一类区间二型模糊PI控制器设计算法

区间二型模糊控制器在处理不确定性方面优于传统的模糊控制器,但带来的一个问题就是区间二型模糊控制器需要降阶过程。常用的KM等迭代式降阶算法效率低下,难以用于实时性较高的场合。本文利用直接降阶算法和动态解模糊化算法,提出了一类区间二型模糊PI控制器设计算法。该算法在降阶过程中考虑偏差和偏差变化量对控制器输出的影响,避免了KM等迭代式降阶过程。通过二阶迟延对象以及一个非线性对象的仿真实验表明,本文算法能够有效降低系统超调,降低系统的稳态时间,控制器在设定值附近的输出更为平滑。     

一种等价于PI的二型模糊控制器设计算法

区间二型模糊集合将次隶属度做了简化,基于KM降阶算法的区间二型模糊控制器实现起来相对简单.虽然区间二型模糊控制器在一定程度上优于传统的一型模糊控制器或者PI控制器等,但区间二型模糊控制器并没有充分利用二型模糊集合的次隶属度信息.为解决这些问题,研究了普通二型模糊控制器的一般结构,提出了一种等价于PI的二型模糊控制器.该...     

一类乘积型区间二型模糊控制器的解析结构

区间二型模糊控制器的降型算法需要使用迭代计算,是导致其解析结构推导困难的主要原因.针对乘积型区间二型模糊控制器,本文提出了一种新的解析结构推导方法.区间二型模糊控制器的配置为:三角形输入模糊集,一型输出模糊单值,集合中心法降型器,平均法解模糊器和基于乘积型"与"操作的规则前件.通过对比传统PID控制器的解析结构,证明了区间二型模糊控制器等效于两个PI(或PD)控制器之和.利用KM算法的迭代终止条件,提出了6步骤IC划分法,保证了激活子空间的正确划分.叠加各个子空间,即可得出全局IC划分图.为了避免重复求解符号数学方程,提出了IC边界线的直接定义法,改进了6步骤IC划分法的便利性.本文方法避开了降型算法的迭代计算,可以保证推导出区间二型模糊控制器的闭环解析表达式.     

一种简化的区间二型模糊系统辨识方法

KM降阶算法是目前区间二型模糊集合常用的降阶算法,针对其效率低、难以用于实时辨识与控制的缺点,提出了一种简化的区间二型模糊系统辨识方法。该方法采用二型T-S模糊模型,前件参数为区间二型模糊集合,后件参数为普通T-S模糊模型形式。二型T-S模糊模型的解模糊化采用简化的降阶算法,提高了模型的辨识效率,可用于实时辨识与控制。仿真实例表明,所提算法在不降低辨识精度的情况下能够有效提高辨识效率。     

一种新的区间二型模糊集合降阶算法

区间二型模糊集合的KM/EKM降阶算法,其效率较低,难以用于二型模糊逻辑的实时控制。而基于切换点计算公式的单调性关系的IASC和EIASC算法虽然其运算时间低于KM/EKM,但其初始值都是从两侧端点开始,其效率也有待提高。本文提出了一种新的二型模糊集合降阶算法,利用切换点计算公式和论域中值的关系以及初始化左右切换点的值来提高计算效率,2个仿真实例验证了本文算法的有效性和实用性。     

基于加权Karnik-Mendel算法的区间二型模糊逻辑系统降型

二型模糊逻辑系统是当前的学术研究的热点问题,而降型是该系统中非常重要的一个模块.Kamik-Mendel(KM)算法是被用来计算和完成区间二型模糊逻辑系统降型的标准算法.通过比较离散版本KM算法中求和运算和连续版本的KM(continuous version ofKM,CKM)算法中求积分运算,本文利用数值积分技术中牛顿-柯斯特求积公式将标准KM算法扩展成3种不同形式的加权KM(weighted KM,WKM)算法.而KM算法只是WKM算法中的一种特殊情况.3个计算机仿真例子用来阐述和分析WKM算法的表现,与传统的KM算法相比,WKM算法有较小的绝对误差和较快的收敛速度,给二型模糊逻辑系统设计者和应用者提供了潜在的应用价值.     

π型隶属函数的典型模糊控制器的解析结构

研究了一种新型的典型模糊控制器,它的输入隶属函数采用π型样条函数,具有二阶逼近特性,而一般典型模糊控制器采用的三角形隶属函数只具有一阶逼近特性,因此研究这种新型的模糊控制器具有重要的意义.文章首先给出了该类典型模糊控制器的定义,推导了它的解析表达式,证明了该类典型模糊控制器可以等效为一个全局的二维继电器和一个局部的非线性PD控制器之和.在此基础上,给出了其极限特性和非线性特性.     

一种新型区间二型模糊神经网络隶属函数的设计

对于区间二型模糊神经网络（IT2FNN）,论文给出了一种新型的模糊隶属函数（FMF）设计方法.通过所设计的模糊隶属函数,可以衍生出三种区间二型模糊隶属函数（IT2FMF）.每种区间二型模糊隶属函数都具有不同的不确定域.论文将三种衍生模糊隶属函数应用于简化区间二型模糊神经网络辨识两个非线性系统.通过仿真,将衍生区间二型模糊隶属函数的辨识性能与高斯和椭圆型模糊隶属函数进行了对比.仿真结果表明,通过调节简化区间二型模糊神经网络的参数,本文所设计的区间二型模糊隶属函数比高斯和椭圆型模糊隶属函数具有更好的辨识性能.     

B样条曲线的降阶公式及近似降阶方法

已有的B样条曲线降阶方法，由于无降阶公式可循，对于可降阶曲线常要通过解一系列线性方程组来实现降阶．该文给出了B样条曲线的降阶公式，使得可直接用降阶公式对可降阶曲线进行降阶．利用降阶公式和约束优化方法，文中进一步给出了B样条曲线的一种近似降阶方法和相应的算法，使得在用约束优化方法求出可降阶的近似曲线后，就可直接用降阶公式求出降阶曲线，简化了降阶过程．该方法应用范围广且简单实用．     

关于二型模糊集合的一些基本问题

采用集合论的方法给出了单位模糊集合和二型模糊集合及其在一点的限制等定义,使得二型模糊集合更易于理解.通过定义嵌入单位模糊集合来描述一般二型模糊集合,并给出离散、半连通二型模糊集合的表达式.根据论域、主隶属度及隶属函数的特性将二型模糊集合分为四种类型:离散、半连通、连通及复合型,并根据连通的特点将连通二型模糊集合分为单连通及多连通两类.利用支集的闭包（Closure of support,CoS）划分法表述主隶属度及区间二型模糊集合.提出了CoS二、三次划分法分别来表述单、复连通二型模糊集合,并使每一个子区域的上下边界及次隶属函数在该子区域上的限制分别具有相同的解析表述式.最后,探讨了二型模糊集合在一点的限制、主隶属度、支集、嵌入单位模糊集合之间的关系.     

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.     

Analytical structure and stability analysis of a fuzzy PID controller

Analytical structure for a fuzzy PID controller is introduced by employing two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. This structure is derived via left and right trapezoidal membership functions for inputs, trapezoidal membership functions for output, algebraic product triangular norm, bounded sum triangular co-norm, Mamdani minimum inference method, and center of sums (COS) defuzzification method. Conditions for bounded-input bounded-output (BIBO) stability are derived using the Small Gain Theorem. Finally, two numerical examples along with their simulation results are included to demonstrate the effectiveness of the simplest fuzzy PID controller.     

基于解析结构的模糊PI圆盘配料控制器

针对圆盘配料过程时变、非线性的特性,设计一种基于解析结构的模糊PI控制器。将料流量偏差和偏差变化率作为输入,采用等差间距的隶属度函数和sum-product推理方法,根据模糊控制规则得到PI参数调整的解析表达式。利用该解析表达式,对圆盘配料控制系统进行仿真,仿真结果验证了该控制器的有效性和实用性。     

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。     

A precise robust fuzzy control of robots using voltage control strategy

Fuzzy control of robot manipulators with a decentralized structure is facing a serious challenge. The state-space model of a robotic system including the robot manipulator and motors is in non-companion form, multivariable, highly nonlinear, and heavily coupled with a variable input gain matrix. Considering the problem, causes and solutions, we use voltage control strategy and convergence analysis to design a novel precise robust fuzzy control (PRFC) approach for electrically driven robot manipulators. The proposed fuzzy controller is Mamdani type and has a decentralized structure with guaranteed stability. In order to obtain a precise response, we regulate a fuzzy rule which governs the origin of the tracking space. The proposed design is verified by stability analysis. Simulations illustrate the superiority of the PRFC over a proprotional derivative like (PD-like) fuzzy controller applied on a selective compliant assembly robot arm (SCARA) driven by permanent magnet DC motors.     

Fuzzy controllers: synthesis and equivalences

It has been proved that fuzzy controllers are capable of approximating any real continuous control function on a compact set to arbitrary accuracy. In particular, any given linear control can be achieved with a fuzzy controller for a given accuracy. The aim of this paper is to show how to automatically build this fuzzy controller. The proposed design methodology is detailed for the synthesis of a Sugeno or Mamdani type fuzzy controller precisely equivalent to a given PI controller. The main idea is to equate the output of the fuzzy controller with the output of the PI controller at some particular input values, called modal values. The rule base and the distribution of the membership functions can thus be deduced. The analytic expression of the output of the generated fuzzy controller is then established. For Sugeno-type fuzzy controllers, precise equivalence is directly obtained. For Mamdani-type fuzzy controllers, the defuzzification strategy and the inference operators have to be correctly chosen to provide linear interpolation between modal values. The usual inference operators satisfying the linearity requirement when using the center of gravity defuzzification method are proposed     

A new approach to fuzzy modeling of nonlinear dynamic systems with noise: relevance vector learning mechanism

This paper presents a new fuzzy inference system for modeling of nonlinear dynamic systems based on input and output data with measurement noise. The proposed fuzzy system has a number of fuzzy rules and parameter values of membership functions which are automatically generated using the extended relevance vector machine (RVM). The RVM has a probabilistic Bayesian learning framework and has good generalization capability. The RVM consists of the sum of product of weight and kernel function which projects input space into high dimensional feature space. The structure of proposed fuzzy system is same as that of the Takagi-Sugeno fuzzy model. However, in the proposed method, the number of fuzzy rules can be reduced under the process of optimizing a marginal likelihood by adjusting parameter values of kernel functions using the gradient ascent method. After a fuzzy system is determined, coefficients in consequent part are found by the least square method. Examples illustrate effectiveness of the proposed new fuzzy inference system.     

Analytical structures and analysis of the simplest fuzzy PI controllers

This paper deals with simplest fuzzy PI controllers which employ two fuzzy numbers on the universe of discourse (UOD) of each input variable, and three fuzzy numbers on the UOD of output variable. Analytical structures of such controllers are derived using triangular membership functions for fuzzification, different combinations of T-norms and T-conorms, different inference methods, and center of area (COA) method for defuzzification. Properties of these controllers are investigated. A comparative study is made on (i) the fuzzy PI controllers derived, and (ii) on the fuzzy PI controllers and their counterpart—conventional PI controller. Moreover, sufficient conditions for bounded-input bounded-output (BIBO) stability of fuzzy PI control systems are established using the well-known small gain theorem.     

模糊控制器在车辆稳定系统中的设计应用

针对车辆安全稳定系统的算法设计中加载于车身的横摆力矩值如何确定的问题,建立了以隶属度函数和运算规则为基础的模糊控制器。本文简述了模糊控制器的一般组成,并阐明此系统控制器针对的输入参考对象是车辆质心的横摆角速度偏差,再通过描述车辆安全稳定控制系统的流程和系统的模糊控制原理设计了需要的隶属度函数和模糊子集。最后,设计了输出力矩的模糊运算规则以满足系统的实际需要。