Stability analysis of direct-detection cooperative optical beam tracking

The system under consideration is a cooperative spatial tracking system between two stations for laser beam communications, using a quadrant photodetector at each station. After determining the equilibrium points of the cooperative system for the case of periodical relative motion, the authors concentrate on the stability of the transient behavior around the equilibrium points for the case of uniform angular relative motion. This case corresponds to an assumption that the steady-state motion is slow with respect to transient phenomena, and is applicable to currently foreseen intersatellite and deep-space optical communications. The analysis is aimed at determining the combined effect of the basic system parameters, such as propagation delay time, tracking loop gains, DC servomotors time constant, and point-ahead velocity error, on the stability and the transient behavior of the overall tracking system. The stability conditions and the transient response around the steady-state trajectory provide a tool for evaluating the consistency of the design parameters for a given propagation delay