柔性梁降阶H_∞控制实验研究

AN EXPERIMENTAL STUDY ON REDUCED ORDER H_∞ CONTROL OF A FLEXIBLE BEAM

研究了压电传感器、作动器非同位配置情况下柔性悬臂梁的降阶H∞振动控制问题。采用频域辨识方法获取低阶名义模型,合理选取权函数,将鲁棒H∞控制问题转化为标准H∞控制问题。采用CCL(Cone Complementarity Lin-earization)算法设计降阶H∞控制器。比较了全阶H∞控制器和降阶H∞控制器的控制效果,实验结果表明,设计的降阶H∞控制器能够有效抑制柔性梁的前三阶模态振动,而且不会产生溢出问题。

The reduced order H∞ control of a flexible cantilever beam is studied. The nominal model is derived using the frequency domain identification method. Appropriate weighted functions for disturbance rejection and robust stability are selected and the robust H∞ control problem is simplified to the standard H∞ control problem. Reduced order H∞ controller involving LMI formulation with the rank constraint is solved using the cone complementarity linearization(CCL) algorithm. The experimental results show that the reduced order H∞ controller can suppress the vibration of the first three modes of the flexible beam effectively and spillover instability doesn't happen.