Artículo

One Approach to the Time–Optimal Strategy Formulation for Analog Circuit Design

Alexander Zemliak¹, Eduardo Rios², Kirill Zemliak³

¹ Departamento de Física y Matemáticas, Universidad Autónoma de Puebla, México. E–mail: azemliak@fcfm.buap.mx

² Departamento de Electrónica, Universidad Autónoma de Puebla, México. E–mail: erios@ece.buap.mx

³ Departamento de Computación, Universidad Autónoma de Puebla, México. E–mail: kzemliak@yahoo.com

Abstract

The formulation of the process of analog system design has been done on the basis of the control theory application. This approach produces many different design strategies inside the same optimization procedure and allows determining the problem of the optimal design strategy existence from the computer time point of view. Different kinds of system design strategies have been evaluated from the operations number. This analysis shows that the traditional approach is not time–optimal at least for the electronic circuit design. General methodology for any analog system design was formulated by means of the optimum control theory. The main equations for this design methodology include the special control functions that are introduced to generalize the design process. The problem of the time–optimal design algorithm construction is defined as the minimal–time problem of the control theory. Numerical results of some nonlinear passive and active electronic circuit design demonstrate the efficiency of the proposed methodology.

Keywords: Time–optimal design strategy, control theory application, minimum–time problem.

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Acknowledgments

This work was supported partially by Universidad Autónoma de Puebla under the project No. VIEP III5G02.

References

1. Brayton R.K., G.D. Hachtel, and A.L. Sangiovanni–Vincentelli, "A survey of optimization techniques for integrated–circuit design", Proc. IEEE, vol. 69, pp. 1334– 1362, 1981.        [ Links ]

2. Bunch J.R., and D.J. Rose, Eds., Sparse Matrix Computations, Acad. Press, N.Y., 1976.        [ Links ]

3. Costello J., "Delivering Quality Delivers Profits", Plenary speech in 2001 IEEE 2^nd Int. Symp. on Quality Electronic Design, San Jose, CA, March 2001, p. 23.        [ Links ]

4. Duff I.S., and J.K. Reid, "Some Design Features of a Sparse Matrix Code", ACM Trans. on Mathematical Software, vol. 5, no. 1, pp. 18–35, 1979.        [ Links ]

5. Fedorenko, R.P., Approximate Solution of Optimal Control Problems, Nauka, Moscow, 1978.        [ Links ]

6. Fletcher, R., and C.M. Reeves, "Function Minimization by Conjugate Gradients", Comput. J., Vol. 7, 1964, pp. 149–154.        [ Links ]

7. Fletcher, R., and M.J.D. Powell, "A Rapidly Convergent Descent Method for Minimization", Comput. J., Vol 6, 1963, pp. 163–168.        [ Links ]

8. Fletcher R., Practical Methods of Optimization, John Wiley and Sons, N.Y., vol. 1, 1980, vol. 2, 1981.        [ Links ]

9. George A., "On Block Elimination for Sparse Linear Systems", SIAM J. Numer. Anal. vol. 11, no.3, 1984, pp. 585–603.        [ Links ]

10. Gill P.E., W. Murray, and M.H. Wright, Practical optimization, Academic Press, London, 1981.        [ Links ]

11. Hooke, R., and T.A. Jeeves, "Direct Search Solution of Numerical and Statistical Problems", JACM, Vol. 8, 1961, pp. 212–229.        [ Links ]

12. Krylov, I.A., and F.L. Chernousko, "Consecutive Approximation Algorithm for Optimal Control Problems", J. of Numer. Math. and Math. Pfysics, Vol 12, No. 1, 1972, pp. 14–34.        [ Links ]

13. Massara R.E., Optimization Methods in Electronic Circuit Design, Longman Scientific & Technical, Harlow, 1991.        [ Links ]

14. Neustadt, L.W., "Synthesis of Time–Optimal Control Systems", J. of Math. Analysis and Applications, Vol. 1, 1960, pp. 484–492.        [ Links ]

15. Osterby O., and Z. Zlatev, Direct Methods for Sparse Matrices, Springer–Verlag, N.Y., 1983.        [ Links ]

16. Pontryagin, L.S., V.G. Boltyanskii, R.V. Gamkrelidze, and E.F. Mishchenko, The Mathematical Theory of Optimal Processes. Interscience Publishers, Inc., New York, 1962.        [ Links ]

17. Rabat N., A.E. Ruehli, G.W. Mahoney, and J.J. Coleman, "A Survey of Macromodeling", IEEE Int. Symp. Circuits Systems, April 1985, pp. 139–143.        [ Links ]

18. Rosen J.B., "Iterative Solution of Nonlinear Optimal Control Problems", J. SIAM, Control Series A, 1966, pp. 223–244.        [ Links ]

19. Ruehli A., A. Sangiovanni–Vincentelli, and G. Rabbat, "Time Analysis of Large–Scale Circuits Containing One–Way Macromodels", IEEE Trans. Circuits Syst., vol. CAS– 29, no. 3, 1982, pp. 185–191.        [ Links ]

20. Ruehli A.E., and G. Ditlow, "Circuit Analysis, Logic Simulation and Design Verification for VLSI", Proc. IEEE, vol. 71, no. 1, 1983, pp. 36–68.        [ Links ]

21. Ruehli A.E., Ed., Circuit Analysis, Simulation and Design, vol. 3, part 2, Elsevier Science Publishers, Amsterdam, 1987.        [ Links ]

22. Sangiovanni –Vincentelli A., L.K. Chen, and L.O. Chua, "An Efficient Cluster Algorithm for Tearing Large–Scale Networks ", IEEE Trans. Circuits Syst., vol. CAS–24, no. 12, 1977, pp. 709–717.         [ Links ]

23. Sepulchre R., M. Jankovic, and P.V. Kokotovic, Constructive Nonlinear Control, Springer–Verlag, N.Y., 1997.        [ Links ]

24. Slotine J.E., and W. Li, Applied Nonlinear Control, Englewood Cliffs, Prentice–Hall, NJ, 1991.        [ Links ]

25. Tabak D., and B.C. Kuo, "Applications of Mathematical Programming in the Design of Optimal Control Systems", Int. Journal of Control, Vol. 10, No. 5, 1969, pp. 548–552.        [ Links ]

26. Wu F.F., "Solution of Large–Scale Networks by Tearing", IEEE Trans. Circuits Syst., vol. CAS–23, no. 12, 1976, pp. 706–713.        [ Links ]

27. Zemliak A., "System Design Strategy by Optimum Control Theory Formulation", in 14th European Conf. on Circuit Theory and Design, Stresa, Italy, Aug. 1999, Vol. 2, 1371–1374.        [ Links ]

28. Zemliak A., "One Approach to Analog System Design Problem Formulation", in 2001 IEEE 2^nd Int. Symp. on Quality Electronic Design, San Jose, CA, March 2001, pp. 273–278.        [ Links ]