Analytic LQR Design for Spacecraft Control System Based on Quaternion Model

Abstract

In this paper, linear-quadratic regulator (LQR) method is proposed for the design of nonlinear spacecraft control systems. The proposed design is based on the linearized spacecraft model that involves only three components of the quaternion. By using a simple and special structure of the linearized reduced quaternion model, an analytical solution for the controller. It is shown that the analytical solution of the state feedback matrix is an explicit function of the cost matrices Q and R. The analytic solution makes it convenient in design practice to tune the feedback matrix and the cost matrices Q and R to balance the requirements between response performance and fuel consumption. It is shown that the designed controller globally stabilizes the nonlinear spacecraft system, whereas it locally optimizes the spacecraft performance. A design example is provided to show the effectiveness of the design method.