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.
This paper presents theoretical and experimental studies of H∞ control for a flexible plate with time delay. Firstly, the time-delay dynamic equation of the plate is established. Secondly, a matrix inequality for system asymptotic stability is derived by using the Lyapunov-Krasovskii functional and free-weighting matrix method. Based on the matrix inequality, two control design problems are solved by using the parameter 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 theoretical results. Simulation and experimental results demonstrate that the designed H∞ controller is effective in reducing the plate vibration and the determined maximum time delay guaranteeing the system stability is close to the real time delay of the system.
出处
《力学学报》
EI
CSCD
北大核心
2011年第6期1043-1053,共11页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金重点项目(11132001)
面上项目(11072146
11002087)资助~~
关键词
柔性板
主动控制
矩阵不等式
时滞
实验
flexible plate, active control, matrix inequality, time delay, experiment