Spacecraft Attitude Stabilization Using Nonlinear Delayed Multiactuator Control and Inverse Dynamics

The dynamics of a rigid spacecraft with nonlinear delayed multiactuator feedback control are studied in this paper. It is assumed that the time delay occurs in one of the actuators, whereas the other actuator has a negligible time delay. Therefore, a nonlinear feedback controller using both delayed and nondelayed states is sought for the controlled system to have the desired linear delayed closed-loop dynamics using an inverse dynamics approach. The closed-loop stability is shown to be approximated by a second-order linear delay differential equation for the modified Rodriguez parameter attitude coordinates for which the Hsu–Bhatt–Vyshnegradskii stability chart can be used to choose the control gains that result in a stable closed-loop response. An analytical derivation of the boundaries of this chart for the case of no derivative feedback control is shown, whereas a numerical method is used to obtain the stability chart for the general case. Then, to achieve a specified performance, the criteria for a critically damped closed-loop response are studied. Further, an integral feedback control is also implemented, which is capable of eliminating the steady-state attitude error caused by any unmodeled external torque.