Finite-Time Sliding Mode Control With Unknown Control Direction

Dongmei Lu

doi:10.1109/access.2021.3078768

Abstract

In this paper, a global nonsingular sliding mode controller is developed for a second order system with unknown control direction. A novel terminal sliding mode hypersurface is presented to compensate for the sign uncertainty in the control input and avoid the singularity issue present in the traditional terminal sliding mode control. In contrast to the Nussbaum gain approach where the equilibrium point is reached asymptotically in the presence of input sign uncertainty, the proposed controller guarantees that the equilibrium point can be reached from any initial state in finite time. Simulation results are provided to validate the proposed controller.

Highlights

Sliding mode control (SMC) is a well known control technique due to its insensitivity to parameter variations and exogenous disturbances [1]
terminal sliding mode (TSM) has been widely accepted due to finite time convergence for systems with model uncertainties and disturbances, the existing TSM solutions do not take into account the unknown control direction, i.e., the sign uncertainty in the input matrix
SIMULATION RESULTS Simulation results are presented for a second order system given in (1)

Summary

Introduction

Sliding mode control (SMC) is a well known control technique due to its insensitivity to parameter variations and exogenous disturbances [1]. TSM has been widely accepted due to finite time convergence for systems with model uncertainties and disturbances, the existing TSM solutions do not take into account the unknown control direction, i.e., the sign uncertainty in the input matrix. Lemma 2 [27]: Let the first order system be given by x = f (x, t) + bu(t) where f (x, t) ∈ R is the disturbance, b ∈ R is the input gain with unknown sign, and the control input u(t) is designed as π u = Msgn sin ε swhere sgn(·) denotes the sign of (·), ε ∈ R+ is a constant, M ∈ R+ is a constant or a positive function, and the hypersurface s(t) is defined as s = s + λ sgn(s)dt with s(t) = x(t) as the sliding surface and λ ∈ R+.

Objectives

Results

Conclusion