The flight dynamics of a spaceplane strongly depends on the flight environment, including the dynamic pressure, angle of attack, and Mach number. In addition, spaceplanes fly at pitch angles around 90 degrees during powered and coasting ascent, and Euler angles are known to be coupled with roll and yaw angles at such pitch angles. In this paper, the control system for a spaceplane based on dynamic inversion theory is proposed. To avoid the problem of the singularity of Euler angles, the equation of state is written in terms of quaternions. The control laws are designed and evaluated in the following three cases: (1) The case where only the attitude error calculation of the control law using the Euler angle is modified. (2) The case where the vector part of the quaternion is used as the control variable. (3) The case where the vector part of the error quaternion is used as the control variable. Finally, the results of the numerical simulation show that Case (3) has the best control performance.
