Attitude control of underactuated small satellites.

Actuator failures onboard satellites have caused severe and even disastrous consequences on several space missions. In this thesis, the problem of the attitude control of a LEO satellite, subject to actuator failures, is addressed. The three axis stabilisation of a satellite with the two remaining control torques on the principal axes, is a challenging problem since the control system is nonholonomic. Such a system has been proven by Brockett to be non-stabilisable using smooth (continuous and time invariant) control laws. Different non-smooth stabilizing control laws for the underactuated attitude control of a satellite are investigated here using pairs of thrusters, and also using reaction wheels. Using two pairs of thrusters, known singular or time varying approaches are applied with a systematic study of the effects of the torque saturation, PWM, singularity avoidance, noise, external disturbances, sampling and angular velocity tracking that intervene in a realistic case. Using two reaction wheels, a novel control strategy based on a singular nonlinear control approach, is mathematically proven and demonstrated by simulation. The 3-axis stability is proven using Rodriguez parameters and then using quaternions. The study of the symmetrical satellite case using thrusters, and the investigation of the effect of a non-zero total momentum using wheels, are done separately. Practical difficulties of the underactuated attitude control of small satellites using two pairs of on/off thrusters are pointed out. Conversely, using two reaction wheels, the possibility of decisive 3-axis manoeuvres is demonstrated (under realistic assumptions). Indeed, using two wheels, the 3-axis stabilisation is achieved with acceptable torque levels and very satisfactory performance. The activation of the non-smooth controller must be done under small momentum conditions. A complete control strategy, (in case of a high initial bias) including a detumbling phase with magnetorquing, and avoiding the non-smooth controller to start from a singularity, is presented. Following the encouraging results from the SSTL's UoSAT-12 simulator, (accounting for noises and external disturbance torques) in-orbit testing of an underactuated control strategy using two wheels has been successfully achieved on UoSAT-12 (by restricting the attitude to sun tracking due to power consumption problems on UoSAT-12). Another in orbit experiment on UK-DMC, for nadir pointing, has been even more successful. Practical results therefore confirm the possibility of using only two control torques for the 3-axis stabilisation of a satellite. One of many interesting consequences of these results is that a fully redundant 3-axis control can be practically envisaged using a 3-wheel configuration.