A smooth attitude-stabilizing control law is derived from which known limits on the control authority of the system are rigorously enforced. Unknown disturbance torques, assumed to be of lesser magnitude than the control limits, are included in the formulation. A smooth control signal containing hyperbolic tangent functions that rigorously obeys a known maximum-torque constraint is introduced. The controller can be viewed as a smooth analog of the variable-structure approach, with the degree of sharpness of the control permitted to vary with time according to a set of user-defined parameters. Lyapunov analysis is employed to ensure global stability, and asymptotic convergence of the angular velocity is guaranteed via the Barbalat lemma. Attitude errors, expressed as Euler parameters, are shown via simulation to vanish whenever certain design parameters are selected appropriately, and guidelines for selection of those parameters are provided in depth.
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Wallsgrove et al. (2005) studied this question.
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