Systematic Approach Towards Computer Aided Non-Linear Control System Analysis Using Describing Function Models

Aparna Sadanand Telang; Prashant Prabhakar Bedekar

doi:doi:10.11648/j.mlr.20190401.13

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Systematic Approach Towards Computer Aided Non-Linear Control System Analysis Using Describing Function Models

Aparna Sadanand Telang, Prashant Prabhakar Bedekar

Published in Machine Learning Research (Volume 4, Issue 1)

Received: 22 March 2019 Accepted: 30 April 2019 Published: 18 June 2019

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Abstract

In recent years, control system problems involving non linearities are important concerns in the framework of automation industries. Actuators with non-linear behavior such as saturation, dead zone, relay, backlash etc. may be responsible for poor control performance in the system. The analysis of these non-linearities is an important task for a control system engineer. Moreover the methods of analyzing these non-linearities are time consuming and non-generic. This paper presents simple and systematic approach for analyzing such kind of non-linearities using user-friendly MATLAB tool “Nonlintool”. This tool saves the time as well as provides visual effects for analysis. Main contribution of this paper is to show how user friendly MATLAB tool “Nonlintool” can extensively be used for quicker and wider interpretation of results based on describing function models. The novelty of this paper lies in analyzing all kinds of non-linearities along with their impact on stability of the nonlinear system. The performance has been evaluated for varying conditions of magnitude and gain of the system as well as on various transfer function models. The results of stability analysis, for which only standard transfer function model is considered, are presented here.

Published in	Machine Learning Research (Volume 4, Issue 1)
DOI	10.11648/j.mlr.20190401.13
Page(s)	13-20
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Nonlinear System, Non-Linearities, Transfer Function, Describing Function (DF), Nonlintool

References

[1]	A. Isidori, “Nonlinear control systems,” New York-Springer-Verlag, 1989.
[2]	M Gopal, “Control Systems Principles and Design,” Tata McGraw- Hill, 2010.
[3]	Giacomo Galuppini, Lalo Magni, Davide Martino Raimondo, “Model predictive control of systems with dead zone and saturation,” Control Engineering Practice, vol. 78, pp. 56–64, 2018.
[4]	Anatoly Gaiduk, Nadežda Stojković, Elena Plaksienko, “Analytical Design of Nonlinear Control Systems,” Automatic Control and Robotics,” vol. 15, no 3, pp. 147-157, 2016.
[5]	R. R. Kadiyala, “A tool box for approximate linearization of nonlinear systems in Control Systems,” IEEE on Control Systems, vol. 13, no. 2, pp. 47-57, April 1993.
[6]	Xueling Song, Chaoying Liu, Zheying Song, Yingbao Zhao, “The Design of Software Platform for Nonlinear System Analysis,” International Conference on Computer Science and Software Engineering, pp. 875-878, 2008.
[7]	R. M. R. Bruns, J. F. P. B. Diepstraten, X. G. P. Schuurbiers, J. A. G. Wouters, “Motion Control of Systems with Backlash,” Master Team Project, pp. 1-50, August 2006.
[8]	P. Shab and J. B. Patel, “Learning of Nonlinear Control System Using nonlintool,” IEEE Fourth International Conference on Technology for education (T4 E), IIIT- Hyderabad, pp. 184-187, 2012.
[9]	Sergey Ul'yanov, N. N. Maksimkin, “Software toolbox for analysis and design of nonlinear control systems and its application to multi-AUV path-following control,” 40th International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO), pp, 1032-1037, May 2017.
[10]	E. A. Freeman, “Dynamic analysis of nonlinear control systems,” PROC. IEE, vol. 114, no. 1, pp. 129-138, January 1967.
[11]	Derek P. Atherton, “Early Developments in Nonlinear Control,” IEEE Control, pp. 34-43, June 1996.
[12]	S. Dormido, F. Gordillo, S. Dormido-Canto, J. Aracil, “An Interactive Tool For Introductory Nonlinear Control Systems Education,” 15th Triennial World Congress, IFAC Elsevier publication, pp. 255-260, 2002.
[13]	Zdeněk Úředníček “Nonlinear systems - describing functions analysis and usings,” MATEC Web of Conferences, pp. 1-10, 2018.
[14]	Alexandro Garro Brito “Computation of multiple limit cycles in nonlinear control systems-a describing function approach,” J. Aerosp. Technol. Manag., vol.3, no.1, pp. 21-28, Apr. 2011.
[15]	Jaydeep Jesur, Ashay Shah and Jignesh B. Patel, “Nonlintools: GUI Tool for Analysis and Design of Nonlinear Control System,” Nirma Universitty Journal of Engineering and Technology, vol.1, no.1, pp. 34-37, Jan-Jun 2010.
[16]	M. Ondera “MATLAB-Based Tool for Non-Linear Systems,” CEEPUS Summer School Intelligent Control Systems, pp. 1-15, 2005.
[17]	Zhitao Liu, Deqing Huang, Yifan Xing, Chuanke Zhang, Zhengguang Wu, and Xiaofu Ji, “ New Trends in Nonlinear Control Systems and Applications,” Hindawi Publishing Corporation and Applied Analysis Volume 1, pp. 1-2, March 2015.

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APA Style

Aparna Sadanand Telang, Prashant Prabhakar Bedekar. (2019). Systematic Approach Towards Computer Aided Non-Linear Control System Analysis Using Describing Function Models. Machine Learning Research, 4(1), 13-20. https://doi.org/10.11648/j.mlr.20190401.13

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ACS Style

Aparna Sadanand Telang; Prashant Prabhakar Bedekar. Systematic Approach Towards Computer Aided Non-Linear Control System Analysis Using Describing Function Models. Mach. Learn. Res. 2019, 4(1), 13-20. doi: 10.11648/j.mlr.20190401.13

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AMA Style

Aparna Sadanand Telang, Prashant Prabhakar Bedekar. Systematic Approach Towards Computer Aided Non-Linear Control System Analysis Using Describing Function Models. Mach Learn Res. 2019;4(1):13-20. doi: 10.11648/j.mlr.20190401.13

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@article{10.11648/j.mlr.20190401.13,
  author = {Aparna Sadanand Telang and Prashant Prabhakar Bedekar},
  title = {Systematic Approach Towards Computer Aided Non-Linear Control System Analysis Using Describing Function Models},
  journal = {Machine Learning Research},
  volume = {4},
  number = {1},
  pages = {13-20},
  doi = {10.11648/j.mlr.20190401.13},
  url = {https://doi.org/10.11648/j.mlr.20190401.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mlr.20190401.13},
  abstract = {In recent years, control system problems involving non linearities are important concerns in the framework of automation industries. Actuators with non-linear behavior such as saturation, dead zone, relay, backlash etc. may be responsible for poor control performance in the system. The analysis of these non-linearities is an important task for a control system engineer. Moreover the methods of analyzing these non-linearities are time consuming and non-generic. This paper presents simple and systematic approach for analyzing such kind of non-linearities using user-friendly MATLAB tool “Nonlintool”. This tool saves the time as well as provides visual effects for analysis. Main contribution of this paper is to show how user friendly MATLAB tool “Nonlintool” can extensively be used for quicker and wider interpretation of results based on describing function models. The novelty of this paper lies in analyzing all kinds of non-linearities along with their impact on stability of the nonlinear system. The performance has been evaluated for varying conditions of magnitude and gain of the system as well as on various transfer function models. The results of stability analysis, for which only standard transfer function model is considered, are presented here.},
 year = {2019}
}

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TY  - JOUR
T1  - Systematic Approach Towards Computer Aided Non-Linear Control System Analysis Using Describing Function Models
AU  - Aparna Sadanand Telang
AU  - Prashant Prabhakar Bedekar
Y1  - 2019/06/18
PY  - 2019
N1  - https://doi.org/10.11648/j.mlr.20190401.13
DO  - 10.11648/j.mlr.20190401.13
T2  - Machine Learning Research
JF  - Machine Learning Research
JO  - Machine Learning Research
SP  - 13
EP  - 20
PB  - Science Publishing Group
SN  - 2637-5680
UR  - https://doi.org/10.11648/j.mlr.20190401.13
AB  - In recent years, control system problems involving non linearities are important concerns in the framework of automation industries. Actuators with non-linear behavior such as saturation, dead zone, relay, backlash etc. may be responsible for poor control performance in the system. The analysis of these non-linearities is an important task for a control system engineer. Moreover the methods of analyzing these non-linearities are time consuming and non-generic. This paper presents simple and systematic approach for analyzing such kind of non-linearities using user-friendly MATLAB tool “Nonlintool”. This tool saves the time as well as provides visual effects for analysis. Main contribution of this paper is to show how user friendly MATLAB tool “Nonlintool” can extensively be used for quicker and wider interpretation of results based on describing function models. The novelty of this paper lies in analyzing all kinds of non-linearities along with their impact on stability of the nonlinear system. The performance has been evaluated for varying conditions of magnitude and gain of the system as well as on various transfer function models. The results of stability analysis, for which only standard transfer function model is considered, are presented here.
VL  - 4
IS  - 1
ER  -

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Author Information

Aparna Sadanand Telang

Department of Electrical Engineering, Faculty of P. R. Patil College of Engineering Management, Sant Gadgebaba Amravati University, Amravati, India
Prashant Prabhakar Bedekar

Department of Electrical Engineering, Faculty of Government College of Engineering, Gondwana University, Chandrapur, India

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Plain Text BibTeX RIS

APA Style

Aparna Sadanand Telang, Prashant Prabhakar Bedekar. (2019). Systematic Approach Towards Computer Aided Non-Linear Control System Analysis Using Describing Function Models. Machine Learning Research, 4(1), 13-20. https://doi.org/10.11648/j.mlr.20190401.13

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ACS Style

Aparna Sadanand Telang; Prashant Prabhakar Bedekar. Systematic Approach Towards Computer Aided Non-Linear Control System Analysis Using Describing Function Models. Mach. Learn. Res. 2019, 4(1), 13-20. doi: 10.11648/j.mlr.20190401.13

Copy | Download

AMA Style

Aparna Sadanand Telang, Prashant Prabhakar Bedekar. Systematic Approach Towards Computer Aided Non-Linear Control System Analysis Using Describing Function Models. Mach Learn Res. 2019;4(1):13-20. doi: 10.11648/j.mlr.20190401.13

Copy | Download

@article{10.11648/j.mlr.20190401.13,
  author = {Aparna Sadanand Telang and Prashant Prabhakar Bedekar},
  title = {Systematic Approach Towards Computer Aided Non-Linear Control System Analysis Using Describing Function Models},
  journal = {Machine Learning Research},
  volume = {4},
  number = {1},
  pages = {13-20},
  doi = {10.11648/j.mlr.20190401.13},
  url = {https://doi.org/10.11648/j.mlr.20190401.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mlr.20190401.13},
  abstract = {In recent years, control system problems involving non linearities are important concerns in the framework of automation industries. Actuators with non-linear behavior such as saturation, dead zone, relay, backlash etc. may be responsible for poor control performance in the system. The analysis of these non-linearities is an important task for a control system engineer. Moreover the methods of analyzing these non-linearities are time consuming and non-generic. This paper presents simple and systematic approach for analyzing such kind of non-linearities using user-friendly MATLAB tool “Nonlintool”. This tool saves the time as well as provides visual effects for analysis. Main contribution of this paper is to show how user friendly MATLAB tool “Nonlintool” can extensively be used for quicker and wider interpretation of results based on describing function models. The novelty of this paper lies in analyzing all kinds of non-linearities along with their impact on stability of the nonlinear system. The performance has been evaluated for varying conditions of magnitude and gain of the system as well as on various transfer function models. The results of stability analysis, for which only standard transfer function model is considered, are presented here.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Systematic Approach Towards Computer Aided Non-Linear Control System Analysis Using Describing Function Models
AU  - Aparna Sadanand Telang
AU  - Prashant Prabhakar Bedekar
Y1  - 2019/06/18
PY  - 2019
N1  - https://doi.org/10.11648/j.mlr.20190401.13
DO  - 10.11648/j.mlr.20190401.13
T2  - Machine Learning Research
JF  - Machine Learning Research
JO  - Machine Learning Research
SP  - 13
EP  - 20
PB  - Science Publishing Group
SN  - 2637-5680
UR  - https://doi.org/10.11648/j.mlr.20190401.13
AB  - In recent years, control system problems involving non linearities are important concerns in the framework of automation industries. Actuators with non-linear behavior such as saturation, dead zone, relay, backlash etc. may be responsible for poor control performance in the system. The analysis of these non-linearities is an important task for a control system engineer. Moreover the methods of analyzing these non-linearities are time consuming and non-generic. This paper presents simple and systematic approach for analyzing such kind of non-linearities using user-friendly MATLAB tool “Nonlintool”. This tool saves the time as well as provides visual effects for analysis. Main contribution of this paper is to show how user friendly MATLAB tool “Nonlintool” can extensively be used for quicker and wider interpretation of results based on describing function models. The novelty of this paper lies in analyzing all kinds of non-linearities along with their impact on stability of the nonlinear system. The performance has been evaluated for varying conditions of magnitude and gain of the system as well as on various transfer function models. The results of stability analysis, for which only standard transfer function model is considered, are presented here.
VL  - 4
IS  - 1
ER  -

Copy | Download