Shape Control of a Carbon Fiber-Reinforced Polymer Reflector and Placement Optimization of the Actuators

Abstract

In this study, a method for the active shape control for carbon fiber-reinforced polymer (CFRC) reflectors using piezoelectric lead zirconate titanate (PZT) actuators is proposed. According to this method, a finite element model considering higher transverse shear deformation with independent voltage degrees of freedom is formulated by the Hamilton principle. An optimal shape controller that minimizes the discrete root mean square (RMS) error of a reflecting surface is applied. Then, the optimal arrangements of the PZT actuators are determined by numerical optimization methods, which are developed by modifying the classical Genetic Algorithm, with both single and multi-objective optimizations being studied. In the single optimization formulation, the number of actuators is considered as a constraint, and the RMS error of the reflector is regarded as the optimizing target. A hybrid method that combines the gradient projection method with an adaptive Genetic Algorithm is proposed to solve this problem. In the multi-objective optimization, the residual RMS errors and power consumption of the actuators are considered as the optimization targets. Pareto optimal solutions are obtained by an improved multi-objective Genetic Algorithm. Numerical examples are provided to show the effectiveness of the proposed methods.