Dual layer barrier functions based adaptive higher order sliding mode control

Abstract

This article presents an adaptive discontinuous higher order sliding mode control (HOSMC) strategy for a disturbed chain of integrators of order n. This strategy employs a barrier function‐based dual layer adaptation and it ensures the convergence of the sliding variable and its (n − 1) first derivatives to zero without requiring any information on the bounds of the disturbances or their derivatives. It consists in applying a barrier function‐based adaptive super‐twisting methodology compensating Lipschitz disturbances with some error, and a growing gain‐based adaptive HOSMC which just needs to counteract this error. Real‐time simulation platform is used to test the efficacy of the proposed strategy to control a linear induction motor considering dynamic end effects.

Adaptive finite‐time super‐twisting sliding mode control for robotic manipulators with control backlash

“…Theorem 1. For a robotic manipulator system (9), positive odd integers 𝛾 1 and 𝛾 2 satisfy 1 < 𝛾 1 𝛾 2 < 2 and define 𝜆 j > 0, j = 1, 2, … , n. With the help of the ATSMS (12) and the designed SMC (16), the finite-time arrival of ATSMS and the finite-time tracking of reference trajectory signal will be achieved.…”

“…By introducing SMC theory into robot control system, it was a reasonable solution to realize the control with strong robustness. [8][9][10] In the 1950s, the former Soviet Union scholars Utkin, Emelyanov, and Taran first proposed the idea of variable structure control which could be divided into two categories. One of the categories was sliding mode being combined with the control, which was referred to SMC, and the other was control law without sliding mode.…”

Asymptotic consensus tracking control of robotic manipulators with disturbance and dead-zone via adaptive sliding mode control

“…Various advanced control approaches are applied to complete the consensus trajectory tracking control. Among them, the SMC method [2] is widely concerned by virtue of the strong robustness and antiinterference.…”

A Lyapunov Approach to Barrier-Function Based Time-Varying Gains Higher Order Sliding Mode Controllers

“…This algorithm provides the convergence of the sliding variable and its r − 1 first derivatives to some unknown neighborhoods of zero. To deal with this drawback, a barrier function-based dual layer strategy which can ensure the convergence of the sliding variable and its r − 1 first derivatives to zero is proposed in [30]. However, the two drawbacks of this strategy are that, on one hand, it cannot be applied in the case of time-dependent control gain, and on the other hand, the convergence can be lost if the perturbation grows suddenly, this means, the states can leave the origin and jump to a unknown big value before re-convergence.…”