A case study on spacecraft attitude control

In this paper, we present a case study on spacecraft attitude control. The plant (spacecraft attitude model) is a second order, nonlinear, multi-input-multi-output system defined by Euler´s equations of rotational motion and the kinematic differential equations. The modified Rodrigues parameter (MRP) is used for kinematic parametrization and is the only measurable variable at the plant output. It is shown that the non-linear plant can be globally asymptotically stabilized by an output feedback control law proposed in the paper. Stability is proved by Lyapunov´s theorem with a new Lyapunov candidate function. In the control scheme design method, the rate of change of the output (attitude) is approximated using a high gain, high pass filter located in the inner feedback loop. In this way, the proposed control scheme possesses the robustness and simplicity of a PD controller, but does not require attitude rate measurement, angular velocity measurement or direct use of differentiators. Furthermore, the control scheme does not require any information about the body principal moments of inertia and is therefore robust with respect to system parametric uncertainty. This makes the approach practically useful and acceptable by practising engineers. The simulations included in the paper show the robust performance and zero tracking error of the overall closed loop, demonstrating the effectiveness of the proposed stabilization approach. Finally, the paper includes a comparison between the controllers designed by the proposed scheme, by an H_¿ loop shaping design procedure and by a mixed sensitivity design, for the same given plant.