Quaternion feedback attitude control system design based on weighted–L2–gain performance

Abstract

The operation and accomplishment of a satellite's mission depend on its capacity to control its attitude. A rotation matrix parameterization, such as a (unit) quaternion, is frequently used to represent the attitude information needed for attitude control. The quaternion can represent the attitude globally. However, the non-uniqueness property of the quaternion causes difficulty in ensuring stability. A quaternion-based attitude control system with an augmented dynamical system is a class of nonlinear continuous quaternion feedback system to tackle that problem. However, tuning the control law's parameters causes further difficulty. This paper addresses the parameters tuning based on weighted–L2–gain performance in the form of linear matrix inequalities such that the equilibrium set of the attitude control system has the guarantee of the asymptotically stable in the large. The proposed parameter tuning method reduces the setting complexity of the controller parameters that comprise scalars and matrices, i.e., from five to two parameters. It is equivalent to reducing from 37 to 4 parameters' elements. In addition, a disturbance observer is proposed as an additional control torque to overcome angular velocity bias and external disturbance bad effects. We proved that the disturbance estimation error is bounded. Simulations verified the effectiveness of the proposed control systems.

Keywords

• Attitude control
• Disturbance observer
• Tuning parameters
• Quaternion
• Weighted-L2-gain performance