Nonlinear rotational maneuver and vibration damping of NASA SCOLE system

Discussion on: Adaptive Variable Structure Maneuvering Control and Vibration Reduction of Three-axis Stabilized Flexible Spacecraft

“…This work presents some variable structure controllers for linear systems of the forṁ x = (A + ∆A)x + (B + ∆B)Φ(u) + f y = Cx (1) with ∆A, ∆B uncertainty matrices, A, B, C the nominal matrices, Φ(u) a nonlinear continuous function, x, u, y the state, input and output of the system, and f ∈ R n a disturbance. The design is based on the adaption of the bounds on the uncertainty matrices and the disturbance, through the application of Barbalat lemma, as common in adaptive control.…”

“…Many contributions can be found in the literature. In fact, in the last decades the research effort has been focused on the nonlinear nature of the spacecraft model, and various works are available either in for rigid [10,17,24,2] or flexible spacecraft [18,20,21,22,1,12,14], also in the digital setting [19,9]. The robustness of these nonlinear controllers has been one of the main issues addressed [23,11,13].…”

“…The application of the theoretical results to the attitude control of flexible spacecraft is weak for various reasons. To begin with, it should be observed that the authors consider some simplifying assumptions under which the model of a flexible spacecraft can be approximated by equations (1). These simplifications are only valid for small rotation angles and small angular velocities, and transform the nonlinear kinematics and the spacecraft dynamics given in equation (44) of the paper to the form (1).…”