Sliding mode active disturbance rejection control for uncertain nonlinear fractional-order systems

• Published in: European journal of control 2021-01, Vol.57, p.54-67
• Main Authors: Djeghali, Nadia, Bettayeb, Maamar, Djennoune, Said
• Format: Article
• Language: English
• Subjects: Active control; Active disturbance rejection control; Closed loops; Control systems; Controllers; Design; Disturbances; Estimates; Extended state observers; Nonlinear control; Nonlinear fractional-order systems; Nonlinear systems; Rejection; Sliding mode control; Stability analysis; State observers; Tracking; Uncertain nonlinear systems; Uncertainty
• ISSN: 0947-3580; 1435-5671
• DOI: 10.1016/j.ejcon.2020.03.008

•Design of a sliding mode active disturbance rejection control for fractional-order nonlinear systems with unknown states and disturbances.•The proposed approach combines the step by step sliding mode extended state observer and the sliding mode control.•Study of the convergence of the proposed control scheme.•The proposed approach has good tracking performance and good ability to disturbance rejection. It is recognized today that active disturbance rejection control (ADRC) is an effective control strategy in the presence of uncertainties and disturbances and especially in the absence of a model. Its advantages and its power have been demonstrated practically on numerous engineering applications. This control technique has been widely developed in the case of integer-order systems. On the other hand, fractional-order systems are gaining more and more interest due to their use in modeling of many physical phenomena. Some works have been dedicated to the design of the ADRC for linear and nonlinear fractional-order systems. However, the sliding mode technique has not yet been used for the design of ADRC of fractional-order systems. The aim of this paper is to propose a sliding mode active disturbance rejection controller (SMADRC) for nonlinear fractional-order systems with uncertainties and external disturbances for stabilization and tracking purposes. First, a step by step sliding mode extended state observer (SMESO) for both state variables and total disturbance (uncertainties and external disturbances) estimation is proposed. The finite time convergence of the proposed extended state observer is established. Then, a sliding mode controller using the estimated states and total disturbance is presented to realize stabilization and desired references tracking with compensation of the total disturbance. The closed loop stability is analyzed. Simulation results of the proposed SMADRC applied to the control of fractional-order chaotic systems are compared to those of the conventional sliding mode control scheme.