A Modified Active-Disturbance-Rejection Control with Sliding Modes for an Uncertain System by Using a Novel Reaching Law

Abstract

This article presents a modified active-disturbance-rejection control (ADRC) combined with a sliding mode control (SMC) regarding the tracking control problems for plants with unmatched uncertainty. The proposed modified active-disturbance-rejection control with sliding mode (ADRC-SM) employs a reduced-order extended state observer (ESO) for estimating various uncertainties of system in time, including unmatched and matched uncertainties. Meanwhile, a novel reaching law of SMC was designed by using the cycloid function as the main controller of ADRC, which ensures the robustness of the uncertain system. Due to the reduced-order ESO tracking and compensating for various uncertainties in the system as a total disturbance, the upper bound of the disturbance in the SMC is relaxed. The gain coefficient of the reaching law only needs to be designed to be larger than the limit of the lumped disturbance; thus, the chattering problem is greatly reduced. The designed new reaching law of the cycloid function shortens the time for the system state’s convergence to the sliding mode’s surface. The cycloid function replaces the switching function in the traditional reaching law, making the actual control input continuous and shortening the approach time. Compared with traditional ADRC-SM, the use of multiple ESOs or intelligent algorithms to approximate plant parameters can be avoided, the design is simplified, its robustness is enhanced, computational costs are reduced, and the convergence time is reduced. The controlled object with unmatched uncertainty is transformed into a system with matched uncertainty using state-space transformation, which reduces the complexity of the controller’s design. In addition, the stability analysis of the closed-loop system is carried out based on the Lyapunov method. Simulations and experiments verify that the modified ADRC-SM has the merits of fast response, small overshoot, small steady-state error, strong anti-interference competence, and high control accuracy.