Adaptive Satellite Attitude Control in the Presence of Inertia and CMG Gimbal Friction Uncertainties

A nonlinear adaptive attitude controller is designed in this paper that compensates for dynamic uncertainties in the spacecraft inertia matrix and unknown dynamic and static friction effects in the control moment gyroscope (CMG) gimbals. Attitude control torques are generated by means of a four single gimbal CMG pyramid cluster. The challenges to develop the adaptive controller are that the control input is multiplied by uncertainties due to dynamic friction effects and is embedded in a discontinuous nonlinearity due to static friction effects. A uniformly ultimately bounded result is proven via Lyapunov analysis for the case in which both static and dynamic gimbal friction is included in the dynamic model, and an extension is provided that illustrates how asymptotic tracking is achieved when only dynamic friction is present in the CMG model. Introduction Through ventures such as NASA’s New Millennium Program and DoD’s Operational Responsive Space [1], the space industry is moving toward smaller satellites and the buses that support them. Some proposed uses of these small satellites (smallsats) include astrophysics research, surveillance, and autonomous servicing, all of which require precision attitude motion. However, due to their smaller sizes, the attitude motion of these small-sats is more susceptible to external disturbances than their larger counterparts. Furthermore, the smaller sizes of these new small-sats limit the mass, power and size budgets allocated to their attitude control systems (ACS). These contradictory requirements necessitate novel solutions for the ACS. Controllers that are based on the assumption that a torque can be directly applied about the body-fixed satellite axes (e.g., [2]–[5]) may not be well-suited for applications that require high-precision attitude control, because the satellite torques are The Journal of the Astronautical Sciences, Vol. 56, No. 1, January–March 2008, pp. 121–134 121 Presented as paper AIAA 2007-6432 at the 2007 AIAA Guidance, Navigation, and Control Conference in Hilton Head, South Carolina, August 20–23, 2007. Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611-6250, USA. E-mail: {mackunis, kdupree, nfc, wdixon}@ufl.edu. generated by actuators with additional dynamics. For example, (especially in small rigid-body satellites), the desired torques are typically generated by a cluster (e.g., [6], [7]) of single gimbal control moment gyroscopes (CMGs) due to their low mass and low power consumption properties. Unfortunately, the torque producing capacity of CMGs can deteriorate over time due to changes in the dynamics such as bearing degradation and increased friction in the gimbals. The ramifications of CMG friction buildup include increased power consumption due to energy dissipation. Examples of actual satellite failures resulting from CMG problems are the Hipparcos satellite and Magellan satellite [8]. Hipparcos failed and “spun down” due to numerous gyroscope failures. One of these failures was due to high and variable drag torque in gyro Number 4, which led to premature degradation. The Magellan satellite was in transit to Venus for five months before it began exhibiting erratic motor current shifts in one of its gyros [8]. The cause of this failure was found to be friction buildup due to a manufacturing process error in which the bearing lubricant was contaminated by a solvent. Motivated by the aforementioned issues, the problem of satellite attitude control in the presence of uncertainties has been investigated by several researchers. In [9], an output feedback structured model reference adaptive controller is developed for spacecraft rendezvous and docking problems. The adaptive controller in [9] accommodates inertia uncertainty in the momentum wheel actuator dynamics; however, no frictional effects were assumed to be present in the actuator model. A quaternionbased, full-state feedback attitude tracking controller was designed in [2] for a rigid satellite in the presence of an unknown satellite inertia matrix. A model-error control synthesis (MECS) approach was used in [3] to cancel the effects of modelling errors and external disturbances on the system. The control law proposed in [3] requires a model-error term to cancel the effects of a time delay, which is inherent to the MECS design. An adaptive control law is designed in [10], which incorporates a velocity-generating filter from attitude measurements. The controller in [10] is shown to achieve asymptotic convergence of the attitude and angular velocity tracking errors despite uncertainty in the satellite inertia, but it assumes no dynamic uncertainty in the control torque. While the aforementioned controllers perform well for applications involving large satellites, they may not be well-suited for attitude control of CMG-actuated small-sats. In this paper, we develop a more suitable control design for such small-sats. A nonlinear adaptive controller is developed in this paper that compensates for inertia uncertainties and uncertain CMG gimbal friction. Instead of developing a control torque to solve the attitude tracking problem, the attitude tracking controller in this paper is developed in terms of the CMG gimbal angular velocity. The development is complicated by the fact that the control input is multiplied by a time-varying, nonlinear uncertain matrix. Additional complications arise because the gimbal velocity control term is embedded inside of a discontinous nonlinearity (i.e., the standard signum function) resulting from the CMG static friction effects. A robust control method is used to mitigate the disturbance resulting from the static friction. In addition, potential singularities may exist in the Jacobian that transforms the torque produced by each CMG to desired torques about the satellite coordinate frame [11]. The singularity problem is circumvented by the use of a particular Jacobian pseudoinverse, coined the “singularity robust steering law,” which was introduced in [12], and has been implemented in several aerospace vehicles (e.g., see [11] and [13]). A uniformly ultimately bounded (UUB) stability 122 MacKunis, Dupree, Fitz-Coy, and Dixon