Fractional control of rigid body attitude dynamics using exponential coordinates

A fractional control law is proposed for feedback stabilization of rigid spacecraft attitude dynamics using exponential coordinates in which the fractional derivative and integral feedback terms have adjustable orders that can be used to tune the closed-loop response. The performance of the controller is studied numerically for different values of the derivative and integral fractional orders in terms of control effort, transient and steady-state response characteristics, and robustness to unmodeled disturbances. The use of fractional PID control allows for greater degree of exibility over its integer order analogue in terms of shaping a desired closed-loop response by tuning the fractional derivative and integral orders. The proposed strategy is also easier to implement numerically than a recently proposed fractional controller using rotation matrices.