Abstract and Applied Analysis

Fractional Order Models of Industrial Pneumatic Controllers

Abolhassan Razminia and Dumitru Baleanu

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


This paper addresses a new approach for modeling of versatile controllers in industrial automation and process control systems such as pneumatic controllers. Some fractional order dynamical models are developed for pressure and pneumatic systems with bellows-nozzle-flapper configuration. In the light of fractional calculus, a fractional order derivative-derivative (FrDD) controller and integral-derivative (FrID) are remodeled. Numerical simulations illustrate the application of the obtained theoretical results in simple examples.

Article information

Abstr. Appl. Anal., Volume 2014 (2014), Article ID 871614, 9 pages.

First available in Project Euclid: 2 October 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Razminia, Abolhassan; Baleanu, Dumitru. Fractional Order Models of Industrial Pneumatic Controllers. Abstr. Appl. Anal. 2014 (2014), Article ID 871614, 9 pages. doi:10.1155/2014/871614. https://projecteuclid.org/euclid.aaa/1412273186

Export citation


  • D. Cafagna, “Past and present–-fractional calculus: a mathematical tool from the past for present engineers,” IEEE Industrial Electronics Magazine, vol. 1, no. 2, pp. 35–40, 2007.
  • K. Ogata, Modern Control Engineering, Prentice Hall, 2010.
  • V. E. Arkhincheev, “Anomalous diffusion in inhomogeneous media: some exact results,” Modelling, Measurement and Control A, vol. 26, pp. 11–29, 1993.
  • B. T. Krishna, “Studies on fractional order differentiators and integrators: a survey,” Signal Processing, vol. 91, no. 3, pp. 386–426, 2011.
  • V. D. Djordjevic and T. M. Atanackovic, “Similarity solutions tononlinear heat conduction and Burgers/Korteweg-deVries fractional equations,” Journal of Computational and Applied Mathematics, vol. 222, no. 2, pp. 701–714, 2008.
  • K. S. Cole, Electric Conductance of Biological Systems, Cold Spring Harbor, New York, NY, USA, 1993.
  • W. G. Glockle and T. F. Nonnenmacher, “A fractional calculus approach to self-similar protein dynamics,” Biophysical Journal, vol. 68, no. 1, pp. 46–53, 1995.
  • N. Laskin, “Fractional market dynamics,” Physica A, vol. 287, no. 3-4, pp. 482–492, 2000.
  • D. Ingman and J. Suzdalnitsky, “Application of differential operator with servo-order function in model of viscoelastic deformation process,” Journal of Engineering Mechanics, vol. 131, no.7, pp. 763–767, 2005.
  • L. Debnath, “Recent applications of fractional calculus to science and engineering,” International Journal of Mathematics andMathematical Sciences, vol. 2003, no. 54, pp. 3413–3442, 2003.
  • S. E. Hamamci, “Stabilization using fractional-order PI and PID controllers,” Nonlinear Dynamics, vol. 51, no. 1-2, pp. 329–343, 2008.
  • X. Jun Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher Limited, HongKong, China,2011.
  • B. W. Andersen, The Analysis Design of Pneumatic Systems, John Wiley & Sons, 1967.
  • T. Miyajima, T. Fujita, K. Sakaki, K. Kawashima, and T. Kagawa, “Development of a digital control system for high-performance pneumatic servo valve,” Precision Engineering, vol. 31, no. 2, pp. 156–161, 2007.
  • Y. Nishioka, K. Suzumori, T. Kanda, and S. Wakimoto, “Multiplex pneumatic control method for multi-drive system,” Sensors and Actuators A, vol. 164, no. 1-2, pp. 88–94, 2010.
  • J.-H. Moon and B.-G. Lee, “Modeling and sensitivity analysis of a pneumatic vibration isolation system with two air chambers,” Mechanism and Machine Theory, vol. 45, no. 12, pp. 1828–1850, 2010.
  • T. M. Atanackovic, S. Pilipovic, and D. Zorica, “Forced oscillations of a body attached to a viscoelastic rod of fractional derivative type,” International Journal of Engineering Science, vol. 64, pp. 54–65, 2013.
  • Z. Xu and W. Chen, “A fractional-order model on new experiments of linear viscoelastic creep of Hami Melon,” Computers & Mathematics with Applications, vol. 66, pp. 677–681, 2013.
  • H. Schiessel, R. Metzler, A. Blumen, and T. F. Nonnenmacher, “Generalized viscoelastic models: their fractional equations with solutions,” Journal of Physics A, vol. 28, no. 23, pp. 6567–6584, 1995.
  • S. A. Bentil and R. B. Dupaix, “Exploring the mechanical behavior of degrading swine neural tissue at low strain rates viathe fractional Zener constitutive model,” Journal of the Mechanical Behavior of Biomedical Materials, vol. 30, pp. 83–90, 2014.
  • S. Holm, S. P. Näsholm, F. Prieur, and R. Sinkus, “Deriving fractional acoustic wave equations from mechanical and thermal constitutive equations,” Computers & Mathematics with Applications, vol. 66, pp. 621–629, 2013.
  • F. Saedpanah, “Well-posedness of an integro-differential equation with positive type kernels modeling fractional order viscoelasticity,” European Journal of Mechanics A, vol. 44, pp. 201–211, 2014.
  • I. Podlubny, Fractional Differential Equations, Academic, New York, NY, USA, 1999.
  • K. B. Oldham and J. Spanier, The Fractional Calculus, Mathematics in Science and Engineering, Academic press, 1974.
  • A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, 2006.
  • T. Pritz, “Analysis of čommentComment on ref. [37?]: Please note that the URL is not accessible[38?] four-parameter fractional derivative model of real solid materials,” Journal of Sound and Vibration, vol. 195, no. 1, pp. 103–115, 1996.
  • http://www.gearseds.com/documents.html.
  • J.-H. Moon and B.-G. Lee, “Modeling and sensitivity analysis of a pneumatic vibration isolation system with two air chambers,” Mechanism and Machine Theory, vol. 45, no. 12, pp. 1828–1850, 2010.
  • A. Oustaloup, F. Levron, B. Mathieu, and F. M. Nanot, “Frequency-band complex noninteger differentiator: characterization and synthesis,” IEEE Transactions on Circuits and Systems I, vol. 47, no. 1, pp. 25–39, 2000. \endinput