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针对具有多面体型参数不确定性和外界扰动的柔性悬臂梁系统,研究其振动的鲁棒控制问题.基于压电柔性悬臂梁系统的状态方程,利用一种扩展LMI(Linear MatrixInequality),对柔性悬臂梁的振动提出了改进的H2/H∞综合状态反馈鲁棒控制方法.此方法针对多面体型参数不确定性系统引入不同的Lyapunov函数,降低了原来H2/H∞综合鲁棒控制方法中由于使用一个公共Lyapunov函数而产生的保守性.通过Matlab分别采用改进和未改进的H2/H∞鲁棒控制方法对柔性悬臂梁系统的振动控制进行了数值仿真.仿真结果表明,2种方法都使柔性悬臂梁的振动得到了良好控制,而改进方法的控制效果更好.
To solve the problem of robust control of flexible cantilever beams with polytopic parameters and external perturbations, a robust extended cantilever beam system (LMI) is proposed based on the state equation of piezoelectric flexible cantilever beam system. The vibration of the beam presents an improved H2 / H∞ synthesis state feedback robust control method. This method introduces different Lyapunov functions for the polytopic-type parametric uncertainty system, which reduces the use of the original H2 / H∞ integrated robust control method due to the use of A public Lyapunov function.The numerical simulations of the vibration control of a flexible cantilever system are carried out by using improved and unmodified H2 / H∞ robust control respectively by Matlab.The simulation results show that both of the two methods make the flexibility Cantilever vibration is well controlled, and the improved method of control is better.