Scientific and Technical Journal


ISSN Print 2221-3937
ISSN Online 2221-3805

The design of electromechanical systems upon application of fractional order controllers significantly enhances possibilities in comparison with the classic controllers. In order to find efficient alternative models for implementing fractional order controllers there has been conducted a research into their dynamic properties on the basis of  Riemann, Riemann-Liouville and Grunwald-Letnikov representations.  When considering electromechanical systems with fractional controllers that generate control actions for different electrical machines, the major problem to be solved is the work of such controllers in real time and with the high speed dynamic processes. Given well-developed implementation of integer order controllers in both analog and digital performance, the problem of synthesized fractional order controllers technical implementation in such systems can be solved on condition of making equivalent substitution (approximation) of their transfer functions into integer order transfer functions. Implementation of integral and differential parts of fractional order PIλDμ – controllers has been carried out on the basis of Oustaloup transformation, which provides significantly higher performance and simplicityof the procedure when compared with computational models, based on Riemann, Riemann-Liouville and Grunwald-Letnikov representations. Computer research of algorithm and implementation program of differential and integral fractional order parts has proven the effectiveness of the proposed approach to implementation of  fractional order controllers that can operate in real time within highly dynamic electromechanical systems. Testing of  frequency converter option of MFC 710 fractional order PIλDμ - controller in the speed control system by using the set of Twerd company has proven its effectiveness in terms of expanding regulatory properties of such controller in comparison with traditional PID - controller.

  1. Maiti, D., Biswas, S. and  Konar, A. (2008). Design of a fractional order PID controller using particle swarm optimization technique. In: 2nd National Conference on Recent Trends in Information Systems (ReTIS-08). [online]. Available at: [Accessed 25 Jan. 2015].
  2. Kennedy, J. and  Eberhart, R. C. (1995). Particle swarm optimization. In: IEEE International Conference on Neural Networks, 4, pp. 1942–1948.
  3. Konar, A. and  Das, S. (2006). Recent advances in evolutionary search and optimization algorithms. In:  International Conference Next Generation Maintenance Systems (NGMS 2006).BESU, Shibpur, Howrah.
  4. Dalir, M. and Bashour, M. (2010). Application of fractional calculus. Applied Mathematical Sciences, 4, pp. 1021–1032.
  5. Busher, V. (2011). Modelling systems with fractional-differentiatial and fractional-integrating parts in SIMULINK [Modelirovanie sistem s drobno- differenciruyushchimi i drobno-integriruyushchimi zvenyami v SIMULINK]. Electromechanical and energysaving systems, 4, pp. 140-143.
  6. Busher, V., Martynyuk, V., Naydenko, E., and Kristo P. (2011). Modeling of supercapacitors with fractionally integrated section in SIMULINK. Electrical and computer systems, 4(80),  pp. 89–92.
  7. Oustaloup, A.,  Levron, F. and Mathieu,  B. (2010). Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47, pp. 25–39.
  8. Marushchak, Y. and  Kopchak, B. (2014). Approximation of fractional order differential-integral controllers by integer order transfer functions.  Computational problems of electrical engineering,1, pp. 29–32.
  9. Kopchak, B. (2016). Development of fractional order differential-integral controller by using Oustaloup transformation. In: XIIth International Conference Perspective Technologies and Methods in MEMS Design (MEMSTECH 2016). Lviv–Polyana; Lviv Polytechnic Publishing House, pp. 62–65.
  10. Kopchak, B., Twerd, M., and Kozlovski, B. (2016). Fractional order PIλDμ-controller for frequency converter MFC 710 [PIλDμ-regulyator drobovogo poryadku dlya peretvoryuvachiv chastoty` ty`pu MFC 710].  Electronics and electromechanics, 4(1), pp. 84–88.
Last download:
2017-07-27 05:21:33

[ © KarelWintersky ] [ All articles ] [ All authors ]
[ © Odessa National Polytechnic University, 2014. Any use of information from the site is possible only under the condition that the source link! ]