Spacecraft attitude stabilization using nonlinear delayed actuator control with an inverse dynamics approach

The dynamics of a rigid body with nonlinear delayed feedback control are studied in this paper. It is assumed that the time delay occurs in one of the actuators while the other one remains is delay-free. Therefore, a nonlinear feedback controller using both delayed and non-delayed states is sought for the controlled system to have the desired linear closed-loop dynamics which contains a time-delay term using an inverse dynamics approach. First, the closed-loop stability is shown to be approximated by a second order linear delay differential equation (DDE) for the MRP attitude coordinate 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 undamped case is shown, and subsequently the Chebyshev spectral continuous time approximation (ChSCTA) method is used to obtain the stable and unstable regions for the damped case. The MATLAB dde23 function is implemented to obtain the closed-loop response which is in agreement with the stability charts, while the delay-free case is shown to agree with prior results.