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模糊辨识、模糊控制和稳定性的若干问题的研究
王守唐
学位类型工学博士
导师高东杰
2001-04-01
学位授予单位中国科学院研究生院
学位授予地点中国科学院自动化研究所
学位专业控制理论与控制工程
关键词模糊辨识 模糊控制 Takagi-sugeno模糊模型 稳定性 圆判据 钝性定理 Fuzzy Identification Fuzzy Control Takagi-sugeno Fuzzy Model Stability Analysis Circle Criterion Pasivity Theorem
摘要模糊建模与控制是非线性建模与控制方法。当前,模糊控制已经成为十分活跃 和富有成果的领域。它之所以受到如此重视是因为复杂系统知识和动念行为往往是 定性的和具有不确定因素。模糊集合理论正好适合表达这样的知识。本文主要的内 容分为三个部分: 1.基于Takagi-sugeno模糊模型的辨识提出了一种新的基于Takagi-Sugeno模糊 模型的辨识算法。该算法可分为二步: 第一步是粗糙的辨识。该部分的主要任务是前件结构的辨识,也就是输入空间 的划分问题。另一个作用规则前后件参数初始值的确定。本文按照子空间的线性程 度来划分输入空间,保留线性程度好的子空间,分割线性程度差的子空间。规则前 件参数的初始值由子空间的中心和大小决定,规则后件线性参数由加权最小二乘法 确定; 第二步是模型的精细调整。利用梯度下降法来调节规则模糊集合的隶属函数和 规则后件的线性参数。优化的目标可以分为以全局误差作为目标函数和强调局部误 差的目标函数两种。算法的本身思想近似于模糊神经网络,但是与模糊神经网络相 比,本文的优化算法不必受到网络结构的限制。 最后,用仿真实验说明了该算法的有效性,并且比较了全局误差目标函数和局 部误差目标函数进行优化所得的结果。 2.基于连续Takag-Sugeno模糊模型的系统化设计方法 给出了模糊控制系统的系统化设计方法。采用Takagi-Sugeno模糊模型来表示被 控对象。利用分解定理,将整个模糊系统稳定性问题分解为几个模糊子系统的稳定 性设计问题。选择占优子系统的局部模型,利用状态反馈进行局部控制器的设计, 综合考虑其它局部模型对占优子系统的影响,给出了保证占优子系统稳定的充分条 件。整个系统的控制器由各个占优子系统反馈控制器组合而成,从而保证了整个模 糊系统的稳定性。本文方法不同于传统的方法需要寻找一个公共正定矩阵。本文使 用的是分段线性二次稳定的方法,在每一个子空间寻找一个正定矩阵,在满足一定 条件下可以保证整个模糊系统的稳定性。最后通过一个典型的非线性倒立摆的例子 验证了该方法是有效的。 3.一维模糊PID控制器的稳定性分析 研究新近提出的一维模糊PID控制器的稳定性问题。该模糊PID控制器结构简 单,具有三个规则,六个调节参数,只要求一个输入,且可以产生不次于相应线性PID控制器的控制效果。该模糊PID控制器的模糊推理部分具有非线性特性,因此 本文采用非线性理论中的稳定性分析方法,主要应用了圆判据和钝性定理稳定性分 析方法
其他摘要Fuzzy modeling and control is one of the methods used for nonlinear systems. Now fuzzy logic control has become one of the most active and fruitful approaches to control complex systems. Because the knowledge and dynamic behaviors of complex systems are qualitative and uncertain, and the fuzzy set theory appears to provide a suitable representation of such knowledge. In my dissertation three subjects are included: 1. Fuzzy Identification Based on the Takagi-Sugeno Model: A new identification algorithm for Takagi-Sugeno fuzzy model is proposed in this section. Identification process consists of two steps: Firstly, coarser identification is carried out. Its tasks are the partition of the fuzzy input space and determination of initial rule parameters. The input space is partitioned according to linear degree of the subspaces. The subspaces whose linear degree is better are held, while the other subspaces are partitioned. The center and size of each subspace determine the parameters of the corresponding rule premise. The consequent parameters of each rule are identified by the weighted least square method. Secondly, the initial rule parameters are fine-tuned by the gradient descent algorithm. There are two objective functions: One is the total error of all the data, the other emphasizes accuracy of local model. The gradient descent method is used to optimize the objective functions. The optimization method is similar to the fuzzy neural networks, but it is not limited to the structure of networks. At last, two simulation examples show effectiveness of the method. The results are compared for the two objective functions. 2. Systematic Design of Fuzzy Control System Based on Continuous Takagi-Sugeno Fuzzy Model A method of stability analysis and systematic design of fuzzy control system is proposed in this section. The plant to be controlled is expressed by Takagi-Sugeno fuzzy model. By the Decomposition Theorem, Stability of the whole fuzzy systems can be transformed to stability of all fuzzy subsystems. Dominant subsystem is chosen to design the feedback controller. Considering the effects of other local models, a sufficient condition is given to guarantee stability of the dominant subsystem. A global controller can be obtained from the local controllers of dominant subsystems. Different from the traditional stability analysis method that require a common positive-definite matrix, the piecewise quadratic stability analysis method is used, that is, in each subspace a positive- definite matrix is required. The simulation result of a nonlinear control system---a inverted pendulum--shows that the method is effective. 3. Stability Analysis of Fuzzy PID Controller with One-Input Stability of a fuzzy PID controller with one input, which is proposed recently, is studied in this section. The controller uses one input inference with three rules and at most six parameters. It can provide the performance no worse than the corr
馆藏号XWLW655
其他标识符655
语种中文
文献类型学位论文
条目标识符http://ir.ia.ac.cn/handle/173211/5718
专题毕业生_博士学位论文
推荐引用方式
GB/T 7714
王守唐. 模糊辨识、模糊控制和稳定性的若干问题的研究[D]. 中国科学院自动化研究所. 中国科学院研究生院,2001.
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