Fuzzy_control
模糊控制基本原理
模糊控制的基本原理模糊控制是以模糊集合理论、模糊语言及模糊逻辑为基础的控制，它是模糊数学在控制系统中的应用，是一种非线性智能控制。
模糊控制是利用人的知识对控制对象进行控制的一种方法，通常用“if条件，then结果”的形式来表现，所以又通俗地称为语言控制。
一般用于无法以严密的数学表示的控制对象模型，即可利用人(熟练专家)的经验和知识来很好地控制。
因此，利用人的智力，模糊地进行系统控制的方法就是模糊控制。
模糊控制的基本原理如图所示：模糊控制系统原理框图它的核心部分为模糊控制器。
模糊控制器的控制规律由计算机的程序实现，实现一步模糊控制算法的过程是：微机采样获取被控制量的精确值，然后将此量与给定值比较得到误差信号E；一般选误差信号E作为模糊控制器的一个输入量，把E的精确量进行模糊量化变成模糊量，误差E的模糊量可用相应的模糊语言表示；从而得到误差E的模糊语言集合的一个子集e(e实际上是一个模糊向量)。
再由e和模糊控制规则R(模糊关系)根据推理的合成规则进行模糊决策，得到模糊控制量u为：式中u为一个模糊量；为了对被控对象施加精确的控制，还需要将模糊量u进行非模糊化处理转换为精确量：得到精确数字量后，经数模转换变为精确的模拟量送给执行机构，对被控对象进行一步控制；然后，进行第二次采样，完成第二步控制……。
这样循环下去，就实现了被控对象的模糊控制。
模糊控制(Fuzzy Control)是以模糊集合理论、模糊语言变量和模糊逻辑推理为基础的一种计算机数字控制。
模糊控制同常规的控制方案相比，主要特点有：(1)模糊控制只要求掌握现场操作人员或有关专家的经验、知识或操作数据，不需要建立过程的数学模型，所以适用于不易获得精确数学模型的被控过程，或结构参数不很清楚等场合。
(2)模糊控制是一种语言变量控制器，其控制规则只用语言变量的形式定性的表达，不用传递函数与状态方程，只要对人们的经验加以总结，进而从中提炼出规则，直接给出语言变量，再应用推理方法进行观察与控制。
高速工况中无人驾驶车辆轨迹跟踪控制技术
引用格式：张泽琪, 杨伟东, 贾鹏飞, 等. 高速工况中无人驾驶车辆轨迹跟踪控制技术[J]. 中国测试，2023, 49(10): 148-155.ZHANG Zeqi, YANG Weidong, JIA Pengfei, et al. Trajectory tracking control of driverless vehicle under high speed steering condition[J]. China Measurement & Test, 2023, 49(10): 148-155. DOI: 10.11857/j.issn.1674-5124.2022050106高速工况中无人驾驶车辆轨迹跟踪控制技术张泽琪1， 杨伟东1,2， 贾鹏飞3， 张云龙4(1. 河北工业大学机械工程学院，天津 300401; 2. 国家技术创新方法与实施工具工程技术研究中心，天津 300401;3. 中汽研（天津）汽车工程研究院有限公司，天津 300300; 4. 国汽（北京）智能网联汽车研究院有限公司，北京 102600)N P N C 摘 要: 为提高无人驾驶车辆在高速工况中轨迹跟踪控制的稳定性，设计一种模糊控制与模型预测控制相结合的车辆轨迹跟踪控制器，针对大曲率或低附着系数道路环境中车辆行驶轨迹易出现偏移与车身失稳问题，应用模糊控制器根据当前车辆相关状态参数对于预测时域与控制时域进行模糊调节，同时给予前轮转角补偿修正。
通过搭建MIL 联合仿真平台，验证该控制器在高速工况中车辆轨迹跟踪控制效果。
结果表明：相比于传统MPC 控制器，该控制器可有效避免车辆高速行驶中响应滞后与轨迹偏移问题，提高无人驾驶轨迹跟踪控制的精确度与稳定性。
关键词: 无人驾驶车辆; 模型预测控制; 轨迹跟踪; 模糊控制中图分类号: U461.99文献标志码: A文章编号: 1674–5124(2023)10–0148–08Trajectory tracking control of driverless vehicle under high speed steering conditionZHANG Zeqi 1, YANG Weidong 1,2, JIA Pengfei 3, ZHANG Yunlong 4(1. School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China; 2. National Engineering Center for Technological Innovation Method and Tool, Tianjin 300401, China; 3. CATARC (Tianjin) Automotive Engineering Research Institute Co., Ltd., Tianjin 300300, China; 4. NationalInnovation Center of Intelligent and Connected Vehicles, Beijing 102600, China)N P N C Abstract : In order to improve the stability of the trajectory tracking control of driverless vehicles in high-speed working conditions, a vehicle trajectory tracking controller combining fuzzy control and model predictive control is designed. Aiming at the problem that the vehicle trajectory is prone to drift and vehicle instability in the road environment with large curvature or low adhesion coefficient, the fuzzy controller is applied to predict the time domain and control time domain to adjust, and at the same time to compensate and correct the front wheel angle. By setting up the mil joint simulation platform, the control effect of the controller in vehicle trajectory tracking under high-speed conditions is verified. The results show that, compared with the traditional MPC controller, the controller effectively avoids the problems of response lag and trajectory offset in high-speed driving, and improves the accuracy and stability of unmanned trajectory tracking control.Keywords : driverless vehicle; model predictive control; trajectory tracking; fuzzy control收稿日期: 2022-05-16；收到修改稿日期: 2022-07-17基金项目: 中汽中心指南类项目（20213402）作者简介: 张泽琪（1996-），男，河北沧州市人，硕士研究生，专业方向为智能驾驶技术。
模糊控制毕业论文
模糊控制考核论文姓名：郑鑫学号：1409814011 班级：149641 题目:模糊控制的理论与发展概述摘要模糊控制理论是以模糊数学为基础,用语言规则表示方法和先进的计算机技术,由模糊推理进行决策的一种高级控制策。
模糊控制作为以模糊集合论、模糊语言变量及模糊逻辑推理为基础的一种计算机数字控制，它已成为目前实现智能控制的一种重要而又有效的形式尤其是模糊控制和神经网络、遗传算法及混沌理论等新学科的融合，正在显示出其巨大的应用潜力。
实质上模糊控制是一种非线性控制，从属于智能控制的范畴。
模糊控制的一大特点是既具有系统化的理论，又有着大量实际应用背景。
本文简单介绍了模糊控制的概念及应用，详细介绍了模糊控制器的设计，其中包含模糊控制系统的原理、模糊控制器的分类及其设计元素。
关键词：模糊控制；模糊控制器；现状及展望Abstract Fuzzy control theory is based on fuzzy mathematics, using language rule representation and advanced computer technology, it is a high-level control strategy which can make decision by the fuzzy reasoning. Fuzzy control is a computer numerical contro which based fuzzy set theory, fuzzy linguistic variables and fuzzy logic, it has become the effective form of intelligent control especially in the form of fuzzy control and neural networks, genetic algorithms and chaos theory and other new integration of disciplines, which is showing its great potential. Fuzzy control is essentially a nonlinear control, and subordinates intelligent control areas. A major feature of fuzzy control is both a systematic theory and a large number of the application background.This article introduces simply the concept and application of fuzzy control and introduces detailly the design of the fuzzy controller. It contains the principles of fuzzy control system, the classification of fuzzy controller and its design elements.Key words: Fuzzy Control; Fuzzy Controller; Status and Prospects.引言传统的常规PID控制方式是根据被控制对象的数学模型建立，虽然它的控制精度可以很高，但对于多变量且具有强耦合性的时变系统表现出很大的误差。
fuzzy_control模糊控制算法
模糊逻辑跟踪控制
模糊控制的基本原理框图如下：
图1 模糊控制的基本原理框图
模糊控制器是模糊控制系统的核心，一个模糊控制系统的性能优劣主要取决于模糊控制器的结构、所采用的模糊控制规则、合成推理算法，以及模糊决策的方法等因素。
文本对应的程序，采用单变量二维模糊控制器，输入分别是 误差和误差的倒数，输出为控制量。
其中基模糊控制器结构如图2所示，模糊规则表如表1所示。
de dt
图2模糊控制器结构
表1 模糊规则表
在本仿真程序中，被控对象为：5
3245.235*10()+87.35 1.047*10G s s s s
=+
采样时间为1ms ，采用z 变换进行离散化，经过z 变换后的离散化对象为：
()(2)(1)(3)(2)(4)(3)(2)(1) (3)(2)(4)(3)
yout k den yout k den yout k den yout k num u k num u k num u k =------+-+-+-
其中，反模糊化采用“Centroid”方法，方波响应及控制器输出结果如图3和图4所示：。
模糊控制理论FuzzyControl
模糊控制理论 Fuzzy Control在传统的控制领域里，控制系统动态模式的精确与否是影响控制优劣的最主要关键， 系统动态的信息越详细，则越能达到精确控制的目的。
然而，对于复杂的系统，由于 变量太多，往往难以正确的描述系统的动态，于是工程师便利用各种方法来简化系统 动态，以达成控制的目的，但却不尽理想。
换言之，传统的控制理论对于明确系统有 强而有力的控制能力，但对于过于复杂或难以精确描述的系统，则显得无能为力了。
因此便尝试着以 模糊数学 来处理这些控制问题。
自从Zadeh 发展出模糊数学之后，对于不明确系统的控制有极大的贡献，自七 年代以后，便有一些实用的模糊控制器相继的完成，使得我们在控制领域中又向前迈 进了一大步，在此将对模糊控制理论做一番浅介。
［编辑本段］概述3.1概念图3.1为一般控制系统的架构，此架构包含了五个主要部分，即 ：定义变量、模糊化、知识库、逻辑判断及反模糊化，底下将就每一部分做简单的说明：(1) 定义变量：也就是决定程序被观察的状况及考虑控制的动作，例如在一般控 制问题上，输入变量有输出误差 E 与输出误差之变化率 CE ，而控制变量则为下一个状态之输入 U 。
其中E 、CE 、U 统称为模糊变量。
xn JftfHZItwj? * }D7MMnstM^r I »?R |pane*n ・R ・M |JTI 于■•|| ----------------------------- ------ - ----模糊控制(2) 模糊化(fuzzify ):将输入值以适当的比例转换到论域的数值，利用口语化变量来描述测量物理量的过程，依适合的语言值( linguisitc value )求该值相对之隶属度，此口语化变量我们称之为模糊子集合( fuzzy subsets )。
(3) 知识库：包括数据库( data base )与规则库(rule base )两部分，其中数据库是提供处理模糊数据之相关定义；而规则库则藉由一群语言控制规则描述控制目标和策略。
模糊控制简介
R=(NBe × PBu ) + ( NSe × PSu ) + (0e × 0u ) + ( PSe × NSu ) + ( PBe × NSu )
NBe × PBu = (1, 0.5, 0, 0, 0, 0, 0) × (0, 0, 0, 0, 0, 0.5,1) NSe × PSu = (0, 0.5,1, 0, 0, 0, 0) × (0, 0, 0, 0,1, 0.5, 0) 0e × 0u = (0, 0, 0.5,1, 0.5, 0, 0) × (0, 0, 0.5,1, 0.5, 0, 0) PSe × NSu = (0, 0, 0, 0,1, 0.5, 0) × (0, 0.5,1, 0, 0, 0, 0) PBe × NSu = (0, 0, 0, 0, 0, 0.5,1) × (1, 0.5, 0, 0, 0, 0, 0) 0 0 0 0 0.5 1 0 0 0 0 0 0.5 0.5 0.5 0 0 0.5 0.5 1 0 0 R= 0 0 0.5 1 0.5 0 0 0 0.5 1 0.5 0.5 0 0 0 0 0 0.5 0.5 0.5 0 1 0.5 0 0 0 0 0
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六．思考
矛盾对立统一规律： 矛盾对立统一规律：两面性 • 优点：模糊逻辑本身提供了由专家构造语 优点： 言信息并将其转化为控制策略的一种系统 的推理方法， 的推理方法，因而能够解决许多复杂而无 法建立精确数学模型系统的控制问题， 法建立精确数学模型系统的控制问题，所 以它是处理推理系统和控制系统中不精确 和不确定性的一种有效方法。从广义上讲， 和不确定性的一种有效方法。从广义上讲， 模糊控制是适于模糊推理， 模糊控制是适于模糊推理，模仿人的思维 方式， 方式，对难以建立精确数学模型的对象实 施的一种控制策略。 施的一种控制策略。它是模糊数学同控制 理论相结合的产物， 理论相结合的产物，同时也是智能控制的 重要组成部分。 重要组成部分。
模糊pid控制-python实现
模糊pid控制 python实现模糊PID控制（Fuzzy PID control）是一种基于模糊逻辑的控制方法，它结合了模糊控制和经典PID控制的优点，可以在复杂和不确定的环境中实现精确的控制。
本文将介绍模糊PID控制的原理、实现方法以及在Python中的应用。
一、模糊PID控制的原理PID控制是一种经典的控制方法，它通过比较实际输出与期望输出之间的误差，根据比例、积分和微分三个参数进行调节，使系统输出逐渐趋近于期望值。
然而，传统的PID控制方法在面对非线性、时变和不确定性系统时表现不佳。
模糊PID控制通过引入模糊逻辑来解决传统PID控制的问题。
模糊逻辑是一种能够处理模糊信息的数学方法，它可以将模糊的输入映射到模糊的输出。
模糊PID控制器通过将误差、误差变化率和误差积分三个输入量模糊化，然后根据一组模糊规则进行推理，得到模糊输出。
最后，通过解模糊化的方法将模糊输出转化为具体的控制量。
二、模糊PID控制的实现方法1. 模糊化模糊化是将具体的输入量映射到模糊集合上的过程。
常用的模糊化方法有三角隶属函数、梯形隶属函数和高斯隶属函数等。
根据具体的问题和经验，选择合适的隶属函数进行模糊化。
2. 规则库规则库是模糊PID控制的核心。
它包含了一组模糊规则，用于根据输入量的模糊值推理出输出量的模糊值。
模糊规则一般采用IF-THEN的形式，例如“IF 误差是A1 AND 误差变化率是B2 THEN 输出是C3”。
规则库的设计需要根据具体问题进行，可以基于经验或者专家知识。
3. 推理机制推理机制是根据模糊规则进行推理的过程。
常用的推理方法有最大最小合成、模糊推理和模糊推理和等。
推理机制将模糊输入与规则库进行匹配，然后根据匹配的程度计算出模糊输出的隶属度。
4. 解模糊化解模糊化是将模糊输出转化为具体的控制量的过程。
常用的解模糊化方法有最大隶属度法、面积法和重心法等。
解模糊化方法根据模糊输出的隶属度分布，计算出具体的控制量。
(英文PPT1)模糊控制讲义第一章(1)
Example 1.1.1 A={ x | x are integers from 1 to 10}
Example 1.1.2 (Human)={Animals who can make and use tools, think, abstract and reason}
1.1.1 Example 1 －“Human” and “Age”
A systemic theory of fuzzy control must be established.
Combining fuzzy control with other control
methods. How to model the fuzzy system and how to establish fuzzy control rules? Further application in industry.
1.2 Fuzzy Control Theory
1.2.1 Incompatibility theory
1.2.2 Development of fuzzy control theory1.2.1 In源自ompatibility theory
“As the complexity of a system increases, our ability to make precise and yet significant statements about its behaviour diminishes until a threshold is reached beyond which precision and significance (or relevance) become almost mutually exclusive characteristics.”
现代控制理论
现代控制理论是在20世纪50年代中期迅速兴起的空间技术的推动下发展起来的。
空间技术的发展迫切要求建立新的控制原理，以解决诸如把宇宙火箭和人造卫星用最少燃料或最短时间准确地发射到预定轨道一类的控制问题。
这类控制问题十分复杂，采用经典控制理论难以解决。
1958年，苏联科学家Л.С.庞特里亚金提出了名为极大值原理的综合控制系统的新方法。
在这之前，美国学者R.贝尔曼于1954年创立了动态规划，并在1956年应用于控制过程。
他们的研究成果解决了空间技术中出现的复杂控制问题，并开拓了控制理论中最优控制理论这一新的领域。
1960～1961年，美国学者R.E.卡尔曼和R.S.布什建立了卡尔曼-布什滤波理论，因而有可能有效地考虑控制问题中所存在的随机噪声的影响，把控制理论的研究范围扩大，包括了更为复杂的控制问题。
几乎在同一时期内，贝尔曼、卡尔曼等人把状态空间法系统地引入控制理论中。
状态空间法对揭示和认识控制系统的许多重要特性具有关键的作用。
其中能控性和能观测性尤为重要，成为控制理论两个最基本的概念。
到60年代初，一套以状态空间法、极大值原理、动态规划、卡尔曼-布什滤波为基础的分析和设计控制系统的新的原理和方法已经确立，这标志着现代控制理论的形成。
学科内容现代控制理论所包含的学科内容十分广泛，主要的方面有：线性系统理论、非线性系统理论、最优控制理论、随机控制理论和适应控制理论。
线性系统理论它是现代控制理论中最为基本和比较成熟的一个分支，着重于研究线性系统中状态的控制和观测问题，其基本的分析和综合方法是状态空间法。
按所采用的数学工具，线性系统理论通常分成为三个学派：基于几何概念和方法的几何理论，代表人物是W.M.旺纳姆；基于抽象代数方法的代数理论，代表人物是R.E.卡尔曼；基于复变量方法的频域理论，代表人物是H.H.罗森布罗克。
非线性系统理论非线性系统的分析和综合理论尚不完善。
研究领域主要还限于系统的运动稳定性、双线性系统的控制和观测问题、非线性反馈问题等。
PID控制与模糊控制比较
PID控制与模糊控制的比较专业：控制理论与控制工程班级：级班姓名：X X X学号：xxxxxxxxxxxxxx摘要：介绍了PID控制系统和模糊控制系统的工作原理。
PID控制器结构简单，实现简单，控制效果良好，已经得到了广泛的应用。
而模糊控制器相对复杂，但在许多的智能化家用电器中也得到了大量应用。
但对于一个简单的系统来讲，哪一种控制方法更好，是不是越智能的控制就能得到越好的效果。
关键词：PID控制，模糊控制，比较Abstract: Introduced the working principle of PID control system and fuzzy control system. PID controller structure is simple, implementation is simple, the control effect is good, has been widely used. And fuzzy controller is relatively complicated, but in a lot of intelligent household appliances also received a large number of applications. But for a simple system, which kind of control method is better, is weather the intelligent control can obtain the good effect.Key words: PID control, fuzzy control, compare目录一、问题的提出 (1)二、PID控制器的设计 (2)1.PID控制原理图： (2)2.PID控制器传递函数的一般表达式 (2)三、模糊控制器的设计 (3)1．模糊控制原理图 (3)2．模糊控制器传递函数一般表达形式 (4)四、系统仿真 (4)五、总结 (14)参考文献： (15)一、问题的提出当今的自动控制技术都是基于反馈的概念。
Fuzzy control for a lamp glass pipe sealing proces
专利名称：Fuzzy control for a lamp glass pipe sealing process发明人：Hishida, Masahiko, c/o MitsubishiGenshiryoku,Yokoyama, Terukuni, c/oMitsubishi Genshiryoku,Atsumi, Yoshihiro,c/o Mitsubishi Genshiryoku,Masui,Motonobu,Ban, Yasuo申请号：EP92116178.2申请日：19920922公开号：EP0534361B1公开日：19961227专利内容由知识产权出版社提供摘要：A fuzzy controller is provided which enables even an unskilled operator to easily adjust various conditions in a glass pipe sealing process. The fuzzy controller (23) has a fuzzy control processor including an image processing unit for processing and calculating image information as a softened state change value of the glass pipe (1) and a combustion state value of burner flame, and a fuzzy control processing unit for calculating and outputting, by receiving a result of this calculation, a suitable control value for controlling parameters relating to the burner flame by fuzzy inference. The fuzzy controller (23) may further have a fuzzy diagnosis support processor which, if there is an abnormality in the sealed portion of the glass pipe and if the state of the glass pipe after sealing is input to the manipulation instruction data input support processor by the operator, automatically ascertains the cause of the abnormality by using fuzzy inference and displays it on a CRT (22). A fuzzy control system and a fuzzy control process are alsoprovided which enable automatization of a lamp glass pipe sealing process by using this fuzzy controller.申请人：MITSUBISHI HEAVY IND LTD,IWASAKI ELECTRIC CO LTD地址：JP,JP国籍：JP,JP代理机构：Lehn, Werner, Dipl.-Ing.更多信息请下载全文后查看。
Fuzzy control system - Wikipedia, the free encyclopedia
Fuzzy control systemFrom Wikipedia, the free encyclopediaA fuzzy control system is a control system based on fuzzy logic—a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of either 1 or 0 (true or false, respectively).Contents1 Overview2 History and applications3 Fuzzy sets3.1 Fuzzy control in detail3.2 Building a fuzzy controller4 Antilock brakes5 Logical interpretation of fuzzy control6 See also7 References8 Further reading9 External linksOverviewFuzzy logic is widely used in machine control. The term "fuzzy" refers to the fact that the logic involved can deal with concepts that cannot be expressed as "true" or "false" but rather as "partially true". Although alternative approaches such as genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases, fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, so that their experience can be used in the design of the controller. This makes it easier to mechanize tasks that are already successfully performed by humans.History and applicationsFuzzy logic was first proposed by Lotfi A. Zadeh of the University of California at Berkeley in a 1965 paper. He elaborated on his ideas in a 1973 paper that introduced the concept of "linguistic variables", which in this article equates to a variable defined as a fuzzy set. Other research followed, with thefirst industrial application, a cement kiln built in Denmark, coming on line in 1975.Fuzzy systems were initially implemented in Japan.Interest in fuzzy systems was sparked by Seiji Yasunobu and Soji Miyamoto of Hitachi, who in 1985 provided simulations that demonstrated the feasibility of fuzzy control systems for the Sendairailway. Their ideas were adopted, and fuzzy systems were used to control accelerating, braking, and stopping when the line opened in 1987.In 1987, Takeshi Yamakawa demonstrated the use of fuzzy control, through a set of simple dedicated fuzzy logic chips, in an "inverted pendulum" experiment. This is a classic control problem, in whicha vehicle tries to keep a pole mounted on its top by a hinge upright by moving back and forth.Yamakawa subsequently made the demonstration more sophisticated by mounting a wine glass containing water and even a live mouse to the top of the pendulum: the system maintained stability in both cases. Yamakawa eventually went on to organize his own fuzzy-systems research lab to help exploit his patents in the field.Japanese engineers subsequently developed a wide range of fuzzy systems for both industrial and consumer applications. In 1988 Japan established the Laboratory for International Fuzzy Engineering (LIFE), a cooperative arrangement between 48 companies to pursue fuzzy research. The automotive company Volkswagen was the only foreign corporate member of LIFE, dispatching a researcher for a duration of three years.Japanese consumer goods often incorporate fuzzy systems. Matsushita vacuum cleaners usemicrocontrollers running fuzzy algorithms to interrogate dust sensors and adjust suction poweraccordingly. Hitachi washing machines use fuzzy controllers to load-weight, fabric-mix, and dirt sensors and automatically set the wash cycle for the best use of power, water, and detergent.Canon developed an autofocusing camera that uses a charge-coupled device (CCD) to measure theclarity of the image in six regions of its field of view and use the information provided todetermine if the image is in focus. It also tracks the rate of change of lens movement duringfocusing, and controls its speed to prevent overshoot. The camera's fuzzy control system uses 12 inputs: 6 to obtain the current clarity data provided by the CCD and 6 to measure the rate of change of lens movement. The output is the position of the lens. The fuzzy control system uses 13 rules and requires 1.1 kilobytes of memory.An industrial air conditioner designed by Mitsubishi uses 25 heating rules and 25 cooling rules. A temperature sensor provides input, with control outputs fed to an inverter, a compressor valve, anda fan motor. Compared to the previous design, the fuzzy controller heats and cools five timesfaster, reduces power consumption by 24%, increases temperature stability by a factor of two, and uses fewer sensors.Other applications investigated or implemented include: character and handwriting recognition;optical fuzzy systems; robots, including one for making Japanese flower arrangements; voice-controlled robot helicopters (hovering is a "balancing act" rather similar to the inverted pendulum problem); control of flow of powders in film manufacture; elevator systems; and so on.Work on fuzzy systems is also proceeding in the US and Europe, though on a less extensive scale than in Japan.The US Environmental Protection Agency has investigated fuzzy control for energy-efficient motors, and NASA has studied fuzzy control for automated space docking: simulations show that a fuzzycontrol system can greatly reduce fuel consumption.Firms such as Boeing, General Motors, Allen-Bradley, Chrysler, Eaton, and Whirlpool have worked on fuzzy logic for use in low-power refrigerators, improved automotive transmissions, and energy-efficient electric motors.In 1995 Maytag introduced an "intelligent" dishwasher based on a fuzzy controller and a "one-stop sensing module" that combines a thermistor, for temperature measurement; a conductivity sensor, to measure detergent level from the ions present in the wash; a turbidity sensor that measuresscattered and transmitted light to measure the soiling of the wash; and a magnetostrictive sensor to read spin rate. The system determines the optimum wash cycle for any load to obtain the best results with the least amount of energy, detergent, and water. It even adjusts for dried-on foods bytracking the last time the door was opened, and estimates the number of dishes by the number of times the door was opened.Research and development is also continuing on fuzzy applications in software, as opposed to firmware, design, including fuzzy expert systems and integration of fuzzy logic with neural-network and so-called adaptive "genetic" software systems, with the ultimate goal of building "self-learning" fuzzy-controlsystems.Fuzzy setsThe input variables in a fuzzy control system are in general mapped by sets of membership functions similar to this, known as "fuzzy sets". The process of converting a crisp input value to a fuzzy value is called "fuzzification".A control system may also have various types of switch, or "ON-OFF", inputs along with its analog inputs, and such switch inputs of course will always have a truth value equal to either 1 or 0, but the scheme can deal with them as simplified fuzzy functions that happen to be either one value or another.Given "mappings" of input variables into membership functions and truth values, the microcontroller then makes decisions for what action to take, based on a set of "rules", each of the form:IF brake temperature IS warm AND speed IS not very fastTHEN brake pressure IS slightly decreased.In this example, the two input variables are "brake temperature" and "speed" that have values defined as fuzzy sets. The output variable, "brake pressure" is also defined by a fuzzy set that can have valueslike "static" or "slightly increased" or "slightly decreased" etc.This rule by itself is very puzzling since it looks like it could be used without bothering with fuzzy logic, but remember that the decision is based on a set of rules:All the rules that apply are invoked, using the membership functions and truth values obtained from the inputs, to determine the result of the rule.This result in turn will be mapped into a membership function and truth value controlling the output variable.These results are combined to give a specific ("crisp") answer, the actual brake pressure, aprocedure known as "defuzzification".This combination of fuzzy operations and rule-based "inference" describes a "fuzzy expert system".Traditional control systems are based on mathematical models in which the control system is described using one or more differential equations that define the system response to its inputs. Such systems are often implemented as "PID controllers" (proportional-integral-derivative controllers). They are the products of decades of development and theoretical analysis, and are highly effective.If PID and other traditional control systems are so well-developed, why bother with fuzzy control? It has some advantages. In many cases, the mathematical model of the control process may not exist, or may be too "expensive" in terms of computer processing power and memory, and a system based on empirical rules may be more effective.Furthermore, fuzzy logic is well suited to low-cost implementations based on cheap sensors, low-resolution analog-to-digital converters, and 4-bit or 8-bit one-chip microcontroller chips. Such systems can be easily upgraded by adding new rules to improve performance or add new features. In many cases, fuzzy control can be used to improve existing traditional controller systems by adding an extra layer of intelligence to the current control method.Fuzzy control in detailFuzzy controllers are very simple conceptually. They consist of an input stage, a processing stage, and an output stage. The input stage maps sensor or other inputs, such as switches, thumbwheels, and so on, to the appropriate membership functions and truth values. The processing stage invokes each appropriate rule and generates a result for each, then combines the results of the rules. Finally, the output stage converts the combined result back into a specific control output value.The most common shape of membership functions is triangular, although trapezoidal and bell curves are also used, but the shape is generally less important than the number of curves and their placement. From three to seven curves are generally appropriate to cover the required range of an input value, or the "universe of discourse" in fuzzy jargon.As discussed earlier, the processing stage is based on a collection of logic rules in the form of IF-THEN statements, where the IF part is called the "antecedent" and the THEN part is called the "consequent". Typical fuzzy control systems have dozens of rules.Consider a rule for a thermostat:IF (temperature is "cold") THEN (heater is "high")This rule uses the truth value of the "temperature" input, which is some truth value of "cold", to generate a result in the fuzzy set for the "heater" output, which is some value of "high". This result is used with the results of other rules to finally generate the crisp composite output. Obviously, the greater the truth value of "cold", the higher the truth value of "high", though this does not necessarily mean that the output itself will be set to "high" since this is only one rule among many. In some cases, the membership functions can be modified by "hedges" that are equivalent to adjectives. Common hedges include "about", "near", "close to", "approximately", "very", "slightly", "too", "extremely", and "somewhat". These operations may have precise definitions, though the definitions can vary considerably between different implementations. "Very", for one example, squares membership functions; since the membership values are always less than 1, this narrows the membership function. "Extremely" cubes the values to give greater narrowing, while "somewhat" broadens the function by taking the square root.In practice, the fuzzy rule sets usually have several antecedents that are combined using fuzzy operators, such as AND, OR, and NOT, though again the definitions tend to vary: AND, in one popular definition, simply uses the minimum weight of all the antecedents, while OR uses the maximum value. There is also a NOT operator that subtracts a membership function from 1 to give the "complementary" function.There are several ways to define the result of a rule, but one of the most common and simplest is the "max-min" inference method, in which the output membership function is given the truth value generated by the premise.Rules can be solved in parallel in hardware, or sequentially in software. The results of all the rules that have fired are "defuzzified" to a crisp value by one of several methods. There are dozens, in theory, each with various advantages or drawbacks.The "centroid" method is very popular, in which the "center of mass" of the result provides the crisp value. Another approach is the "height" method, which takes the value of the biggest contributor. The centroid method favors the rule with the output of greatest area, while the height method obviously favors the rule with the greatest output value.The diagram below demonstrates max-min inferencing and centroid defuzzification for a system with input variables "x", "y", and "z" and an output variable "n". Note that "mu" is standard fuzzy-logic nomenclature for "truth value":Notice how each rule provides a result as a truth value of a particular membership function for the output variable. In centroid defuzzification the values are OR'd, that is, the maximum value is used and values are not added, and the results are then combined using a centroid calculation.Fuzzy control system design is based on empirical methods, basically a methodical approach to trial-and-error. The general process is as follows:Document the system's operational specifications and inputs and outputs.Document the fuzzy sets for the inputs.Document the rule set.Determine the defuzzification method.Run through test suite to validate system, adjust details as required.Complete document and release to production.As a general example, consider the design of a fuzzy controller for a steam turbine. The block diagram of this control system appears as follows:The input and output variables map into the following fuzzy set:—where:N3: Large negative.N2: Medium negative.N1: Small negative.Z: Zero.P1: Small positive.P2: Medium positive.P3: Large positive.The rule set includes such rules as:rule 1: IF temperature IS cool AND pressure IS weak,THEN throttle is P3.rule 2: IF temperature IS cool AND pressure IS low,THEN throttle is P2.rule 3: IF temperature IS cool AND pressure IS ok,THEN throttle is Z.rule 4: IF temperature IS cool AND pressure IS strong,THEN throttle is N2.In practice, the controller accepts the inputs and maps them into their membership functions and truth values. These mappings are then fed into the rules. If the rule specifies an AND relationship between the mappings of the two input variables, as the examples above do, the minimum of the two is used as the combined truth value; if an OR is specified, the maximum is used. The appropriate output state is selected and assigned a membership value at the truth level of the premise. The truth values are then defuzzified. For an example, assume the temperature is in the "cool" state, and the pressure is in the "low" and "ok" states. The pressure values ensure that only rules 2 and 3 fire:The two outputs are then defuzzified through centroid defuzzification:__________________________________________________________________| Z P21 -+ * *| * * * *| * * * *| * * * *| * 222222222| * 22222222222| 333333332222222222222+---33333333222222222222222-->^+150__________________________________________________________________The output value will adjust the throttle and then the control cycle will begin again to generate the next value .Building a fuzzy controllerConsider implementing with a microcontroller chip a simple feedback controller:A fuzzy set is defined for the input error variable "e", and the derived change in error, "delta", as well as the "output", as follows:LP: large positiveSP: small positiveZE: zeroSN: small negativeLN: large negativeIf the error ranges from -1 to +1, with the analog-to-digital converter used having a resolution of 0.25, then the input variable's fuzzy set (which, in this case, also applies to the output variable) can be described very simply as a table, with the error / delta / output values in the top row and the truth values for each membership function arranged in rows beneath:_______________________________________________________________________-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1_______________________________________________________________________mu(LP) 0 0 0 0 0 0 0.3 0.7 1mu(SP) 0 0 0 0 0.3 0.7 1 0.7 0.3mu(ZE) 0 0 0.3 0.7 1 0.7 0.3 0 0mu(SN) 0.3 0.7 1 0.7 0.3 0 0 0 0mu(LN) 1 0.7 0.3 0 0 0 0 0 0_______________________________________________________________________—or, in graphical form (where each "X" has a value of 0.1):LN SN ZE SP LP+------------------------------------------------------------------+| |-1.0 | XXXXXXXXXX XXX : : : |-0.75 | XXXXXXX XXXXXXX : : : |-0.5 | XXX XXXXXXXXXX XXX : : |-0.25 | : XXXXXXX XXXXXXX : : |0.0 | : XXX XXXXXXXXXX XXX : |0.25 | : : XXXXXXX XXXXXXX : |0.5 | : : XXX XXXXXXXXXX XXX |0.75 | : : : XXXXXXX XXXXXXX |1.0 | : : : XXX XXXXXXXXXX || |+------------------------------------------------------------------+Suppose this fuzzy system has the following rule base:rule 1: IF e = ZE AND delta = ZE THEN output = ZErule 2: IF e = ZE AND delta = SP THEN output = SNrule 3: IF e = SN AND delta = SN THEN output = LPrule 4: IF e = LP OR delta = LP THEN output = LNThese rules are typical for control applications in that the antecedents consist of the logical combination of the error and error-delta signals, while the consequent is a control command output. The rule outputs can be defuzzified using a discrete centroid computation:SUM( I = 1 TO 4 OF ( mu(I) * output(I) ) ) / SUM( I = 1 TO 4 OF mu(I) )Now, suppose that at a given time we have:e = 0.25delta = 0.5Then this gives:________________________e delta________________________mu(LP) 0 0.3mu(SP) 0.7 1mu(ZE) 0.7 0.3mu(SN) 0 0mu(LN) 0 0________________________Plugging this into rule 1 gives:rule 1: IF e = ZE AND delta = ZE THEN output = ZEmu(1) = MIN( 0.7, 0.3 ) = 0.3output(1) = 0-- where:mu(1): Truth value of the result membership function for rule 1. In terms of a centroid calculation, this is the "mass" of this result for this discrete case.output(1): Value (for rule 1) where the result membership function (ZE) is maximum over the output variable fuzzy set range. That is, in terms of a centroid calculation, the location of the "center of mass" for this individual result. This value is independent of the value of "mu". It simplyidentifies the location of ZE along the output range.The other rules give:rule 2: IF e = ZE AND delta = SP THEN output = SNmu(2) = MIN( 0.7, 1 ) = 0.7output(2) = -0.5rule 3: IF e = SN AND delta = SN THEN output = LPmu(3) = MIN( 0.0, 0.0 ) = 0output(3) = 1rule 4: IF e = LP OR delta = LP THEN output = LNmu(4) = MIN( 0.0, 0.3 ) = 0output(4) = -1The centroid computation yields:—for the final control output. Simple. Of course the hard part is figuring out what rules actually work correctly in practice. If you have problems figuring out the centroid equation, remember that a centroid is defined by summing all the moments (location times mass) around the center of gravity and equating the sum to zero. So if is the center of gravity, is the location of each mass, and is each mass, this gives:In our example, the values of mu correspond to the masses, and the values of X to location of the masses (mu, however, only 'corresponds to the masses' if the initial 'mass' of the output functions are all the same/equivalent. If they are not the same, i.e. some are narrow triangles, while others maybe wide trapizoids or shouldered triangles, then the mass or area of the output function must be known or calculated. It is this mass that is then scaled by mu and multiplied by its location X_i).This system can be implemented on a standard microprocessor, but dedicated fuzzy chips are now available. For example, Adaptive Logic INC of San Jose, California, sells a "fuzzy chip", the AL220, that can accept four analog inputs and generate four analog outputs. A block diagram of the chip is shown below:+---------+ +-------+analog --4-->| analog | | mux / +--4--> analogin | mux | | SH | out+----+----+ +-------+| ^V |+-------------+ +--+--+| ADC / latch | | DAC |+------+------+ +-----+| ^| |8 +-----------------------------+| | || V || +-----------+ +-------------+ |+-->| fuzzifier | | defuzzifier +--++-----+-----+ +-------------+| ^| +-------------+ || | rule | |+->| processor +--+| (50 rules) |+------+------+|+------+------+| parameter || memory || 256 x 8 |+-------------+ADC: analog-to-digital converterDAC: digital-to-analog converterSH: sample/holdAntilock brakesAs a first example, consider an anti-lock braking system, directed by a microcontroller chip. The microcontroller has to make decisions based on brake temperature, speed, and other variables in the system.The variable "temperature" in this system can be subdivided into a range of "states": "cold", "cool", "moderate", "warm", "hot", "very hot". The transition from one state to the next is hard to define.An arbitrary static threshold might be set to divide "warm" from "hot". For example, at exactly 90 degrees, warm ends and hot begins. But this would result in a discontinuous change when the input value passed over that threshold. The transition wouldn't be smooth, as would be required in braking situations.The way around this is to make the states fuzzy. That is, allow them to change gradually from one state to the next. In order to do this there must be a dynamic relationship established between different factors.We start by defining the input temperature states using "membership functions":With this scheme, the input variable's state no longer jumps abruptly from one state to the next. Instead, as the temperature changes, it loses value in one membership function while gaining value in the next. In other words, its ranking in the category of cold decreases as it becomes more highly ranked in the warmer category.At any sampled timeframe, the "truth value" of the brake temperature will almost always be in some degree part of two membership functions: i.e.: '0.6 nominal and 0.4 warm', or '0.7 nominal and 0.3 cool', and so on.The above example demonstrates a simple application, using the abstraction of values from multiple values. This only represents one kind of data, however, in this case, temperature.Adding additional sophistication to this braking system, could be done by additional factors such as traction, speed, inertia, set up in dynamic functions, according to the designed fuzzy system.[1]Logical interpretation of fuzzy controlIn spite of the appearance there are several difficulties to give a rigorous logical interpretation of the IF-THEN rules. As an example, interpret a rule as IF (temperature is "cold") THEN (heater is "high") by the first order formula Cold(x)→High(y) and assume that r is an input such that Cold(r) is false. Then the formula Cold(r)→High(t) is true for any t and therefore any t gives a correct control given r.A rigorous logical justification of fuzzy control is given in Hájek's book (see Chapter 7) where fuzzy control is represented as a theory of Hájek's basic logic. Also in Gerla 2005 a logical approach to fuzzy control is proposed based on fuzzy logic programming. Indeed, denote by f the fuzzy function arising of an IF-THEN systems of rules. Then we can translate this system into fuzzy program in such a way that f is the interpretation of a vague predicate Good(x,y) in the least fuzzy Herbrand model of this program. This gives further useful tools to fuzzy control.See alsoDynamic logicBayesian inferenceFunction approximationFuzzy markup languageNeural networksNeuro-fuzzyFuzzy control languageType-2 fuzzy sets and systemsReferences1. ^ Vichuzhanin, Vladimir (12 April 2012). "Realization of a fuzzy controller with fuzzy dynamic correction".Central European Journal of Engineering2 (3): 392–398. doi:10.2478/s13531-012-0003-7(/10.2478%2Fs13531-012-0003-7).Gerla G., Fuzzy Logic Programming and fuzzy control, Studia Logica, 79 (2005) 231-254.Bastian A., Identifying Fuzzy Models utilizing Genetic Programming, Fuzzy Sets and Systems 113,333–350, 2000Hájek P., Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998.Mamdani, E. H., Application of fuzzy algorithms for the control of a simple dynamic plant. In Proc IEEE (1974), 121-159.Further readingKevin M. Passino and Stephen Yurkovich, Fuzzy Control, Addison Wesley Longman, Menlo Park, CA, 1998 (522 pages) (/~passino/FCbook.pdf)Kazuo Tanaka; Hua O. Wang (2001). Fuzzy control systems design and analysis: a linear matrixinequality approach. John Wiley and Sons. ISBN 978-0-471-32324-2.Cox, E. (Oct. 1992). Fuzzy fundamentals. Spectrum, IEEE, 29:10. pp. 58–61.Cox, E. (Feb. 1993) Adaptive fuzzy systems. Spectrum, IEEE, 30:2. pp. 7–31.Jan Jantzen, "Tuning Of Fuzzy PID Controllers", Technical University of Denmark, report 98-H 871, September 30, 1998. [1] (http://www.iau.dtu.dk/~jj/pubs/fpid.pdf)Jan Jantzen, Foundations of Fuzzy Control. Wiley, 2007 (209 pages) (Table of contents)(/WileyCDA/WileyTitle/productCd-0470029633,descCd-tableOfContents.html)Computational Intelligence: A Methodological Introduction by Kruse, Borgelt, Klawonn, Moewes,Steinbrecher, Held, 2013, Springer, ISBN 9781447150121External linksIntroduction to Fuzzy Control (/~msimoes/documents/Intro_Fuzzy_Logic.pdf) Fuzzy Logic in Embedded Microcomputers and Control Systems(/downloads/fuzlogic.pdf)IEC 1131-7 CD1 (/binaries/ieccd1.pdf) IEC 1131-7 CD1 PDFRetrieved from "/w/index.php?title=Fuzzy_control_system&oldid=630783009" Categories: Fuzzy logic Control engineeringThis page was last modified on 23 October 2014 at 12:17.Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is aregistered trademark of the Wikimedia Foundation, Inc., a non-profit organization.。
模糊控制算法单片机实现
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20020101
摘要
押出机是电线电缆工业中的核心设备，现行的电线电缆成套设备生产厂家广 泛采用基于ＰＬＣ的自动控制系统。一方面，由于被控对象建模复杂，输入输出变 量多，并且输出变量之间关联性强等原因，基于ＰＬＣ的控制系统普遍存在着自动 化程度低的突出问题。另一方面，这种系统采用传统的模拟量和开关量控制，致‘ 使系统的生产精度低，可靠性差。本文从模糊控制的基础理论出发，对模糊控制 器的设计方法、模糊控制的单片机实现方法进行了分析和对比研究，在此基础上 提出了基于ＭＯＴＯＲＯＬＡ ＭＣ６８ＨＣ０５８６单片机的押出机模糊控制系统。文章首先设 计出了４输入２输出的模糊控制器，其模糊控制规则能够比较有效地模仿熟练操 作人员的经验，合理解决输出的强关联性问题。然后利用模糊逻辑推理的方法， 结合大量的数学运算，离线计算出了简洁方便的模糊控制查询表。最后给出了模 糊控制查询的单片机实现方法及押出机模糊控制系统的核心控制部分的硬件电 路和软件流程。采用模糊控制的押出机自动控制系统，能够大大提高生产的自动 化程度，可实现～个操作工人轻松控制多条生产流水线，较大地提高劳动生产率。 另外，系统采用基于ＳＣＩ串行通信总线的数字控制，代替原系统中的模拟量和丌 关量控制，能够有效提高系统的生产精度，改善系统的可靠性。本文的研究对我 国电线电缆工业成套设备的设计和生产具有一定的指导意义，如做进一步的研究 和调试，将具有较大的经济价值。
智能控制--模糊控制论文【范本模板】
华北电力大学科技学院智能控制论文模糊控制的概述及模糊控制的应用姓名：班级:学号：日期:模糊控制的概述及模糊控制在污水处理中的应用摘要:模糊控制技术对工业自动化的进程有着极大地推动作用，本文简要讲述了模糊控制的定义、特点、原理和应用,简介模糊控制在污水处理中的应用.并讲诉了模糊控制的发展.关键词：模糊控制；污水处理。
An overview of the fuzzy control and fuzzy control in application ofwastewater treatmentAbstract：Fuzzy control of industrial process automation has greatly promoted the role, the paper briefly describes the definition of fuzzy control，characteristics, principles and applications，Introduction to fuzzy control in wastewater treatment applications. And complaints about the development of fuzzy control.Keywords: fuzzy control；sewage treatment。
1 引言传统的自动控制控制器的综合设计都要建立在被控对象准确的数学模型(即传递函数模型或状态空间模型)的基础上，但是在实际中,很多系统的影响因素很多，油气混合过程、缸内燃烧过程等) ，很难找出精确的数学模型。
这种情况下，模糊控制的诞生就显得意义重大.因为模糊控制不用建立数学模型不需要预先知道过程精确的数学模型。
2 概述刘金琨在《智能控制》教材里提到模糊控制的定义和特点：2。
1定义：从广义上，可将模糊控制定义为：“以模糊集合理论、模糊语言变量及模糊推理为基础的一类控制方法”,或定义为:“采用模糊集合理论和模糊逻辑，并同传统的控制理论相结合，模拟人的思维方式,对难以建立数学模型的对象实施所谓一种控制方法"。
4_FuzzyControl讲解
模糊化 Fuzzifier
模糊化 信号
推理单元 Reasoning
解模糊
Defuzzifier
清晰输 出信号
e
de/dt
第一步： 模糊化
偏差（E），偏差的变化率（EC）。 要采用模糊控制的技术，首先把它们转换成模糊集 合的隶属函数。 为了便于工程实现，通常把变量范围人为的定义为 离散的若干级，所定义的级数多少取决于输入量的 分辨率。 使用最多的为三角隶属函数。
鲁棒性：
– 模糊控制系统的鲁棒性强，干扰和参数变化对控制
效果的影响被大大减弱，尤其适合于非线性、时变 及纯滞后系统的控制。
模糊控制的突出特点
1. 控制系统的设计不要求知道被控对象的精确数学 模型。 2. 控制系统的鲁棒性强，适应于解决常规控制难以 解决的非线性、时变及大纯滞后等问题。 3. 以语言变量代替常规的数学变量，易于形成专家 的“知识”。
4. 控制推理采用“不精确推理”，推理过程模仿人 的思维过程，能够处理复杂甚至“病态”系统。
模糊控制简史
1973年 Zadeh在论文Outline of a new approach
to the analysis of complex systems and decision proccesses（IEEE Trans On Systems,
模糊控制简史
1987年 the Sendai City subway成为第一个成 功应用模糊控制的大型工程 ； 模糊控制的发展最初在西方遇到了较大的阻力； 然而在东方尤其是在日本，却得到了迅速而广 泛的推广应用。 近30年来，模糊控制不论从理论上还是技术上 都有了长足的进步，成为自动控制领域中一个 非常活跃而又硕果累累的分支。
揭秘模糊控制在洗衣机中的运行机制详解
揭秘模糊控制在洗衣机中的运行机制详解Revealing the Detailed Mechanism of Fuzzy Control in Washing MachinesWashing machines have become an indispensable appliance in modern households, revolutionizing the way we wash our clothes. Behind their seamless operation lies a complex control mechanism, with fuzzy control playing a crucial role. In this article, we will delve into the workings of fuzzy control in washing machines, demystifying its operation.Fuzzy control, a subset of artificial intelligence, is a control system that imitates human decision-making. Unlike traditional control systems that rely on precise numerical inputs, fuzzy control utilizes linguistic variables to handle uncertainty and imprecision. This feature makes it suitable for applications where human-like decision-making is required, such as in washing machines.The main objective of fuzzy control in washing machines is to optimize the washing process by adjusting various parameters, such as water temperature, washing time, and detergent dosage, based on the input variables, such as the type of fabric, dirtiness level,and desired washing outcome. These input variables are transformed into linguistic terms, such as "lightly soiled" or "heavily soiled," using fuzzy sets.The fuzzy control system in a washing machine consists of three main components: the fuzzifier, the inference engine, and the defuzzifier. The fuzzifier converts the crisp input variables into fuzzy sets, assigning membership degrees to each linguistic term. The inference engine applies a set of fuzzy rules, which are predefined by experts or learned through machine learning algorithms, to determine the appropriate control actions. Finally, the defuzzifier converts the fuzzy output into crisp control signals that can be directly applied to the washing machine's actuators.The fuzzy rules in a washing machine's control system are typically defined based on expert knowledge and experience. For example, a rule could state that if the fabric type is delicate and the dirtiness level is high, then the washing time should be increased and the water temperature should be decreased. These rules are represented in the form of "if-then" statements and are combined using fuzzy logic operators, such as "AND" and "OR."One of the advantages of fuzzy control in washing machines is its adaptability to varying conditions. By continuously monitoring the input variables, the fuzzy control system can dynamically adjust the control actions to achieve optimal washing performance. For example, if the dirtiness level suddenly increases during the washing process, the fuzzy control system can increase the detergent dosage and extend the washing time accordingly.In conclusion, fuzzy control plays a vital role in optimizing the washing process in washing machines. By imitating human decision-making and handling uncertainty, it allows for adaptable and efficient control actions. Understanding the detailed mechanism of fuzzy control in washing machines provides valuable insights into the technology behind this everyday appliance.洗衣机中模糊控制的运行机制详解洗衣机已成为现代家庭中不可或缺的家电，彻底改变了我们洗衣服的方式。
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Fuzzy control model in the hospitality industrySonja Petrovic-Lazarevic and Amy WongMonash University,Churchill,Victoria,AustraliaIntroductionFuzzy set theory was created 30years ago (Zadeh,1968).Fuzzy logic as a part of fuzzy set theory has been implemented in many industrial topics characterised byuncertainty and vagueness.Fuzzy logic implementation varies from numerous commercial products to decisionmakin g support (Zimmerman,1991;1993;Kruse et al.,1994;Bandemar and Gottwald,1995).The applicationof fuzzy set theory inthe differen t industries has been mainly visible in decisionmakin g support area (Ahmad,1990;Prascevic and Petrovic-Lazarevic,1992;1996;1997;1998).Service quality process plays a significant role in the hospitality industry (Johnston et al.,1990).In today's changing global environment,many businesses in the hospitality industry are faced withintensifying competition.In order to outdo its competitors,each hospitality industry's business must seek profitable ways to achieve competitive advantage andefficiency.One approach to competitive advantage is the delivery of high service quality (Rao and Kelkar,1997).This concept has been the subject of many conceptual and empirical studies,and it is generally accepted that quality has positive implications for an organisation'sperformance and competitive position.However,despite the vast amount of research done in the area of service quality,quality related issues have received little research attention within the hospitality context(Harrington and Akehurts,1996).In addition,it seems that there is a lack of fuzzy logic applicationinthe hospitality in dustry.According to recent research conducted by Wong et al.(1999),it was found that the best parameters of overall service quality areattributes relating to human resources (polite and knowledgeable employees,willingness to help)and tangibles (up-to-date-equipment,comfort,cleanliness andattractiveness of a hotel).The level of service quality influences customers'behavioural intentions towards the hotel.Parameters of customers'behavioural intentions include:.loyalty to the hospitality industry business unit;.propensity to switch to another business unit;and .willingness to pay for the service provided by the business unit.Both groups of parameters do not necessarily need to be highly predicted.The parameters canbe easily estimated for measuremen t.Such statements can help to develop the fuzzy logic approach to the hospitality industry.The approach should have two parts:1control model that relates to the service quality process;and2fuzzy logic model that explains behavioural intentions.The aim of this paper is to underline the significance of an application of fuzzy control inthe hospitality in dustry inorder to achieve or sustaincompetitive advan tage.The authors'approach to SQHI fuzzy control is partially based onthe work of Kacprzyk (1997)and Bojadziev and Bojadziev (1995).The first part of this paper deals with the definition of fuzzy control model.The second part presents the SQHI fuzzy control model.This model is based onanexpert system an d therefore,should be time absorbing.The final part of this paper provides a case study of the applicability and usefulness of the SQHI fuzzy control model.Concludingremarks give a directioninwhich the model should be further developed and applied.Fuzzy control modelFuzzy control model is a fuzzy model applied to control problems.Fuzzy controlmodelThe current issue and full text archive of this journal is available at [156]International Journal of Agile Management Systems 2/2[2000]156±162#MCB University Press [ISSN 1465-4652]KeywordsFuzzy sets,Service quality,Employees,Tangible factors,Hospitality industryAbstractFuzzy set theory supports business decision-making processes.So far it has been implemented in many industries,but not in thehospitality industry.An attempt is made to apply general fuzzy control model to service quality processes in the hospitality industry (SQHI).In this respect,the SQHI fuzzy control model is created.The case studyunderlines a possible practical use of the model in controlling service quality processes in order to achieve or sustain competitive advantage.replaces mathematical models for complex processes in an environment of uncertainty and imprecision (Bojadziev and Bojadziev,1995).It is effective for a system simulation where:.high precision is not required;and .control object has parameters available for estimationor measuremen t.Fuzzy control model is based on the fuzzy expert system implying a collection offuzzy membership functions and rules (see Figure 1).Fuzzy control process proceeds in several steps.These are:1Fuzzification .Linguistic variables that present inputs and output of the model are defined.Membership functions areapplied to their actual values to determine the degree of truth for each rule premise.2Inference .Setting the ``If F F F and F F F then''rules.One fuzzy subset is assigned to each output variable for each ually,it relates to fuzzy logic AND or fuzzy logic OR.3Rules evaluation .The real input numbers,called readings,are translated to proper terms of the corresponding linguistic variables.4Aggregation (conflict resolution).Choosing control action as a result of the applicationof a con trol rule.t relates to fuzzy logic MAX or fuzzy logic SUM.5Defuzzification .Decoding the output.This is the operation that produces a nonfuzzy control action presenting the membership function of an aggregated fuzzy action in the form of a single crisp value.SQHI fuzzy control modelThe control of service quality process seems to be the indicator to every business in thehospitality industry to achieving orsustaining competitive advantage.Such an indicator usually relies on strategic decision making process or implication of possible investment options.The indicator contains parameters that are to be monitored.Parameters are subject to expert knowledge estimations.Hence,the SQHI fuzzy control model can be applied in order to support strategic decisionmakin g.FuzzificationIt is assumed that linguistic variables of the SQHI fuzzy model are:A f A 1;F F F A i ;F F F A n gB f B 1;F F F B j ;F F F B m gC f C 1;F F F C k ;F F F C l g1where A i ,an d B j are inputs of human resources (or attributes that relate toemployees)and tangibles respectively,while C k is the level of service quality (SQ):A i f x ; A i x j x P A i &U 1g i 1;F F F ;n B j f y ; B j y j y P B j &U 2g j 1;F F F ;m C k f z ; C k z j z P C k &U 3gk 1;F F F ;l2 InferenceRenamed elements of the set (C 1F F F C l )are presented in Table I.Figure 1Fuzzy controlmodelTable IDecision table:``If F F F and F F F then rulesB 1F F F B j F F F B m A 1C 11F F F C 1,j F F F C 1,m F F F F F F F F F F F F F F F F F F A i±1C i±1,1F F F C i±1,j F F F C i±1,m A i C i,1F F F C i,j F F F C i,m A i+1C i+1,1F F F C i+1,j F F F C i+1,m F F F F F F F F F F F F F F F F F F A nC n1F F FC n,jF F FC n,m[157]Amy WongFuzzy control model in the hospitality industryInternational Journal of Agile Management Systems 2/2[2000]156±162If x is A i and y is B j thenz is C k3denotingp i Áx is A i ;q j Áy is B j ;r k Áz is C k4where Áindicates ``defined as''.It can be writtenas:If p i and q j thenr k5Preconditions (containing ``and''part)(3)and (5)are composition conjunction .A ÂB U 1ÂU 2that istrue value of p and q p q A ÂB x ;y min A x ;B y ; x ;y P A ÂB6where A ÂB (x,y)is the membership function of the direct minproduct.A ÂB f x ;y ;min A x ; B y ; x ;yP A ÂB g7Hence:p i q j r k min A i x ; B j y ; C ij zi 1;F F F n j 1;F F F mk 1;F F F lx ;y ;z P A ÂB ÂC P U 1ÂU 2ÂU 38where U is universal set U ={U 1,U 2,U 3F F F }, u (x)=1,and (x)=0for (indicating an empty set).Rules evaluationCoding the inputs or fuzzification indicates creationof Table .The following step is conflict resolution relating to the application of a control rule:Rule 1:If x is A 0 i À1and B 0j À1thenz is C i À1;j À1.Rule 2:If x is A 0i À1and B 0 jthenz is C i À1;j .Rule 3:If x is A 0 i À1and B 0j 1thenz is C i À1;j 1.Rule 4:If x is A 0 i and B 0j À1thenz is C i ;j À1.Rule 5:If x is A 0 i and B 0 jthenz is C i ;j .Rule 6:If x is A 0 iand B 0 j 1thenz is C i ;j 1.Rule 7:If x is A 0 i 1and B 0j À1thenz is C i 1;j À1.Rule 8:If x is A 0 i 1and B 0jthenz is C i 1;j .Rule 9:If x is A 0i 1and B 0j 1thenz is C i 1;j 1.a i À1;j À1 A i À1 x 0 B j À1min A i À1 x 0 ; B j À1a i À1;j A i À1 x 0 B jmin A i À1 x 0 ; B ja i À1;j 1 A i À1 x 0 B j 1min A i À1 x 0 ; B j 1a i ;j À1 A i x 0 B j À1min A i x 0 ; B j À1a i ;j A i x 0 B jmin A i x 0 ; B ja i ;j 1 A i x 0 B j 1min A i x 0 ; B j 1a i 1;j À1 A i 1 x 0 B j À1min A i 1 x 0 ; B j À1a i 1;j A i 1 x 0 B jmin A i 1 x 0 ; B ja i 1;j 1 A i 1 x 0 B j 1min A i 1 x 0 ; B j 19Now Table canbe created.The difference between Table II and Table I I I is that the active cells inTable I I are fuzzy outputs while the active cells inTable represent strength of the rules.The control output (CO)of each rule is defined by the operation conjunction applied on its strength and conclusion:CO of Rule 1:a i À1;j À1 c i À1;j À1 z=min a i À1;j À1; c i À1;j À1 z .CO of Rule 2:a i À1;j c i À1;j z=min a i À1;j ; c i À1;j z .CO of Rule 3:a i À1;j 1 c i À1;j 1 z=min a i À1;j 1; c i À1;j 1 z .CO of Rule 4:a i ;j À1 c i ;j À1 z=min a i ;j À1; c i ;j À1 z .CO of Rule 5:a i À1;j c i À1 z=min a i À1;j ; c i À1 z .CO of Rule 6:a i À1;j 1 c i À1;j 1 z=min a i À1;j 1; c i À1;j 1 z .CO of Rule 7:a i 1;j À1 c i 1;j À1 z=min a i 1;j À1; c i 1;j À1 z .CO of Rule 8:a i 1;j c i 1;j z=min a i 1;j ; c i 1;j z .CO of Rule 9:a i 1;j 1 c i 1;j 1 z=min a i 1;j 1; c i 1;j 1 z .The control output presented in a table form is showninTable V.Aggregation (conflict resolution)norder to produce the con trol output with aggregated membership function agg (z),the operator (or)is used for aggregation:The induced decision table and active cellsF F F B j À1 B j F F F B j 1000F F FF F F0F F F A i À1 C i À1;j À1 C i À1;j C i À1;j 1 A i 0 C i ;j À1 C i ;j C i ;j 10 A i 1 C i 1;j À1C i 1;j C i 1;j 1F F F F F F F F F F F F 0F F F 0F F F 0[158]Amy WongFuzzy control model in the hospitality industryInternational Journal of Agile Management Systems 2/2[2000]156±162agg z a i À1;j À1 c i À1;j À1 za i À1;j c i À1;j za i À1;j 1 c i À1;j 1 z a i ;j À1 c i ;j À1 z a i ;j c i À1; z a i ;j 1 c i À1;j 1 z a i 1;j À1 c i 1;j À1 z a i 1;j c i 1;j z a i 1;j 1 c i 1;j 1 z m x f a i À1;j À1 c i À1;j À1 z ; a i À1;j 12 c i À1;j z ; a i À1;j 1 c i À1;j 1 z ; a i ;j À1 c i ;j À1 z ; a i ;j c i À1 z ; a i ;j 1 c i À1;j 1 z ; a i 1;j À1 c i 1;j À1 z ; a i 1;j c i 1;j z ; a i 1;j 1 c i 1;j 1 z g10DefuzzificationThe membership function agg z should be decoded to a single crisp value z*.There are several methods of decoding (Bojadziev and Bojadziev,1995).The ``centre of area method''is used presuming this is appropriate for the applicationof the SQHI fuzzy con trol model.Suppose the aggregate control rules result in:agg z ;z P z 0;z gThe crisp value z*is the midpoint of the interval (Â1,Â2)presuming the fuzzynumbers are presented in a triangle form.The interval (z 0,z q )is subdivided into q subintervals (see Figure 2).The crisp value is:z ÃcPq À1k 1z k agg z kPq À1k 1agg z k11Fuzzy numbers could also be presented asbell shaped,or other fuzzy numbers forms (Bandemar and Gottwald,1995).Case studyFuzzificationThe luxury-to-mid-luxury hotel managers are looking for the given pair of input variables:A i :employees'attributes;B j :tangibles j ;and a correspondingC l :output or a service quality (SQ)level.Attributes of employees are defined as:A f A 1;A 2;A 3gwhere L relates to responsiveness,M relates to L +assurance,and H relates to M +empathy.Attributes of tangibles are defined as:B f B 1;B 2;B 3gwhere L relates to the appeal of the hotel,M relates to L +the attractiveness of the hotel,and H relates to M +up-to-date equipment.SQ level is defined as:C f C 1;C 2;C 3gwhere L relates to low SQ level,Me relates to medium SQ level,and H relates to high SQ level.A ,B andC are fuzzy numbers with supporting intervals belonging to the universal sets U 1={x /0 x 100},U 2=(y /0 y 100},U 3={z /0 z 100}.The numbers are taken from the hospitality industry system scale.Graphically,they look as showninFigure 3.L v1for 0 v 2050Àv =30for 20 x 50M vv À20 =30for 20 v 50 80Àv =30for50 v 80H vv À50 =30for 50 v 801for 80 v 100InferenceThe induced decision table and active cells are showninTable V.The variable C has three levels as shownin Table VI,with the rules defined as:The control outputs of Rules 1-9F F FF F FF F FF F FF F Fa i À1;j À1 c i À1;j À1 z a i À1;j c i À1;j z a i À1;j 1 c i À1;j 1 z a i ;j À1 c i ;j À1 z a i À1;j c i À1;j z a i À1;j 1 c i À1;j 1 z a i 1;j À1 c i 1;j À1 z a i 1;j c i ;j z a i 1;j 1 c i 1;j 1 z F F FF F FF F FF F FThe rules strength table0F F F B j À1 y 0 B j y 0 B j 1 y 0 1 F F F 0F F F 00F F F 0A i À10 C i À1;j À1 C i À1;j a i À1;j 10 A i 0 C i ;j À1 C i ;j a i ;j 10 A i 10C i 1;j À1C i 1;j a i 1;j 10F F F F F F F F F F F F F F F F F F F F F 00F F F000F F F 0[159]Amy WongFuzzy control model in the hospitality industryInternational Journal of Agile Management Systems 2/2[2000]156±162Rule 1:If Employees (E)are only responsive(L)and Tangibles relate only to the appeal of the hotel (L),thenSQ level is low L.Rule 2:if E is L and T is M,then SQ is L.Rule 3:if E is L and T is M,then SQ is Me.Rule 4:if E is M and T is M,then SQ is L.Rule 5:if E is M and T is M,then SQ is Me.Rule 6:if E is M and T is M,then SQ is H.Rule 7:if E is H and T is M,then SQ is Me.Rule 8:if E is H and T is M,then SQ is H.Rule 9:if E is H and T is M,then SQ is H.The above rules could be presented in the following form:Rule 1:p 1 q 1 r 11=min (( L (x), L (y), L (z)).Rule 2:p 1 q 2 r 12=min (( L (x), M (y), L (z)).Rule 3:p 1 q 3 r 13=min (( L (x), H (y), Me (z)).Rule 4:p 2 q 1 r 21=min (( M (x), L (y), L (z)).Rule 5:p 2 q 2 r 22=min (( M (x), M (y), Me (z)).Rule 6:p 2 q 3 r 23=min (( M (x), H (y), H (z)).Rule 7:p 3 q 1 r 31=min (( H (x), L (y), Me (z)).Figure 2Defuzzification by the ``centre of areamethod''Figure 3Terms of inputs and the output ofSQHIThe induced decision table and active cellsF F F B j À1 B j F F F B j 1000F F FF F F0 A i À1 C i À1;j À1 C i À1;j C i À1;j 1 A i 0 C i ;j À1 C i ;j C i ;j 10 A i 1 C i 1;j À1C i 1;j C i 1;j 1F F F F F F F F F F F F 0F F F 0F F F 0Table VIThe three levels of output SQ Tangibles Employees L M H L L L Me M L Me H HMeHH[160]Amy WongFuzzy control model in the hospitality industryInternational Journal of Agile Management Systems 2/2[2000]156±162Rule 8:p 3 q 2 r 32=min (( H (x), M (y), H (z)).Rule 9:p 3 q 3 r 33=min (( H (x), H (y), H (z)).Rules evaluationWe shall code the inputs through the use of the induced decision table (see Figures 4a and 4b and Table VII).The strength of active rules is:11 L 40 L 25 min 1=3;5=6 1=3 12 L 40 M 25 min 1=3;1=6 1=621 M 40 L 25 min 2=3;5=6 2=3 22 M 40 M 25 min 2=3;1=6 1=6That is as showninTable VI .Aggregation (conflict resolution)The control output (CO)for Rules 1-4is obtained as follows:Rule 1: 11 L z min 1=3; L z .Rule 2: 12 L z min 1=6; L z .Rule 3: 21 L z min 2=3; L z .Rule 4: 22 Me z min 1=3; Me z .This is equivalent to performing operation min on the corresponding cells from the induced decision table and the rule strength table.The control output for SQ is presented in Table IX.Accordingly:agg m x f min 1=6; L z ;min 2=3; Mo z Mo z gDefuzzificationThe single value z Ãc that represents agg z of an aggregate control action for the following interval can be seen in Figure 5and Table X.Table X represents crisp output:z Ãc 46:11%46The luxury-to-mid-luxury hotel managerscould estimate the service quality level,givenits employees attributes,are 40an d tangibles are 25,to be 46on a scale from 0toFigure 4aTerms of the inputemployeesTerms of the inputtangiblesTable VIIThe induced decision table of SQHIL (25)=5/6M (25)=1/60 L (40)=1/3 L (z) L (z)0 M (40)=2/3 L (z) Me (z)00The rule strength table of SQHIL (25)=1/3M (25)=1/60 L (40)=1/31/31/60 L (40)=1/32/31/600Table IXControl output for SQHI F F F F F F F F F F F F F F F 1=3 L z 1=6 L z F F F F F F 2=3 L z1=6 Me zF F F F F FF F FF F FF F F Defuzzification by the centre of areamethod[161]Amy WongFuzzy control model in the hospitality industryInternational Journal of Agile Management Systems 2/2[2000]156±162100.Accordingly,they could suggestmoderate service quality improvement in order to sustainits competitive advan tage.ConclusionThe methodology and procedure proposed in this paper may be easily used by managers in the hospitality industry to monitor and control their level of service qualityprovided.Applied SQHI fuzzy control model can support strategic decisions.Being based onexpert system the model should be time absorbing.If further developed towards fuzzy logic modelling of customers'behavioural intentions the model may contribute to creationof overall hospitality in dustry fuzzy logic model.Ahmad,I.(1990),``Decision-support system 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