,提高响应速度,从而证实了这种方法的正确性及优越性,并且该方法适用于具有任何特点的模糊控制系统。     

基于变论域模糊PID的分解炉温度控制研究

分解炉温度控制系统具有非线性、时变、纯滞后的特点,针对传统PID控制及模糊.PID控制难以很好地满足控制要求,提出了一种变论域模糊自适应PID控制方法。利用变论域思想,设计了一种基于函数模型的伸缩因子控制器,动态地调整模糊控制器的量化因子和比例因子,提高了控制精度。在Matlab环境下分别对PID控制、模糊PID控制和变论域模糊PID控制方法进行了仿真对比,结果表明变论域模糊PID控制方法具有更好的动静态性能和自适应能力。     

基于变论域模糊增量理论的质子交换膜燃料电池温度控制

质子交换膜燃料电池(PEMFC)内部的电化学反应过程直接表现为温度的变化,所以有效的温度控制是保证燃料电池可靠性和耐久性的关键.本文将模糊增量控制用于PEMFC热管理系统中,将PEMFC的温度和电堆出入口温度差保持在设定值.首先,建立PEMFC热管理系统的动态模型,包括PEMFC电堆模型和辅助散热设备模型.然后,基于建立的系统模型,设计了一种变论域的模糊增量控制器.该控制器通过伸缩因子来动态调节模糊控制器中的量化因子和比例因子,实现对模糊论域的调节,从而提高控制的灵敏性和精确度.最后,将该温度控制方法用于10 kW燃料电池系统中,实验结果表明变论域模糊增量控制器相比于其他模糊控制方法,不仅具有更快的动态响应速度,还具有更强的鲁棒性和更高的控制精度.     

Design of Mamdani fuzzy logic controllers with rule base minimisation using genetic algorithm

This paper presents a design procedure for Mamdani fuzzy logic controller including rule base minimisation. The rules are modelled with binary weights on which constraints are imposed in order to ensure consistency. A genetic algorithm is used for finding stabilising controllers that minimise the number of rules. The cost function includes a stability/performance coefficient which insures that stable, performance satisfying controllers are given the highest possible fitness. The number of fuzzy sets for the input and the control variables are set by the user and the design procedure is concerned only with the rule base and the distribution of the fuzzy sets in the universes of discourses. Two examples were studied: the control of the pole and cart system and the control of the concentration in CSTR. In both cases, the fuzzy sets were isosceles triangles evenly distributed, in the universe of discourses.     

变论域智能积分控制器设计

结合模糊控制理论,从优化模糊控制器的角度出发,将论域伸缩因子和智能积分结合起来,设计开发了基于可变论域的智能积分模糊控制器。利用LPC2132 ARM嵌入式芯片作为模糊控制器的核心,LabVIEW搭建监测平台。并针对带有纯滞后的温度控制系统给出了仿真结果。仿真结果表明,对于带有纯滞后的系统,变论域智能积分模糊控制器能够很好地改善纯滞后系统的缺点,对于大延迟、时变、非线性的工业过程系统能够很好的控制效果,其控制效果优于常规的模糊控制器,有较高的工程实用价值。     

Genetic algorithm for the design of a class of fuzzy controllers:an alternative approach

A simple, easy to implement alternative method for designing fuzzy logic controllers (FLCs) with symmetrically distributed fuzzy sets in a universe of discourse is introduced. The design parameters include the parameters of the membership functions of the inputs and outputs and the rule base. The method is based on a network implementation of the FLC with real and binary weights with constraints. Due to the presence of the binary weights the backpropagation technique cannot be used. The learning problem is cast as a mixed integer constrained dynamic optimization problem and solved using the genetic algorithm (GA). The crossover and mutation are slightly disrupted in order to cope with the constraints on the binary weights. Training of the controller is carried out in a closed-loop simulation with the controller in the loop     

空天飞空天飞行器的自适应变论域模糊预测控制行器的自适应变论域模糊预测控制

考虑一类非线性不确定系统的变论域模糊预测控制问题.根据跟踪误差在线调整伸缩因子,使变论域模糊系统一致逼近被控对象中的未知干扰和不确定因素.通过引入鲁棒自适应控制器,消除了模糊建模误差,提高了系统的动态性能.基于泰勒展开的非线性预测控制律,避免了繁重的计算负担.基于Lyapunov理论,给出了伸缩因子的σ调整律,并证明了闭环系统一致最终有界.最后,将该算法用于空天飞行器(ASV)姿态控制系统的设计,仿真结果表明了该算法的有效性.     

变论域自适应模糊控制及其在Chua's混沌电路中的应用

本文研究输出反馈自适应变论域模糊控制方法.变论域模糊控制通过自适应调节伸缩因子,生成大量规则,提高了系统的控制精度.由于状态的不完全可测,本文首先通过构造状态观测器实现输出反馈控制.然后,为了抑制外部扰动和参数变化,通过监督控制将系统的状态约束在给定的范围之内,从而提高了控制器的精度和鲁棒性.进而利用Lyapunov函数证明了观测器-控制器系统的稳定性;在所有状态一致有界的前提下,整个自适应控制算法保证闭环系统的稳定性.最后将所提算法应用于Chua s混沌电路,仿真结果证明了控制方法的有效性.     

变论域自适应模糊控制器失真率的计算

变论域自适应模糊控制器已经成功应用在许多领域,然而它的参数难以准确估计,因此其失真率计算十分困难.本文基于Markov过程,提出一个新的计算方法.该方法通过一个特殊的Markov链模拟变论域自适应模糊控制器工作过程,解决了它的失真率计算问题,并证明这个方法是可行的.同时,通过两个算例验证这个方法的有效性.     

三相四线APF直流侧的T-S模糊均压控制

电容分裂中点式三相四线有源电力滤波器（APF）是解决三相四线电力系统谐波治理的有效方法,由于直流侧两组电容电压需要单独控制,增加了均压控制难度并直接影响补偿的效果。分析了该APF的电路拓扑,采用T-S模糊控制的方法对电容分裂中点式三相四线APF的直流侧均压控制进行建模,将直流侧两组电容电压分别作为输入前件变量,对电源电流实施反馈控制。设计的T-S模糊反馈控制器使APF直流侧两组电容电压实现自动均压,满足了APF对负载谐波的补偿控制要求。仿真及实验结果验证了所建立T-S模糊均压控制模型的有效性,APF直流侧两组电容的电压保持均衡,具有较高的稳态精度和良好的动态性能。     

电阻点焊的变论域模糊控制方法

为提高电阻点焊模糊控制适应性和稳定性差的缺点, 根据变论域控制理论, 提出了电阻点焊的变论域模糊控制方法. 首先, 讨论了变论域模糊控制的基本原理. 其次, 设计了输入隶属函数、输出隶属函数、模糊控制规则、伸缩因子, 开发了一种基于规范化因子的电阻电焊变论域模糊控制器, 并使用模糊规则选择变论域的伸缩因子,给出了算法实现的具体步骤. 最后, 进行了不同控制方案的实验研究, 分析了实验结果, 验证了该控制算法的优越 性.     

On generalized fuzzy rough sets

In this paper, a class of generalized fuzzy rough sets based on two universes are studied. Some new set-valued mappings and fuzzy set-valued mappings are introduced to discuss properties of the known model, and a new model for fuzzy rough sets is proposed which provides a new selection of interval structure for uncertainty reasoning using rough set theory. Some properties of the new model are revealed. The new model seems to be more natural in the sense that fuzzy sets are approximated by fuzzy sets on the same universe.     

一种改进的三级倒立摆变论域模糊控制器设计

在传统变论域模糊控制系统中, 论域随着输入的变化实时改变, 论域的反复调整降低了控制的实时性, 同时伸缩因子的函数结构和参数也不易确定. 基于上述问题本文设计了基于改进型变论域算法的三级倒立摆模糊控制器: 首先提出了相对变论域控制思想, 然后采用模糊逻辑推理器构造了伸缩因子, 实时调整输入变量, 从而相对性地改变论域大小, 避免了传统伸缩因子的函数结构和参数不易确定的问题, 并根据系统闭环响应曲线设计了控制 器输出调整因子. 最后采用极点配置方法对状态变量进行综合, 避免了规则爆炸问题. 三级倒立摆的仿真结果表明了该方法具有较好的控制效果.     

一种变论域模糊控制器伸缩因子选择的新方法

对变论域模糊控制器伸缩因子选取的易实现性和输出的实时性问题进行了讨论,给出了一种选择伸缩因子的新方法。该方法与积分型伸缩因子和指数型伸缩因子选择相比具有计算量小、参数少的特点。通过仿真给出了该伸缩因子参数选择的原则。结合间歇反应釜工程应用,将此伸缩因子设置在变论域模糊控制器模糊推理的前件和后件,验证了此伸缩因子的有效性：在保证高精度的基础上,输出能快速跟踪系统的输入,为变论域模糊控制器实际应用提供了一种有效的解决方案。     

模糊控制器输出值不变的两个充分条件

模糊控制器通常由模糊化、模糊推理以及清晰化三部分构成, 而模糊推理决定了一个由输入论域到输出论域的模糊映射. 当模糊映射为常值映射时, 任意选择模糊化和去模糊化方式, 模糊控制器的输出值不因输入信号变化而改变. 本文给出了模糊映射为常值映射的两个充分条件, 并将结论从单入单出模糊系统推广到多入单出模糊系统.     

A hybrid frequency—time domain adaptive fuzzy control scheme for flexible link manipulators

This paper addresses the implementation of an adaptive fuzzy controller for flexible link robot arms. The design technique is a hybrid scheme involving both frequency and time domain techniques. The eigenvalues of the open loop plant can be estimated through application of a frequency domain based identification algorithm. The region of the eigenvalue space, within which the system operates, is partitioned into fuzzy cells. Membership function are assigned to the fuzzy sets of the eigenvalue universe of discourse. The degree of uncertainty on the estimated eigenvalues is encountered through these membership functions. The knowledge data base consists of feedback gains required to place the closed loop poles at predefined locations. A rule based controller infers the control input variable weighting each with the value of the membership functions at the identified eigenvalue. The afore-mentioned controller is compared through simulation with conventional techniques, namely pole placement and gain scheduling.     

基于多层蚁群算法的变论域模糊控制

针对模糊控制器控制精度不高、自适应能力有限等问题,提出一种变论域自适应模糊控制方式.首先在对离散蚁群算法改进的基础上,提出用于连续域寻优的多层蚁群算法.其通过将解空间分成有限网格,并且算法在迭代过程中采用三个阶段的搜索策略,每个阶段采用异构搜索机制.然后根据系统性能利用改进算法动态调整伸缩因子,从而构成基于多层蚁群算法的变论域自适应模糊控制器.最后将此控制器用于中厚板液压位置伺服系统中.仿真结果表明,采用自适应模糊控制器的伺服系统收敛速度明显加快,此控制策略在适应能力与鲁棒性好于其它控制方式.