Variable structure attitude controller design for solely magnetically actuated small satellites subject to environmental disturbances

Sliding mode control algorithms with classical and modified discontinuous reaching laws for purely magnetic attitude control of small satellites are proposed and compared with each other in this work. They are designed by following the steps characteristic to the variable structure control method and the magnetic attitude control problem. The asymptotical stability of the control laws is proven by using theoretical and intuitive approaches together. The stability of the controllers is verified by converging simulation results of the states. The aim is to obtain a controller superior to the sliding mode magnetic controller with continuous reaching law in terms of steady state error under environmental disturbance effects. The time responses of Euler angles and angular velocities indicate that the aim is reached. The necessity of modifying the classical discontinuous reaching law is made clear by comparing states' responses obtained by using the classical and the modified sliding mode algorithms.