Geometric Modeling and Robust Control of a Gyroscopic System

Gyroscopic systems are multi-body systems which present coupled three dimensional motion. The configuration space and the state space are differentiable manifolds, and differential geometric concepts are frequently useful in the process of modeling. This paper deals with a Control Moment Gyroscope (CMG), which is not asymptotically stable, so it needs a stabilizing control law. We apply a new methodology of modeling kinematics and dynamics of rigid multi-body systems, based in the concept of Cartan’s connection and covariant derivative. The systems has two inputs (torques) and two outputs (angles) that will be controlled by a robust linear closed-loop control technique (LQG/LTR). Experimental results are presented in order to validate the proposal.