In a variety of fields, system inversion is often required in order to determine inputs from measured or for desired outputs. However, inverse systems are often non-proper in the sense that they require differentiators in their realization. This leads to numerical difficulties associated with the computer implementation of their mathematical models. To overcome these problems, approximate inversion (also referred to as filtered inversion) is proposed for systems modelled by bond graphs. Generic configurations of right and left filtered inverse bond graph models are proposed with dynamic structural conditions on the filters so that the resulting composite bond graph represents a proper system suitable for effective numerical implementation.
BrockettR. W.MesarovicM. D.The reproducibility of multivariable systems. J. Math. Anal. Appl., 1965, 11, 548–563.
2.
SilvermanL. M.Inversion of multivariable linear systems. IEEE Trans. Automat. Contr., 1969, AC-14(3), 270–276.
3.
SainM. K.MasseyJ. L.Invertibility of linear time-invariant dynamical systems. IEEE Trans. Automat. Contr., 1969, AC-14(2), 141–149.
4.
SerajiH.Minimal inversion, command matching and disturbance decoupling in multivariable systems. Int. J. Contr., 1989, 49(6), 2093–2121.
5.
YeY.WangD.Clean system inversion learning control law. Automatica, 2005, 41(9), 1549–1556.
6.
NgwompoR. F.ScavardaS.ThomassetD.Physical model-based inversion in control systems design using bond graph representation – part 2: applications. Proc. IMechE, Part I: J. Systems and Control Engineering, 2001, 215(I2), 105–112.
7.
ThomsonD.BradleyR.Inverse simulation as a tool for flight dynamics research – principles and applications. Prog. Aero. Sci., 2006, 42(3), 174–210.
8.
YoshikawaT.SugieT.Filtered inverse systems. Int. J. Contr., 1986, 43(6), 1661–1671.
9.
YamadaK.WatanabeK.ShuZ. B.A specification-based design method of stable filtered inverse systems and its application to H2 suboptimal internal model control. In Proceedings of 13th Triennial IFAC World Congress, San Francisco, USA, 1996, 379–384.
10.
KarnoppD. C.MargolisD. L.RosenbergR. C.System dynamics: a unified approach, 1990 (John Wiley, New York).
11.
GawthropP. J.SmithL.Metamodelling: bond graphs and dynamic systems, 1996 (Prentice Hall, Hemel Hempstead, UK).
12.
GawthropP. J.Bicausal bond graphs. In Proceedings of 1995 International Conference on Bond graph modelling and simulation (ICBGM’95), simulation series, 27 (Eds CellierF. E.GrandaJ. J.), Las Vegas, 1995, pp. 83–88 (Society for Computer Simulation).
13.
GawthropP. J.Physical interpretation of inverse dynamics using bicausal bond graphs. J. Franklin Inst., 1999, 337, 743–769.
14.
NgwompoR. F.ScavardaS.ThomassetD.Physical model-based inversion in control systems design using bond graph representation – part 1: theory. Proc. IMechE, Part I: J. Systems and Control Engineering, 2001, 215(I2), 95–103.
15.
NgwompoR. F.GawthropP. J.Bond graph based simulation of nonlinear inverse systems using physical performance specifications. J. Franklin Inst., 1999, 336(8), 1225–1247.
16.
BonillaM.MalabreM.FonsecaM.On the approximation of non-proper control laws. Int. J. Contr., 1997, 68(4), 775–796.
17.
PachecoM. J.BonillaM. E.MalabreM.Proper exponential approximation of non-proper compensators: the MIMO case. In Proceedings of 42nd IEEE Conference on Decision and control, Maui, Hawaii, USA, December 2003, 1, pp. 110–115.
18.
KamiyamaS.FurutaK.Integral invertibility of linear time invariant systems. Int. J. Contr., 1977, 25(3), 403–412.
19.
CommaultC.DescusseJ.DionJ. M.LafayJ. F.MalabreM.New decoupling invariants: the essential orders. Int. J. Contr., 1986, 44(3), 689–700.
20.
CremerM.A precompensator of minimal order for decoupling a linear multivariable systems. Int. J. Contr., 1971, 14(6), 1089–1103.
21.
MasseyJ. L.SainM. K.Inverses of linear sequential circuits. IEEE Trans. Comput., 1968, C-17(4), 330–337.
22.
El FekiM.Di LoretoM.BideauxE.ThomassetD.NgwompoR. F.Structural properties of inverse models represented by bond graph. In Proceedings of 17th World Congress (IFAC’08), Seoul, Korea, 6–11 July 2008.
23.
El FekiM.Di LoretoM.BideauxE.ThomassetD.Marquis-FavreW.On the role of essential orders on feedback decoupling and model inversion: bond graph approach. In Proceedings of 22nd European Conference on Modelling and simulation, Nicosia, Cyprus, June 2008 (Eds LoucaL. S.ChrysanthouY.OplatkovaZ.Al-BegainK.).
24.
BreedveldP. C.Elimination of time derivatives of sources inputs. In Proceedings of 2005 International Conference on Bond graph modelling and simulation, simulation series, 37(1) (Eds CellierF. E.GrandaJ. J.), New Orleans, 2005, pp. 39–42 (Society for Computer Simulation).
