848 research outputs found
Implicit Euler numerical simulations of sliding mode systems
In this report it is shown that the implicit Euler time-discretization of
some classes of switching systems with sliding modes, yields a very good
stabilization of the trajectory and of its derivative on the sliding surface.
Therefore the spurious oscillations which are pointed out elsewhere when an
explicit method is used, are avoided. Moreover the method (an {\em
event-capturing}, or {\em time-stepping} algorithm) allows for accumulation of
events (Zeno phenomena) and for multiple switching surfaces (i.e., a sliding
surface of codimension ). The details of the implementation are given,
and numerical examples illustrate the developments. This method may be an
alternative method for chattering suppression, keeping the intrinsic
discontinuous nature of the dynamics on the sliding surfaces. Links with
discrete-time sliding mode controllers are studied
Analysis of explicit and implicit discrete-time equivalent-control based sliding mode controllers
Different time-discretization methods for equivalent-control based sliding
mode control (ECB-SMC) are presented. A new discrete-time sliding mode control
scheme is proposed for linear time-invariant (LTI) systems. It is error-free in
the discretization of the equivalent part of the control input. Results from
simulations using the various discretized SMC schemes are shown, with and
without perturbations. They illustrate the different behaviours that can be
observed. Stability results for the proposed scheme are derived
Dissipative Systems Analysis and Control, Theory and Applications: Addendum/Erratum
This is an up-dated addendum/erratum to the second edition of the book Dissipative Systems Analysis and Control, Theory and Applications, Springer-Verlag London, 2nd Edition, 2007
Dissipative Systems Analysis and Control, Theory and Applications: Addendum/Erratum
This is an up-dated addendum/erratum to the second edition of the book Dissipative Systems Analysis and Control, Theory and Applications, Springer-Verlag London, 2nd Edition, 2007
Stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme
Here we present well-posedness results for first order stochastic
differential inclusions, more precisely for sweeping process with a stochastic
perturbation. These results are provided in combining both deterministic
sweeping process theory and methods concerning the reflection of a Brownian
motion. In addition, we prove convergence results for a Euler scheme,
discretizing theses stochastic differential inclusions.Comment: 30 page
Identification of delays and discontinuity points of unknown systems by using synchronization of chaos
In this paper we present an approach in which synchronization of chaos is
used to address identification problems. In particular, we are able to
identify: (i) the discontinuity points of systems described by piecewise
dynamical equations and (ii) the delays of systems described by delay
differential equations. Delays and discontinuities are widespread features of
the dynamics of both natural and manmade systems. The foremost goal of the
paper is to present a general and flexible methodology that can be used in a
broad variety of identification problems.Comment: 11 pages, 3 figure
On the control of complementary-slackness juggling mechanical systems
International audienceThis paper studies the feedback control of a class of complementary-slackness hybrid mechanical systems. Roughly, the systems we study are composed of an uncontrollable part (the "object") and a controlled one (the "robot"), linked by a unilateral constraint and an impact rule. A systematic and general control design method for this class of systems is proposed. The approach is a nontrivial extension of the one degree-of-freedom (DOF) juggler control design. In addition to the robot control, it is also useful to study some intermediate controllability properties of the object's impact Poincaré mapping, which generally takes the form of a non-linear discrete-time system. The force input mainly consists of a family of dead-beat feedback control laws, introduced via a recur-sive procedure, and exploiting the underlying discrete-time structure of the system. The main goal of this paper is to highlight the role of various physical and control properties characteristic of the system on its stabilizability properties and to propose solutions in certain cases
On the Control of a One Degree-of-Freedom Juggling Robot
International audienceThis paper is devoted to the feedback control of a one degree-of-freedom (dof) juggling robot, considered as a subclass of mechanical systems subject to a unilateral constraint. The proposed approach takes into account the whole dynamics of the system, and focuses on the design of a force input. It consists of a family of hybrid feedback control laws, that allow to stabilize the object around some desired (periodic or not) trajectory. The closed-loop behavior in presence of various disturbances is studied. Despite good robustness properties, the importance of good knowledge of the system parameters, like the restitution coefficient, is highlighted. Besides its theoretical interest concerning the control of a class of mechanical systems subject to unilateral constraints, this study has potential applications in non-prehensile manipulation, extending pushing robotic tasks to striking-and-pushing tasks
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