智能桁架结构最优振动控制与作动器优化配置

研究了智能桁架结构最优振动控制和作动器的优化配置问题。首先采用有限元方法,根据Hamilton原理推导了智能桁架结构的机电耦合动力学方程,根据线性二次型最优控制理论,推导了结构振动控制的数学模型,通过最小化性能泛函,求解黎卡提矩阵代数方程确定了最优控制输入。然后通过对最优控制性能指标函数的修正,得到了与初始状态无关的性能指标,以修正的性能指标为目标函数,应用模拟退火算法对作动器位置进行了优化配置。最后给出了空间智能桁架结构振动控制算例验证建模过程和算法。算例结果表明,通过最优振动控制可以使结构振动快速衰减,达到振动抑制的效果,而且通过模拟退火算法可以确定最佳的作动器布置方式。

Optimal Vibration Control and Actuator Placement for Intelligent Truss Structures

The optimal vibration control and actuator placement for intelligent truss structures is investigated. Firstly, the mech-electric coupling dynamic formulation of piezoelectric intelligent truss structures based on the Hamilton principle is presented. The mathematical model of vibration control for truss structures is derived using Linear Quadratic Gauss optimal control theory. The input of optimal control is determined by minimizing performance function and solving Riccati algebraic equation. Then, the performance criterion unrelated to initial state is obtained through correcting the performance criterion of optimal control. The optimization of actuator position is performed using simulated annealing algorithm so as to minimize the corrected performance criterion. Finally, a numerical example of vibration control for spatial intelligent truss structure is given to verify the modeling process and optimization algorithm. Simulations results indicate that the suppression effect of vibration is obvious and the vibration responses decrease quickly by optimal vibration control. The optimal position of actuators can be determined by using simulated annealing algorithm.