Input–output linearization minimum sliding-mode error feedback control for spacecraft formation with large perturbations

Abstract

To improve the control precision of nonlinear spacecraft formation flying, the input–output linearization minimum sliding-mode error feedback controller is presented based on the linear-decoupled spacecraft formation model by input–output linearization method incorporating the sliding-mode control. This paper proposes a new strategy to estimate and offset the system-control errors, which include various kinds of uncertainties and disturbances. To facilitate the analysis, the linear-decoupled spacecraft formation model is first given; on which basis, the concept of equivalent control error is introduced to define the entire model error. Based on the minimum sliding-mode covariance constraint, a cost function is formulated to estimate the equivalent control error and fed back to the conventional sliding-mode control. It is shown that the sliding mode after the input–output linearization minimum sliding-mode error feedback controller will approximate to the ideal sliding mode with high-control precision. In addition, the new methodology is applied to spacecraft formation flying. It guarantees global asymptotic convergence of the relative-tracking error in the presence of the large perturbations. More exactly, the two input–output linearization minimum sliding-mode error feedback controller laws (continuous sliding-mode control and nonsingular terminal sliding-mode control) are developed for this spacecraft formation flying system. Several fault-tolerant scenarios are considered to verify that the input–output linearization minimum sliding-mode error feedback controller is still effective in the presence of faults in spacecraft thrusters. Numerical simulations are performed to demonstrate the efficacy of the proposed methodology to maintain and reconfigure the spacecraft formation with existence of initial offsets and large perturbations effects.