Simulation of a PARASOL Microsatellite control system model based on the Linear Quadratic Regulator (LQR)

The Parasol microsatellite control system model aims to enhance the stability and performance of small satellite operations in low Earth orbit (LEO). This paper presents a simulation framework based on the Linear Quadratic Regulator (LQR) methodology, which is a widely recognized optimal control strategy. The LQR approach is particularly suited for systems requiring precise control with minimal energy expenditure, making it ideal for microsatellites that operate under strict power constraints. The simulation using the MATLAB/Simulink environment incorporates dynamic models of the microsatellite’s attitude and orbital mechanics, allowing for an assessment of the LQR controller’s effectiveness in maintaining desired orientation and trajectory. In this study, we first of all detailed the mathematical model of the Parasol’s position, including state-space representation, cost function definition, and feedback gain computation. Then we implemented the Linear Quadratic Regulatorcontroller in a closed-loop model in MATLAB/Simulink. After we provided attitude control data in the context of the Parasol microsatellite scenario and his geographic coordinates. Finally, the simulation results demonstrate the effectiveness of the implemented Linear Quadratic Regulator controller in stabilizing Parasol’s position. It shows the trajectory of the Parasol microsatellite in DCI coordinates and the simulation of the geographic coordinate with latitude equal to 61.9756 and longitude 108.119 correspondant to northeastern Siberia, Russia, within Yakutia. And the latitude equal to 1.41449 and longitude -57.7824 is located in Brazil near the Amazon rainforest region.