Solutions for handling control magnitude bounds in adaptive dynamic inversion controlled satellites

Abstract

Traditional adaptive control assumes full control authority and lacks an adequate theoretical treatment for control in the presence of actuator saturation limits. The adaptive dynamic inversion control methodology, which uses dynamic inversion to calculate the control and adaptation to compensate for errors in the inversion due to model uncertainties, also lacks an adequate theoretical treatment for saturation. This paper investigates the problems introduced in adaptive dynamic inversion control schemes due to bounds on the control, and develops a three component control scheme to overcome them. The main contribution of the paper is determination of the maximum possible domain of attraction with respect to the control position limit, and development of a control switching strategy to contain the plant within the maximum possible domain of attraction. This strategy ensures boundedness of the state by restricting it within the Domain of Control Authority. A direction consistent control constraint mechanism was also developed, to maintain the resultant direction of the rate of change of state to be the same as that of the desired, even in the presence of control saturation. Finally, a modified adaptation mechanism was implemented to prevent incorrect adaptation arising from trajectory errors due to control saturation. Mathematical development of the control laws and the adaptation mechanisms is presented, along with proofs for convergence of the tracking error and stability of the overall control scheme. To demonstrate the control scheme, two different numerical simulations for rigid spacecraft attitude tracking with uncertain inertias and saturated controls are presented. Results show that the control scheme successfully handles adaptive dynamic inversion control of systems with dynamics that are nonlinear in terms of the state, with uncertain parameters that appear linearly, in the presence of initial condition errors and control position bounds, and nonlinear saturation constraints on the components of the control.