Nonlinear regulation of Space Station - A geometric approach

This paper presents a new approach to control system design for the nonlinear regulation and angular momenta management of the space station in the presence of disturbance torque based on geometric control theory. The aerodynamic disturbance torque is treated as the output of an exosystem that is Poisson stable. An output zeroing submanifold for the pitch, yaw, and roll dynamics is obtained. A control law is obtained such that in the closed-loop system the trajectories converge to this manifold and the desired equilibrium state is attained. For the synthesis of the controller, the states associated with the exosystem are generated using measurement on the attitude angles and angular rates. Simulation results are presented to show that in the closed-loop system, attitude regulation and momenta management are accomplished in spite of the presence of the aerodynamic disturbance inputs. TTITUDE control of space vehicles employing control moment gyros (CMGs) is an interesting problem. The equations of motion of the space station are described by nonlinear differential equations. Often, attitude control system design using linear control theory1'9 is obtained. However, linear control systems are designed based on the assumption that the perturbation in attitude angles are small. For large changes in orientation of space vehicles employing momentum exchange devices, nonlinear controllers have been described in the literature.10'14 An adaptive control design has been presented in Ref. 15. In recent papers1'3'9 interesting approaches to CMG momentum management and attitude control of the space station using linear quadratic optimization, pole assignment techniques, and game theory have been reported. However, these control system designs are based on linearized models of the space station. An exact feedback linearization technique has been used in Ref. 16 to derive an attitude control system. This control law has a singularity at 45-deg pitch angle. Input-output feedback linearization has been used in Ref. 17 to design a controller for the space station. However, the effect of disturbance torque has not been treated in Refs. 16 and 17. We present in this paper a new approach to attitude control system design of the space station employing control moment gyros. For simplicity, here CMGs are considered as ideal torquers; however, the CMG gimbal dynamics should be included in the further development of control systems. A geometric approach18'19 to control system design is taken for the nonlinear pitch, yaw, and roll axis regulation of the space station and for the momentum management in the presence of aerodynamic disturbance torque inputs. The unknown disturbance torques contain sinusoidal functions of the orbital frequency and twice the orbital frequency, besides constant terms, and can be considered to be generated by a dynamic system called an exosystem. This exosystem is Poisson stable in the neighborhood of the origin. The output variables chosen for regulation are the roll CMG momentum and the pitch and yaw angles. An output zeroing submanifold (a hypersurface) is obtained by solving an associated partial differential equation in the closed form. A control law is derived such that the output zeroing manifold is attractive. The system trajectories are thus attracted to this manifold. On this manifold the roll CMG momentum and the pitch and yaw angles are constant, whereas the space station rocks about the roll axis in spite of continuously acting aerodynamic torque. Since the