Non-linear control with Lyapunov stability applied to spacecraft with flexible structures

The method of input-output feedback linearization incorporating the Lyapuno v stability analysis was applied in this study to design a stable control l aw for the problem of reorienting a spacecraft with flexible appendages. On ly three mutually orthogonal torque actuators on the hub are required for t he proposed control law to perform a desired simultaneous multi-axis reorie ntation. Mathematical modelling of the system gives a set of coupled ordina ry and partial differential equations, which includes attitude dynamics of the spacecraft and dynamics of the flexible structures. To simplify the sys tem equations for controller design, deformations of the flexible structure s were assumed to be small and mode-shape functions were applied first. Fur thermore, the set of non-linear equations governing the attitude motions wa s transformed into a Euler parameters representation. Through the method of feedback linearization and vector subtraction in the Euler parameters spac e, the dynamics of the attitude errors were formulated as a set of stable s econd-order ordinary differential equations with constant coefficients, whi ch are the gains of the attitude feedback control law. Vibration control of the flexible structures in the form of adaptive damping was also derived f rom the procedure of Lyapunov stability analysis and becomes a part of the attitude feedback control law. The stability of the overall dynamic system can be achieved by tuning the selected control gains in the Lyapunov analys is. Attitude manoeuvre of a model spacecraft was tested using the proposed control law and the simulation results were compared for the cases with and without adaptive structural damping. This study also shows that, by select ing the adaptive damping coefficients, the optimal time and torque manoeuvr e of the flexible spacecraft can be determined.