C. Sueur

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.

Duality in system analysis for bond graph models

Duality as a general notion has been discussed previously in multiple domains. The field of system modeling, analysis and control has used it for quite some time. The duality between the controllability and the observability is well known, especially in the case of the linear time-invariant systems. But when it comes to the linear systems in general, time-invariant or otherwise, the definitions become ambiguous. Even though there have been papers which use the state space representation or the module theoretical approach, a unified description has not been found yet. This paper is meant to fill in this gap, by using the bond graph representation. The bond graph perspective offers a global overview because the bond graph is a graphical tool which can be seen both as a state space representation and as a module.

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.

Bond Graph and Flatness-Based Control of a Salient Permanent Magnetic Synchronous Motor

Abstract This paper deals with flatness-based control of a salient permanent-magnet synchronous motor in the bond graph (BG) domain. It develops two main points. The first proposes and develops a new flat outputs identification procedure valid for multiple-input non-linear BG models without elements in derivative causality assignment. This procedure exploits a variational (tangent) BG model obtained by using Kähler differentials. The second deals with control design based on physical system decomposition into electrical, mechanical, and coupling submodels. Each loop of the decomposition tracks a reference for the local flat output of the corresponding subsystem. This decomposition enables the designing of a control block for each submodel by means of system inversion using the concept of bicausality. Then, the resulting blocks are concatenated in order to build the global controller. Finally, the global stability of the feedback system for both cases (known and unknown load torques) is tested and the control scheme is assessed through simulations in order to illustrate the performances of the method.

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.

Unknown Input Observer for control design: a bond graph approach

Abstract The objective of this paper is the development of a bond graph approach for the control of linear systems subject to unknown inputs (disturbances or failures) with a new unknown input observer. At the analysis step, a causal approach is proposed and intrinsic solvability conditions which do not require the knowledge of the value of parameters are given. The synthesis of the estimator is proposed with formal calculus. A DC motor example is studied with a flatness based control with the estimation of an unknown load.

Infinite zero of linear time varying bond-graph models : Graphical rules

The study of the infinite structure of linear time varying systems modeled by bond-graph is proposed in the paper. Firstly, a new bond-graph ring model is presented and the correspondence between the bond graph ring model and the module theory is proposed. Secondly, the Riegle rule is used in order to obtain the input-output representation. Graphical rules are proposed to study the infinite structure of the model. Finally, one application on a thyristor circuit model TCSC used in the power electronics is achieved, showing the efficiency and the simplicity of the approach.

FLATNESS BASED CONTROL OF LINEAR TIME VARYING BOND GRAPHS

Abstract A general flatness based control design and parametrization procedure for single input time varying systems modelled by bond graphs is presented. The methodology is introduced in an algebraic framework provided by differential rings and modules theory. The method is applied to a flatness based control design of separately excited DC motor.

Bond-Graph Modeling and Geometric Approach: Input-Output Decoupling with Stability

Abstract In this paper, the geometric approach and the bond-graph methodology are combined to characterize the structure of square linear systems modeled by bond-graph. A new concept is thus defined to emphasize the symbolic expressions of the fixed modes of the decoupled model and to design decoupling state feedbacks.

Flat control of a torsion bar with unknown input estimation

The main purpose of this paper is to design a flat control of a real torsion bar system subject to unknown input variables using the concept of unknown input observer. The bond graph approach is used due to its structural and causal properties. Three main points are developed: modeling of the dynamical system with model simplification using an integrated approach, application of an unknown input observer with estimation of physical variables and application of a flat control on the experimental system.