Underactuated Attitude Control of Small Spacecraft.

Actuator failures onboard spacecraft often lead to unsatisfied control performances or even the lose of the whole mission. The aim of this thesis is to find an optimal and generic backup strategy for attitude control in the case of actuator failure. With UoSAT-12 as an example, two existing backup strategies are compared using different combinations of the remaining magnetorquers and reaction wheels. The ’’constant gain like” control law shows poor performances when actuator fails. A Lyapunov-based discontinuous control law is modified with the consideration on capacity of actuators and adopted for underactuated attitude control with two reaction wheels. The simulation results indicate that Lyapunov-based underactuated attitude control law can achieve better performances and is promising to deal with actuator failures. To improve the performances, two new underactuated attitude control laws are proposed based on feedback linearization technology. The two new underactuated attitude control laws can provide higher accuracy and faster attitude response. However, robustness and attitude tracking are still problems for underactuated attitude control design. Nonlinear H ∞ theory is utilized in this thesis to further improve the performances of underactuated attitude control since it can deal with external disturbances and unmodeled errors. A new energy-compensation based approach, which can guarantee a solution of Hamiltonian-Jacobi-Isaacs (HJI) equation for a controllable system, is proposed. Its applications on UoSAT-12 fully active attitude control show that the control law via this approach needs smaller control inputs but against larger disturbances compared with existing approaches. It is also proven both mathematically and numerically with cascade discontinuous control law as an example in this thesis that nonlinear H ∞ theory can be used to improve control accuracy against disturbances and to estimate the region of convergence. Based on that, new underactuated attitude control laws are proposed via different approaches of solving HJI inqualities. The simulations with two reaction wheels onboard UoSAT-12 indicate that nonlinear H control design is a much simpler way for underactuated attitude control problem. It can not only stabilize the attitude of the satellite, but also solve the problem of attitude tracking. It also shows that the control laws based on nonlinear H ∞ theory can attenuate the disturbances from both external environment and un-modelled system errors. It provides a systematic approach with well defined methods for specifying performances and capacities of onboard actuators