Adaptive Spacecraft Attitude Tracking Control with Actuator Uncertainties

An adaptive control algorithm for the spacecraft attitude tracking problem when the spin axis directions and/or the gains of the flywheel actuators are uncertain is developed. A smooth projection algorithm is applied to keep the parameter estimates inside a singularityfree region and avoid parameter bursting. Numerical examples show that the controller successfully deals with unknown misalignments of the axis directions as well as the unknown gains of the flywheel actuators. Introduction Adaptive attitude control of spacecraft with uncertain parameters has been studied intensively in the past decade [1–8]. However, most (if not all) of the previous research deals only with uncertainties in the inertia matrix of the spacecraft, assuming that an exact model of the actuators is available. The only exemption the authors are aware of seems to be reference [9], in which disturbances caused by defects of flywheels are estimated and compensated using recursive filtering. However, the control law presented in that work can be applied only for the special case when the reference attitude is the local-vertical-local-horizonal frame for a circular orbit. Subsequently, most results in the literature hinge on the assumption that the torque axis directions and/or input scalings of the actuators (e.g., gas jets, reaction wheels, or CMGs/VSCMGs etc.) are exactly known. This assumption is rarely satisfied in practice because of misalignment of the actuators during installation, aging and wearing out of the mechanical and electrical parts, etc. For most cases the effect of these uncertainties on the overall system performance is not significant. However, for the case of flywheels used as “mechanical batteries” in an Integrated Power and Attitude Control System (IPACS) [8, 10, 11], even small misalignments of the flywheel axes can be detrimental. Flywheels for IPACS applications spin at very high speeds and subsequently have large amounts of stored kinetic energy The Journal of the Astronautical Sciences, Vol. 56, No. 2, April–June 2008, pp. 251–268 251 Presented as paper AIAA-2005-6392 at the 2005 AIAA Guidance, Navigation, and Control Conference. NRC Research Associate, Naval Postgraduate School, Monterey, CA 93943. E-mail: [email protected]. Professor, School of Aerospace Engineering. E-mail: [email protected]. (and hence angular momentum). Precise attitude control requires proper momentum management, while minimizing spurious output torques. This can be achieved with the use (in the simplest scenario) of at least four flywheels, whose angular momenta have to be canceled or regulated with high precision. If the exact direction of the axes (hence also the direction of the angular momenta) are not known with sufficient accuracy, large output torque errors will impact the attitude of the spacecraft. Similarly, accurate information of the actuator gains are necessary for exact cancelation of the angular momenta. In this article, an adaptive control law is designed for spacecraft attitude tracking using Variable Speed Control Moment Gyros (VSCMGs) [8, 11, 12], whose moments of inertia and gimbal axes directions are not exactly known. A VSCMG is a spacecraft attitude actuator, which has been recently introduced as an alternative to conventional control moment gyros (CMGs) and reaction wheels (RWs). A conventional CMG has a regulator to keep its flywheel spinning at a constant rate, whereas a VSCMG—as its name implies—is essentially a singlegimbal control moment gyro (CMG), with the flywheel allowed to have variable speed. The VSCMGs are especially suitable for IPACS applications [8], because the variable speed of the flywheels can be used to store/release mechanical (i.e., kinetic) energy at will, while gimbal angle changes can be used to generate the necessary torques for attitude control in an efficient manner owing to the torque amplification effect. The VSCMGs are also suitable for developing and implementing singularity-free steering laws in lieu of standard CMGs, thanks to their additional degrees of freedom [11, 12]. One of the difficulties encountered when designing adaptive controllers dealing with actuator uncertainties for the spacecraft attitude tracking problem is the Multi-Input/Multi-Output (MIMO) form of the equations of motion. The controller has to track at least the three attitude states for full three-axis attitude control. Complete control requires, in general, three or more actuator torques. Much research has been devoted to the adaptive attitude tracking problem. Most previous results in this area have dealt only with the Single-Input/Single-Output (SISO) or the uncoupled Multi-Input case. Slotine et al [1, 13]. proposed adaptive controllers for MIMO systems, but these systems must be Hamiltonian. Furthermore, the uncertainties should appear in the inertia of the spacecraft and/or the Coriolis/centrifugal terms, but not in the actuators. Ge [14] derived an adaptive control law for multi-link robot manipulators with uncertainties in the control input term, but the uncertainty must be in the input scalings and the uncertainty matrix must be diagonal when represented in multiplicative form. Recently, Chang [15] provided an adaptive, robust tracking control algorithm for nonlinear MIMO systems. His work is based on the “smooth projection algorithm,” which has also been used in references [16] and [17] for adaptive control of SISO systems. This algorithm plays a key role in our developments by keeping the parameter estimates inside a properly defined convex set, so that the estimates neither drift into a region where the control law may become singular nor diverge to very large values. Problem Statement Consider a spacecraft with a VSCMG cluster of N flywheels, as shown in Fig. 1. The definition of the axes in Figure 1 is as follows ( ): i 1, . . . , N 252 Yoon and Tsiotras