Active Shape Control of Satellite Antenna Reflectors with Limited Power Supplies

Abstract

This paper proposes an active shape control method for an antenna control system under a limited number of power supplies with a reduction in weight and cost. An analytical model of a grid reflector with embedded piezoelectric actuators was first established, from which an influence coefficient matrix was derived for controller design. A shape controller was designed by synergistically optimizing the actuator group and power supply voltage. The optimization objectives include the root-mean-square (RMS) error, control energy consumption, and a multiobjective combination of both. The design variables include the actuator group and power supply voltage. A dynamic actuator group design with a detached power supply is proposed to improve the control performance, which also significantly increases the design domain of this optimization problem. A hybrid optimization method is proposed based on the general genetic algorithm and least-squares method to reduce the difficulty and complexity of this optimization problem with a large-dimensional design domain. Numerical simulations were carried out to illustrate the effect of the proposed hybrid optimization control method. The results indicate that the RMS error can be reduced by more than 90%, even if only two power supplies are used. The introduction of a group design with a detached power supply can clearly improve the control performance, especially by reducing the energy consumption. By employing multiobjective optimization with a uniform consideration of the RMS error and control energy consumption, a series of Pareto-optimal results can be obtained, and these results can provide meaningful references for engineering designers.