Abstract
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.