Abstract
A new non-linear tracking control algorithm based on an attitude error quaternion is studied in this paper. The control law developed here uses the commanded attitude rate without transformation into the body frame. The direct use of the commanded attitude rate simplifies the calculation of its derivative, which is used in the control law. The solutions and the equilibrium points of the closed-loop system, which is a time-varying non-linear system, are obtained in different scenarios. In order to analyse the stability of the system and the tracking performance, two different forms of perturbation dynamics with seven state variables are introduced. Local stability and performance analysis shows that the eigenvalues of the linearized perturbation dynamics are determined only by the gain matrices in the control algorithm and the inertia matrix. The existence of globally stable tracking control is proved using a Lyapunov function. Simulation results show that the spacecraft can track the commanded attitude and rate quickly for a non-zero acceleration rate command.
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