Damien Eberard

Robust stability for delayed port-Hamiltonian systems using improved Wirtinger-based inequality

This paper addresses robust stability issues of interconnected port-Hamiltonian systems with polytopic uncertainty and time-varying delay. On the basis of a Lyapunov-Krasovskii functional and the Wirtingers inequality (known to be less conservative than the popular Jensens inequality) we show the improvements of the newly proposed criterion with respect to other existing ones. The stability analysis is derived based on a delay independent criterion. A classical nonlinear example taken from the literature illustrates the relevance of the results.

Approximation of distributed delays

In this paper, we address the approximation problem of distributed delays. These elements are convolution operators with kernel having bounded support and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and working on the convolution Banach algebra, a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control for time-delay systems.

Canonical interconnection of discrete linear port-Hamiltonian systems

This paper deals with the canonical interconnection of discrete-time linear port-Hamiltonian systems. A conservative discrete linear port-Hamiltonian dynamics involving a modified conjugate port-output is introduced. It is shown that the projection yielding the discrete dynamics and the composition by canonical interconnection commute. As a by-product, symplecticity of the numerical flow is preserved by interconnection whenever input vector fields are Hamiltonian vector fields, which is analogous to the continuous case. The negative feedback interconnection of two circuits illustrates the results.

Discrete IDA-PBC design for 2D port-Hamiltonian systems

We address the discrete-time passivity-based control laws synthesis within port-Hamiltonian framework. We focus on IDA-PBC design for canonical port-Hamiltonian systems with separable energy being quadratic in momentum. For this class of systems, we define a discrete Hamiltonian dynamics that exactly satisfies a discrete energy balance. We then derive a discrete controller following the IDA-PBC procedure. The proposed methodology relies on an energy discretization scheme with suitable discrete conjugate port variables. The main result is illustrated on two examples: a nonlinear pendulum in order to compare with some simulation results of the literature, and the impact oscillator which requires robust discretization scheme.

A dual-user teleoperation system with Online Authority Adjustment for haptic training

This paper introduces a dual-user teleoperation system for hands-on medical training. A shared control based architecture is presented for authority management. In this structure, the combination of control signals is obtained using a dominance factor. Its main improvement is Online Authority Adjustment (OAA): the authority can be adjusted manually/automatically during the training progress. Experimental results are provided to validate the performances of the system.

Hamiltonian systems discrete-time approximation: Losslessness, passivity and composability

Abstract In this paper a passive integrator dedicated to input/output Hamiltonian systems approximation is presented. In a first step, a discrete Hamiltonian framework endowed with a Lie derivative-like formula is introduced. It is shown that the discrete dynamics encodes energy conservation and passivity. Additionally, the characterization of the discrete dynamics in terms of Dirac structure is shown to be invariant by interconnection. The class is thus composable: networked systems belong to the class. In a second step, the discrete dynamics is considered as a one-step integration method. The method is shown to be convergent and provides a discrete-time approximation of an input/output Hamiltonian system. Accordingly, the discrete dynamics inherits intrinsic energetic characteristics (storage function and dissipation rate) from the original system. The method is thus tagged as passive integrator. As an illustration, the closed-loop behavior of interconnected subsystems and the stabilization of a rigid body spinning around its center of mass are presented.

Tolerance synthesis using bond graph inversion and fuzzy logic

In the context of mechatronic systems design, this paper addresses a parameter tolerance synthesis with respect to specifications including output epistemic uncertainties. The methodology proposed here concerns uncertainties modelled with fuzzy logic. The procedure relies on output uncertainties propagation through an inverse model. Design parameter tolerance is then synthesized. The results are validated injecting designed parameters in the direct model. The methodology is illustrated on a linear model with specifications including combined uncertainties.

An energy based approach for passive dual-user haptic training systems

This paper introduces a new controller for dual-user training systems, designed by way of an energy based approach. Dual-user training systems are useful for supervised hands-on training when a trainer shows the right gestures to a trainee and where the forces to apply on the tools are difficult to dose. An energy shared control (ESC) based architecture is proposed, based on an intrinsically passive authority sharing mechanism which is enhanced to provide a full force feedback to both users. As this enhancement may violate the natural passivity of the system, a passivity controller is introduced. A task based comparative study with two other dual-user schemes (Complementary Linear Combination (CLC) and Masters Correspondence with Environment Transfer (MECT) from is conducted, which reveals analogous performances. Real-time experiments demonstrate good tracking performances.

Bond Graph Model Of A Water Heat Exchanger.

This paper presents a Bond Graph (BG) modellingapproach to add and exploit on existing Modelica mod-els some information on the energy structure of thesystems. The developed models in the ThermosysProlibrary (Modelica-based) are already validated againstthe experimental data in previous works. A plate heatexchanger (PHE), which is equipment for nuclear powerplants, is considered as a case study in this paper.Simulation results of the BG model for the counterflowPHE are compared with simulation results of the testedModelica model. Comparisons show good agreementbetween both model results.

Approximation of linear distributed parameter systems by delay systems

The present work addresses continuous-time approximation of distributed parameter systems governed by linear one-dimensional partial differential equations. While approximation is usually realized by lumped systems, that is finite dimensional systems, we propose to approximate the plant by a time-delay system. Within the graph topology, we prove that, if the plant admits a coprime factorization in the algebra of BIBO-stable systems, any linear distributed parameter plant can be approximated by a time-delay system, governed by coupled differential-difference equations. Considerations on stabilization and state-space realization are carried out. A numerical method for constructive approximation is also proposed and illustrated.