Nonlinear Model Reduction for Dynamic and Automotive System Descriptions

[+] Author and Article Information
Zeyu Liu, John Wagner

Automotive Research Laboratory, Department of Mechanical Engineering, 212 Fluor Daniel Engineering Building, Clemson University, Clemson, SC 29634-0921

J. Dyn. Sys., Meas., Control 124(4), 637-647 (Dec 16, 2002) (11 pages) doi:10.1115/1.1515327 History: Received June 01, 2001; Revised January 01, 2002; Online December 16, 2002
Copyright © 2002 by ASME
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Mizutani, S., 1992, Car Electronics, Sankaido Co., LTD.
Setlur, P., Wagner, J., Dawson, D., and Samuels, B., 2001, “Modeling and Control of a Continuously Variable Power Split Transmission,” Proc. of American Control Conference, Arlington, VA, June.
Kelly,  D., and Shannon,  G., 1990, “Automotive Electronics and Engine Management Systems-A Review,” J. Electr. Electron. Eng., Aust., 10(4), pp. 286–299.
Watanabe,  K., and Tumer,  M., 1984, “Automotive Engine Calibration System Using Microcomputer,” IEEE Trans. Veh. Technol., 33(2), pp. 45–50.
Skogestad, S., and Postlethwaite, I., 1996, Multivariable Feedback Control-Analysis and Design, John Wiley and Sons, New York.
Fortuna, L., Nunnari, G., and Gallo, A., 1992, Model Order Reduction Techniques With Applications in Electric Engineering, Springer-Verlag, London.
Van Woerkom,  P., 1990, “Mathematical Models of Flexible Spacecraft Dynamics: A Survey of Order Reduction Approaches,” Control Theory and Advanced Technology, 6(4), pp. 609–632.
Hahn, J., and Edgar, T. F., 2000, “Reduction of Nonlinear Models using Balancing of Empirical Gramians and Galerkin Projections,” Proc. of American Control Conf., Chicago, IL, June.
Scherpen,  J. M. A., 1993, “Balancing for Nonlinear Systems,” Systems and Controls, 21(2), pp. 143–153.
Shamash,  Y., 1975, “Model Reduction Using Routh Stability Criterion and the Pade Approximation Technique,” Int. J. Control, 21(3), pp. 275–484.
Shamash, Y., 1973, “Order Reduction of Pade Approximation Methods,” Ph.D Thesis, Imperial College of Science and Technology, Univ. of London.
Pal,  J., 1979, “Stable Reduced-Order Pade Approximants Using the Routh-Hurwitz Array,” Electron. Lett., 15(8), pp. 25–226.
Goldman,  M. J., Porrasm,  W. J., and Leondes,  C. T., 1981, “Multivariable Systems Reduction via Cauer Forms,” Int. J. Control, 34(4), pp. 623–650.
Chen,  C. F., 1994, “Model Reduction of Multivariable Control Systems by Means of Matrix Continued Fractions,” Int. J. Control, 20(2), pp. 225–238.
Hutton,  M. F., and Friedland,  B., 1975, “Routh Approximation for Reducing Order of Linear, Time-Invariant Systems,” IEEE Trans. Autom. Control, 20(3), pp. 329–337.
Shieh,  L. S., and Gaudiano,  F. F., 1974, “Matrix Continued Fraction Expansion and Inversion by the Generalized Matrix Routh Algorithm,” Int. J. Control, 20(5), pp. 727–737.
Aoki,  M., 1978, “Some Approximation Methods for Estimation and Control of Large Scale Systems,” IEEE Trans. Autom. Control, 23(2), pp. 173–182.
Jamashidi, M., 1981, “An Overview on the Aggregation on Large-Scale Systems,” Proc. of IFAC World Congress, Kyoto, Japan.
Siret,  J. M., Michailesco,  G., and Bertrand,  P., 1977, “Representation of Linear Dynamic Systems by Aggregation Models,” Int. J. Control, 26(1), pp. 121–128.
Moore,  B. C., 1981, “Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction,” IEEE Trans. Autom. Control, 26(1), pp. 17–32.
Pernebo,  L., and Silverman,  L. M., 1982, “Model Reduction via Balanced State-Space Representation,” IEEE Trans. Autom. Control, 27(2), pp. 382–387.
Kokotovic,  P. V., and Sannuti,  P., 1986, “Singular Perturbation Method for Reducing the Model Order in Optimal Control Design,” IEEE Trans. Autom. Control, 13(4), pp. 145–156.
Wilson,  D. A., and Mishra,  R. N., 1979, “Optimal Reduction of Multivariable Systems,” Int. J. Control, 29(2), pp. 267–278.
Glover,  K., 1984, “All Optimal Hankel-Norm Approximations of Linear, Multivariable Systems and Their L Error Bounds,” Int. J. Control, 39(6), pp. 1115–1193.
Louca, L., and Stein, J., 1999, “Energy-based Model Reduction of Linear Systems,” Proc. of Int. Conf. on Bond Graph Modeling and Simulation, San Francisco, CA.
Desrocher,  A. A., and AI-Jaar,  R. Y., 1985, “A Method for High Order Linear System Reduction and Nonlinear Signification,” Automatica, 21(1), pp. 93–100.
Lall, S., Marsden, J., and Glavaski, S., 1999, “Empirical Model Reduction of Controlled Nonlinear Systems,” Proc. of 14th IFAC World Congress, Beijing, China.
Ma, X., and Abram-Garcia, J. A., 1998, “On the Computation of Reduced Order Models of Nonlinear Systems Using Balancing Techniques,” Proc. of 27th IEEE CDC, Austin, TX.
Milnor, J., 1969, Morse Theory, Princeton University Press.
Newman, A., and Krishnaprasad, P. S., 2000, “Computing Balanced Realization for Nonlinear Systems,” 14th Int. Symp. of Mathematical Theory Networks and Systems, Perpignan, France.
Liu, Z., and Wagner, J., 2001, “Nonlinear Model Reduction in Automotive System Component Descriptions,” Proc. of ASME IMECE DSC Division, New York, NY.
Redfield,  R. C., and Karnopp,  D. C., 1989, “Performance Sensitivity of an Actively Damped Vehicle Suspension to Feedback Variation,” ASME J. Dyn. Syst., Meas., Control, 111(1), pp. 51–59.
Khalil, H. K., 1996, Nonlinear Systems, Prentice Hall, NJ.
Karnopp,  D. C., 1983, “Active Damping in Road Vehicle Suspension Systems,” Veh. Syst. Dyn., 12(6), pp. 291–312.
Butler, K. R., and Wagner, J. R., 1994, “A Strategy to Demonstrate the Compliance of Automotive Controller Software to Systems Requirements,” SAE Paper No. 940492.
Vaughan,  N., and Gamble,  J., 1996, “The Modeling and Simulation of a Proportional Solenoid Valve,” ASME J. Dyn. Syst., Meas., Control, 118(1), pp. 120–125.
Palm, W. J., 1999, Modeling, Analysis, and Control of Dynamic Systems, John Wiley and Sons.
Kotwicki, A. J., and Russell, J., 1998, “Vacuum EGR Valve Actuator Model,” SAE Paper No. 981438.


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Powertrain control systems functions
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Model reduction strategies for linear and nonlinear systems
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Balanced realization based model reduction method
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Empirical gramian balancing method for nonlinear systems
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Vehicle suspension system with sprung and unsprung masses
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Comparison of the nonlinear and linearized full-order systems for the vehicle suspension (solid: nonlinear; dashed: linearized)
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Transient response of the linearized full-order and reduced-order systems for the vehicle suspension (solid: full-order; dashed: reduced-order)
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Summary of the vehicle suspension system transient responses (solid:full-order nonlinear; dashed: reduced nonlinear; dash-dot: reduced linear)
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Exhaust gas recirculation (EGR) valve schematic
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Comparison of the nonlinear and linearized full-order systems for the EGR valve (solid: nonlinear; dashed: linearized)
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Transient response of the linearized full-order and reduced order systems for the EGR valve (solid: full-order; dashed: reduced-order)
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Summary of the exhaust gas recirculation valve transient responses (solid: full-order nonlinear; dotted: reduced nonlinear; dash-dot: reduced linear)



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