Active disturbance rejection control with adaptive input gain using dynamic inversion approach

This paper addresses the problem of adaptive output feedback trajectory tracking for plants with an unknown input gain. To tackle this issue, a control method is proposed, which stems from the Active Disturbance Rejection Control (ADRC) and employs the dynamic inversion approach to generate the auxiliary control law in a transient state, while simultaneously taking advantage of the adaptive input gain identification to produce the tracking controller, ensuring asymptotic tracking in the steady state. Specifically, a smoothly saturated gradient law with projection is used to ensure the desired properties of the parameter estimates dynamics, and eliminate the parameter instability in the transient states. The boundedness of the trajectories of the system is established in the most general case, and an asymptotic convergence of tracking and estimation errors for a disturbance-free system is proven. The theoretical findings are validated by experimental trials employing two laboratory testbeds.