Adaptive Control and Moment of Inertia Estimation for a Sliding-Mass Actuated 5 Degree of Freedom Testbed with Concurrent Learning

In this work, we present the theory for an adaptive controller capable of estimating the moment of inertia of a 5 degree-of-freedom spacecraft testbed while tracking a desired reference frame using only sliding masses as the control input. First, the dynamics of the testbed are modeled using Euler’s rotational equations of motion followed by the derivation of the desired frame. Consequently, an adaptive controller with a concurrent learning modification is designed to drive the body frame to the desired in the presence of an unknown time-varying moment of inertia. In this work, the stability of the closed-loop system is proven using Lyapunov stability analysis. The standard persistency of excitation condition is relaxed through the use of a concurrent learning update law, to allow for the exact estimation of the moment of inertia. Finally, this paper concludes with a numerical simulation to demonstrate the efficacy of the proposed method.