Abstract
This note presents a novel methodology for reduction of high order linear time-invariant commensurate non-integer interval systems. It is shown first that the fractional-order interval system is reconstructed to integer interval system and further a hybrid technique is applied as a model reduction scheme. In this scheme, the reduced denominator is acquired by applying a modified least square method and the numerator is achieved by time moment matching. This formulated reduced interval integer model is reconverted to a reduced fractional interval model. As a final point, the results of a numerical illustration are verified to show the relevance and superiority of the proposed technique.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Monje CA, Chen Y, Vinagre BM, Xue D, Feliu-Batlle V (2010) Fractional-order systems and controls fundamental and applications advances in industrial control. Springer
Maiti D, Konar A (2008) Approximation of a Fractional order system by an integer model using particle swarm optimization technique. In: IEEE sponsored conference on computational intelligence, control and computer vision in robotics and automation, pp 149–152
Saxena S, Hote YV (2013) Load frequency control in power systems via internal model control scheme and the model-order reduction. IEEE Trans Power Syst 28(3):2749–2757
Oprzedkiewicz K, Mitkowski W, Gawin E (2015) Application of fractional order transfer functions to the modeling of high-Order systems. In: 20th International conference on methods and models in automation and robotics MMAR, 24–27
Valerio D, Sa da Costa J (2011) Introduction to single-input, single output fractional control. IET Control Theory Appl 5(8):1033–1057
Chen YQ, Petráš I, Xue D (2009) Fractional order control-a tutorial. In: American control conference, pp 1397–1411
Tavakoli-Kakhki M, Haeri M (2009) Model reduction in commensurate fractional-order linear systems. ProF. IMechE Part I: J Syst Control Eng 223
Pollok A, Zimmer D, Casella F (2015) Fractional-Order Modelling in Modelica. In: Proceedings of the 11th international Modelica conference, Versailles, France, 21–23. ISBN: 978-91-7685-955-1
Schilders WH, Van der Vorst HA, Rommes J (2008) Model order reduction theory, research aspects and applications. Springer
Sahaj, Saxena., Yogesh., V., Arya, Pushkar Prakash. “Reduced-Order Modeling of Commensurate Fractional-Order Systems”, 14th International Conference on Control, Automation, Robotics & Vision, Phuket, Thailand (2016)
Lanusse P, Benlaoukli H, Nelson-Gruel D, Oustaloup A (2008) Fractional-order control and interval analysis of SISO systems with time-delayed state. IET Control Theory Appl 2(1)
Sunaga T (2009) Theory of interval algebra and its application to numerical analysis. Jpn J Indust Appl Math 26:125–143
Kiran Kumar K, Sastry GVKR (2012) A new method for order reduction of high order interval systems using least squares method. Int J Eng Res Appl 2(2):156–160
Kiran Kumar K, Sastry GVKR (2012) An approach for interval discrete-time systems using least squares method. Int J Eng Res Appl 2(5):2096–2099
Sondhi S, Hote YV (2015) Relative stability test for fractional order interval systems using Kharitonov’s theorem. J Control, Autom Electr Syst 27(1):1–9
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Kiran Kumar, K., Sangeeta, K., Prasad, C. (2020). A New Algorithm for Reduction of High Order Commensurate Non-integer Interval Systems. In: Deepak, B., Parhi, D., Jena, P. (eds) Innovative Product Design and Intelligent Manufacturing Systems. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-2696-1_66
Download citation
DOI: https://doi.org/10.1007/978-981-15-2696-1_66
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-2695-4
Online ISBN: 978-981-15-2696-1
eBook Packages: EngineeringEngineering (R0)