柔性梁结构的时滞主动控制

Active control of a flexible beam with time delay

对考虑时滞影响的柔性悬臂梁的离散最优控制进行了研究。首先采用独立模态空间方法给出包含有时滞项的控制模态方程,然后将之离散化并通过状态变量增广转化成不含时滞的标准离散形式。离散形式的性能指标也转化成增广形式。则离散时滞最优控制律可以针对增广的系统进行设计。因在最初的系统动力方程中就考虑了时滞项,且在推导离散模态控制律的过程中无近似处理,因而所给控制方法易于保证控制系统的稳定性。另外,文中还给出了从实际测量中提取模态坐标和将模态控制力转换成实际控制力的方法。最后通过数值仿真对本文所提控制方法的可行性和效果进行了验证。仿真结果显示,采用本文所提控制方法能够有效地抑制结构的振动。若在控制设计中忽略时滞,有可能引起动力失稳。

In this paper,an active vibration controller for a flexible cantilever beam with time delay is studied.The dynamic equation of the controlled mode with time delay is first presented using the independent modal space method,then it is discretized and transformed into a standard discrete form with no explicit time delay by augmenting the state variables.The discrete performance index is also transformed into an augmenting form.Discrete optimal control algorithm can be designed based on the augmented state system.Since time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations are made in the control algorithm derivation,the system stability is guaranteed.Furthermore,the extraction of modal coordinate from actual physical measurements and the conversion of actual control force from modal one are developed.The feasibility and efficiency of the proposed control algorithm are demonstrated by numerical simulation studies,which indicate that the vibration of the structure may be suppressed significantly using the proposed control algorithm.Instability may occur if the time delay is neglected in the control design.