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 引用本文: 赵童 陈龙祥 蔡国平. 柔性板的时滞H∞控制的理论与实验研究[J]. 力学学报, 2011, 43(6): 1043-1053.
Tong Zhao Longxiang Chen Guoping Cai. Theoretical and experimental studies of H∞ control for a flexible plate with time delay[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(6): 1043-1053.
 Citation: Tong Zhao Longxiang Chen Guoping Cai. Theoretical and experimental studies of H∞ control for a flexible plate with time delay[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(6): 1043-1053.

## Theoretical and experimental studies of H∞ control for a flexible plate with time delay

• 摘要: 以柔性板为对象, 开展时滞H∞控制的理论与实验研究. 首先给出柔性板的时滞动力学方程; 然后利用Lyapunov-Krasovskii泛函和自由权矩阵法, 推导了闭环时滞系统渐近稳定的矩阵不等式;进而根据该矩阵不等式采用参数调节法及遗传算法, 研究了如下两类控制设计问题: 已知控制律求解最大稳定时滞量, 已知最大稳定时滞量求解H∞控制律; 最后对理论研究成果进行了数值仿真和实验验证. 结果显示, 获得的H∞控制律能够有效地抑制板的弹性振动, 所确定出的保证系统稳定性的时滞区间更接近实际情况.

Abstract: This paper presents theoretical and experimental studiesof H∞ control for a flexible plate with time delay. Firstly, thetime-delay dynamic equation of the plate is established. Secondly, a matrixinequality for system asymptotic stability is derived by using theLyapunov-Krasovskii functional and free-weighting matrix method. Based onthe matrix inequality, two control design problems are solved by using theparameter adjustment method and genetic algorithm: (1) H∞controller design with known maximum time delay of the system; (2)determination of maximum time delay with known controller. Finally,simulation and experiments are carried out to verify the theoreticalresults. Simulation and experimental results demonstrate that the designedH∞ controller is effective in reducing the plate vibration and thedetermined maximum time delay guaranteeing the system stability is close tothe real time delay of the system.

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