RGC Newsletter - Research Frontiers

Attitude control of spacecraft provides the spacecraft the capabilities of rapid acquisition, tracking, and pointing, and it is also a benchmark control problem in the control community. A common challenge in spacecraft attitude control is the attenuation/ rejection of external disturbances caused by control moment gyroscopes (CMGs) or by the excitation of flexible appendages. Over the past two decades, various advanced nonlinear control methods have been proposed to handle the attitude control and disturbance rejection problem. For example, the sliding model method was employed to regulate attitude tracking errors into a small region of the origin. Also, nonlinear H infinity optimal or suboptimal control was applied to attenuate the effect of the external disturbance to the attitude of the spacecraft to some degree quantified by the L2 gain, while achieving global attitude tracking. However, this approach can only completely reject such disturbances with bounded energy.

In practical situations, external disturbances may not be energy bounded. For example, the disturbance caused by control moment gyroscopes (CMGs) is modelled by a multitone sinusoidal function which is not energy bounded. In this project, we aimed to consider the attitude tracking and disturbance rejection problem of spacecraft systems for such disturbance which is a multi-tone sinusoidal function with arbitrarily unknown amplitudes, unknown initial phases, and unknown frequencies. For this purpose, we first converted the attitude control and disturbance rejection problem of the spacecraft systems into an adaptive stabilization problem of a so-called augmented system. This process involves several coordinate and input transformations and the use of internal model design from the robust output regulation theory to compensate for the unknown external disturbance. The augmented system is a complex nonlinear system containing both time-varying static uncertainty and dynamic uncertainty. Moreover, the dynamic uncertainty is not input-to-state stable due to the presence of some perturbation term. Thus, the existing methods cannot handle the stabilization problem of the augmented system. To overcome this difficulty, we devised a dynamic extension technique to obtain an extended augmented system. This dynamic extension eliminates the perturbation term in the dynamic uncertainty of the extended augmented system so that the dynamic uncertainty of the extended augmented system is input-to-state stable. As a result, we have managed to solve the adaptive stabilization problem of the extended augmented system by combining some techniques in adaptive control and robust control, thus leading to the solution of the attitude tracking and disturbance rejection problem of spacecraft systems subject to a multi-tone sinusoidal disturbance.