Quaternion-based satellite attitude control—A direct parametric approach

In this paper, the dynamical model in a matrix second-order nonlinear form with respect to the quaternion coordinates is firstly established for the attitude system of a satellite, which is complete in the sense that no approximation is taken. Then, with the help of a recently proposed general parametric design approach for general fully-actuated second-order nonlinear systems, a direct parametric approach for satellite attitude control via proportional plus derivative quaternion feedback is proposed, which gives a complete parametrization of the pair of feedback gains. The approach possesses two important features. Firstly, with the proposed controller parametrization, the satellite attitude system, though highly nonlinear, can be turned into a constant linear system with desire eigenstructure. Secondly, in such a design there are still degrees of freedom which may be further utilized to improve the system performance. An example is considered to demonstrate the use of the proposed approach.