Robust fractional Active Disturbance Rejection Control: A unified approach

Abstract This paper presents an adaptation of the Active Disturbance Rejection Control (ADRC) method within the fractional calculus context. This ADRC version is characterized by a single active cancellation of the lumped effects of all the unmodeled dynamics, external disturbances and parameter uncertainty associated with the linear model of commensurate fractional order. This methodology proposes suitable simplifications to fit the resulting system to one of appropriate commensurate fractional order. The design is reduced to a linear observer-based control of fractional order that estimates the unified disturbance. A numerical stability analysis is presented to quantify the tracking and estimate errors bounds and provide guidelines in the in the parameters of observer-based controller configuration. The proposed control strategy is experimentally validated in linear and nonlinear cases of fractional order by means of approximate analog implementations.