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.
Issue Section:
Research Papers
References
1.
Cremer
, M.
, 1971
, “A Precompensator of Minimal Order for Decoupling a Linear Multi-Variable System
,” Int. J. Control
, 14
(6
), pp. 1089
–1103
.10.1080/002071771089321172.
Commault
, C.
, Descusse
, J.
, Dion
, J. M.
, Lafay
, J. F.
, and Malabre
, M.
, 1986
, “New Decoupling Invariants: The Essential Orders
,” Int. J. Control
, 44
(3
), pp. 689
–700
.10.1080/002071786089336273.
Dion
, J. M.
, and Commault
, C.
, 1982
, “Smith-McMillan Factorizations at Infinity of Rational Matrix Functions and Their Control Interpretation
,” Syst. Control Lett.
, 1
, pp. 312
–320
.10.1016/S0167-6911(82)80029-74.
Vardulakis
, A. I. G.
, Limebeer
, D. J. N.
, and Karcanias
, N.
, 1982
, “Structure and Smith-MacMillan Form of a Rational Matrix at Infinity
,” Int. J. Control
, 35
(4
), pp. 701
–725
.10.1080/002071782089226495.
Lafay
, J. F.
, Zagalak
, P.
, Herrera
, A.
, Icart
, S.
, 1990
, “Structural Results About the Interactor
,” Proceedings of the 29th IEEE
Conference on Decision and Control, Vol. 2
, pp. 1048
–1049
.10.1109/CDC.1990.2037606.
Herrera
, A. N.
, and Lafay
, J. F.
, 1993
, “New Results About Morgan’s Problem
,” IEEE Trans. Autom. Control
, 38
(12
), pp. 1834
–1838
.10.1109/9.2505617.
Commault
, C.
, and Dion
, J. M.
, 1982
, “Structure at Infinity of Linear Multivariable Systems: A Geometric Approach
,” IEEE Trans. Autom. Control
, 27
(3
), pp. 693
–696
.10.1109/TAC.1982.11029998.
Descusse
, J.
, Lafay
, J. F.
, and Malabre
, M.
, 1985
, “Solution of the Static-State Feedback Decoupling Problem for Linear Systems With Two Outputs
,” IEEE Trans. Autom. Control
, 30
(9
), pp. 914
–918
.10.1109/TAC.1985.11040899.
Descusse
, J.
, Lafay
, J. F.
, and Malabre
, M.
, 1988
, “Solution to Morgan Problem
,” IEEE Trans. Autom. Control
, 33
(8
), pp. 732
–739
.10.1109/9.128910.
van der Woude
, J. W.
, 1991
, “On the Structure at Infinity of a Structured System
,” Linear Algebra Appl.
, 148
, pp. 145
–169
.10.1016/0024-3795(91)90091-A11.
Dion
, J. M.
, and Commault
, C.
, 1993
, “Feedback Decoupling of Structured Systems
,” IEEE Trans. Autom. Control
, 38
(7
), pp. 1132
–1135
.10.1109/9.23147112.
Karcanias
, N.
, Sagianos
, E.
, and Milonidis
, E.
, 2005
, “Structural Identification: The Computation of the Generic McMillan Degree
,” Proceedings of the 44th IEEE
Conference on Decision and Control and European Control Conference, pp. 7222
–7227
.10.1109/CDC.2005.158332613.
Karcanias
, N.
, Sagianos
, E.
, and Milonidis
, E.
, 2007
, “Structured Transfer Function Matrices and Integer Matrices: The Computation of the Generic McMillan Degree and Infinite Zero Structure
,” Int. J. Control
, 80
(9
), pp. 1404
–1420
.10.1080/0020717070131663214.
Reinschke
, K. J.
, 1988
, Multivariable Control: A Graph-Theoretic Approach (Lecture Notes in Control Information Sciences)
, Springer-Verlag, Berlin
.15.
Rahmani
, A.
, Sueur
, C.
, and Dauphin-Tanguy
, G.
, 1992
, “Formal Determination of Controllability/Observability Matrices for Multivariable Systems Modelled by Bond Graph
,” Proceedings of IMACS/SICE International Symposium of Robotics, Mechatronics and Manufacturing Systems,
pp. 573
–580
.16.
Wu
, S. T.
, and Youcef-Toumi
, K.
, 1995
, “On Relative Degrees and Zero Dynamics From Physical System Modeling
,” ASME J. Dyn. Sys., Meas., Control
, 117
(2
), pp. 205
–217
.10.1115/1.283518117.
Rahmani
, A.
, Sueur
, C.
, and Dauphin-Tanguy
, G.
, 1996
, “On the Infinite Structure of Systems Modelled by Bond Graph: Feedback Decoupling
,” IEEE
International Conference on Systems, Man and Cybernetics, Vol. 3
, pp. 1617
–1622
.10.1109/ICSMC.1996.56533718.
Bertrand
, J. M.
, Sueur
, C.
, and Dauphin-Tanguy
, G.
, 1997
, “On the Finite and Infinite Structures of Bond-Graph Models
,” Proceedings of the IEEE
Conference on Computational Cybernetics and Simulation, Vol. 3
, pp. 2472
–2477
.10.1109/ICSMC.1997.63530219.
Murota
, K.
, 2000
, Matrices and Matroids for Systems Analysis (Algorithms and Combinatorics)
, Vol. 20
, Springer-Verlag, Berlin
.20.
Brockett
, R. W.
, 1965
, “Poles, Zeros, and Feedback: State Space Interpretation
,” IEEE Trans. Autom. Control
, 10
, pp. 129
–135
.10.1109/TAC.1965.109811821.
Dauphin-Tanguy
, G.
, 2000
, Les Bond Graphs,
Hermès Sciences
, Paris
.22.
Descusse
, J.
, and Dion
, J. M.
, 1982
, “On the Structure at Infinity of Linear Square Decoupled Systems
,” IEEE Trans. Autom. Control
, 27
(4
), pp. 971
–974
.10.1109/TAC.1982.110304123.
Gilbert
, E. G.
, 1969
, “Decoupling of Multivariable Systems by State Feedback
,” SIAM J. Control
, 7
(1
), pp. 50
–63
.10.1137/030700424.
Ngwompo
, R. F.
, Scavarda
, S.
, and Thomasset
, D.
, 1997
, “Structural Inversibility and Minimal Inversion of Multivariable Linear Systems—A Bond Graph Approach
,” Simul. Counc. Proc. Ser.
, 29
(1
), p. 109
.25.
Ngwompo
, R. F.
, and Scavarda
, S.
, 1999
, “Dimensioning Problems in System Design Using Bicausal Bond Graphs
,” Simul. Pract. Theory
, 7
(5–6
), pp. 577
–587
.10.1016/S0928-4869(99)00013-026.
Ngwompo
, R. F.
, and Gawthrop
, P. J.
1999
, “Bond Graph-Based Simulation of Non-Linear Inverse Systems Using Physical Performance Specifications
,” J. Franklin Inst.
, 336
(8
), pp. 1225
–1247
.10.1016/S0016-0032(99)00032-027.
Ngwompo
, R. F.
, Scavarda
, S.
, and Thomasset
, D.
, 2001
, “Physical Model-Based Inversion in Control Systems Design Using Bond Graph Representation, Part 1: Theory
,” Proc. ImechEJ. Syst. Control Eng.
, 215
(12
), pp. 95
–103
.10.1243/095965101154088828.
Gawthrop
, P. J.
, 1995
, “Bicausal Bond Graphs
,” Proceedings of the, International Conference on Bond Graph Modeling and Simulation (ICBGM’95),
pp. 83
–88
.29.
Gawthrop
, P. J.
1997
, “Bicausal Bond Graphs
,” Proceedings of the International Conference on Bond Graph Modeling and Simulation (ICBGM’97),
pp. 97
–102
.30.
El Feki
, M.
, Di Loreto
, M.
, Bideaux
, E.
, Thomasset
, D.
, and Ngwompo
, R. F.
, 2008
, “Structural Properties of Inverse Models Represented by Bond Graph
,” Proceedings of the 17th IFAC World Congress
, Vol. 17
, pp. 236
–241
.31.
El Feki
, M.
, Di Loreto
, M.
, Bideaux
, E.
, Thomasset
, D.
, and Marquis-Favre
, W.
, 2008
, “On the Role of Essential Orders on Feedback Decoupling and Model Inversion: Bond Graph Approach
,” Proceedings of the European Conference of Modelling and Simulation (ECMS’08),
pp. 457
–463
.32.
Sueur
, C.
, and Dauphin-Tanguy
, G.
, 1992
, “Poles and Zeros of Multivariable Linear Systems: A Bond Graph Approach
,” Bond Graph for Engineers,
Elsevier Science Publishers B.V.
, Amsterdam
, pp. 211
–228
.33.
Karnopp
, D. C.
, Margolis
, D. L.
, and Rosenberg
, R. C.
, 2006
, System Dynamics: Modeling and Simulation of Mechatronic Systems,
4th ed., John Wiley & Sons
, Hoboken, NJ
.34.
Jardin
, A.
, El Feki
, M.
, Marquis-Favre
, W.
, Thomasset
, D.
, and Bideaux
, E.
, 2008
, “Use of Structural Analysis in a Bond Graph-Based Methodology for Sizing Mechatronic Systems
,” Proceedings of the 7th edition of France-Japan, and 5th Europe-Asia Congress on Mechatronics
.35.
Ngwompo
, R. F.
, Bideaux
, E.
, and Scavarda
, S.
, 2005
, “On the Role of Power Lines and Causal Paths in Bond Graph-Based Model Inversion
,” Proceedings of the International Conference on Bond Graph Modeling and Simulation (ICBGM’05),
pp. 78
–85
.36.
Glumineau
, A.
, and Moog
, C. H.
, 1992
, “Nonlinear Morgan’s Problem: Case of (p + 1) Inputs and p Outputs
,” IEEE Trans. Autom. Control
, 37
(7
), pp. 1067
–1072
.10.1109/9.14837537.
Wonham
, W. M.
, 1979
, Linear Multivariable Control: A Geometric Approach,
Springer-Verlag
, Berlin
.38.
Eldem
, V.
, 1994
, “The Solution of Diagonal Decoupling Problem by Dynamic Output Feedback: The General Case
,” IEEE Trans. Autom. Control
, 39
(3
), pp. 503
–511
.10.1109/9.28074939.
Rahmani
, A.
, 1993
, “Etude structurelle des systèmes lineaires par l’approche Bond Graph
,” Ph.D. thesis
, Université des Sciences et Technologies de Lille
, France
.40.
Achir
, A.
, Junco
, S.
, Donaire
, A.
, and Sueur
, C.
, 2006
, “A Bond-Graph Method for Flatness-Based Dynamic Feedback Linearization Controller Synthesis: Application to a Current-Fed Induction Motor
,” Proceedings of the European Conference of Modelling and Simulation (ECMS ‘06).
41.
Glumineau
, A.
, and Moog
, C. H.
, 1989
, “Essential Orders and the Non-Linear Decoupling Problem
,” Int. J. Control
, 50
(5
), pp. 1825
–1834
.10.1080/0020717890895346842.
Achir
, A.
, and Sueur
, C.
, 2005
, “Non Commutative Ring Bond Graphs: Application to Flatness
,” Proceedings of the International Conference on Bond Graph Modeling and Simulation (ICBGM’05)
, Vol. 37
, pp. 59
–64
.43.
Lichiardopol
, S.
, and Sueur
, C.
, 2006
, “Decoupling of Non-Linear Bond-Graph Models
,” Proceedings of the IEEE
International Conference on Control Applications, pp. 2237
–2242
.10.1109/CACSD-CCA-ISIC.2006.4776988Copyright © 2012 by ASME
You do not currently have access to this content.