Design of an adaptive chattering avoidance global sliding mode tracker for uncertain non-linear time-varying systems

Abstract

In this paper, a novel adaptive global sliding mode control technique is suggested for the tracking control of uncertain and non-linear time-varying systems. The proposed scheme composed of a global sliding mode control structure to eliminate reaching mode and an adaptive tracker to construct the auxiliary control term for eliminating the impacts of unwanted perturbations. Using the Lyapunov direct method, the tracking control of the non-linear system is guaranteed. Moreover, superior position tracking performance is obtained, the control effort is considerably decreased and the chattering phenomenon is removed. Furthermore, using adaptation laws, information about the upper bounds of the system perturbations is not required. To indicate the effectiveness of the suggested scheme, three simulation examples are presented. Simulation results demonstrate the superiority and capability of the offered control law to improve the transient performance of a closed-loop system using online adaptive parameters.

Adaptive Observer‐Based Global Sliding Mode Control for Uncertain Discrete‐Time Nonlinear Systems with Time‐Delays and Input Nonlinearity

“…Lemma 1. If the observer error dynamics (5), the sliding manifold (6) and the auxiliary control (14) with the adaptation law (15) are employed, then the sliding manifold σ 1 (k) converges into a residual set of the origin.…”

“…Hence, the problem of robust stabilization and tracking control for uncertain nonlinear systems has been widely investigated. Over the past decades, a range of research has been undertaken in this field . However, these studies assumed that all system states are known.…”

“…It is well known that SMC is an effective robust control scheme and has been extensively used to improve the stability, performance, and robustness of uncertain linear and nonlinear systems. Many studies on adaptive SMC have been presented in the literature . However, none of the above methods can deal with the robustness against parameter uncertainties, time‐delays, and input nonlinearity by using partial known state information in discrete‐time domain.…”

“…Over the past decades, a range of research has been undertaken in this field. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] However, these studies assumed that all system states are known. From a practical point of view, the system states may not be available and only the system outputs can be measured in many systems.…”

Nonsingular fast terminal sliding-mode stabilizer for a class of uncertain nonlinear systems based on disturbance observer

“…Sliding-Mode Control (SMC) is e ciently applied for the stabilization and controller design of various linear and nonlinear dynamical systems such as singular systems [2], robotic manipulators [3], nonholonomic mobile robots [4,5], fractional order systems [6], chaotic systems [7,8], under-actuated systems [9], etc. SMC is an in uential control technique, which has access to the favorite responses in spite of the uncertainties and disturbances [10,11].…”