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Arie Levant

Bio: Arie Levant is an academic researcher from Tel Aviv University. The author has contributed to research in topics: Sliding mode control & Differentiator. The author has an hindex of 40, co-authored 143 publications receiving 17103 citations. Previous affiliations of Arie Levant include École centrale de Lille & Ben-Gurion University of the Negev.


Papers
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Journal ArticleDOI
Arie Levant1
TL;DR: In this article, the authors proposed arbitrary-order robust exact differentiators with finite-time convergence, which can be used to keep accurate a given constraint and feature theoretically-infinite-frequency switching.
Abstract: Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...

2,954 citations

Journal ArticleDOI
TL;DR: It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay and a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced.
Abstract: The synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered. Usually, what is called sliding mode is employed in such synthesis. This sliding mode is characterized, in practice, by a high-frequency switching of the control. It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay. A new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced. These algorithms feature a bounded control continuously depending on time, with discontinuities only in the control derivative. It is also shown that the sliding accuracy is proportional to the square of the switching time delay.

2,714 citations

Journal ArticleDOI
TL;DR: In this paper, an order of the maximal differentiation error to the square root of the maximum deviation of the measured input signal from the base signal from Lipschitz's constant of the derivative was proposed.

1,958 citations

Book
01 Jun 2013
TL;DR: The sliding mode control and observation (SOMO) approach has proven to be effective in dealing with complex dynamical systems affected by disturbances, uncertainties and unmodeled dynamics as discussed by the authors.
Abstract: The sliding mode control methodology has proven effective in dealing with complex dynamical systems affected by disturbances, uncertainties and unmodeled dynamics. Robust control technology based on this methodology has been applied to many real-world problems, especially in the areas of aerospace control, electric power systems, electromechanical systems, and robotics. Sliding Mode Control and Observation represents the first textbook that starts with classical sliding mode control techniques and progresses toward newly developed higher-order sliding mode control and observation algorithms and their applications.The present volume addresses a range of sliding mode control issues, including:*Conventional sliding mode controller and observer design*Second-order sliding mode controllers and differentiators*Frequency domain analysis of conventional and second-order sliding mode controllers*Higher-order sliding mode controllers and differentiators*Higher-order sliding mode observers *Sliding mode disturbance observer based control *Numerous applications, including reusable launch vehicle and satellite formation control, blood glucose regulation, and car steering control are used as case studiesSliding Mode Control and Observation is aimed at graduate students with a basic knowledge of classical control theory and some knowledge of state-space methods and nonlinear systems, while being of interest to a wider audience of graduate students in electrical/mechanical/aerospace engineering and applied mathematics, as well as researchers in electrical, computer, chemical, civil, mechanical, aeronautical, and industrial engineering, applied mathematicians, control engineers, and physicists. Sliding Mode Control and Observation provides the necessary tools for graduate students, researchers and engineers to robustly control complex and uncertain nonlinear dynamical systems. Exercises provided at the end of each chapter make this an ideal text for an advanced coursetaught in control theory.

1,774 citations

Journal ArticleDOI
TL;DR: The super-twisting second-order sliding-mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems and the finite time convergence of the observer is proved.
Abstract: The super-twisting second-order sliding-mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems. The finite time convergence of the observer is proved. Thus, the observer can be designed independently of the controller. A discrete version of the observer is considered and the corresponding accuracy is estimated.

1,040 citations


Cited by
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Journal ArticleDOI
Arie Levant1
TL;DR: In this article, the authors proposed arbitrary-order robust exact differentiators with finite-time convergence, which can be used to keep accurate a given constraint and feature theoretically-infinite-frequency switching.
Abstract: Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...

2,954 citations

Journal ArticleDOI
TL;DR: Two types of nonlinear control algorithms are presented for uncertain linear plants, stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions.
Abstract: Two types of nonlinear control algorithms are presented for uncertain linear plants. Controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions. The control design procedure uses block control principles and finite-time attractivity properties of polynomial feedbacks. Controllers of the second type are modifications of the second order sliding mode control algorithms. They provide global finite-time stability of the closed-loop system and allow to adjust a guaranteed settling time independently on initial conditions. Control algorithms are presented for both single-input and multi-input systems. Theoretical results are supported by numerical simulations.

2,380 citations

Journal ArticleDOI
TL;DR: In this paper, an order of the maximal differentiation error to the square root of the maximum deviation of the measured input signal from the base signal from Lipschitz's constant of the derivative was proposed.

1,958 citations

Journal ArticleDOI
TL;DR: The super-twisting second-order sliding-mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems and the finite time convergence of the observer is proved.
Abstract: The super-twisting second-order sliding-mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems. The finite time convergence of the observer is proved. Thus, the observer can be designed independently of the controller. A discrete version of the observer is considered and the corresponding accuracy is estimated.

1,040 citations

Journal ArticleDOI
TL;DR: A new solution to the problem of chattering elimination in variable structure control (VSC) is presented, inspired by the classical bang-bang optimal control strategy, and extended to the case of nonlinear systems with uncertainties of more general types.
Abstract: Relying on the possibility of generating a second-order sliding motion by using, as control, the first derivative of the control signal instead of the actual control, a new solution to the problem of chattering elimination in variable structure control (VSC) is presented. Such a solution, inspired by the classical bang-bang optimal control strategy, is first depicted and expressed in terms of a control algorithm by introducing a suitable auxiliary problem involving a second-order uncertain system with unavailable velocity. Then, the applicability of the algorithm is extended, via suitable modifications, to the case of nonlinear systems with uncertainties of more general types. The proposed algorithm does not require the use of observers and differential inequalities and can be applied in practice by exploiting such commercial components as peak detectors or other approximated methods to evaluate the change of the sign of the derivative of the quantity accounting for the distance to the sliding manifold.

992 citations