Electronic Circuit Emuling a First-order Time-delay Differential Equation

Authors

  • César Jiménez IICO - Universidad Autónoma de San Luis Potosí
  • I. Campos-Canton Universidad Autónoma de San Luis Potosí
  • L. J. Ontañón-García Universidad Autónoma de San Luis Potosí

DOI:

https://doi.org/10.31349/RevMexFisE.19.010202

Keywords:

Time delay, phase shift, analog circuits, differential equation, circuit theory.

Abstract

This article provides undergraduates a useful tool for a better understanding of the time delay eect on a electronic circuit. The time delay eect is analyzed on this paper in a rst order dierential equation. This linear time delay is associated with the amplitude of a first-order dierential equation and is responsible of three responses: one of the responses is an dierential equation type in first-order without delay, another one of the responses is a dierential equation type in second-order and nally we have the response of a harmonic oscillator.The proposed circuit is an emulator that develop the three different responses mentioned above. Simulink-Matlab software was used to implement the time delay and simulate the dierential equation. This simulation results coincide with the theoretical results. In the same manner, the experimental results match those of the theory. The electronical circuits suggested consist of three blocks: an integrator block, a phase shift block and a gain block. The electrical circuit is composed of resistors, capacitors and operational ampliers.

References

A. Gonzalez Sorribes, (2011). Sistemas Din ´ amicos con Retardos Temporales, Departamento de Ingenier´ıa de Sistemas y Automatica, Universidad Politécnica de Valencia.

K. Shujaee, B. Lehman, Vibrational feedback control of time delay systems, IEEE Trans. Autom. Control, 42 (1997) 1529. DOI:10.1109/9.649695

E. Fridman, U. Shaked, An improved stabilization method for linear systems with time-delay, IEEE Trans. Autom. Control, 47 (2002) 1931. DOI: 10.1109/TAC.2002.804462

E.C. Heyde, Theoretical methodology for describing active and passive recirculating delay line systems, Electron. Lett., 31 (1995) 2038. DOI: 10.1049/el:19951356

G. Groenewold, Noise and group delay in active filters, IEEE Trans. Circuits Syst. I, Regul. Pap., 54 (2007) 1471, DOI:10.1109/TCSI.2007.900181.

C. Wijenayake et al., RF analog beamforming fan filters using CMOS all-pass time delay approximations, IEEE Trans. Circuits Syst. I, Regul. Pap., 59 (2012) 1061, DOI:10.1109/TCSI.2012.2185294.

E. Fridman, Introduction to Time-Delay Systems-Analysis and Control. (Springer2014).

G. Mungu´ıa and M. Garc Antonioia, Ecuaciones diferenciales con retardo, Memorias de la XVII semana regional de investigacion y docencia en matemáticas, 20 (2007) 137.

Downloads

Published

2022-01-01