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.
The recent radio frequency communication system developments are generating the need for creating space antennas with lightweight and high precision. The carbon fiber reinforced composite (CFRC) materials have been used to manufacture the high precision reflector. The wave-front errors caused by fabrication and on-orbit distortion are inevitable. The adaptive CFRC reflector has received much attention to do the wave-front error correction. Due to uneven stress distribution that is introduced by actuation force and fabrication, the high order wave-front errors such as print-through error is found on the reflector surface. However, the adaptive CFRC reflector with PZT actuators basically has no control authority over the high order wave-front errors. A new design architecture assembled secondary ribs at the weak triangular surfaces is presented in this paper. The virtual experimental study of the new adaptive CFRC reflector has conducted. The controllability of the original adaptive CFRC reflector and the new adaptive CFRC reflector with secondary ribs are investigated. The virtual experimental investigation shows that the new adaptive CFRC reflector is feasible and efficient to diminish the high order wave-front error.
The trend in future space high precision reflectors is going towards large aperture, lightweight and actively controlled
deformable antennas. An adaptive shape control system for a Carbon Fiber Reinforced Composite (CFRC) reflector is
conducted by Piezoelectric Ceramic Transducer (PZT) actuators. This adaptive shape control system has been shown to
effectively mitigate common low order wave-front error, but it is inevitably plagued by high order wave-front error
control. In order to improve the controllability of the adaptive CFRC reflector control system for high order wave-front
error, the design of adaptive CFRC reflector requires optimizing further. According to numerical and experimental
results, the print-through error induced by manufacturing and PZT actuators actuation is a type of predominant high
order wave-front error. This paper describes a design which some secondary rib elements are embedded within the
triangular cells of the primary ribs. These small secondary ribs are designed to support the reflector surface’s weak
region. Controllability of this new adaptive CFRC reflector control system with small secondary ribs is evaluated by
generalized Zernike functions. This new design scheme can reduce high order residual error and suppress the high order
wave-front error such as print-through error. Finally, design parameters of the adaptive CFRC reflector control system
with small secondary ribs, such as primary rib height, secondary rib height, cut-out height of primary rib, are optimized.
An adaptive control system for correcting wave-front error of a CFRC reflector has been studied. Errors investigated in this paper were mainly introduced by fabrication and gravity. 72 Piezoelectric Ceramic Transducer (PZT) actuators were integrated to the CFRC reflector to conduct wave-front error control. The adaptive CFRC reflector was fixed on an optical platform without any external loads. The temperature and humidity were well controlled during the experimental study. The wave-front error correction algorithm is based on influence matrix approach coupled with least squares optimization method. The linear relationship between the PZT actuator’s input voltage and the output displacement of the adaptive CFRC reflector surface is validated. A laser displacement sensor was used for measuring the displacements. The influence matrix was obtained experimentally by measuring the displacements of the associated points while each actuator was activated separately. The wave-front error and influence matrix were measured using a V-Stars photogrammetry system. Experimental investigation validated that this adaptive control system is capable to significantly reduce the reflector surface geometry error. Experimental results are correlated very well with simulation results which were obtained by using a multidisciplinary analytical approach. Conclusions of this study suggest that the adaptive CFRC reflector technology can provide a low cost method to significantly increase the precision of a CFRC reflector.
Maintaining geometrical high precision for a graphite fiber reinforced composite (GFRC) reflector is a challenging task. Although great efforts have been placed to improve the fabrication precision, geometry adaptive control for a reflector is becoming more and more necessary. This paper studied geometry adaptive control for a GFRC reflector with piezoelectric ceramic transducer (PZT) actuators assembled on the ribs. In order to model the piezoelectric effect in finite element analysis (FEA), a thermal analogy was used in which the temperature was applied to simulate the actuation voltage, and the piezoelectric constant was mimicked by a Coefficient of Thermal Expansion (CTE). PZT actuator’s equivalent model was validated by an experiment. The deformations of a triangular GFRC specimen with three PZT actuators were also measured experimentally and compared with that of simulation. This study developed a multidisciplinary analytical model, which includes the composite structure, thermal, thermal deformation and control system, to perform an optimization analysis and design for the adaptive GFRC reflector by considering the free vibration, gravity deformation and geometry controllability.