Adaptive control of multibody systems with unknown mass distribution.

Abstract

The performance of rigid body systems is degraded by unknown mass distribution. In rotating mechanisms, for example, mass imbalance to some degree is always present resulting from manufacturing errors, assembly misalignment or material imperfections. The dynamic effect of imbalance is unwanted disturbance forces or undesired motion of the rotor. Another instance where the mass properties of a rigid body may be unknown is in spacecraft. Spacecraft require attitude control systems that provide rapid acquisition, tracking and pointing capabilities and since the mass properties of the spacecraft may be uncertain or may change due to fuel usage and articulation, it is necessary for the control system to be able to adapt to changes in mass distribution. We consider three rigid body systems: a spacecraft, a control-moment gyro, and a planar rotor. In each of these cases, the control objective is to counteract the effects of unknown mass distribution. For the spacecraft and the control-moment gyro (CMG) we develop an adaptive control algorithm based on Lyapunov methods that permits tracking a desired commanded motion in the absence of any knowledge of the mass distribution of the system. As part of the dissertation a CMG has been designed and fabricated and we apply our adaptive controller to the experimental setup and provide experimental results. In the case of the planar rotor we develop an adaptive control law that asymptotically stabilizes a rotor with mass imbalance without knowledge of the location of the center of mass.