Sliding mode control of the X-33 vehicle in launch and re-entry modes

Abstract

This work develops a sliding mode controller for the X-33 vehicle in launch and re-entry mode. The resulting controller utilizes two-loop sliding mode controller and provides robust, de-coupled tracking of both the required angular velocity profiles and the desired vehicle orientation angles. The motion in sliding of both the angular velocity and the orientation angles is described by linear de-coupled homogeneous vector valued differential equations with desired eigenvalues placement. An optimal control allocation algorithm is employed to allocate torque commands into end- effector deflection commands, which are executed by the actuators. Simulation of the X-33 vehicle in launch and re-entry modes demonstrated accurate, robust, de- coupled tracking performance. provides robust de-coupled multivariable tracking of the desired X-33 vehicle re-entry profiles. A sliding mode control system was designed and analyzed for the WB001 reusable launch vehicle design*'5. This work develops a sliding mode controller (SMC) for the X-33 launch and re-entry modes. The design consists of two basic steps. First, the required angular velocity profile is determined in the outer (guidance) loop such that the given vehicle mission angle profiles are followed if the angular velocity profile is tracked. This is achieved by designing an outer-loop SMC for the kinematics equation of angular motion and taking the angular velocity as the virtual control input. Second, a suitable inner-loop SMC is designed for the dynamic equation of motion such that the required angular velocity profile is tracked. The inner-loop SMC produces control signals in terms of roll, pitch and yaw torque commands. The inner loop transient response must be much faster than the outer loop response. A control allocation algorithm is employed to allocate torque commands into end- effector deflection commands, which are executed by the actuators. The resulting two-loop SMC provides robust, de-coupled tracking of both the angular velocity profiles and the desired vehicle mission angle profiles and takes full advantage of the cascade form of the equations of motion. The motion in sliding of both the angular velocity and the mission angles is described by linear de-coupled homogeneous vector valued differential equations with desired eigenvalues placement. Simulation results demonstrating the substantive effectiveness of this controller design for the X-33 launch and re-entry modes and utilizing realistic desired angular profiles provided in table lookup format are presented.