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Radio astronomical observations put stringent requirements on the tracking and pointing accuracy of radio telescope antennas. High inertia, low stiffness, underdamped, and multi-resonant frequencies of a large aperture radio telescope's antenna make the high-accuracy control difficult. It is not easy to satisfy control performance using only conventional PID controllers. A low-order Active Disturbance Rejection-based double-loop controller for large antenna is designed in this paper and tested on the Green Bank Telescope model. First, the first-order Linear Active Disturbance Rejecting Controller (LADRC) cascading a first-order low-pass filter and a notch filter is designed for the antenna's velocity loop to achieve the dual-objective optimal velocity tracking. Second, the position loop controller is designed to realize the antenna's position-tracking control by combining the PD controller and a low-pass filter. Further optimization of the position-loop controller helps improve the dynamic performance of the system. The simulation results indicate that the response curves of the proposed PD-LADRC control are smother than those of the Quantitative Feedback Theory (QFT) based controller; the settling time of the PD-LADRC system is 10.1 s and reduces by about 8.2 s than that of the QFT. While using a better position controller reduces settling time to 5 s. The PD-LADRC system also has better wind-disturbance rejection; the worst disturbance response reduces at the gearbox by 68.3% and 60% at the dish, and the recovery time reduces by more than 15 s than the QFT-based controller. In addition, besides easier parameter tuning, the proposed PD-LADRC has better robustness to systematic parameter perturbations and minor tracking error rms in position tracking. [ABSTRACT FROM AUTHOR]