基于本征正交分解模型降阶的索杆结构振动主动控制

ACTIVE VIBRATION CONTROL OF CABLE-STRUT STRUCTURE USING POD-BASED REDUCED-ORDER INTRINSIC ORTHOGONAL MODEL

  • 摘要: 索杆结构具有低刚度弱阻尼的特点,在动态激励作用下振动响应较大,基于主动控制方法通过作动器输入最优控制力,可有效降低结构的振动水平。由于结构模型的复杂性、控制器设计参数的多样性以及算法鲁棒性设计需求等客观因素的存在,主动控制算法的计算成本日益增长。为了降低主动控制算法的计算成本,该文提出了基于本征正交分解(Proper Orthogonal Decomposition, POD)模型降阶的索杆结构线性二次型最优控制(Linear Quadratic Regulator, LQR)方法,即POD-LQR方法。基于结构位移、速度或加速度响应数据,实现了数据驱动的投影子空间的提取。实现了基于能量精度指标的降阶模型阶数自动选择。确定了基于投影关系的POD-LQR控制器设计参数,使其控制性能指标不随降阶模型阶数的大小而变化。降阶模型的应用大幅缩短了POD-LQR控制器的设计时长。验证算例采用Levy索穹顶和30杆球形张拉整体,结果表明所提方法在计算效率和控制效果方面均具有优势。

     

    Abstract: The cable-strut structures have the characteristics of weak stiffness and low damping, which exhibit high vibration levels under dynamic excitations. By inputting appropriate control force into the structure through the embedded actuators, an active vibration control can be achieved. The computational efficiency of active control algorithms faces more severe challenges due to the existence of objective factors such as the complexity of structural model, the diversity of controller design parameters, and the need for algorithmic robustness design. Thusly, the proper orthogonal decomposition (POD) method is proposed to achieve a data-driven reduced-order model (ROM) for improving the computational efficiency of the active control algorithm. The reduced-order space is constructed by using the structural displacement, velocity, or acceleration response data. The order of the ROM is selected automatically upon an energy-based accuracy index. The design parameters of the linear quadratic regulator (LQR) using POD-based ROM (POD-LQR) are determined according to the projection relationship, thus the control performance index does not change with the order of the ROM. The application of ROM greatly reduces the design time of POD-LQR controller. The verification example uses the Levy cable dome and 30-strut spherical tensegrity. The findings indicate that the POD-LQR controller exhibits a superior design efficiency and a vibration control effect.

     

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