Nonlinear Dynamic Inversion Controller Design for a Satellite, Considering the Dynamics of Magnetorquers

In this paper, a nonlinear inverse dynamic controller is designed for a magnetic actuated satellite. Since the stability of linear control laws in nonlinear dynamics is not guaranteed far from the equilibrium point, a global stabilizing nonlinear control law is necessary. In this method, by changing the system parameters, the nonlinear dynamics of the system is converted to linear dynamics and the input controller compensates the changes. The stability of the closed loop system was, then, investigated and proved by the Lyapunov method. Dynamic and kinematic equations of satellite are also developed in the presence of aerodynamic disturbance, gravity gradient, magnetic and radiation moments, and the linearization of the motion equations is done around the equilibrium point. In order to evaluate the performance of the dynamic inverse controller, the proportional-derivative linear control law and linear quadratic regulator optimal control law are designed and the results are compared. By modeling satellite orbit, the disturbance moments and the local magnetic field vector are calculated instantaneously according to the satellite's position in the orbit. Finally, the system response is presented by considering the saturation range of magnetic actuators. The results show a better performance of the nonlinear dynamic inversion controllers in both accuracy and convergence time.