轴向受压梁非线性随机最优电压有界控制

Nonlinear stochastic optimal voltage bounded control for axial compressed beam

针对轴向受压细长结构容易在外界扰动下产生低频大幅振动的问题,基于几何非线性理论、压电耦合场理论和拉格朗日方程,推导表面贴附压电作动片的轴向受压梁的机电能量表达式,建立轴向受压梁的非线性随机振动压电主动控制模型;考虑压电作动器工作电压的限制因素,利用随机平均法和动态规划方程导出改进型的非线性随机最优电压有界控制策略.该策略包括无界最优电压和bang-bang控制电压,因而较bang-bang电压控制律具有更好的连续性.对简支轴向受压梁在多种情况下的非线性随机振动最优控制进行数值仿真,与bangbang电压控制律进行比较,结果表明本研究导出的改进型电压控制律所需的压电作动器控制电压大幅下降,而振动控制效果略有降低.

The electromechanical energy expressions of axial compressed beam with surface attached piezoelectric actuators were derived,and then a nonlinear stochastic vibration active control model of axial compressed beam was developed,based on the geometric nonlinear theory,multi-physics coupling theory of piezoelectric materials and Lagrange's equation.The purpose is to deal with the low-frequency nonlinear stochastic vibration of the axial compressed slim structures which is easily led by the external disturbance.A modified nonlinear stochastic optimal voltage bounded control strategy was derived by the stochastic average method and dynamical programming equation,in consideration of the voltage limitation of piezoelectric actuators.This voltage control strategy consists of unbounded optimal voltage control and bang-bang voltage control,so that has a better continuity than bang-bang voltage control strategy.The derived optimal voltage bounded control strategy were applied to control the nonlinear stochastic vibration of an axial compressed simply supported beam.Numerical results of various parameters cases show that the required control voltage of piezoelectric actuators is lower than that of bang-bang voltage control,with slight loss of vibration control effectiveness.