A new two-step iterative method for optimal reduction of linear SISO systems

Journal of the Franklin Institute

Volumn 333, Issue 5, 1996, Pages 631-645

  Hwang, Chyi ^a   Hwang, Jyh Haur ^a  

^a NATIONAL CHUNG CHENG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; LINEAR CONTROL SYSTEMS; MATHEMATICAL MODELS; OPTIMIZATION; POLYNOMIALS; VECTORS;

GRADIENT BASED SEARCH TECHNIQUE; LINEAR TIME INVARIANT SINGLE INPUT SINGLE OUTPUT SYSTEMS; NUMERATOR DYNAMICS; OPTIMAL REDUCED ORDER MODELING; ROUTH STABILITY PARAMETERS;

ITERATIVE METHODS;

EID: 0030243853     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/0016-0032(96)00049-X     Document Type: Article

References (41)

1. M. Bosley and F. Lees, "A survey of simple transfer function derivations from high-order state-variable models", Automatica, Vol. 8, No. 6, pp. 765-775, 1972.
2. M. Decoster and A. R. van Cauwenberghe, "A comparative study of different reduction methods", Pt. I, Journal A, Vol. 17, pp. 68-74; Pt,. II, Journal A, Vol. 17, pp. 125-134, 1976.
3. M. Decoster and A. R. van Cauwenberghe, "A comparative study of different reduction methods", Pt. I, Journal A, Vol. 17, pp. 68-74; Pt,. II, Journal A, Vol. 17, pp. 125-134, 1976.
4. R. Genesio and M. Milanese, "A note on the derivation and use of reduced-order models", IEEE Trans. Automat. Contr., Vol. AC-21, pp. 118-122, 1976.
5. A. Bultheel and M. van Barel, "Padé techniques for model reduction in linear system theory: A survey", J. Comput. and Appl. Math., Vol. 14, pp. 401-438, 1986.
6. D. J. Davison, "A method for simplifying linear dynamic systems", IEEE Trans. Automat. Contr., Vol. AC-11, No. 1, pp. 93-101, 1966.
7. S. A. Marshall, "An approximate method for reducing the order of a linear system", Control, Vol. 10, pp. 642-643, 1966.
8. S. C. Chuang, "Homographic transformation for the simplification of discrete-time transfer functions by Padé approximation", Int. J. Control, Vol. 22, No. 5, pp. 721-728, 1975.
9. S. C. Chuang, "Homographic transformation for the simplification of continuous-time transfer functions by Padé approximation", Int. J. Control, Vol. 23, No. 6, pp. 821-826, 1976.
10. C. F. Chen and L. S. Shieh, "A novel approach to model simplification", Int. J. Control, Vol. 8, pp. 561-570, 1968.
11. M. Bosley and F. P. Lees, "The reduction of the order of state variable models using the method of moments", Chem. Eng. Sci., Vol. 28, pp. 2071-2077, 1973.
12. F. P. Lees, "The derivation of simple transfer function models of oscillating and inverting processes from the basic transformed equations using the method of moments", Chem. Eng. Sci., Vol. 26, pp. 1179-1186, 1971.
13. M. F. Hutton and B. Friedland, "Routh approximations for reducing order of linear systems", IEEE Trans. Automat. Contr., Vol. AC-20, pp. 329-337, 1975.
14. A. S. Rao, S. S. Lamba and S. V. Rao, "Routh-approximant time-domain reduced-order modeling for single-input, single-output systems", Proc. IEE, Vol. 125, pp. 1059-1063, 1978.
15. B. C. Moore, "Principal component analysis in linear systems: controlability, observability, and model reduction", IEEE Trans. Automat. Contr., Vol. AC-26, pp. 17-32, 1981.
16. S. Y. Kung and D. W. Lin, "Optimal Hankel norm model reductions: multivariable systems", IEEE Trans. Automat. Contr., Vol. AC-26, pp. 832-852, 1981.
17. 2 error bounds", Int. J. Control, Vol. 39, pp. 1115-1193, 1984.
18. A. S. S. R. Reddy, "A method for frequency domain simplification of transfer functions", Int. J. Control, Vol. 23, pp. 403-408, 1976.
19. A. H. Whitfield and N. G. Williams, "Integral least-squares techniques for frequency-domain model reduction", Int. J. Systems Sci., Vol. 19, No. 8, pp. 1355-1371, 1988.
20. R. Luus, "Optimization in model reduction", Int. J. Control, Vol. 32, No. 5, pp. 741-747, 1980.
21. D. A. Wilson, "Optimum solution of model-reduction problems", Proc. IEE, Vol. 117, pp. 1161-1165, 1970.
22. N. K. Sinha and G. T. Bereznai, "Optimum approximation of high-order systems by low-order models", Int. J. Control, Vol. 14, No. 5, pp. 951-959, 1971.
23. J. Aplevich, "Approximation of discrete linear systems", Int. J. Control, Vol. 17, No. 3, pp. 565-575, 1973.
24. F. D. Galiana, "On the approximation of multiple input-multiple output constant linear systems", Int. J. Control, Vol. 17, No. 6, pp. 1313-1324, 1973.
25. J. Aplevich, "Gradient methods for optimal linear systems reduction", Int. J. Control, Vol. 18, No. 4, pp. 767-772, 1973.
26. D. A. Wilson, "Model reduction for multivariables systems", Int. J. Control, Vol. 20, No. 1, pp. 57-64, 1974.
27. J. Riggs and T. F. Edgar, "Least squares reduction of linear systems using impulse responses", Int. J. Control, Vol. 20, No. 2, pp. 213-223, 1974.
28. T. F. Edgar, "Least squares model reduction using unit step response", Int. J. Control, Vol. 22, No. 2, pp. 261-270, 1975.
29. G. Hirzinger and G. Kreisselmeier, "On optimal approximation of high-order linear systems by low-order models", Int. J. Control, Vol. 22, No. 3, pp. 399-408, 1975.
30. J. M. Siret, G. Michailesco and P. Bertrand, "Optimal approximation of high-order systems subject to polynomial inputs", Int. J. Control, Vol. 26, No. 6, pp. 963-971, 1977.
31. D. A. Wilson and R. N. Mishra, "Optimal reduction of multivariables systems", Int. J. Control, Vol. 29, No. 2, pp. 267-278, 1979.
32. F. F. Shoji, R. R. Mohler and T. C. Hsia, "Simplification of large linear systems using a two-step iterative method", J. of Franklin Inst., Vol. 310, No. 3, pp. 155-188, 1980.
33. F. F. Shoji, "Comments on 'Simplification of large linear systems using a two-step iterative method': A two-step projection algorithm", J. of Franklin Inst., Vol. 313, No. 5, pp. 267-271, 1982.
34. F. F. Shoji, K. Abe and H. Takeda, "A two-step iterative method for discrete-time systems reduction", J. of Franklin Inst., Vol. 315, No. 4, pp. 247-257, 1983.
35. S. A. Marshall, "System simplification and control system design: application of the two-step iterative algorithm of Shoji", J. of Franklin Inst., Vol. 316, No. 4, pp. 327-328, 1983.
36. A. E. Bryson, "Second-order algorithm for optimal model order reduction", J. Guidance, Control, and Dynamics, Vol. 13, No. 5, pp. 887-892, 1990.
37. C. Hwang, T. Y. Guo and L. S. Shieh, "Model reduction using new optimal Routh approximant technique", Int. J. Control, Vol. 55, No. 4, pp. 989-1007, 1992.
38. K. J. Aström, "Introduction to Stochastic Control Theory", Academic Press, New York, 1970.
39. C. Hwang and Y. H. Chuang, "Computation of optimal reduced-order models with time delay", Chem. Eng. Sci., Vol. 49, No. 19, pp. 3291-3296, 1994.
40. A. Talbot, "The evaluation of integrals of products of linear system responses, Part I", Quart. J. Mech. and Applied Math., Vol. 12, Pt. 4, pp. 488-502, 1959.
41. A. Talbot, "The evaluation of integrals of products of linear system responses, Part II. Continued-fraction methods", Quart. J. Mech. and Applied Math., Vol. 12, Pt. 4, pp. 503-520, 1959.