Geneviève Dauphin-Tanguy

Bond graph aided design of controlled systems

Abstract An active or controlled system is generally composed of two parts: a passive basis and a control architecture containing actuators and sensors. When dealing with such a system, the first point usually considered is the study of the system without control. To do this, we need a model in order to get simulation-based results on the frequency domain and dynamical behaviour for dimensioning purpose. The second step is then to design a control architecture, with its actuators and sensors, specified in a way allowing the objectives to be reached as accurately and cheaply as possible. Since many years, the bond graph methodology has shown its qualities for modelling and generation of physical insight, specially when applied to multidisciplinary systems. The aim of this paper is to show how a bond graph model may be used for analysis of structural properties, i.e., properties depending only on the model structure and on the type of elements composing it, but not on the numerical values of the parameters. The properties pointed out in this way are generic, and can be used for “integrated design”, i.e., the simultaneous design of the passive system model, its control architecture and control laws for specific aims. The proposed methodology depends on causal manipulations on the bond graph model (assignment of integral and derivative causality, causal path and loops); its application may necessitate a return to the model in order to check and sometimes modify the modelling hypotheses. The proposed procedure is implemented on an example, which will be the guideline of the presentation.

Bond graph models of structured parameter uncertainties

Taking into account uncertainties in model parameter values is a crucial point for studying robustness in modeling and in control. This paper proposes to construct in a systematic and graphical procedure two forms of the linear state equation usually found in the literature for dealing with the robustness problem in the case of structured uncertainties on parameters. It is shown how to model uncertainties in a bond graph approach, in the case of additive or multiplicative parametric variations.

Bond graph modelling of a photovoltaic system feeding an induction motor-pump

Abstract Water pumping using induction motors has become one of the most feasible photovoltaic (PV) applications. A bond graph model to enable testing the PV system performance by computer simulation was developed. The PV-powered water pumping system investigated in this paper consists mainly of a PV generator, DC–DC and DC–AC converters, and induction motor-pump. The DC–DC converter control strategy is based on pulse width modulation (PWM). However, the oriented field control is used for the induction machine control. Computer simulations were carried out for maximum power point tracking (MPPT).

Pole assignment for systems modelled by bond graph

Abstract In this paper, the pole assignment problem is considered for linear systems modelled by bond graphs. A procedure for the formal determination of the controllability matrix is proposed. This matrix is used to transform the state and control matrices into a controllability form. It allows us to formally assign the poles of the system.

Proportional-integral observer for systems modelled by bond graphs

Abstract In the present work a bond graph approach to build full-order proportional–integral (PI) observers is shown. The proposed approach is based on the bond graph method defined for designing classical linear observers (Luenberger observers). The method is extended to build a second type of integral observers more robust to the presence of sensor noise. As application, the method is used over the pseudo bond graph model of a continuous stirred tank reactor (CSTR). Simulation results show the performance of the PI observers with respect to the presence of modelling errors and the robustness of integral observers when sensor noise is present.

Pseudo bond graph model of coupled heat and mass transfers in a plastic tunnel greenhouse

Abstract In greenhouses, models built are classified into two kinds; heterogeneous approaches based on computational fluid dynamics (CFD) codes and homogeneous one based on heat and mass balance equations. Bond graph modelling was not seriously introduced in greenhouse modelling in spite of the concordance of the energetic based approach of bond graphs with the nature of the greenhouse plant. In this research work, a pseudo bond graph model of a greenhouse was elaborated to simulate temperature and relative humidity inside. The model proposed is an energetic lumped approach which describes coupled heat and mass transfers in a plastic tunnel greenhouse. This model includes convection, evaporation/condensation phenomena, air change flow and soil heat and mass transfer. Multiport (3 ports) bond graph elements are introduced to describe the state of the two elements (dry air and water vapor) fluid. New bond graph schemes are used to characterize the coupling effect between heat and mass transfer, and for modelling free evaporation/condensation mechanism. Big leaf assumption was used to model the canopy. New boundary layer elements are added in the model, these elements allow a separation of the different phenomena inside greenhouse and thus a simplification of the modelling task. The practical results obtained from an experimental tunnel greenhouse are used here as validation elements for the greenhouse bond graph model. A good correlation is observed between measured and predicted samples.

Incremental bond graph approach to the derivation of state equations for robustness study

Aiming at an automated bond graph based determination of unnormalized frequency domain sensitivities in symbolic form Borutzky and Granda proposed the systematic construction of a so-called incremental bond graph from an initial bond graph for the increments ðDeÞðtÞ, ðDf ÞðtÞ of power variables eðtÞ and f ðtÞ associated with each bond. This paper shows that the incremental bond graph can serve also as a starting point for setting up symbolically the canonical form as well as the standard interconnection form of state equations used for robustness study. The approach applicable to general linear time-invariant systems is illustrated by means of a fairly small example. 2003 Elsevier B.V. All rights reserved.

Controllability indices for structured systems

Abstract A new methodology is proposed for the characterization of the controllability indices of linear multivariable systems. Related to the state space representation, a new symbolism dealing only with numbers associated with the position of nonnull terms of matrices is proposed. This symbolism, associated with the graphical digraph representation model, allows one to highlight, from a structural point of view, a list of dimensions of controllable subspaces corresponding one to one with the list of controllability indices.

Luenberger observers for linear time-invariant systems modelled by bond graphs

This paper shows how to build Luenberger observers for linear time-invariant systems modelled by bond graph. The methods are based on Luenbergers algebraic methods to design both full-order and reduced-order observers. The procedure for reduced-order observers uses the bicausality concept to simplify some classical matrix calculations (the calculation of matrix inverses is not needed), which is an important improvement mainly for large-scale systems. The calculation of the observer gains is based on the pole-placement techniques for linear systems modelled by bond graphs. As an application, both observers are designed for a vehicle suspension modelled by bond graphs.

How to derive a bond graph model from a transfer matrix

Abstract A methodology is presented based on the alpha-beta expansion, so as to derive a bond graph model from any transfer function (resp. matrix) found, most of the time, using special techniques for the identification of dynamical systems. The object is to take advantage of the whole set of bond graph techniques for structural analysis, sensors assignment, model reduction and control.