Audrey Jardin

Optimal control problem in bond graph formalism

This paper presents a new way to derive an optimal control system for a specific optimisation problem, based on bond graph formalism. The procedure proposed concerns the optimal control of linear time invariant MIMO systems and can deal with both cases of the integral performance index, these correspond to dissipative energy minimization and output error minimization. An augmented bond graph model is obtained starting from the bond graph model of the system associated with the optimal control problem. This augmented bond graph, consisting of the original model representation coupled to an optimizing bond graph, supplies, by its bicausal exploitation, the set of differential-algebraic equations that analytically give the solution to the optimal control problem without the need to develop the analytical steps of Pontryagins method. The proof uses the Pontryagin Maximum Principle applied to the port-Hamiltonian formulation of the system.

Bond Graphs and Inverse Modeling for Mechatronic System Design

This chapter is concerned with the design of mechatronic systems on dynamic and energy criteria. Compared to the traditional trial–error–correction approach a methodology is presented that drastically decreases the number of simulation iterations and ensures more relevant solutions with respect to the specifications. Moreover, early in the design stages, this methodology enables to check if the design problem is well posed before any simulation. This verification is possible according to the structural analysis concept that points out the characteristic properties of the design models independently of the parameter numerical values. Also, the methodology is based on model inversion that uses straightforwardly the information written in the specifications. Finally, because of its ability to represent multidisciplinary physical systems, to acausally describe a model and to easily undertake a structural analysis, and to visualize the results of this analysis, the bond graph language is well dedicated to this methodology. In this chapter topics like design model validity, specifications validity, structural analysis, technological component specifications, selection and validation, and open-loop control determination will be discussed.

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.

A medical simulator for subcutaneous contraceptive implant insertion

New contraceptive methods like the subcutaneous implant offers a new kind of comfort for women with an efficiency similar to the contraceptive pill. Unfortunately the few numbers of unintended pregnancies that have been reported are generally due to a bad insertion of the implant. In order to give more security to patients, we have designed, in close collaboration with physicians, a new kind of medical simulator. This paper focuses on a device dedicated to a specific subcutaneous implant but it is worth noting that this simulator is relatively generic since it will be used for other subcutaneous techniques or other implant instruments. This simulator can be used for two purposes: one for training novice physicians in the correct manipulation and the other for physician certification which will help determine if they are capable of inserting the implant in vivo. This paper describes the approach which has led to the design of this simulator. It describes its functionalities, its several components but also methods used to analyze the manipulation of the implant insertion inside the patient. Finally first experimental results are reported and discussed. The system used in this paper makes possible to carry out training in a constraint-free context and provides the first mean of visualizing a maneuver that, until now, has been performed blindly.

Structural analysis by bond graph approach: duality between causal and bicausal procedures

The infinite structure of linear time-invariant systems has been principally used to solve control problems. Nevertheless, this system characterization appears interesting in the design and sizing of mechatronic systems as well. Indeed, based on the bond graph language and inverse modelling, a methodology has already been developed for sizing mechatronic systems according to energy and dynamic criteria. One of the novelties of this methodology is its structural analysis step. This step enables structural properties to be deduced and helps in the formulation of the specifications. The aim of this paper is to add new graphical procedures to the structural analysis step to determine some structural properties (infinite pole orders and relative orders) from the inverse model (bicausal bond graph model). The structural analysis of the inverse model remains interesting since the essential orders are immediately obtained on the bicausal model. A discussion is carried out regarding the duality between the causal and bicausal procedures.