Quaternion-Based LQR Spacecraft Control Design Is a Robust Pole Assignment Design

AbstractRecently, a fully controllable quaternion spacecraft model was proposed. Based on this controllable quaternion model, an analytic linear-quadratic regulator (LQR) design for a spacecraft control system was obtained. Although the LQR design is based on the linearized quaternion model, it was shown that the design of the LQR control system globally stabilizes the original nonlinear spacecraft system. Because in spacecraft design practice engineers normally use models with simplified system dynamics and cost function (which has diagonal structure and excludes external torques) to make the design complexity manageable, this paper will show that the LQR control design is a robust pole assignment design; therefore, the controller is insensitive to the modeling error and external disturbances of nonlinear spacecraft systems. All these properties make this design very attractive. First, the designed controller locally achieves the desired performance because LQR design is optimal for the linearized system...