Journal ArticleDOI
Higher-order sliding modes, differentiation and output-feedback control
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TLDR
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...read more
Citations
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Journal ArticleDOI
Command Filtered Backstepping
TL;DR: A filtering approach is presented that significantly simplifies the backstepped implementation, analyzes the effect of the command filtering, and derives a compensated tracking error that retains the standard stability properties of backstepping approaches.
Journal ArticleDOI
Homogeneity approach to high-order sliding mode design
TL;DR: It is shown that a general uncertain single-input-single-output regulation problem is solvable only by means of discontinuous control laws, giving rise to the so-called high-order sliding modes, and homogeneity features significantly simplify the design and investigation of a new family of high- order sliding-mode controllers.
Journal ArticleDOI
Principles of 2-sliding mode design
TL;DR: A recently developed robust exact differentiator being applied, robust output-feedback controllers with finite-time convergence are produced, capable to control any general uncertain single-input-single-output process with relative degree 2.
Journal ArticleDOI
A novel adaptive-gain supertwisting sliding mode controller: Methodology and application
TL;DR: A novel super-twisting adaptive sliding mode control law is proposed for the control of an electropneumatic actuator using dynamically adapted control gains that ensure the establishment, in a finite time, of a real second order sliding mode.
Journal ArticleDOI
Higher order sliding modes
TL;DR: So-called sliding modes are introduced, which become main operation modes in the variable structure systems (VSS) and reveal their main drawback: the so-called chattering effect, i.e., dangerous high-frequency vibrations of the controlled system.
References
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Book
Applied Nonlinear Control
TL;DR: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
Book
Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
Journal ArticleDOI
Sliding order and sliding accuracy in sliding mode control
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.
Journal ArticleDOI
Robust exact differentiation via sliding mode technique
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.
Journal ArticleDOI
Nonholonomic motion planning: steering using sinusoids
TL;DR: Methods for steering systems with nonholonomic c.onstraints between arbitrary configurations are investigated and suboptimal trajectories are derived for systems that are not in canonical form.