A Hybrid Model Reference Adaptive and Regressive‐Form Sliding Mode Control in Discrete Domain: Robustness Under System Uncertainty

ABSTRACT This paper presents a discrete‐time model reference adaptive sliding mode control (MRASMC), with a sliding surface formulated based on regressive structure. Stability and convergence are rigorously proven using Lyapunov theory. The effectiveness of the MRASMC is demonstrated via both simulation and experiments on differential‐drive mobile robots (DMRs) equipped with magnetic adhesion. In the simulation, the MRASMC is applied to the DC motor for angular velocity control under model variation in the presence and absence of external disturbances. The model parameters are predefined and vary significantly in each stage to evaluate the controller's adaptability. In all cases, the system responses achieve settling times below 0.6 s and recover from disturbances or model changes within approximately 0.25 s. The adaptation process remains stable, with control parameters converging rapidly after each event. Output oscillations are effectively controlled and remain largely unaffected by disturbance, owing to the support of the adaptive triggering condition. In the experiment scenario, tests are conducted on a DMR operating on vertical steel surfaces under challenging conditions, including strong magnetic adhesion (up to 4000 N), uneven contact surfaces, and the presence of weld seams. Three reference speed levels—15, 12, and 20 rpm—are tested, with a sampling interval of 0.5 s. The adaptive gain is set to 0.01, the sliding coefficient to 40, and the triggering condition is defined as a deviation threshold of 0.5 rpm and a counter limit of one step. As a result, the DMR successfully tracks the reference speed, achieving a settling time of about 2.5 s after each change. Steady‐state oscillations range between 1.27 and 3.6 rpm, and the maximum error remains below 2.12 rpm. The adaptive control parameters exhibit clear convergence and maintain stability despite sensor disturbance and surface irregularities.