CFRP反射器型面主动控制和作动器位置优化

研究了运用压电陶瓷作动器对碳纤维增强复合材料（CFRP）格栅反射器的型面主动控制。首先，采用了一种具有独立电压自由度的梁单元，以及考虑高阶剪切变形的板单元，对主控格栅反射器进行有限元建模；运用能量变分哈密尔顿原理推导了主控格栅反射器的有限元控制方程，并给出了反射面型面残余均方根（RMS）误差最小的电压最优控制方法。然后，研究了在典型载荷下，反射面残余RMS误差最小的PZT作动器位置分布的优化配置问题；提出了一种将遗传算法和梯度投影方法相结合的改进优化方法，用来求出在限定作动器数量的条件下，作动器几何位置的优化配置，使控制后反射面的残余RMS误差最小；给出的数值算例验证了方法的正确性和有效性。最后，研制了格栅反射器型面主动控制的实验样机，针对反射器的初始制造误差进行了型面主动控制，验证了控制方法的可行性和有效性。

Shape active control of a CFRP reflector and placement optimization of actuator

In this paper, the piezoelectric ceramic transducer actuators are used to perform active shape control for Carbon Fiber Reinforced Polymer (CFRP) rib reflector. Firstly, a beam element with independent degrees of voltage and a plate element with higher transverse shear deformation are used to conduct a finite element modeling of the CFRP reflector. Using Hamilton variation formulation, the governing equation of the finite element model is derived, developing an optimized reflector surface shape controller that minimizes the Root Mean Square (RMS) error. Then, the placement optimization of PZT actuators is investigated under several typical loads. To minimizing the residual RMS error of the reflector, an optimization method combining the adaptive genetic algorithm with the gradient projection method is proposed to solve the placement optimization of the actuators with a certain number. Numerical examples show the validity and the effectiveness of the proposed method. Finally, an experimental prototype is made to verify the proposed controlling method. The results proved the feasibility and the effectiveness of the proposed method.