High-precision identification of a tip–tilt control system for the compensation of time delay

The resolution of ground-based large aperture telescopes is decreased severely due to the effect of atmospheric turbulence. Adaptive optics systems (AOSs) have been widely used to overcome this, and low-order aberrations [tip–tilt (TT)] are corrected by a TT mirror. In the tip/tilt TT correction loop, the time delay affects the correction performance significantly and a predicted signal compensation method (PSCM) has been used to reduce its effect. However, the performance of the PSCM is reduced obviously due to the low identification accuracy of the TT AOS model. In this paper, a nonlinear least squares subspace identification (NLSSI) method is presented to obtain a high-precision model of the TT AOS. The system is identified with the subspace method first, and then the identified parameters are modified in the frequency domain. By using this method, a TT correction system is identified. Compared with the subspace identification method, the identification accuracies of the time domain and frequency response are increased 2 and 5 times, respectively, with the NLSSI method. Furthermore, with the NLSSI method, the −3  dB error rejection bandwidth is increased from 69 to 76 Hz. Finally, an adaptive correction experiment is performed on a 1.23 m telescope, and the astronomical observation results show that the correction accuracy is increased to 1.5 times with the NLSSI method. Moreover, the peak intensity of the image is improved by 11% with the NLSSI method. This work is very helpful to improve the TT correction accuracy of AOS, particularly for extreme adaptive optics and faint target observation.