Youla–Kucera Parameterization-Based Optimally Closed-Loop Control for Tip–Tilt Compensation

Abstract

In this paper, we develop a new method based on Youla-Kucera parameterization in frequency domain to reduce tip and tilt vibrations of astronomical telescopes. This proposed method can be implemented in real time and can also achieve optimal correction when frequencies of vibrations are provided. Based on this parameterization, the closed-loop stability is easily assured, which can relax the stability condition to design control parameters. Due to being plugged into an existing feedback control loop, the sensitivity function of the tip-tilt mirror control system can be minimized by optimizing Q-filter for adapting the changes of vibrations. Two types of Q-filter are introduced to deal with low-frequency and large-magnitude narrowband vibrations. Because of not being restricted by an accurate model of tip-tilt mirror, this improved control mode cannot lead to a compromise between vibrations rejection and noise propagation in the control loop. Although on-line identification of disturbances models is not required, finding the vibration frequencies is crucial. Simulations and experiments demonstrate that the Youla-Kucera controller has a clear improvement of the closed-loop performance in comparison with the original method.