On Time-optimal procedure for analog system design

 

A. Zemliak, E. Rios, P. Miranda, K. Zemliak

 

Facultad de Ciencias Físico Matemáticas, Universidad Autónoma de Puebla Av. San Claudio y 18 sur s/n, Ciudad Universitaria, C.P. 72570, Puebla, Pue. México, Tel. 222-2295-500 Ext. 2123 E-Mail: azemliak@fcfm.buap.mx

 

Received: October 23^th, 2001.
Accepted: February 4^th, 2003.

 

Abstract

The process of any analog system design has been formulated 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. The general methodology for the analog system design was formulated by means of the optimum control theory. The main equations for this design methodology were elaborated. These equations include the special control functions that are introduced artificially. This approach generalizes the design process and generates an infinite number of the different design strategies. The problem of the optimum design algorithm construction is defined as the minimum-time problem of the control theory. Numerical results of some electronic circuit design demonstrate the efficiency and perspective of the proposed methodology. These examples show that the computer time gain of the optimal design strategy with respect to the traditional design strategy increases when the size and complexity of the system increase. An additional acceleration effect of the design process has been discovered by the analysis of various design strategies with the different initial points. This effect is displayed for all analyzed circuits and it reduces additionally the total computer time for the system design.

Keywords: Time-optimal system design, Control theory approach, acceleration effect.

 

Resumen

El proceso de diseño de un sistema análogo ha sido formulado en la base de aplicación de la teoría de control. Esta concepción produce varias estrategias del diseño dentro del mismo procedimiento de optimización y permite determinar el problema de existencia de una estrategia óptima de diseño de punto de vista en el tiempo de cómputo. Diferentes estrategias de diseño fueron evaluadas desde el punto de vista del número de operaciones. La metodología general del diseño de sistemas análogos fue desarrollada en la base de la teoría de control óptimo. Las ecuaciones principales de esta metodología fueron elaboradas. Estas ecuaciones incluyen las funciones de control especiales. Este enfoque generaliza el proceso de diseño y produce un número infinito de diferentes estrategias de diseño. El problema de la construcción de un algoritmo óptimo está definido como un problema de tiempo mínimo de la teoría de control óptimo. Los resultados numéricos del diseño de varios circuitos electrónicos muestran la eficiencia y la perspectiva de una nueva metodología. Estos ejemplos exponen que la ganancia del tiempo de cómputo para la estrategia óptima con respecto a la estrategia tradicional crece cuando el tamaño y la complejidad del sistema se aumentan. Un efecto de aceleración adicional del proceso de diseño ha sido descubierto en la base del análisis de diferentes estrategias con varios puntos iniciales. Este efecto aparece en todos los ejemplos analizados y puede reducir adicionalmente el tiempo total de diseño de sistemas.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Acknowledgments

This work was supported partially by the Universidad Autonoma de Puebla, under project VIEPIII05G02.

 

References

[1] Bunch J.R. and Rose D.J., (Eds), Sparse Matrix Computations, New York: Academic Press, 1976.         [ Links ]

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

[3] Osterby O. and Zlatev Z., Direct Methods for Sparse Matrices, New York: Springer-Verlag, 1983.         [ Links ]

[4] George A., "On Block Elimination for Sparse Linear Systems", SIAMJ. Numer. Anal Vol. 11, No.3, pp. 585-603. 1984.         [ Links ]

[5] Wu F.F., "Solution of Large-Scale Networks by Tearing", IEEE Trans. Circuits Syst., Vol. CAS-23, No. 12, pp. 706-713. 1976.         [ Links ]

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

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

[8] Ruehli A.E., Sangiovanni-Vincentelli A. and Rabbat G., "Time Analysis of Large-Scale Circuits Containing One-Way Macromodels", IEEE Trans. Circuits Syst., Vol. CAS-29, No. 3, pp. 185-191. 1982.         [ Links ]

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

[10] Fletcher R., Practical Methods of Optimization, New York: John Wiley and Sons, Vol. 1, 1980, Vol. 2, 1981.         [ Links ]

[11] Brayton R.K., Hachtel G.D. and Sangiovanni-Vincentelli A.L., "A survey of optimization techniques for integrated-circuit design", Proceedings IEEE, Vol. 69, pp. 1334-1362. 1981.         [ Links ]

[12] Ruehli A.E., (Ed.), Circuit Analysis, Simulation and Design, Vol. 3, part 2, Amsterdam: Elsevier Science Publishers, 1987.         [ Links ]

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

[14] Zemliak A., "System Design Problem Formulation by Control Theory", Proceedings of the IEEE Int. Symp. Circuits Systems, Sydney, Australia, May, Vol. 5, pp. 5-8. 2001.         [ Links ]

[15] Zemliak A., "General Methodology for System Design", in Modern Applied Mathematics Techniques in Circuits, Systems and Control, N. Mastorakis (ed), Athens: Word Scientific and Engineering Society Press, pp.150-155. 1999.         [ Links ]

[16] Zemliak A., "Analog System Design Problem Formulation by Optimum Control Theory", IEICE Trans, on Fundamentals of Electronics, Comunications and Computer Sciencies, Vol. E 84-A, No. 8, pp. 2029-2041. 2001.         [ Links ]

[17] Fletcher R and Powell M.J.D., "A Rapidly Convergent Descent Method for Minimization", Comput. J., No. 6, pp. 163-168. 1963.         [ Links ]

[18] Kashirskiy I.S. and Trokhimenko Ya.K., General Optimization for Electronic Circuits, Kiev: Tekhnika, 1979.         [ Links ]

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

[20] Neustadt L.W., "Synthesis of Time-Optimal Control Systems", J. of Math. Analysis and Applications, No. 1, pp. 484-492. 1960.         [ Links ]

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

[22] Krotov V.F., Global Methods in Optimal Control Theory, New York: Marcel Dekker, Inc., 1996.         [ Links ]

[23] Sepulchre R., Jankovic M., and Kokotovic P.V., Constructive Nonlinear Control, New York: Springer-Verlag, 1997.         [ Links ]

[24] Pytlak R., Numerical Methods for Optimal Control Problems with State Constraints, Berlin: Springer-Verlag, 1999.         [ Links ]