Adaptive Backstepping Approach for 2-DOF Telescopes Despite Unknown Wind Disturbance

Abstract

Small ground telescopes on the marked are widely used in many space observatories and scientific researches. There are three main problems in such telescopes; positioning of the focal point and the need of tuning for both different seasonal wind speeds and mass changes of the telescope arm. This study focuses on eliminating those problems for 2-DOF altazimuth configuration small telescopes. An adaptive controller is designed to create a set and forget system. The mathematical model of the telescope is derived based on RR type joint configuration. For a realistic approach, motor dynamics is considered in the mathematical model. The wind disturbance is modeled according to the Wind-Gust model which is a sum of sinusoidal with unknown amplitude, frequency and phase. The controller aims to cancel the effect of the disturbance on focal point of the telescope while positioning. The asymptotic stability is proven with the Lyapunov approach. The numerical study is illustrated to success of the proposed controller.