Generalised dynamic inversion spacecraft control design methodologies

Generalised dynamic inversion control design methodologies for realisation of linear spacecraft attitude servo-constraint dynamics is introduced. A prescribed stable linear second-order time-invariant ordinary differential equation in a spacecraft attitude deviation norm measure is evaluated along solution trajectories of the spacecraft equations of motion, yielding a linear relation in the control variables. Generalised inversion of the relation results in a control law that consists of particular and auxiliary parts. The particular part works to drive the spacecraft attitude variables in order to nullify the attitude deviation norm measure, and the auxiliary part provides the necessary spacecraft internal stability by proper design of the involved null-control vector. Two constructions of the null-control vector are made, one by solving a state-dependent Lyapunov equation, yielding global spacecraft internal stability. The other is globally perturbed feedback linearising, but yields local stability of the spacecraft internal dynamics. The control designs utilise a damped generalised inverse to limit the growth of the controls coefficient Moore-Penrose generalised inverse as the steady-state response is approached. Both designs guarantee uniformly ultimately bounded attitude trajectory tracking errors. The null-control vector design freedom furnishes an advantage of the approach over classical inverse dynamics, because it can be used to reduce dynamic inversion control signal magnitude. The design methodologies are illustrated by two spacecraft slew and trajectory tracking manoeuvres.