层合压电智能结构振动主动控制数值模拟及其优化
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摘要
压电材料具有将机械能转化为电能的能力及其逆效用,常被制作成薄片形状的致动器/传感器,粘贴在主结构表面或埋置于主结构内部,构成具有自检测、自诊断、自修复及自适应等功能的层合压电智能结构。层合压电智能结构在航空航天、机械和土木工程等领域中的应用和现代控制理论的发展,极大的推动了国内外学者对柔性层合智能结构振动控制的研究热情。层合压电智能结构是一个具有不连续密度分布、不连续材料性质、机电耦合的动力系统。因此,精确而有效的分析压电材料的力电耦合行为,探索力学场,电场的耦合作用;兼顾求解计算效率,建立能准确描述层合压电智能结构在干扰荷载作用下的动态响应分析模型;揭示致动器/传感器分布位置、几何尺寸和复合材料层间铺设角度对层合智能结构振动特性的影响;分析控制器参数、结构配置对控制系统品质和性能的影响,移动荷载作用下智能结构的振动控制;研究智能结构主动控制的理论和算法,提高智能结构控制系统稳定性;压电致动器/传感器位置优化的程序设计及实现;实现层合压电智能结构多阶目标模态振动控制等,这些都是亟待解决的问题。
论文从Hamilton原理和压电材料的力-电耦合本构方程出发,建立了线弹性压电体的动力有限元状态空间方程,基于ANSYS/APDL参数化语言编制了能够准确描述层合压电智能结构力-电耦合场的有限元数值模型。揭示了智能悬臂梁自振频率及阵型随致动器/传感器位置、尺寸、复合层合角度改变的变化规律。深入研究了压电致动器/传感器位置、数量及控制器参数对PID闭环系统控制性能的影响,引入先进的积分分离、变速积分、不完全微分PID控制有效解决了经典PID控制器参数选择不当造成的系统发散失稳等现象,提高了系统的稳定性,扩大了控制器参数选择范围。分析了移动荷载作用下层合压电智能梁系统不同振动阶段控制器参数、荷载移动速度对系统控制性能的影响。
提出了一种根据系统输出误差实时调整修正反馈增益的自学习控制(SLC)算法。将模糊逻辑和迭代学习控制的基本思想相结合,提出了以系统输出误差及其变化量作为模糊控制器的输入,以迭代学习增益作为模糊控制器的输出,采用模糊控制实时确定迭代学习增益的模糊自学习控制(FSLC)方法,提高了自学习控制的收敛速度。建立了上下表面对称粘贴有三对压电致动器/传感器压电智能悬臂板动力分析有限元模型,通过仿真试验,证明了SLC和FSLC均能有效地控制了闭环系统振动响应,结果表明FSLC控制效果比SLC控制效果更好,为智能结构振动控制理论算法和迭代学习控制增益的确定增加了新的思路。基于线性二次型最优控制与迭代学习控制相结合的思想,研究线性二次型迭代学习混合控制方法,加快了迭代学习控制的收敛速度。基于MATLAB软件建立了多点致动一维层合压电悬臂梁动力分析的有限元数值模型,实现了层合智能梁的经典最优控制和线性二次型最优迭代学习混合控制,证明了线性二次型最优迭代学习混合控制方法能够有效控制层合压电智能结构的振动,并且控制效果得到了一定的改进。
以离散分布压电致动器/传感器的位置参数为优化变量,压电智能结构闭环控制系统阻尼比为目标函数,提出了层合压电智能结构振动控制及压电致动器/传感器位置优化的遗传算法程序。通过有限元数值模拟,研究了悬臂板自由端在瞬时荷载和简谐荷载作用下振动控制问题,数值仿真结果验证了压电致动器/传感器位置优化程序的正确性,说明采用遗传算法搜索压电智能结构振动控制中压电致动器/传感器的最优位置是十分有效的,并具有较高的计算效率。
基于数值仿真实验的方法,研究了复合层合压电梁比例反馈控制系统中,比例反馈增益、层间铺设方式对闭环系统控制性能的影响。基于复合层合板模态应变能分布大小,提出了一种简单易行的压电致动器/传感器位置确定方法,适用于层合智能结构多阶目标模态的振动控制。数值试验结果证明了基于模态应变能分布确定压电致动器/传感器进而实现复合层合压电智能板多阶模态振动控制的可行性和正确性。
Piezoelectric materials have been manufactured into thin actuators/sensors because of their ability to transform mechanical energy to electrical energy and vice versa. Laminated piezoelectric smart structures with piezoelectric actuators/sensors bonded on the surface or embedded in host structures have self-detection, self-diagnosis, self-healing and adaptive functions. Application of laminated piezoelectric smart structures in the fields of aerospace, mechanical as well as civil engineering and modern control theory development have greatly promoted the domestic and foreign scholars to poure enthusiasm into their vibration control research. Laminated piezoelectric smart structure is a discrete density distribution, discontinuous material properties and electro-mechanical coupling dynamic model system. Therefore, accurately and effectively analyzing the behavior of piezoelectric material electro-mechanical coupling, exploring the mechanical and electric field coupling action, taking into account of solving efficiency when establishing the accurate dynamic response model of laminated piezoelectric smart structure under disturbance loading, revealing the effect of acturators/sensors distribution location, geometry size as well as compsite material lay-ups on laminated smart structure vibration characteristics, controller parameters and structure configuration impact on system quality and performance, vibration control of smart structures undering moving load are problems to be solved. Investigating active control theory and algorithm of smart structure to improve system stability, optimization of pizeoelectirc actuator/sensor locations, realizing multi target mode vibration control and so on, all these problems mentioned above are also urgent to be solved.
In this paper, finit element dyanimc state-space equation of linear elastic piezoelectric is derived from Hamilton principle and electro-mechanical coupling constitutive of piezoelectric materials. Numerical models are established to accurately describe the mechanich-electric coupling field based on ANSYS/APDL parameter language. The variation of natural frequency and mode shape of smart cantilever beam as actuator/sensor location, size and composite material lay-ups changing has been explored. The impact of piezoelectric actuator/sensor location, number and controller parameters on PID closed-loop control system performance is studied. The introduction of advanced PID controller with separated integration, changing rate integration and partial differential effectively settled the divergency and instability appearance of system caused by inappropriate parameters of classic PID controller. The impact of controller parameters and load moving speed on control performance is also analyzed at different vibration stages of laminated piezoelectric smart system under moving load.
A self-learning control (SLC) algrothm able to real-time adjust and amend control feedback gain is presented according to system output error. Taking system output error with its variation and the gain of iterative learning as the input and output of fuzzy controller respectively, the fuzzy self-learning control (FSLC) method is also proposed to speed up the convergence of SLC. The numerical simulation results of piezoelectric smart cantilever plate prove that both SLC and FSLC could effectively reduce the vibration response of closed-loop system, and FSLC quality is better than SLC. Based on the idea of combining the linear quadratic optimal control with iterative learning (IL) control, the paper puts forward a new hybrid control strategy which is named linear quadratic iterative learning control to improve the iterative learning control convergence. The numerical model for dynamic analyzing of one-dimensional laminated piezoelectric cantilever beam is created by MATLAB software. And then the classic optimal control and linear quadratic optimal iterative learning hybrid control are achieved, thus the control property is improved.
Taking the location parameters of discrete distribution piezoelectric actuators/sensors and the damping ratio of piezoelectric smart structure closed-loop control system as optimization variables and objective function respectively, the actuator/sensor optimization program based on genetic algorithm (GA) is presented. The finite element numerical simulation is conducted to consider the vibration control of cantilever plate exited by transient and harmonic loading at the free end of it. Numerical results show the validity and effectiveness of using GA for searching optimal placement of the actuator /sensor pairs in active structural vibration control.
This paper discussed proportional feedback gain and lay-ups effect on the closed-loop system performance of composite laminated piezoelectric beam by numerical simulation method. A simple and easy to implement way to determinate actuator/sensor locations is raised based on distribution of modal strain energy for multi target modes vibration control of laminated smart structures. Numerical results proved the feasibility and correctness of the method metioned above.
论文从Hamilton原理和压电材料的力-电耦合本构方程出发,建立了线弹性压电体的动力有限元状态空间方程,基于ANSYS/APDL参数化语言编制了能够准确描述层合压电智能结构力-电耦合场的有限元数值模型。揭示了智能悬臂梁自振频率及阵型随致动器/传感器位置、尺寸、复合层合角度改变的变化规律。深入研究了压电致动器/传感器位置、数量及控制器参数对PID闭环系统控制性能的影响,引入先进的积分分离、变速积分、不完全微分PID控制有效解决了经典PID控制器参数选择不当造成的系统发散失稳等现象,提高了系统的稳定性,扩大了控制器参数选择范围。分析了移动荷载作用下层合压电智能梁系统不同振动阶段控制器参数、荷载移动速度对系统控制性能的影响。
提出了一种根据系统输出误差实时调整修正反馈增益的自学习控制(SLC)算法。将模糊逻辑和迭代学习控制的基本思想相结合,提出了以系统输出误差及其变化量作为模糊控制器的输入,以迭代学习增益作为模糊控制器的输出,采用模糊控制实时确定迭代学习增益的模糊自学习控制(FSLC)方法,提高了自学习控制的收敛速度。建立了上下表面对称粘贴有三对压电致动器/传感器压电智能悬臂板动力分析有限元模型,通过仿真试验,证明了SLC和FSLC均能有效地控制了闭环系统振动响应,结果表明FSLC控制效果比SLC控制效果更好,为智能结构振动控制理论算法和迭代学习控制增益的确定增加了新的思路。基于线性二次型最优控制与迭代学习控制相结合的思想,研究线性二次型迭代学习混合控制方法,加快了迭代学习控制的收敛速度。基于MATLAB软件建立了多点致动一维层合压电悬臂梁动力分析的有限元数值模型,实现了层合智能梁的经典最优控制和线性二次型最优迭代学习混合控制,证明了线性二次型最优迭代学习混合控制方法能够有效控制层合压电智能结构的振动,并且控制效果得到了一定的改进。
以离散分布压电致动器/传感器的位置参数为优化变量,压电智能结构闭环控制系统阻尼比为目标函数,提出了层合压电智能结构振动控制及压电致动器/传感器位置优化的遗传算法程序。通过有限元数值模拟,研究了悬臂板自由端在瞬时荷载和简谐荷载作用下振动控制问题,数值仿真结果验证了压电致动器/传感器位置优化程序的正确性,说明采用遗传算法搜索压电智能结构振动控制中压电致动器/传感器的最优位置是十分有效的,并具有较高的计算效率。
基于数值仿真实验的方法,研究了复合层合压电梁比例反馈控制系统中,比例反馈增益、层间铺设方式对闭环系统控制性能的影响。基于复合层合板模态应变能分布大小,提出了一种简单易行的压电致动器/传感器位置确定方法,适用于层合智能结构多阶目标模态的振动控制。数值试验结果证明了基于模态应变能分布确定压电致动器/传感器进而实现复合层合压电智能板多阶模态振动控制的可行性和正确性。
Piezoelectric materials have been manufactured into thin actuators/sensors because of their ability to transform mechanical energy to electrical energy and vice versa. Laminated piezoelectric smart structures with piezoelectric actuators/sensors bonded on the surface or embedded in host structures have self-detection, self-diagnosis, self-healing and adaptive functions. Application of laminated piezoelectric smart structures in the fields of aerospace, mechanical as well as civil engineering and modern control theory development have greatly promoted the domestic and foreign scholars to poure enthusiasm into their vibration control research. Laminated piezoelectric smart structure is a discrete density distribution, discontinuous material properties and electro-mechanical coupling dynamic model system. Therefore, accurately and effectively analyzing the behavior of piezoelectric material electro-mechanical coupling, exploring the mechanical and electric field coupling action, taking into account of solving efficiency when establishing the accurate dynamic response model of laminated piezoelectric smart structure under disturbance loading, revealing the effect of acturators/sensors distribution location, geometry size as well as compsite material lay-ups on laminated smart structure vibration characteristics, controller parameters and structure configuration impact on system quality and performance, vibration control of smart structures undering moving load are problems to be solved. Investigating active control theory and algorithm of smart structure to improve system stability, optimization of pizeoelectirc actuator/sensor locations, realizing multi target mode vibration control and so on, all these problems mentioned above are also urgent to be solved.
In this paper, finit element dyanimc state-space equation of linear elastic piezoelectric is derived from Hamilton principle and electro-mechanical coupling constitutive of piezoelectric materials. Numerical models are established to accurately describe the mechanich-electric coupling field based on ANSYS/APDL parameter language. The variation of natural frequency and mode shape of smart cantilever beam as actuator/sensor location, size and composite material lay-ups changing has been explored. The impact of piezoelectric actuator/sensor location, number and controller parameters on PID closed-loop control system performance is studied. The introduction of advanced PID controller with separated integration, changing rate integration and partial differential effectively settled the divergency and instability appearance of system caused by inappropriate parameters of classic PID controller. The impact of controller parameters and load moving speed on control performance is also analyzed at different vibration stages of laminated piezoelectric smart system under moving load.
A self-learning control (SLC) algrothm able to real-time adjust and amend control feedback gain is presented according to system output error. Taking system output error with its variation and the gain of iterative learning as the input and output of fuzzy controller respectively, the fuzzy self-learning control (FSLC) method is also proposed to speed up the convergence of SLC. The numerical simulation results of piezoelectric smart cantilever plate prove that both SLC and FSLC could effectively reduce the vibration response of closed-loop system, and FSLC quality is better than SLC. Based on the idea of combining the linear quadratic optimal control with iterative learning (IL) control, the paper puts forward a new hybrid control strategy which is named linear quadratic iterative learning control to improve the iterative learning control convergence. The numerical model for dynamic analyzing of one-dimensional laminated piezoelectric cantilever beam is created by MATLAB software. And then the classic optimal control and linear quadratic optimal iterative learning hybrid control are achieved, thus the control property is improved.
Taking the location parameters of discrete distribution piezoelectric actuators/sensors and the damping ratio of piezoelectric smart structure closed-loop control system as optimization variables and objective function respectively, the actuator/sensor optimization program based on genetic algorithm (GA) is presented. The finite element numerical simulation is conducted to consider the vibration control of cantilever plate exited by transient and harmonic loading at the free end of it. Numerical results show the validity and effectiveness of using GA for searching optimal placement of the actuator /sensor pairs in active structural vibration control.
This paper discussed proportional feedback gain and lay-ups effect on the closed-loop system performance of composite laminated piezoelectric beam by numerical simulation method. A simple and easy to implement way to determinate actuator/sensor locations is raised based on distribution of modal strain energy for multi target modes vibration control of laminated smart structures. Numerical results proved the feasibility and correctness of the method metioned above.
引文
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