Spacecraft Dynamics Linearizing and Optimal Control Based on Operational Research and LQI

This paper presents a new feasible methodology for linearizing the spacecraft's dynamics, a key idea for space mission design and implementation. First, a “symbolic vectorial derivative operator” is proposed based on operational research and vectorial analysis; the defined operator is used to linearize the spacecraft dynamics, providing a new feasible approach for spacecraft dynamics linearizing. Second, a Geostationary Orbit (GEO) spacecraft is used to analyze the limitations of the proposed linear approach; incremental analysis is used to describe the proposed new GEO linear model regarding orbit deviation parameters. In the end, the Linear Quadratic Integral (LQI) optimal control algorithm is implemented to analyze the controllability of the proposed GEO approach. The simulation results show that the proposed linearization method can be implemented for spacecraft dynamics modeling, analysis, and control. Consequently, the proposed operator can be used for linearizing any non-linear vectorial model.