Nonlinear proportional-derivative-type controller for flexible spacecraft attitude stabilization under bounded disturbances

A semi-globally input-to-state stable (ISS) control law is derived for flexible spacecraft attitude maneuvers in the presence of parameter uncertainties and external disturbances. The Modified Rodrigues Parameters (MRP) are used as the kinematic variables since they are nonsingular for all possible rotations. This novel simple control is a proportional-plus-derivative (PD) type controller plus a sign function through a special Lyapunov function construction involving the sum of quadratic terms in the angular velocities, kinematic parameters, modal variables and the cross state weighting. A sufficient condition under which this nonlinear PD-type control law can render the system semi-globally input-to-state stable is provided such that the closed-loop system is robust with respect to any disturbance within a quantifiable restriction on the amplitude, as well as the set of initial conditions, if the control gains are designed appropriately. In addition to detailed derivations of the new controllers design and the associated stability and attitude convergence proofs, simulation studies have been conducted to validate the design and the results are presented to highlight the ensuring closed-loop performance benefits when compared with the conventional control schemes.