Application of a PID-like control to the problem of triaxial electrodynamic attitude stabilization of a satellite in the orbital frame

The problem of triaxial attitude stabilization of a satellite in the orbital frame is considered. The problem is raised about the possibility of implementing such a system of electrodynamic attitude control by the type of a PID controller in which the restoring component of the control torque contains a distributed delay. A constructive analytical approach to the nonlinear stability analysis in the problem of triaxial attitude stabilization of a satellite is presented. A theorem on the asymptotic stability of the stabilized angular position of the satellite is proved. The theorem substantiates the possibility of constructing the indicated control system. Nonlinear analysis is based on the Lyapunov direct method and an original construction of Lyapunov–Krasovskii functional. The effectiveness of the designed attitude control with a distributed delay is confirmed by a computer modeling.