Dynamic Modeling and Controller Design for a Space Vehicle with Fuel Sloshing

This paper is dedicated to modeling of fuel sloshing dynamics and its effect on the stability and control of the space vehicle. Sloshing due to the liquid movement in the fuel tank of a space vehicle's propulsion system can be effective on the vehicle’s control and stability. Force and moment interaction between fuel sloshing and space vehicle’s control system will be appeared as a feedback in the control system. Analyzing of a rigid body's equations of motion is simpler in comparison with a fluid dynamics equations which can be led to reduction in computational efforts. Consequently, it is possible to apply a mechanical model instead. So in this paper fuel sloshing is modelled as a linear mechanical system to investigate its effect on the stability and control of the vehicle. For this purpose, two mechanical models, mass-spring and pendulum systems, are applied to model dynamics of a space vehicle with fuel sloshing and each system’s parameters are evaluated for simulation of dominant sloshing modes. Nonlinear dynamic equations of both systems are simplified and linearized in MAPLE and then an LQR controller is applied for the state space equations of the systems in MATLAB. Finally time response of states and control inputs demonstrate the stability of the system.