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. ©, 2015, AAAS Press of Chinese Society of Aeronautics and Astronautics. All right reserved.