Optimal FPID Control Approach for a Docking Maneuver of Two Spacecraft: Translational Motion

Abstract

This paper studies the use of a fuzzy proportional integral derivative (PID) controller based on a genetic algorithm (GA) in a docking maneuver of two spacecraft in the space environment. The docking maneuver consists of two parts: translation and orientation. To derive governing equations for the translational phase, Hill linear equations in a local vertical–local horizontal (LVLH) frame will be used. In fuzzy PID (FPID) controller design, two fuzzy inference motors will be utilized. The single input fuzzy inference motor (SIFIM) is the first to have only one input, and for each state variable, a separate SIFIM is defined. Another fuzzy inference motor, the preferrer fuzzy inference motor (PFIM), represents the control priority order of each state variable and a supervisory role in large deviations. This FPID controller covers a servicer’s translation of a docking maneuver, which tries to dock with a stable nonrotating target. Various conflicting objective functions are distance errors from the set point and control efforts. To enter the control limit in an optimization problem, the maximal value of the thrust force is constrained. Considering these objective functions, a statistical analysis on the GA parameters will be performed, and the test with the best minimum fuel consumption and minimum deviations of the servicer from the equilibrium point will be chosen as the best test. The three-dimensional (3D) Pareto frontiers corresponding to the best test will be plotted, and the optimal points related to the objective functions will be demonstrated on them; the time response figures corresponding to these points will then be generated. The results prove that this controller shows an efficient performance in the docking maneuver of the servicer spacecraft. In comparison with similar work, a number of system performance parameters (e.g., settling time) will be improved, and overshoot (as a critical parameter in docking maneuver) will be truncated.