Respuesta en frecuencia para sistemas en espacio de estados

Efraín  Alcorta García; David Alejandro  Díaz Romero; Rodolfo  Castillo Martínez; Luis Humberto  Rodríguez Alfaro

doi:10.29105/ingenierias26.94-790

Authors

Efraín Alcorta García Universidad Autónoma de Nuevo León
David Alejandro Díaz Romero Universidad Autónoma de Nuevo León
Rodolfo Castillo Martínez Universidad Autónoma de Nuevo León
Luis Humberto Rodríguez Alfaro Universidad Autónoma de Nuevo León https://orcid.org/0000-0001-5047-0455

DOI:

https://doi.org/10.29105/ingenierias26.94-790

Keywords:

Frequency response, state space, linear system, Sylvester equation

Abstract

The frequency response of linear systems is a popular tool used in the analysis and design of automatic control systems. The common way to obtain the frequency response is from the input-output representation (transfer function) of a system. In this paper we present a novel way to obtain the frequency response from the state space representation. The result is obtained by characterizing the input signal (sine function) by means of an additional external system, as well as the evaluation of the steady state. The determination of phase and magnitude is obtained from the solution to a Sylvester equation repeatedly for different values of the frequency in a specific interval together with some algebraic manipulations and use of trigonometric identities. The procedure is shown by examples and compared with classical ways of obtaining the frequency response.

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Author Biographies

Efraín Alcorta García, Universidad Autónoma de Nuevo León

He is an Engineer and Master of Science from the Universidad Autónoma de Nuevo León (UANL), and the degree of Dr.-Ing. in Electrical Engineering from the Gerhard Mercator University of Duisburg, Germany, 1999. Since 1999 he has been a professor in control. Areas of interest include automatic control and fault-tolerant control.

David Alejandro Díaz Romero, Universidad Autónoma de Nuevo León

PhD in automatic control and systems from the University of Sheffield, United Kingdom, bachelor's and master's degrees from UANL in related subjects. Full-time professor in the control department of the Facultad de Ingeniería Mecánica y Eléctrica de la UANL. Areas of interest: automatic control, topology and applications.

Rodolfo Castillo Martínez, Universidad Autónoma de Nuevo León

Master of Science in Electrical Engineering and Control and Computing Engineer from UANL 1995 and 1976 respectively. Professor in the area of Control since 1976. His areas of interest include issues of automatic control and power electronics.

https://orcid.org/0000-0002-3893-5042

Luis Humberto Rodríguez Alfaro, Universidad Autónoma de Nuevo León

He obtained a PhD in Electrical Engineering from the Universidad Autónoma de Nuevo León (UANL) in 2014. Since 2013 he has been a professor at the Facultad de Ingeniería Mecánica y Eléctrica at UANL. His areas of interest are the design and application of control algorithms for electrical systems.

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