Suppressing high-order surface errors of an active carbon fiber reinforced composite reflector using two types of actuators

Abstract

Active feedback control is a feasible approach for maintaining the desired shape of a reflector. An architecture for an active reflector is presented in which both piezoelectric ceramic transducer (PZT) and macrofiber composite (MFC) actuators are introduced to reduce both the global and local (high-order) surface errors. An electromechanical finite element model with two types of actuators is developed using the Hamilton principle. An optimal shape controller is then developed to minimize the reflector surface error. Lower-order orthogonal Zernike polynomials are derived in a unit hexagon. The polynomials are considered to be the basic error modes of a reflector and are used to optimize the length of the PZT actuators. The arrangement of MFC actuators can be optimized in a single triangular component of the reflector because the deflections they induced are very local. An experiment is conducted to verify the performance of MFC actuators in a triangular component. The improvement in the control efficiency of the active reflector is demonstrated by two numerical examples.