考虑时滞影响的柔性悬臂梁的离散最优控制

Discrete-Time Optimal Control of a Flexible Cantilever Beam with Time Delay in Control

对考虑时滞影响的柔性悬臂梁的离散最优控制进行研究。首先给出包含有时滞项的控制模态方程 ,然后将控制模态方程离散化和标准化 ;连续时间形式的性能指标也离散成标准离散形式 ,则最优控制律可按离散最优控制理论进行设计。所得出的时滞最优控制律中 ,除了包含有当前的状态反馈 ,还包含有前若干步控制的线性组合。因在由控制模态方程推导时滞最优控制律的过程中无近似处理 ,所给控制方法易于保证控制系统的稳定性。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。

This paper studies the discrete-time optimal control of a flexible cantilever beam with time delay in control. The mode-controlled equation with time delay is presented and then discretized and transformed into the standard discrete form which contains no time delay. The continuous performance index is also discretized into the standard discrete form. Thus the discrete optimal controller can be designed based on the discrete optimal control theory. Since no approximation is made in the derivation of the time-delay optimal controller from the mode-controlled equation, the system stability is easy to guarantee. In addition, the extraction of modal coordinates from actual measurement and the transformation into the actual control force from the modal control force are presented in this paper too. The feasibility and effectiveness of the proposed control algorithm are illustrated by numerical simulations at the end of this paper.