Realization-preserving structure and order reduction of nonlinear energetic system models using energy trajectory correlations

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Volumn 131, Issue 3, 2009, Pages 1-8

  Ersal, Tulga ^a   Fathy, Hosam K ^a   Stein, Jeffrey L ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Bond graphs; Karhunen Lo ve expansion; Model order structure reduction; Nonlinear systems

Indexed keywords

BOND GRAPH; DYNAMIC SYSTEM MODELS; ENERGY TRAJECTORY; MODEL COMPONENTS; MODEL ORDER; ORDER REDUCTION; RELATIVE IMPORTANCE; SIMULTANEOUS MODEL; STATE TRANSFORMATION; STRUCTURAL REDUCTION; SYSTEM MODELS;

EXPANSION; GRAPH THEORY; NONLINEAR SYSTEMS;

DYNAMICAL SYSTEMS;

EID: 77955909224     PISSN: 00220434     EISSN: 15289028     Source Type: Journal    
DOI: 10.1115/1.3072128     Document Type: Article

References (21)

1. Wilson, B. H., and Stein, J. L., 1995, "An Algorithm for Obtaining Proper Models of Distributed and Discrete Systems," ASME J. Dyn. Syst., Meas., Control, 117(4), pp. 534-540.
2. Skelton, R. E., and Yousuff, A., 1983, "Component Cost Analysis of Large Scale Systems," Int. J. Control, 37(2), pp. 285-304.
3. Moore, B. C., 1981, "Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction," IEEE Trans. Autom. Control, 26(1), pp. 17-32.
4. Shieh, L.-S., Chang, F.-R., and Yates, R. E., 1986, "The Generalized Matrix Continued-Fraction Descriptions and Their Application to Model Simplification," Int. J. Syst. Sci., 17(1), pp. 1-19.
5. Hutton, M. F., and Friedland, B., 1975, "Routh Approximations for Reducing Order of Linear, Time-Invariant Systems," IEEE Trans. Autom. Control, 20(3), pp. 329-337.
6. Shamash, Y., 1975, "Model Reduction Using the Routh Stability Criterion and the Pade Approximation Technique," Int. J. Control, 21(3), pp. 475-484.
7. Glover, K., 1984, "All Optimal Hankel-Norm Approximations of Linear Multivariable Systems and Their L-Infinity Error Bounds," Int. J. Control, 39(6), pp. 1115-1193.
8. Wilson, D. A., 1970, "Optimum Solution of Model-Reduction Problem," Proc. Inst. Electr. Eng., 117, pp. 1161-1165.
9. Hyland, D. C., and Bernstein, D. S., 1985, "The Optimal Projection Equations for Model Reduction and the Relationships Among the Methods of Wilson, Skelton, and Moore," IEEE Trans. Autom. Control, 30(12), pp. 1201-1211.
10. Lumley, J. L., 1967, "The Structure of Inhomogeneous Turbulent Flow," Atmospheric Turbulence and Radio Wave Propagation, A. M. Yaglom and V. I. Tatarski, eds., Nauka, Moscow, pp. 166-178.
11. Holmes, P., Lumley, J. L., and Berkooz, G., 1996, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, Cambridge.
12. Kokotovic, P., Khalil, H. K., and O'Reilly, J., 1986, Singular Perturbation Methods in Control: Analysis and Design, Academic, London.
13. Margolis, D. L., and Young, G. E., 1977, "Reduction of Models of Large Scale Lumped Structures Using Normal Modes and Bond Graphs," J. Franklin Inst., 304(1), pp. 65-79.
14. Fertis, D. G., 1995, Mechanical and Structural Vibrations, Wiley, New York.
15. Ersal, T., Fathy, H. K., Louca, L. S., Rideout, D. G., and Stein, J. L., 2008, "A Review of Proper Modeling Techniques," ASME J. Dyn. Syst., Meas., Control, 130(6), pp. 061008.
16. Rosenberg, R. C. and Zhou, T., 1988, "Power-Based Model Insight," Proceedings of Automated Modeling for Design, Chicago, IL, Nov. 27-Dec. 2 1988, American Society of Mechanical Engineers (ASME), New York, Vol. 8, pp. 61-67.
17. Louca, L. S., Stein, J. L., Hulbert, G. M., and Sprague, J., 1997, "Proper Model Generation: An Energy-Based Methodology," Proceedings of 1997 International Conference on Bond Graph Modeling, Phoenix, AZ, Vol. 29, pp. 44-49.
18. Rideout, D. G., Stein, J. L., and Louca, L. S., 2004, "System Partitioning and Physical-Domain Model Reduction Through Assessment of Bond Graph Junction Structure," Proceedings of IMAACA '04, Bond Graph Techniques for Modeling Dynamic Systems, Genoa, Italy, Oct. 28-30.
19. Ersal, T., Fathy, H. K., and Stein, J. L., 2009, "Structural Simplification of Modular Bond-Graph Models Based on Junction Inactivity," Simul. Model. Pract. Theory, 17(1), pp. 175-196.
20. Ersal, T., Fathy, H. K., and Stein, J. L., 2009, "Orienting Body Coordinate Frames Using Karhunen-Loève Expansion for More Effective Structural Simplification," Simul. Model. Pract. Theory, 17(1), pp. 197-210.
21. Karnopp, D., and Rosenberg, R. C., 1975, System Dynamics: A Unified Approach, Wiley. New York.