基于线性矩阵不等式方法的建筑结构H∞控制
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摘要
随着社会经济的发展,越来越多的土木建筑物结构形式向着大跨高耸的体型发展。为了减小这些大型复杂结构的振动,新型材料、新型阻尼器和各种附属结构不断地发展并应用于结构的振动控制中。随着混合控制和主动控制技术分别投入到广州电视塔与京基100两栋超高层建筑中来减振控制,主动控制技术已经开始受到重视。对于高耸大跨等大型结构,与被动地增大刚度相比,主动控制会大量减小其投入的经济成本。为了适应今后的发展趋势,本文考虑了在土木结构中采用主动控制可能带来的一些问题,进行了相关的研究工作,目的在于减小主动控制技术在土木工程中应用所带来的问题。本文的控制算法为Hoo控制,计算理论为LMI方法,作者所做的工作如下：
(1)考虑控制系统本身传感器出现故障的情况,设计了故障检测器对故障进行了诊断,并且隔离(即FDI),再对控制策略进行重组,使其具有容错的功能(即FTC)。文中通过建立动态控制器设计方法和基于Kalman滤波器的静态控制器设计方法分别设计了动态故障检测器和静态故障检测器,应用静态估值检测器对控制策略进行了重组。设计过程中,均是将设计目标设定为系统传递函数的Hoo范数,并通过LMI方法进行求解。通过数值算例分别对动态、静态故障检测器、容错控制器进行了验证,用以说明文中提出的方法对传感器故障的识别和容错的有效性。
(2)考虑土木结构尺度大导致的主动控制反馈时间延迟的问题,采用了分散控制来解决,通过双同伦法将BMI问题近似为了LMI问题,最后解得Hoo分散控制器。通过6层框架数值算例和带有2个AMD的双层框架振动台试验对文中提出的Hoo分散控制器设计方法进行了验证,用以说明Hoo分散控制在处理大尺度的土木建筑结构振动控制中的适用性。
(3)由于土木结构在使用中存在附加荷载,振动中刚度阻尼会变化,本文考虑了结构参数的不确定,提出了基于D-K迭代方法和LMI方法的Hoo鲁棒控制器设计方法。通过4层框架数值算例和带有1个AMD的双层框架振动台试验进行了验证,用以说明文中提出的Hoo鲁棒控制是可以考虑到结构参数变化并保证控制的鲁棒性的。
(4)对于大尺度土木结构,同时考虑主动控制反馈时间延迟和结构参数的不确定,提出了对结构参数不确定具有鲁棒性的Hoo分散控制器设计方法,融合了D-K迭代方法与双同伦方法。通过4层框架数值算例对此方法进行了验证,用以说明文中提出的控制器设计方法可以同时考虑反馈时间延迟和结构参数不确定等因素。
In recent decades, the economy is developed very fast. There are a lot of infrastructures with large span or extra high, which can be damaged due to the vibration. In order to reduce the vibration of these structures, many new materials, dampers and accessory structures have been utilized to control the structural vibration. Nowadays, the hybrid control and active control were used in Guangzhou TV tower (Canton Tower) and KingKey Financial Center (KK100), respectively. Compared with increasing the structural stiffness, active control can save a lot of money. So it is necessary to do some research on active control. In this dissertation, some active control problems caused by civil structural characteristics are considered. And some research on how to make the active control robust are performed. The reaseach is all based on the Hoo theory and linear matrix inequality (LMI) approach. The primary innovative contents are as follows:
(1) Considering the faults in the sensors of the control system, the filters are designed to conduct the fault detection and isolation (FDI). The control strategy is reformed to have the fault tolerant control (FTC) performance. The dynamic filter and static filter are designed. The former one is based on the dynamic H∞controller design theorem. The later one is motivated by Kalman filter theorem. These two filters are both solved by LMI approach. The static filter is then used to reform the control strategy, which can execute the fault tolerant control. Their performance are validated by numerical examples, respectively.
(2) Considering the time delay for control system in the large scale civil structures, the Hoo decentralized controller is designed through double homotopy approach. The proposed method is first studied numerically with a six-story building example, and then validated experimentally through shaking table tests of a two-story frame with active mass dampers.
(3) Considering the structural parametric uncertainties, the Hoo robust controller is designed based on the D-K iteration method and LMI approach, The proposed algorithm is first theoretically validated by a four-story structure numerical example, and then experimentally corroborated by a shaking table test of a two-story frame with one active mass damper.
(4) Considering the time delay and the parametric uncertainties simultaneously, a innovative control strategy is proposed to design the Hoo robust decentralized controller. This new method combines D-K iteration and double homotopy approach. Finally, the proposed method is validated numerically with a four-story building example.
(1)考虑控制系统本身传感器出现故障的情况,设计了故障检测器对故障进行了诊断,并且隔离(即FDI),再对控制策略进行重组,使其具有容错的功能(即FTC)。文中通过建立动态控制器设计方法和基于Kalman滤波器的静态控制器设计方法分别设计了动态故障检测器和静态故障检测器,应用静态估值检测器对控制策略进行了重组。设计过程中,均是将设计目标设定为系统传递函数的Hoo范数,并通过LMI方法进行求解。通过数值算例分别对动态、静态故障检测器、容错控制器进行了验证,用以说明文中提出的方法对传感器故障的识别和容错的有效性。
(2)考虑土木结构尺度大导致的主动控制反馈时间延迟的问题,采用了分散控制来解决,通过双同伦法将BMI问题近似为了LMI问题,最后解得Hoo分散控制器。通过6层框架数值算例和带有2个AMD的双层框架振动台试验对文中提出的Hoo分散控制器设计方法进行了验证,用以说明Hoo分散控制在处理大尺度的土木建筑结构振动控制中的适用性。
(3)由于土木结构在使用中存在附加荷载,振动中刚度阻尼会变化,本文考虑了结构参数的不确定,提出了基于D-K迭代方法和LMI方法的Hoo鲁棒控制器设计方法。通过4层框架数值算例和带有1个AMD的双层框架振动台试验进行了验证,用以说明文中提出的Hoo鲁棒控制是可以考虑到结构参数变化并保证控制的鲁棒性的。
(4)对于大尺度土木结构,同时考虑主动控制反馈时间延迟和结构参数的不确定,提出了对结构参数不确定具有鲁棒性的Hoo分散控制器设计方法,融合了D-K迭代方法与双同伦方法。通过4层框架数值算例对此方法进行了验证,用以说明文中提出的控制器设计方法可以同时考虑反馈时间延迟和结构参数不确定等因素。
In recent decades, the economy is developed very fast. There are a lot of infrastructures with large span or extra high, which can be damaged due to the vibration. In order to reduce the vibration of these structures, many new materials, dampers and accessory structures have been utilized to control the structural vibration. Nowadays, the hybrid control and active control were used in Guangzhou TV tower (Canton Tower) and KingKey Financial Center (KK100), respectively. Compared with increasing the structural stiffness, active control can save a lot of money. So it is necessary to do some research on active control. In this dissertation, some active control problems caused by civil structural characteristics are considered. And some research on how to make the active control robust are performed. The reaseach is all based on the Hoo theory and linear matrix inequality (LMI) approach. The primary innovative contents are as follows:
(1) Considering the faults in the sensors of the control system, the filters are designed to conduct the fault detection and isolation (FDI). The control strategy is reformed to have the fault tolerant control (FTC) performance. The dynamic filter and static filter are designed. The former one is based on the dynamic H∞controller design theorem. The later one is motivated by Kalman filter theorem. These two filters are both solved by LMI approach. The static filter is then used to reform the control strategy, which can execute the fault tolerant control. Their performance are validated by numerical examples, respectively.
(2) Considering the time delay for control system in the large scale civil structures, the Hoo decentralized controller is designed through double homotopy approach. The proposed method is first studied numerically with a six-story building example, and then validated experimentally through shaking table tests of a two-story frame with active mass dampers.
(3) Considering the structural parametric uncertainties, the Hoo robust controller is designed based on the D-K iteration method and LMI approach, The proposed algorithm is first theoretically validated by a four-story structure numerical example, and then experimentally corroborated by a shaking table test of a two-story frame with one active mass damper.
(4) Considering the time delay and the parametric uncertainties simultaneously, a innovative control strategy is proposed to design the Hoo robust decentralized controller. This new method combines D-K iteration and double homotopy approach. Finally, the proposed method is validated numerically with a four-story building example.
引文
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