Robust control of nonlinear uncertain systems via sliding mode with backstepping design

Abstract

This paper presents a new combination of sliding mode and backstepping for output tracking of coupled two tank system. The proposed controller can greatly reduce chattering of sliding modes of the system, and it has certain robustness with respect to the external disturbances and good adaptability with respect to the parametric uncertainty. It is proved that the proposed systematic backstepping design method is able to guarantee global uniformly ultimately boundedness of all the signals in the closed-loop system. The tracking error is proven to converge to a small neighborhood of the origin. Finally, some experimental results are demonstrated to validate the proposed controllers.

ISS-based vehicle yaw stability controller design in backstepping framework

“…(9) to above equation, ∆V1(Sr(k)) = βr 2 − 1 2 Sr(k) 2 +βrSr(k)Λ1(k)+ 1 2 Λ1(k) 2 (15) According to Young's inequality,…”

“…(6) is r and its input is T b2 (k), so it is in single-input-single-output strict-feedback form and it is convenient to implement backstepping control theory, which is a systematic method for designing a controller to track reference signal step-by-step through calculating control (virtual control) at each step. Furthermore, to improve robustness of control systems, backstepping and sliding mode control (SMC) have been combined and implemented [15]. In the section, the proposed controller is designed according to the integration of backstepping and sliding mode control theory and the closed loop system stability is testified through input-to-state stability theory, which is well developed for analyzing systems with uncertainties.…”

Robust Control Design of Nonlinear System by Using Back-Stepping-GSA and Sliding Mode Technique

“…In [25] integrate these two controllers to increase the tracking performance of permanent magnet synchronous motor control system. Combination of these two controllers also been proved too has robustness to the exterior disturbances and virtuous flexibility to variation of the parameter of a coupled-tank system [26]. A vane-type air motor X-Y table motion system also adapts these two control techniques for tracking purpose [27] and to overcome chaotic problem [28].…”