基于压电致动器的柔性构件振动主动控制技术研究
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摘要
对柔性构件的振动主动控制问题，结合国家自然科学基金项目，针对一类空间柔性杆系统的扭转振动及一类两连杆柔性构件系统中的柔性梁、柔性杆之间的弯曲-扭转耦合振动进行系统、深入的理论与实验研究。
第一章概述了课题研究的背景与意义。从柔性构件的系统建模、典型柔性构件的研究、智能材料的应用、致动器／传感器的优化配置、振动控制中的常用控制算法方面，综述了柔性构件主动控制的研究现状。最后阐述了本文的主要研究内容。
第二章阐述了压电材料的压电方程及压电应用。设计了一种采用轴向极化方式的压电扭转致动器，导出了此致动器的输出扭矩，分析了其谐振频率，探讨了此类致动器的制作加工工艺。分析了电阻应变片测量扭转振动的基本原理，推导了其扭转角与电桥输出电压之间的关系。
第三章简要分析了柔性杆的扭转振动。提出一种由柔性杆、压电扭转致动器、电阻应变片传感器所组成的空间柔性杆件系统。针对该柔性杆系统中压电致动器／传感器的位置优化配置问题，推导了系统的动力学方程，建立了系统的状态空间表达式。提出一种基于最小输入能量、最大能量传递、Grammian矩阵最小奇异值最大化的复合优化配置算法，运用遗传算法对压电扭转致动器／传感器的布局位置进行了优化。最后，进行了数值优化仿真研究，确定了致动器／传感器的最优配置位置，并与其它位置作了比较研究。
第四章基于线性二次型最优控制基本理论，研究了线性二次型最优控制理论中的加权矩阵Q的选择策略，提出一种基于遗传算法并具有约束条件的加权矩阵选择方法。以第三章所建立的系统为例进行了优化仿真研究，表明所提出的加权矩阵选择策略是有效的、可行的。同时也作了致动器／传感器在不同位置的控制研究，验证了相关优化理论的正确性。
第五章构建了一种由柔性梁与柔性杆所组成的具有弯扭耦合特性的空间两连杆柔性构件系统，将两种不同极化方式的压电致动器应用于此柔性构件系统的弯扭耦合振动主动控制。运用拉格朗日方程和假设模态法推导了此柔性系统的动力学方程。在柔性杆上粘贴压电扭转致动器抑制柔性杆的扭转振动，在柔性梁上粘贴压电弯曲致动器抑制柔性梁的弯曲振动。提出了两种控制策略，第一种是基于Lyapunov稳定性的速度反馈控制策略，第二种是带有饱和环节及低通滤波器的滑模变结构控制策略，对提出的两种控制策略，分别进行了主动控制数值仿真研究，并作了对比分析。
第六章构建了基于工业PC机为核心的柔性构件实验系统，对实验系统的软、硬件进行了阐述，分别进行了柔性杆系统及两连杆柔性构件系统的主动控制实验研究。实验结果验证了相关位置优化理论及控制理论应用的正确性。
第七章对全文进行了总结，并对未来的工作进行了展望。
Aiming at the active vibration control of space flexible structures and combined with the National Natural Science Foudation Project, the torsional vibration of a space flexible bar and the bending-torsional-coupled vibration of a two-link flexible structure were investigated theoretically and experimentally.
In chapter one, the background information and significance of the dissertation were presented. And then the up-to-date research status of the flexible structures was given in the following aspects which are the system modeling of the flexible structures, studies on the typically flexible structures, application of smart materials, optimization placement of the actuators/sensors and conventional control algorithms in active vibration control. At last, the main research content of this dissertation was presented.
In chapter two, the piezoelectric constitutive equations and the application of piezoelectric materials were presented. A piezoelectric torisonal actuator was designed using axial poling method, and the output torque of the actuator was derived. The torisonal resonant frequency of the piezoelectric torsional actuator was analyzed and its fabrication method was discussed. The fundamental of the strain gauge in testing torsional vibration was investigated and the relationship between the torsional angle and output voltage of the electric bridge was founded.
In chapter three, the torsional vibration of the flexible bar was analyzed. A space flexible structure consiting of a flexible bar, a piezoelectric torsional actuator and strain gauges was proposed. Aiming at the optimization placement of the actuator/sensor, the dynamic governing equation of the system was derived, and the state-space expression of the dynamic system was developed. A hybrid optimization algorithm combined with minimum input energy, maximum energy transferring and maximum of minmum singular value of controllability Grammian was proposed. The optimization process was carried out using genetic algorithm. And optimal placement position of the actuator/sensor was obtained. Also a comparable research was implemented compared with other positions.
In chapter four, linear quadratic optimal control theory was summarized. Choosing method of the weight matrix was investigated. A method based on genetic algorithm combined with constraints was proposed. Simulations were implemented using the model founded in chapter three. The results show the proposed choosing method of the weighting matrix is effective and feasible. Also an active control was implemented when the actuator/sensor was placed in other position. Results validate the optimization conclusions made in chapter three.
In chapter five, a two-link space flexible structure system consisting of a flexible beam and a flexible bar was proposed. Two piezoelectric actuators with different poling methods were used to suppress the bending-torsional-coupled vibration of the system. The dynamic governing equation of the system was derived using Lagrange equation and assumed mode method. Piezoelectric torsional actuators were bonded on the flexible bar to suppress the torsional vibraition of the bar, and piezoelectric bending actuators were bonded on the flexible beam to suppress the bending vibration of the beam. Two control strategies were proposed, the first was a modal velocity control strategy based on the Lyapunov stability. The second was a variable structure control method combined with a saturation element and a low-pass filter. Simulations were carried out. At last, the proposed two control methods were compared.
In chapter six, experimental system of the flexible structure was founded, and the corresponding soft ware and hard ware of the experimental system were summarized. Active vibration control research of the flexible bar system and the two-link flexible structure system were carried out respectively.
In chapter seven, some conclusions were made, and the future work was proposed.
第一章概述了课题研究的背景与意义。从柔性构件的系统建模、典型柔性构件的研究、智能材料的应用、致动器／传感器的优化配置、振动控制中的常用控制算法方面，综述了柔性构件主动控制的研究现状。最后阐述了本文的主要研究内容。
第二章阐述了压电材料的压电方程及压电应用。设计了一种采用轴向极化方式的压电扭转致动器，导出了此致动器的输出扭矩，分析了其谐振频率，探讨了此类致动器的制作加工工艺。分析了电阻应变片测量扭转振动的基本原理，推导了其扭转角与电桥输出电压之间的关系。
第三章简要分析了柔性杆的扭转振动。提出一种由柔性杆、压电扭转致动器、电阻应变片传感器所组成的空间柔性杆件系统。针对该柔性杆系统中压电致动器／传感器的位置优化配置问题，推导了系统的动力学方程，建立了系统的状态空间表达式。提出一种基于最小输入能量、最大能量传递、Grammian矩阵最小奇异值最大化的复合优化配置算法，运用遗传算法对压电扭转致动器／传感器的布局位置进行了优化。最后，进行了数值优化仿真研究，确定了致动器／传感器的最优配置位置，并与其它位置作了比较研究。
第四章基于线性二次型最优控制基本理论，研究了线性二次型最优控制理论中的加权矩阵Q的选择策略，提出一种基于遗传算法并具有约束条件的加权矩阵选择方法。以第三章所建立的系统为例进行了优化仿真研究，表明所提出的加权矩阵选择策略是有效的、可行的。同时也作了致动器／传感器在不同位置的控制研究，验证了相关优化理论的正确性。
第五章构建了一种由柔性梁与柔性杆所组成的具有弯扭耦合特性的空间两连杆柔性构件系统，将两种不同极化方式的压电致动器应用于此柔性构件系统的弯扭耦合振动主动控制。运用拉格朗日方程和假设模态法推导了此柔性系统的动力学方程。在柔性杆上粘贴压电扭转致动器抑制柔性杆的扭转振动，在柔性梁上粘贴压电弯曲致动器抑制柔性梁的弯曲振动。提出了两种控制策略，第一种是基于Lyapunov稳定性的速度反馈控制策略，第二种是带有饱和环节及低通滤波器的滑模变结构控制策略，对提出的两种控制策略，分别进行了主动控制数值仿真研究，并作了对比分析。
第六章构建了基于工业PC机为核心的柔性构件实验系统，对实验系统的软、硬件进行了阐述，分别进行了柔性杆系统及两连杆柔性构件系统的主动控制实验研究。实验结果验证了相关位置优化理论及控制理论应用的正确性。
第七章对全文进行了总结，并对未来的工作进行了展望。
Aiming at the active vibration control of space flexible structures and combined with the National Natural Science Foudation Project, the torsional vibration of a space flexible bar and the bending-torsional-coupled vibration of a two-link flexible structure were investigated theoretically and experimentally.
In chapter one, the background information and significance of the dissertation were presented. And then the up-to-date research status of the flexible structures was given in the following aspects which are the system modeling of the flexible structures, studies on the typically flexible structures, application of smart materials, optimization placement of the actuators/sensors and conventional control algorithms in active vibration control. At last, the main research content of this dissertation was presented.
In chapter two, the piezoelectric constitutive equations and the application of piezoelectric materials were presented. A piezoelectric torisonal actuator was designed using axial poling method, and the output torque of the actuator was derived. The torisonal resonant frequency of the piezoelectric torsional actuator was analyzed and its fabrication method was discussed. The fundamental of the strain gauge in testing torsional vibration was investigated and the relationship between the torsional angle and output voltage of the electric bridge was founded.
In chapter three, the torsional vibration of the flexible bar was analyzed. A space flexible structure consiting of a flexible bar, a piezoelectric torsional actuator and strain gauges was proposed. Aiming at the optimization placement of the actuator/sensor, the dynamic governing equation of the system was derived, and the state-space expression of the dynamic system was developed. A hybrid optimization algorithm combined with minimum input energy, maximum energy transferring and maximum of minmum singular value of controllability Grammian was proposed. The optimization process was carried out using genetic algorithm. And optimal placement position of the actuator/sensor was obtained. Also a comparable research was implemented compared with other positions.
In chapter four, linear quadratic optimal control theory was summarized. Choosing method of the weight matrix was investigated. A method based on genetic algorithm combined with constraints was proposed. Simulations were implemented using the model founded in chapter three. The results show the proposed choosing method of the weighting matrix is effective and feasible. Also an active control was implemented when the actuator/sensor was placed in other position. Results validate the optimization conclusions made in chapter three.
In chapter five, a two-link space flexible structure system consisting of a flexible beam and a flexible bar was proposed. Two piezoelectric actuators with different poling methods were used to suppress the bending-torsional-coupled vibration of the system. The dynamic governing equation of the system was derived using Lagrange equation and assumed mode method. Piezoelectric torsional actuators were bonded on the flexible bar to suppress the torsional vibraition of the bar, and piezoelectric bending actuators were bonded on the flexible beam to suppress the bending vibration of the beam. Two control strategies were proposed, the first was a modal velocity control strategy based on the Lyapunov stability. The second was a variable structure control method combined with a saturation element and a low-pass filter. Simulations were carried out. At last, the proposed two control methods were compared.
In chapter six, experimental system of the flexible structure was founded, and the corresponding soft ware and hard ware of the experimental system were summarized. Active vibration control research of the flexible bar system and the two-link flexible structure system were carried out respectively.
In chapter seven, some conclusions were made, and the future work was proposed.
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