Nonlinear Controller Design for a Flexible Spacecraft

Abstract

This paper combines the nonlinear Udwadia-Kalaba control approach with the Assumed Mode Method to model flexible structures and derives an attitude controller for a spacecraft. The study case of this paper is a satellite with four flexible cantilever beams attached to a rigid central hub. Two main topics are covered in this paper. The first one is the formulation of the equation of motion and the second one is the nonlinear controller design. The combination of these two techniques is able to provide a controller that damps the vibration of a flexible structure while achieving the desired rigid-motion state.

Modeling Flexible Multi-Body Systems Within the Udwadia–Kalaba Framework, a Lumped Parameter Approach

“…Examples include Antunes et al [16][17][18] who demonstrated a modelling strategy for continuous flexible systems by transforming the U-K formulation into modal coordinate space. Gutiérrez and Heidecker [19] combined the assumed modes method within the U-K framework to model flexible structures by approximating the differential equation model of continuous systems. Pennestri et al [20] assessed the numerical efficiency of the U-K formulation in analysing the dynamics of a flexible linkage against an alternative coordinate partitioning scheme through an application study of a slider-crank mechanism; as an additional element of novelty, Pennestri et al modelled the coupler by a single Timoshenko beam element.…”