Nested adaptive integral terminal sliding mode control for high‐order uncertain nonlinear systems

Abstract

This paper aims to develop a nested adaptive integral terminal sliding mode control scheme for high‐order uncertain nonlinear systems. To achieve this goal, a recursive‐structure integral terminal sliding mode (ITSM) is presented, which consists of a nonsingular terminal sliding mode and a fractional power integral terminal sliding mode. Based on the ITSM, the reaching phase is eliminated and simultaneously, the system is stabilized in finite time. Moreover, due to the full‐order sliding mode inherent in ITSM, the reaching control input is obtained in an integral form instead of a signum function. To remove the needs for the upper bounds of the disturbance or its derivatives, a nested dual‐layer adaptive law is introduced to update the level of the control gain according to the disturbance variations without overestimation. Stability analysis demonstrates that under the proposed control, the system state starts on the sliding surface and then converges to the origin in finite time in the presence of system uncertainties. The novelty of the proposed method lies in its finite‐time origin convergence without reaching phase, nonoverestimation, nonsingular and chattering‐free control signal, and those properties have not yet been achieved by any other existing methods. A simulation example is provided to illustrate the superiorities of the proposed control by comparison to conventional method.

Chattering-free nested adaptive terminal sliding mode control for PEMFC air supply system with event-triggered communication

“…Remark 1. As discussed in Shao 32 and Hong et al, 34 it can be inferred that if the sliding mode function S = 0 in equation (26), then the sliding variable δ will converge to zero from the initial value δ ( t S ) in finite time t δ…”

Neural network based recursive terminal sliding mode control and its application to active power filters

“…Remark For the compensation control term defined in (), in order to reduce the impact of chattering on system performance, this study adopts the boundary layer technique and replaces the sign function with a saturation function, namely $$$$ {u}_1=\left\{\begin{array}{ll}& -\frac{1}{b}\Big({k}_1s+{k}_2 sig{(s)}^{\nu }+{u}_s\mathit{\operatorname{sgn}}(s)\kern0.90em \mid s\mid >\phi, \\ {}& -\frac{1}{b}\Big({k}_1s+{k}_2 sig{(s)}^{\nu }+{u}_s\frac{s}{\phi}\kern2.70em \mid s\mid \le \phi, \end{array}\right. $$$$ In the above formula, $$$ \phi $$$ is a constant, representing the thickness of the boundary layer 34,35 …”

Terminal time regulator‐based exact‐time sliding mode control for uncertain nonlinear systems

“…[2][3][4] The TSM achieves finite-time convergence but the upper bound of the settling time (UBST) is associated with the system's initial condition. 5,6 In other words, the actual convergence time cannot be exactly determined unless the initial condition is given. As a result, the actual system may have converged significantly earlier than the time bound, which may lead to unessential control effort.…”

“…To improve the convergence speed and control precision of conventional sliding mode, terminal sliding mode (TSM) has been developed 2‐4 . The TSM achieves finite‐time convergence but the upper bound of the settling time (UBST) is associated with the system's initial condition 5,6 . In other words, the actual convergence time cannot be exactly determined unless the initial condition is given.…”

“…System state and control input responses (t f = 1). (A) control (3), q=0.5; (B) control (4), 𝛾 1 = 3, 𝛾 2 = 5; and (C) control(5) …”