Active Control Model for the “FAST” Reflecting Surface Based on Discrete Methods

Abstract

Radio telescopes are important for the development of society. With the advent of China’s Five-hundred-meter Aperture Spherical radio Telescope (FAST), adjusting the reflector panel to improve the reception ability is becoming an urgent problem. In this paper, an active control model of the reflector panel is established that considers the minimum sum of the radial offset of the actuator and the non-smoothness of the working paraboloid. Using the idea of discretization, the adjusted position of the main cable nodes, the ideal parabolic equation, and the expansion of each actuator are obtained by inputting the elevation and azimuth angle of the incident electromagnetic wave. To find the ideal parabola, a univariate optimization model is established, and the Fibonacci method is used to search for the optimal solution $h=-0.33018$ (offset in the direction away from the sphere’s center) and the focal diameter ratio $f=0.4671$ of the parabolic vertex. The ideal two-dimensional parabolic equation is then determined as $x^2-555.25z-166757.2=0$, and the ideal three-dimensional paraboloid equation is determined to be $z=\left(x^2+y^2\right)/555.25-300.33018$. Moreover, the amount of the nodes and triangular reflection panels are calculated, which were determined to be 706 and 1325, respectively. The ratio reception of the working paraboloid and the datum sphere are $9.434\%$ and $1.3898\%$, respectively. The latter is calculated through a ray tracing simulation using the optical system modeling software LightTools.