Numerous ground-based observatories are using small sized ground telescopes for scientific research purposes. The telescopes that are available on the market have three main problems. These issues can be listed as: positioning repeatability, tuning requirement according to different wind speeds for different seasons, and the mass changing via different scientific equipments added to the telescope. This study is aimed at resolving these issues for ground based small alt-azimuth telescopes. Establishing of a set and forget system is performed by designing an adaptive controller. Motor dynamics are taken into consideration for a realistic mathematical model. The Wind-Gust model that consists of a sum of sinusoidal disturbances with unknown phase, amplitude and frequency is used for the wind model. The purposed controller cancels the disturbance effects on the plant while operational positioning and also the makes the plant insensitive to mass changes. The Lyapunov approach is utilised when proving the asymptotic stability. The proposed controller's success is illustrated with thorough numerical evaluation.