Singularity Analysis of Variable Speed Control Moment Gyros

Abstract

Single-gimbal control moment gyros (CMGs) have many advantages over other actuators for attitude control of spacecraft. For instance, they act as torque amplifiers and, thus, are suitable for slew maneuvers. However, their use as torque actuators is hindered by the presence of singularities, that, when encountered, do not allow a CMG cluster to generate torques about arbitrary directions. One method to overcome this drawback is to use variable-speed single-gimbal control moment gyros (VSCMGs). Whereas the wheel speed of a conventional CMG is constant, VSCMGs are allowed to have variable wheel speed. Therefore, VSCMGs have extra degrees of freedom that can be used to achieve additional objectives, such as singularity avoidance and/or power tracking, as well as attitude control. The singularity problem of a VSCMGs cluster is studied in detail for the cases of attitude tracking, with and without a power tracking requirement. A null motion method to avoid singularities is presented, and a criterion is developed to determine the momentum region over which this method will successfully avoid singularities. This criterion can be used to size the wheels and develop appropriate momentum damping strategies tailored to the specific mission requirements.

Combines Attitude Control and Energy Storage for Small Satellites using Variable Speed Control Moment Gyroscopes

“…Yoon and Tsiotras furthered the VSCMGs for ESACS efforts by examining the singularity space for cases where power demands are too high and redundancy in VSCMGs for ACS is too low [110]. This lays needed ground work for developing robust, fault-tolerant system controllers.…”

Nonlinear Spacecraft Control with Applications to Combined Attitude and Energy Storage

“…2 More challenging is the singularity analysis of a VSCMG cluster with power tracking. In this case, the occurrence of escapable and inescapable singular configurations is completely characterized by the rank of the following matrix [21] M^ (1) where Sj is spin axis vector, I^si is the axial moment of inertia and Vli is the speed of the i-th wheel. In (1) u denotes the singular direction vector.…”

“…For elliptic singular states the best one can expect is to avoid them altogether by proper sizing of the wheels. In [21,25] we found a simple condition which can be used for this purpose. Simply put, this condition states that a VSCMG system used for both attitude and power tracking (in a standard pyramid configuration) will encounter an elliptic singularity in the interval 0 < f < fy^ if and only if there exist i S [0, tf] such that mm ^ sj^^mi.…”

“…The calculation of the envelopes (B) and (C) requires the solution of a constrained maximization problem. The details are given in [21]. …”

Inertia-Independent Generalized Dynamic Inversion Control of Spacecraft Attitude Maneuvers

“…Several remedies for the problem of generalized inversion instability due to MPGI singularity have been offered in the literature of robotics and control moment gyroscopic devices, in what has become known as the singularity avoidance problem. Remedies are either nullspace parametrization-based, made by proper choices of the null-vector in the auxiliary part of the Greville formula, e.g., (Liegeois, 1977;Mayorga et al, 1995;Yoon & Tsiotras, 2004), or approximation-based, made by modifying the definition of the generalized inverse itself in the particular part of the formula, e.g., (Nakamura & Hanafusa, 1986;Wampler II, 1986;Oh & Vadali, 1991). A series of solutions to the GDI closed loop instability due to MPGI singularity have been provided in the context of GDI control.…”