基于状态微分控制算法的空间结构主动振动控制分析

对于主动振动控制器的设计,传统的控制算法以速度和位移作为系统的输入量,但速度和位移难以观测,给实际应用带来了较大的误差.本文在振动状态空间方程的基础上,对其进行矩阵运算,形成以加速度为系统输入的状态微分反馈控制方程.构造具有约束条件的目标函数,根据Lagrange乘子法和泛函极值运算确定了状态反馈矩阵和状态反馈估计值,从而构造了闭环的状态微分控制算法.根据此算法对一直径为1m的环形空间结构进行了振动控制仿真,利用时域内的模态参数识别方法,对控制效果进行了评价,并以三层剪切型框架结构为对象,对状态微分控制算法和传统的LQR算法进行了控制效果的对比分析.结果表明,利用状态微分控制算法在空间结构上的振动控制是可行的,且减振效果明显,同时优于传统的LQR控制算法.

Active vibration control analysis of spatial structures by state-derivative feedback algorithm

For the design of active vibration controller,the measurement of the traditional algorithm are velocity and displacement.It brings errors because velocity and displacement is difficult to be measured.So this paper proposed state-derivative feedback equation in which measurement is acceleration based on state space equation.The feedback gain matrix and state-derivative estimator can be determined by Lagrange multiplier method and functional minimization method.State-derivative feedback algorithm of closed-loop control system is formed.According to this algorithm,vibration control of a annular space truss with diameter of one meter is analyzed,and effect of vibration control is evaluated by modal parameter identification of time domain.The control effect on LQR algorithm and state-derivative feedback algorithm is compared by a three layers of shear frame structure.The results show that effectiveness on vibration control is apparent and the algorithm of state-derivative feedback control can apply to active vibration control on spatial structure.And also,state-derivative feedback algorithm is superior over LQR algorithm.