压电智能反射面静态形状控制与作动器位置优化

为了提高反射面的精度,建立了压电智能反射面的形状控制模型,对该结构的力学建模方法、形状控制方法和作动器优化配置算法进行了研究。首先,将蜂窝夹层结构的压电智能反射面等效为多层复合板,根据虚功原理推导了结构的有限元方程。然后,根据建立的有限元方程,推导了反射面变形的均方根误差与作动器控制电压的关系式,以均方根误差最小为优化目标,建立了形状控制优化模型,将作动器控制电压的优化转化为约束优化问题的求解。最后,采用模拟退火算法对压电作动器进行了优化配置。为了验证形状控制的可行性及优化算法的有效性,以300mm口径的平面压电智能反射面为例进行仿真,分析结果表明,通过压电作动器的控制,可以使反射面的重力变形误差减小97%以上,对于给定数目的作动器,通过模拟退火算法优化,可使其布置在最佳的位置。

Static shape control of piezoelectric smart reflector and optimization of actuators' placement

In order to improve the precision of reflector, the static shape control model of smart reflector is presented, and the methods of structural mechanics modeling and shape control and the optimization algorithms of actuators'' placement are investigated. Firstly, the smart reflector with the honeycomb core is modeled with the equivalent laminate plate theory, and the finite element formulation of flexible piezoelectric smart reflector is derived according to virtual work theory. Then, the relationship between mean square root error of reflector''s deformation and control voltages of actuators is derived, and the optimization model for static shape control is created with the objective of minimizing mean square root error of shape, and the optimization of control voltage can be transformed to a constrained optimization problem. The actuator''s placement is implemented using simulated annealing algorithm. Finally, a numerical example of plane piezoelectric smart reflector with a diameter of 300 mm is given to demonstrate the feasibility of shape control model and the effectiveness of optimization algorithm. Simulation results indicate that the square root error of smart reflector''s deformation under gravity can be reduced by above 97% by controlling the piezoelectric actuators, and the actuators can be placed in the optimal position for a given number actuators using simulated annealing algorithm.