Principles of 2-sliding mode design

By Arie Levant. at - Automatisierungstechnik, 2007

846 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/4bdedd47206b997a894254fe508d4707ba0e3494

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In Control and Systems Engineering

Citations in the corpus

Finite-time and fixed-time stabilization: Implicit Lyapunov function approach (2015, background): “Most of them are restricted to the second order sliding mode systems (Cruz-Zavala, Moreno, & Fridman, 2011; Levant, 2007; Polyakov, 2012; Polyakov & Poznyak, 2009).”
A linear framework for the robust stability analysis of a Generalized Super-Twisting Algorithm (2009, methodology): “In order to simplify the STA convergence proof, the idea of homogeneity was used initially in [12], [1], [15], [13].”
Lyapunov Approach for Analysis and Design of Second Order Sliding Mode Algorithms (2011, methodology): “Finite time convergence and robustness for the STA has been proved by geometrical methods [16], [9],[19], or by means of the Homogeneity properties [3] of the algorithm [18, 34], [19], [35].”
Continuous Integral Terminal Third-Order Sliding Mode Motion Control for Piezoelectric Nanopositioning System (2017, background): “Among these approaches, higher order sliding mode [18], [19] is an efficient way to eliminate the chattering.”
A Lyapunov approach to second-order sliding mode controllers and observers (2008, background): “Levant [14], [16] defines the sliding mode order by means of a smooth dynamic system with a smooth output function σ, closed by some possibly dynamical discontinuous feedback, with an output σ to be forced to zero.”
Strict Lyapunov Functions for the Super-Twisting Algorithm (2012, background): “The states of the plant follow the typical limit cycle behavior, slightly perturbed by the presence of the perturbations and .”
Robust Voltage Control of Floating Interleaved Boost Converter for Fuel Cell Systems (2018, methodology): “The inductor current is controlled by using the super-twisting (ST) sliding mode control [13], [14], and the corresponding sliding surface is defined as the error between the reference inductor current and the measured value.”
A New Adaptive Sliding-Mode Control Scheme for Application to Robot Manipulators (2016, methodology): “These methods include the boundary layer setting [20], [21], low-pass filtering [22], [23], and higher order control [24], [25].”
Chattering free full-order sliding-mode control (2014, methodology): “A number of methods for attenuating chattering have been proposed, such as boundary layer method (Utkin, 1992), high-order sliding-mode method (Bartolini, Ferrara, & Usai, 1998; Levant, 1998, 2001, 2005, 2007), and disturbance estimation method (Shtessel, Shkolnikov, & Brown, 2003).”
Finite-time convergence analysis for “Twisting” controller via a strict Lyapunov function (2010, neutral): “This work was supported by CONACyT project no. 56819 PAPIIT IN111208, FONCICyT project 93302.”
New methodologies for adaptive sliding mode control (2010, methodology): “A second way to decrease the chattering phenomenon is the use of higher order sliding mode controller [14, 1, 15, 16, 12, 19].”
Chattering Analysis (2007, background): “Following the main idea of the high-order sliding mode control [22]–[25], the controller is known in advance; only one gain is adjusted here.”
Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems (2012, methodology): “To overcome this problem the paper introduces a special modification of the socalled ”nested” (terminal) second order sliding mode control algorithm [17] that provides fixedtime stability of the origin and allows to adjust the global settling time of the closed-loop system.”