Wilfrid Marquis-Favre

Equilibrium set investigation using bicausality

The introduction of the bicausality concept in the bond graph language has allowed new analytical methodologies, for instance in the context of model inversion, mechatronic system sizing and control. The bicausality concept is here applied for solving the equilibrium state of a mechatronic system. We propose a new method, which permits us to determine the size of the equilibrium set and the algebraic system to be solved. The proposed method is applied to linear systems in a first step, and a generalization is also given for some non-linear systems. Several examples are included in order to explain the method.

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.

Determination of Essential Orders From a Bond Graph Model

The notion of essential orders was first introduced for the handling of decoupling problems. This paper focuses more on their interpretation, namely on the fact that each essential order corresponds to the highest time-differentiation order of a specific output appearing in the inverse model. During inverse modeling, this can in particular be useful for checking whether the specifications are appropriate to the structure of the given model. The aim of this paper is to define two procedures to graphically determine the essential orders directly from a bond graph (BG) model of a linear time-invariant system. Their usefulness is then justified in the context of a bond-graph based methodology for design problem analysis.

On the role of essential orders on feedback decoupling and model inversion : bond graph approach

The essential orders have an important role in the study of the systems decouplability as well as in the inverse model characterization. The aim of this paper is first to define essential orders on the bond graph model. Secondly, static and dynamic decoupling by bond graph approach is discussed and the dynamic extension order is defined. Finally, the dynamic compensation is physically located on the bond graph model and an approach to synthesize a model statically decouplable is suggested in order to define an adequate structure to the control requirements.

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.

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.

Combined Kinetic and Potential Energy Recovery Solution Applied to a Reach Stacker

Reach stackers are heavy duty mobile machines mainly used for container handling on intermodal terminals or harbors. The increasingly restrictive legislation on pollutant emissions as well as the need to reduce fuel costs for operators motivate manufacturers to design more efficient machines. Previous studies highlighted three ways to improve the fuel consumption, namely: (i) improving the engine efficiency; (ii) recuperating the potential energy of elevated containers; (iii) recovering the kinetic energy of the vehicle during decelerations. The architecture proposed in this paper combines these three requirements while preserving most of the conventional components. It results in a moderately priced solution. Control strategies are also studied, especially focusing on the potential energy recovery system where an input-output linearization method is compared to a conventional linear controller. Simulation conducted on several duty cycles shows fuel savings of up to 18.4% and a good robustness to cycle variations.Copyright

Discrete IDA-PBC control law for Newtonian mechanical port-Hamiltonian systems

This paper deals with the stability of discrete closed-loop dynamics arising from digital IDA-PBC controller design. This work concerns the class of Newtonian mechanical port-Hamiltonian systems (PHSs), that is those having separable energy being quadrating in momentum (with constant mass matrix). We first introduce a discretization scheme which ensures a passivity equation relatively to the same storage and dissipation functions as the continuous-time PHS. A discrete controller is then obtained following the IDA-PBC design procedure applied to the discrete PHS system. This method guarantees that, from an energetic viewpoint, the discrete closed-loop behavior is similar to the continuous one. Under zero-state observability assumption, closed-loop stability then follows from LaSalle principle. The method is illustrated on an inertia wheel pendulum model.