Exact differentiator based sliding mode control for large optical astronomical telescopes

Abstract

Large astronomical optical telescopes are badly needed in order to learn more remote universe. There exist some key problems of the control systems of large astronomical optical telescopes. Since they have voluminous bodies that would encounter heavy external disturbance, one of the key problems is focused on how to accurately control them. Additionally, in order to get nicer ultra-low velocity performance and a steady field of view, friction drive is widely applied in contemporary large optical telescopes. One serious disadvantage of friction drive is that it will cause some nonlinear uncertainties to influence telescope controls because of the mechanical characteristics between the principal and subordinate friction wheels. These two aspects of external and internal disturbances will make a telescope very difficult to be controlled. In this paper, we introduce a method of higher order sliding modes (HOSM) to control telescopes, which overcome these two disadvantages of traditional Proportional-Integral-Derivative approach and can achieve excellent control performance. Conventional sliding mode approach has been applied in many other mechanical control systems owing to its high accuracy in anti-jamming. By discontinuous switching, it is invariable to disturbances based on keeping some constraints with a sufficiently energetic effort. However, such conventional sliding mode approach may cause dangerous high-frequency vibrations in the corresponding control system，which may influence systemic control performance or even lead the system unstable. In this work, we use the newly developed HOSM approach in the control systems of the large astronomical optical telescopes. The HOSM approach inherits the dominant merits of conventional sliding mode. Moreover, it acts on the higher order time derivatives of the system deviation from the constraint. And the discontinuous dynamics are restricted to the highest state while the counterpart in standard sliding mode is in first derivative. Thus the HOSM approach can mostly removes high-frequency vibration effects on telescope control. This control approach needs all states of the system to be observable. We use robust exact differentiator to estimate the immeasurable state. Simulations have been done in the environment of MATLAB language. The results show that this approach can realize the tracking performance of accurate ultra-low velocity for telescope control.