空间分布动态系统的3-D模糊控制设计与分析
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摘要
工业生产过程中的多数系统都具有空间分布特性,但实际应用过程中通常忽略系统的空间分布特性,采用发展较为成熟、实现较为简单的集总参数控制理论去解决存在的控制问题。然而,随着现代工业的发展,人们对生产过程提出了越来越严格的要求,除了考虑生产安全外,还要满足日益增长的环保、产品质量、能耗等要求。传统集总参数控制方法已不能满足实际控制要求,研究空间分布系统控制理论已成为现代控制理论的热点之一。经典分布参数系统控制方法是过去几十年中针对空间分布系统发展起来的方法,其不但需要系统的精确数学模型,并且需要设计人员掌握大量的、复杂的涉及到分布参数系统理论的数学知识,这为其在工程实践中的应用带来困难。模糊控制由于具有两个优点(设计控制器不需要被控系统的数学模型以及可以通过实际经验而非复杂数学推导获得令人满意的控制器),在现实生活中得到广泛应用。然而传统模糊集固有的二维信息特征,使得传统模糊控制器并不能有效地解决空间分布系统的控制问题。空间分布系统模糊控制仍然是个有待解决的问题。为此,本论文基于空间分布系统的空间分布特性,从模糊集及模糊控制策略着手对空间分布系统的模糊控制问题进行了研究。
主要工作包括以下几个方面:
针对传统二维模糊集不能表征空间信息的特点,提出了具有三维信息(分别用于基本变量的论域、隶属度及空间信息)的空间模糊集,使其具有表征空间信息的能力。介绍了空间模糊集运算法则,并且给出了由空间模糊集延伸出的两个概念:空间输入变量与空间模糊化。根据系统的空间分布特点,提出了基于空间模糊集的模糊控制策略,使得控制器能够模拟人类操作员知识或者专家经验从整个空间角度去控制一个空间分布的场。作为基于空间模糊集的模糊控制策略的初步尝试,设计了区间值模糊控制器,仿真例子表明了该控制器的有效性。
针对单控制源空间分布系统,提出了一种新型模糊控制器-3-D模糊控制器。它是在基于空间模糊集的模糊控制思想指导下设计而成的自成体系的模糊控制器。它具有与传统模糊控制器相似的结构,由空间模糊化、空间模糊规则推理及去模糊化构成,但却有着其独特的特点:①它可将来自空间域上的多个传感器输入作为空间分布输入,然后采用空间模糊集构造空间信息;②它具有能够处理空间信息的模糊规则推理机制;③规则数目不会随着测量传感器的数目增加而增加。由于3-D模糊控制器结构简单,空间模糊集与3-D推理均物理意义明确,计算并不复杂,使得对其作进一步研究分析成为可能。仿真例子表明了该控制器的有效性。
推导了两项输入3-D模糊控制器的数学解析模型,并且对其作了结构分析。利用传统模糊控制器所使用的一种图形化解析法(规则库平面分解的方法),推导并得到3-D模糊控制器的数学解析模型。从数学解析的角度揭示了3-D模糊控制器在空间上具有全局滑模变结构特点以及与传统模糊控制器存在着一个空间等价关系,并且根据这个空间等价关系,揭示了3-D模糊控制本身固有的一些属性。
在3-D模糊控制器数学解析模型的基础上,研究了3-D模糊控制系统的稳定性问题。利用3-D模糊控制器在空间域上的全局滑模变结构特性,研究了3-D模糊控制系统的Lyapunov稳定性,给出了全局稳定性条件以及据此设计控制器参数的方法。利用3-D模糊控制与传统模糊控制的空间等价关系以及离散时间系统的某些特点,研究了离散时间3-D模糊逻辑控制系统的BIBO稳定性,给出了全局BIBO稳定性条件以及据此设计控制器参数的方法。两个例子的仿真研究分别验证了依据不同稳定性条件所设计的控制器参数的有效性。
针对空间分布更为复杂的多控制源空间分布系统,提出了基于分解协调的3-D模糊控制策略,使得3-D模糊控制能够处理一般的空间分布系统的控制问题。基于分解协调的3-D模糊控制采用了分层结构。首先处于底层的分解模块利用系统的局部影响特性,将空间域分解成多个子区域,进而将复杂多控制源空间分布系统分解成多个相对简单的单控制源空间分布子系统。在中间层,每个子系统均采用3-D模糊控制器。在顶层,针对子系统之间不可忽略的较强耦合,协调模块对空间邻近子系统之间进行局部协调,形成了协调式3-D模糊控制。将基于分解协调的3-D模糊控制应用于RTCVD系统,仿真结果表明了该控制方法的有效性。
Many of industrial processes and systems are inherently characterized by the presence of strong spatial variations, however, in the actual application the spatial distribution is usually ignored and the traditional control methods developed for lumped parameter systems are used. With the development of modern industry, higher requirements are brought forward for those industrial processes, including safety regulation, increasingly stringent environmental regulation, tighter product quality, and energy specification. For the spatially distributed systems that commonly exist in the industrial processes, control methods used for traditional lumped parameter systems couldn’t satisfy the actual control requirement any more, thus, research on the control theory of spatially distributed systems has become one of the highlights in the modern control theory. Classical distributed parameter control methods were developed for spatially distributed systems during the past several decades. Since the methods require the precise mathematical models of the systems to be controlled and expect the control designers to grasp plentiful, complicated mathematical knowledge involved in the theory of distributed parameter systems, they are difficultly employed in the practical engineering applications. In contrast, fuzzy logic control has achieved worldwide success in countless commercial products and applications, because it has two practical advantages: no requirement of the mathematical model of the system, and satisfactory nonlinear controller developed by utilizing human control knowledge and experience without a complicated mathematics. However, due to the inherent two-dimensional feature of the traditional fuzzy set, the traditional fuzzy logic controller cannot solve the control problem of spatially distributed systems effectively. Fuzzy logic control for spatially distributed system is still an open problem. Thus, on the basis of the spatial distribution nature, this dissertation begins with new fuzzy set and new fuzzy logic control strategy, and then concentrates on the study on the fuzzy logic control for spatially distributed systems.
The main contents are as follows:
A novel three-dimensional fuzzy set, called as spatial fuzzy set, is proposed, since traditional two-dimensional fuzzy set is not able to express the spatial information effectviely. The spatial fuzzy set is inherently defined to express the spatial information, and has three coordinates: one is for the universe of discourse of the variable, another is for the spatial information, and a third is for the membership degree. Additionally, the set-theoretic operation of spatial fuzzy sets is introduced, and then spatial input variable and spatial fuzzification,two concepts extended from the spatial fuzzy set, are given. In terms of the feature of spatial distribution, a novel fuzzy logic control strategy based on spatial fuzzy set is proposed. The fuzzy logic control strategy can make a fuzzy logic controller control a spatially-distributed field by emulating human knowledge and experience from the point of view of the entire space domain. As a tentative application of the fuzzy logic control strategy based on spatial fuzzy set, an interval-valued fuzzy logic controller is designed. An example is illustrated to verify the effectiveness of the controller by simulation experiments.
A three domain fuzzy logic controller (3-D FLC) is proposed based on the spatial fuzzy set for the spatially distributed systems with one control source. The controller is designed under the framework of the fuzzy logic control strategy based on spatial fuzzy set, and it has a self-contained structure. Similar to the traditional FLC, the 3-D FLC consists of spatial fuzzification, 3-D fuzzy rule inference, and defuzzifier, however, it has its unique nature:①it takes the spatially distributed inputs from multiple sensors in the space domain and expresses the spatial information with the help of the spatial fuzzy set.②it processes the inference mechanism which can cope with the spatial information.③rules will not increase as sensors increase for spatial measurement. The 3-D FLC is designed with a simple configuration. Additionally, the spatial fuzzy set as well as the 3-D rule inference has certain physical meanings, and the involved computation is not complicated. Thus, 3-D FLC can be further investigated analytically. An example is finally illustrated to verify the effectiveness of the controller by simulation experiments.
The analytical mathematical model of the 3-D two-term fuzzy logic controller is derived, and then controller structure is explained with the help of the existing conventional control techniques. The graphic analytical method (rule base plane decomposition) for the traditional two-term fuzzy logic controller is used for the analytical model derivation. The derived results expose that on the one hand, the 3-D FLC has a global sliding mode structure over the spatial domain; on the other hand, it has a spatial equivalent structure with the traditional fuzzy logic controller over the space domain. In terms of the spatial equivalent structure, some properties of the controller are further presented.
The stability issue of the 3-D fuzzy logic control system is discussed, based on the analytical mathematical model of the 3-D FLC. In virtue of the global sliding mode feature of 3-D FLC, the Lyapunov stability of fuzzy logic control system is investigated, where a global stability condition is derived and an approach for designing the controller parameters is given. Utilizing the spatial equivalent structure and some feature of discrete time systems, the BIBO stability of discrete time fuzzy logic control system is investigated, where a global BIBO stability condition is derived and an approach for designing the controller parameters is given. Two examples are presented respectively to demonstrate the effectiveness of the two kinds of controller parameter designs by simulation experiments.
A 3-D fuzzy logic control strategy based on decomposition and coordination is proposed for the spatially distributed systems with multiple sources. It extends the 3-D FLC to solve the control problem of the general spatially distributed systems. The control system has a hierarchical structure with three hierarchies. Firstly, the decomposition module decomposes the whole space domain into sub-space domains and decomposes the complex spatially-distributed process with multiple sources into several relatively simple subsystems. Then, on the middle layer, a 3-D FLC is used for each subsystem. Finally, on the top layer, the coordination module carries out a strategy of local coordination among adjacent subsystems, and formulates a coordinated 3-D fuzzy logic control. The proposed control method is successfully applied to a Rapid Thermal Chemical Vapor Deposition (RTCVD) system, and the simulation results demonstrate its effectiveness.
主要工作包括以下几个方面:
针对传统二维模糊集不能表征空间信息的特点,提出了具有三维信息(分别用于基本变量的论域、隶属度及空间信息)的空间模糊集,使其具有表征空间信息的能力。介绍了空间模糊集运算法则,并且给出了由空间模糊集延伸出的两个概念:空间输入变量与空间模糊化。根据系统的空间分布特点,提出了基于空间模糊集的模糊控制策略,使得控制器能够模拟人类操作员知识或者专家经验从整个空间角度去控制一个空间分布的场。作为基于空间模糊集的模糊控制策略的初步尝试,设计了区间值模糊控制器,仿真例子表明了该控制器的有效性。
针对单控制源空间分布系统,提出了一种新型模糊控制器-3-D模糊控制器。它是在基于空间模糊集的模糊控制思想指导下设计而成的自成体系的模糊控制器。它具有与传统模糊控制器相似的结构,由空间模糊化、空间模糊规则推理及去模糊化构成,但却有着其独特的特点:①它可将来自空间域上的多个传感器输入作为空间分布输入,然后采用空间模糊集构造空间信息;②它具有能够处理空间信息的模糊规则推理机制;③规则数目不会随着测量传感器的数目增加而增加。由于3-D模糊控制器结构简单,空间模糊集与3-D推理均物理意义明确,计算并不复杂,使得对其作进一步研究分析成为可能。仿真例子表明了该控制器的有效性。
推导了两项输入3-D模糊控制器的数学解析模型,并且对其作了结构分析。利用传统模糊控制器所使用的一种图形化解析法(规则库平面分解的方法),推导并得到3-D模糊控制器的数学解析模型。从数学解析的角度揭示了3-D模糊控制器在空间上具有全局滑模变结构特点以及与传统模糊控制器存在着一个空间等价关系,并且根据这个空间等价关系,揭示了3-D模糊控制本身固有的一些属性。
在3-D模糊控制器数学解析模型的基础上,研究了3-D模糊控制系统的稳定性问题。利用3-D模糊控制器在空间域上的全局滑模变结构特性,研究了3-D模糊控制系统的Lyapunov稳定性,给出了全局稳定性条件以及据此设计控制器参数的方法。利用3-D模糊控制与传统模糊控制的空间等价关系以及离散时间系统的某些特点,研究了离散时间3-D模糊逻辑控制系统的BIBO稳定性,给出了全局BIBO稳定性条件以及据此设计控制器参数的方法。两个例子的仿真研究分别验证了依据不同稳定性条件所设计的控制器参数的有效性。
针对空间分布更为复杂的多控制源空间分布系统,提出了基于分解协调的3-D模糊控制策略,使得3-D模糊控制能够处理一般的空间分布系统的控制问题。基于分解协调的3-D模糊控制采用了分层结构。首先处于底层的分解模块利用系统的局部影响特性,将空间域分解成多个子区域,进而将复杂多控制源空间分布系统分解成多个相对简单的单控制源空间分布子系统。在中间层,每个子系统均采用3-D模糊控制器。在顶层,针对子系统之间不可忽略的较强耦合,协调模块对空间邻近子系统之间进行局部协调,形成了协调式3-D模糊控制。将基于分解协调的3-D模糊控制应用于RTCVD系统,仿真结果表明了该控制方法的有效性。
Many of industrial processes and systems are inherently characterized by the presence of strong spatial variations, however, in the actual application the spatial distribution is usually ignored and the traditional control methods developed for lumped parameter systems are used. With the development of modern industry, higher requirements are brought forward for those industrial processes, including safety regulation, increasingly stringent environmental regulation, tighter product quality, and energy specification. For the spatially distributed systems that commonly exist in the industrial processes, control methods used for traditional lumped parameter systems couldn’t satisfy the actual control requirement any more, thus, research on the control theory of spatially distributed systems has become one of the highlights in the modern control theory. Classical distributed parameter control methods were developed for spatially distributed systems during the past several decades. Since the methods require the precise mathematical models of the systems to be controlled and expect the control designers to grasp plentiful, complicated mathematical knowledge involved in the theory of distributed parameter systems, they are difficultly employed in the practical engineering applications. In contrast, fuzzy logic control has achieved worldwide success in countless commercial products and applications, because it has two practical advantages: no requirement of the mathematical model of the system, and satisfactory nonlinear controller developed by utilizing human control knowledge and experience without a complicated mathematics. However, due to the inherent two-dimensional feature of the traditional fuzzy set, the traditional fuzzy logic controller cannot solve the control problem of spatially distributed systems effectively. Fuzzy logic control for spatially distributed system is still an open problem. Thus, on the basis of the spatial distribution nature, this dissertation begins with new fuzzy set and new fuzzy logic control strategy, and then concentrates on the study on the fuzzy logic control for spatially distributed systems.
The main contents are as follows:
A novel three-dimensional fuzzy set, called as spatial fuzzy set, is proposed, since traditional two-dimensional fuzzy set is not able to express the spatial information effectviely. The spatial fuzzy set is inherently defined to express the spatial information, and has three coordinates: one is for the universe of discourse of the variable, another is for the spatial information, and a third is for the membership degree. Additionally, the set-theoretic operation of spatial fuzzy sets is introduced, and then spatial input variable and spatial fuzzification,two concepts extended from the spatial fuzzy set, are given. In terms of the feature of spatial distribution, a novel fuzzy logic control strategy based on spatial fuzzy set is proposed. The fuzzy logic control strategy can make a fuzzy logic controller control a spatially-distributed field by emulating human knowledge and experience from the point of view of the entire space domain. As a tentative application of the fuzzy logic control strategy based on spatial fuzzy set, an interval-valued fuzzy logic controller is designed. An example is illustrated to verify the effectiveness of the controller by simulation experiments.
A three domain fuzzy logic controller (3-D FLC) is proposed based on the spatial fuzzy set for the spatially distributed systems with one control source. The controller is designed under the framework of the fuzzy logic control strategy based on spatial fuzzy set, and it has a self-contained structure. Similar to the traditional FLC, the 3-D FLC consists of spatial fuzzification, 3-D fuzzy rule inference, and defuzzifier, however, it has its unique nature:①it takes the spatially distributed inputs from multiple sensors in the space domain and expresses the spatial information with the help of the spatial fuzzy set.②it processes the inference mechanism which can cope with the spatial information.③rules will not increase as sensors increase for spatial measurement. The 3-D FLC is designed with a simple configuration. Additionally, the spatial fuzzy set as well as the 3-D rule inference has certain physical meanings, and the involved computation is not complicated. Thus, 3-D FLC can be further investigated analytically. An example is finally illustrated to verify the effectiveness of the controller by simulation experiments.
The analytical mathematical model of the 3-D two-term fuzzy logic controller is derived, and then controller structure is explained with the help of the existing conventional control techniques. The graphic analytical method (rule base plane decomposition) for the traditional two-term fuzzy logic controller is used for the analytical model derivation. The derived results expose that on the one hand, the 3-D FLC has a global sliding mode structure over the spatial domain; on the other hand, it has a spatial equivalent structure with the traditional fuzzy logic controller over the space domain. In terms of the spatial equivalent structure, some properties of the controller are further presented.
The stability issue of the 3-D fuzzy logic control system is discussed, based on the analytical mathematical model of the 3-D FLC. In virtue of the global sliding mode feature of 3-D FLC, the Lyapunov stability of fuzzy logic control system is investigated, where a global stability condition is derived and an approach for designing the controller parameters is given. Utilizing the spatial equivalent structure and some feature of discrete time systems, the BIBO stability of discrete time fuzzy logic control system is investigated, where a global BIBO stability condition is derived and an approach for designing the controller parameters is given. Two examples are presented respectively to demonstrate the effectiveness of the two kinds of controller parameter designs by simulation experiments.
A 3-D fuzzy logic control strategy based on decomposition and coordination is proposed for the spatially distributed systems with multiple sources. It extends the 3-D FLC to solve the control problem of the general spatially distributed systems. The control system has a hierarchical structure with three hierarchies. Firstly, the decomposition module decomposes the whole space domain into sub-space domains and decomposes the complex spatially-distributed process with multiple sources into several relatively simple subsystems. Then, on the middle layer, a 3-D FLC is used for each subsystem. Finally, on the top layer, the coordination module carries out a strategy of local coordination among adjacent subsystems, and formulates a coordinated 3-D fuzzy logic control. The proposed control method is successfully applied to a Rapid Thermal Chemical Vapor Deposition (RTCVD) system, and the simulation results demonstrate its effectiveness.
引文
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