基于MBC的复杂结构振动控制研究
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摘要
自1972年华裔学者Yao提出了土木工程结构振动控制的概念以来,结构振动控制理论研究和应用技术取得了迅猛的发展,目前已被广泛应用于土木工程控制的各个领域,效果显著。伴随着科技的进步和发展,高层、高耸、大跨等复杂结构形式不断涌现,结构自由度的增加以及大量控制装置和传感器的应用,使得土木工程控制系统趋于复杂化,导致结构控制方法发生转变,传统的集中控制策略逐渐暴露出局限性。为了解决集中控制方法处理复杂结构方面的不足,20世纪70年代分散控制策略应运而生。基于市场竞争机制的控制策略(Market-based control,MBC)作为一种分散控制方法,是一种多目标优化算法。MBC策略是将自由经济市场中的价格机制引入到控制系统中,以市场模拟控制系统,以销售商和消费者分别替代能量源系统和受控结构,通过模拟自由市场中的经济行为完成控制能量的最优分配,以解决不同领域的控制问题。
目前,已有MBC理论主要用于解决结构处于弹性状态下的控制问题,对于进入弹塑性状态的结构振动控制研究较少。此外,MBC策略应用时主要基于精确的结构计算模型,而对于复杂结构而言,由于结构本身存在的非线性、时变性、不确定性和复杂性等因素,往往很难建立精确的计算模型,使得MBC策略的应用受到限制。鉴于以上原因,本文主要开展了以下几方面的研究工作:
(1)总结了MBC理论的发展历程和研究现状,介绍了MBC理论的经济学基础,概括了结构控制系统市场模型的理论基础,同时对工程中常用的MBC供需函数模型予以总结和分析,为MBC策略在土木工程振动控制中的应用提供理论平台。
(2)在已有MBC理论的基础上考虑复杂结构的非线性问题,以拟力法为结构非线性求解平台,解决结构动力分析中计算时间长、求解速度慢、存储空间大等问题,实现了MBC策略在结构非线性控制领域中的应用。通过数值算例验证了该方法的正确性和有效性。
(3)将模糊逻辑理论引入MBC策略中,利用模糊逻辑不需要建立精确计算模型的优点,提出了基于MBC理论的模糊价格规则提取方法;在此基础上,建立了基于MBC理论的模糊控制方法。数值算例展示了模糊价格提取方法的操作流程,将模糊控制方法用于结构控制中取得了较好的控制效果。
Since the conception of vibration control in civil engineering structure was proposed by scholars Yao in 1972, the theoretical studies and application technology of vibration control had made considerable advancement in the past 30 years, and was widely used in all aspects of civil engineering control, Moreover, achieving good results. With the development of science and technology, the complicated large-scale systems were built (such as high-raise building, long-span structure). Owing to the increase of structure dimensions and the massive application of control devices and sensors, the system tend to complicate, the structure control method was transformed, and the traditional centralized-control strategy gradually revealed limitations. During 1970s, decentralized control strategy was proposed, and was used to compensate the shortage of centralized-control strategy in dealing with the complicated large-scale system.
As a decentralized control strategy, Market-based control (MBC) is a multipurpose optimal method. MBC strategy is that price mechanism in the free-market economy is introduced to the control system, and achieve the optimal allocation of the control energy via simulating economic behavior in the free-market economy, resolve the control problem in different fields. Moreover, the market simulate the control system, and the seller and consumer respectively substitute the energy system and controlled structure.
Currently, the existing MBC strategy is mostly used to resolve the control problem of linear elastic structure, but can't do anything about the non-linear control problem in the elastic-plastic structure. Furthermore, the application of MBC strategy is based upon accurate model of the buildings, because of the complicated structure's nonlinear, time variant, uncertainty and complexity, the accurate models are difficultly built, and the use of MBC strategy is limited. For these reasons, the paper's contents include :
(1) retrospect and summarize the development and current situation of the MBC strategy, introduce the Theoretical foundation of economics, sum up the ideological foundation of the structure control system market model. Moreover, this paper summarizes the demand and supply function widely used in engineering, laying the theoretical foundation for the practical application of the MBC strategy.
(2) the structural nonlinear deformation problem is considered upon MBC strategy. Force analogy method (FAM) is proposed to analyze the structural nonlinear problem. The new method fills in the blank of structural nonlinear deformation upon MBC theory, and compared with traditional method of variable stiffness, FAM reduces storage spaces and enhances computing speed. At last, an example is given to demonstrate the accuracy and efficiency of the proposed computational method.
(3) Fuzzy logic is introduced into MBC strategy, a new extraction method of fuzzy price rules upon MBC theory is built, and a new fuzzy control strategy based on MBC theory is proposed. The extraction method of fuzzy price rules are carried out by an example, and the fuzzy control strategy obtain the better control effects in the course of being used in the structure control.
目前,已有MBC理论主要用于解决结构处于弹性状态下的控制问题,对于进入弹塑性状态的结构振动控制研究较少。此外,MBC策略应用时主要基于精确的结构计算模型,而对于复杂结构而言,由于结构本身存在的非线性、时变性、不确定性和复杂性等因素,往往很难建立精确的计算模型,使得MBC策略的应用受到限制。鉴于以上原因,本文主要开展了以下几方面的研究工作:
(1)总结了MBC理论的发展历程和研究现状,介绍了MBC理论的经济学基础,概括了结构控制系统市场模型的理论基础,同时对工程中常用的MBC供需函数模型予以总结和分析,为MBC策略在土木工程振动控制中的应用提供理论平台。
(2)在已有MBC理论的基础上考虑复杂结构的非线性问题,以拟力法为结构非线性求解平台,解决结构动力分析中计算时间长、求解速度慢、存储空间大等问题,实现了MBC策略在结构非线性控制领域中的应用。通过数值算例验证了该方法的正确性和有效性。
(3)将模糊逻辑理论引入MBC策略中,利用模糊逻辑不需要建立精确计算模型的优点,提出了基于MBC理论的模糊价格规则提取方法;在此基础上,建立了基于MBC理论的模糊控制方法。数值算例展示了模糊价格提取方法的操作流程,将模糊控制方法用于结构控制中取得了较好的控制效果。
Since the conception of vibration control in civil engineering structure was proposed by scholars Yao in 1972, the theoretical studies and application technology of vibration control had made considerable advancement in the past 30 years, and was widely used in all aspects of civil engineering control, Moreover, achieving good results. With the development of science and technology, the complicated large-scale systems were built (such as high-raise building, long-span structure). Owing to the increase of structure dimensions and the massive application of control devices and sensors, the system tend to complicate, the structure control method was transformed, and the traditional centralized-control strategy gradually revealed limitations. During 1970s, decentralized control strategy was proposed, and was used to compensate the shortage of centralized-control strategy in dealing with the complicated large-scale system.
As a decentralized control strategy, Market-based control (MBC) is a multipurpose optimal method. MBC strategy is that price mechanism in the free-market economy is introduced to the control system, and achieve the optimal allocation of the control energy via simulating economic behavior in the free-market economy, resolve the control problem in different fields. Moreover, the market simulate the control system, and the seller and consumer respectively substitute the energy system and controlled structure.
Currently, the existing MBC strategy is mostly used to resolve the control problem of linear elastic structure, but can't do anything about the non-linear control problem in the elastic-plastic structure. Furthermore, the application of MBC strategy is based upon accurate model of the buildings, because of the complicated structure's nonlinear, time variant, uncertainty and complexity, the accurate models are difficultly built, and the use of MBC strategy is limited. For these reasons, the paper's contents include :
(1) retrospect and summarize the development and current situation of the MBC strategy, introduce the Theoretical foundation of economics, sum up the ideological foundation of the structure control system market model. Moreover, this paper summarizes the demand and supply function widely used in engineering, laying the theoretical foundation for the practical application of the MBC strategy.
(2) the structural nonlinear deformation problem is considered upon MBC strategy. Force analogy method (FAM) is proposed to analyze the structural nonlinear problem. The new method fills in the blank of structural nonlinear deformation upon MBC theory, and compared with traditional method of variable stiffness, FAM reduces storage spaces and enhances computing speed. At last, an example is given to demonstrate the accuracy and efficiency of the proposed computational method.
(3) Fuzzy logic is introduced into MBC strategy, a new extraction method of fuzzy price rules upon MBC theory is built, and a new fuzzy control strategy based on MBC theory is proposed. The extraction method of fuzzy price rules are carried out by an example, and the fuzzy control strategy obtain the better control effects in the course of being used in the structure control.
引文
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