Abstract
This paper investigates the dynamic properties and chaos control in a fractional order brushless DC (BLDC) motor. The fractional order model of the brushless DC motor has been derived from its integer order model. Then the qualitative properties of the fractional order BLDC motor are derived. Bifurcation analysis of the BLDC motor with the fractional order has been also discussed. Fractional order chaos control in the BLDC motor is achieved using sliding mode control, robust control and extended back-stepping control.
Similar content being viewed by others
References
Vaidyanathan S, Volos C (2016) Advances and applications of chaotic systems. Springer, Berlin
Li Z, Park JB, Joo YH, Zhang B, Chen G (2002) Bifurcations and chaos in a permanent-magnet synchronous motor. IEEE Trans Circuit Syst I Theor Appl 49:383–387
Jing ZJ, Yu C, Chen GR (2004) Complex dynamics in a permanent-magnet synchronous motor model. Chaos Solitons Fractals 22(4):831–848
Jabli N, Khammari H, Mimouni MF, Dhifuoui R (2010) Bifurcation and chaos phenomena appearing in induction motor under variation of PI controller parameters. WSEAS Trans Syst 9(7):784–793
Tavazoei MS, Haeri M (2009) A note on the stability of fractional order systems. Math Comput Simul 79(5):1566–1576
Cao Y, Li Y, Ren W, Chen YQ (2010) Distributed coordination of networked fractional order systems. IEEE Trans Syst Man Cybern Part B 40(2):362–370
Podlubny I (1999) Fractional differential equations. Academic Press, San Diego, USA
Yau HT (2004) Design of adaptive sliding mode controller for chaos synchronization with uncertainities. Chaos Solut Fractals 22(2):341–347
Asada H, Youcef-Toumi K (1987) Direct drive robots. MIT Press, Cambridge, USA
Murugesan S (1981) An overview of electric motors for space applications. IEEE Trans Ind Electron Control Instrument 28(4):260–265
Uyaroglu Y, Cevher B (2013) Chaos control of single time-scale brushless DC motor with sliding mode control method. Turkish J Elect Eng Comput Sci 21:649–655
Krause PC (1986) Analysis of electric machinery. McGraw-Hill, New York, USA
Hemati N, Leu MC (1992) A complete model characterization of brushless DC motors. IEEE Trans Ind Appl 28(1):172–180
Premkumar K, Manikandan BV (2015) Speed control of brushless DC motor using bat algorithm optimized adaptive neuro-fuzzy inference system. Appl Soft Comput 32:403–419
Ibrahim HEA, Hassan FN, Shomer AO (2014) Optimal PID control of a brushless DC motor using PSO and BF techniques. Ain Shams Eng J 5(2):391–398
Li CL, Yu SM, Luo XS (2012) Fractional-order permanent magnet synchronous motor and its adaptive chaotic control. Chin Phys B, vol 21, no. 10. Article ID 100506
Vaidyanathan S (2016) Global chaos control of the generalized Lotka–Volterra three-species system via integral sliding mode control. Int J PharmTech Res 9(4):399–412
Vaidyanathan S (2016) Anti-synchronization of Duffing double-well chaotic oscillators via integral sliding mode control. Int J ChemTech Res 9(2):297–304
Si-Ammour A, Djennoune S, Bettayeb M (2009) A sliding mode control for linear fractional systems with input and state delays. Commun Nonlinear Sci Num Simul 14:2310–2318
Efe MO (2010) Fractional order sliding mode control with reaching law approach. Turkish J Electr Eng Comput Sci 18(5):731–747
Barembones O, De Durana JMG, De La Sen M (2012) Robust speed control for a variable speed wind turbine. Int J Innov Comput Inform Control 8(11):7627–7640
Onma OS, Olusola OI, Njah AN (2014) Control and synchronization of chaotic and hyperchaotic Lorenz systems via extended backstepping techniques. J Nonlinear Dyn 2014. Article ID 861727
Samko SG, Klibas AA, Marichev OI (1993) Fractional integrals and derivatives: theory and applications. Gordan and Breach, Amsterdam, Netherlands
Caputo M (1967) Linear models of dissipation whose Q is almost frequency independent-II. Geophys J Int 13:529–539
Pezeshki C (1990) Bispectral analysis of systems possessing chaotic motions. J Sound Vibr 137(3):357–368
Author information
Authors and Affiliations
Corresponding author
Additional information
In the original publication of this article one of the corresponding author names was published incorrectly as “Sundarapandian Vaidhyanathan”, this error has now been corrected.
An erratum to this article is available at http://dx.doi.org/10.1007/s00202-016-0462-6.
Rights and permissions
About this article
Cite this article
Rajagopal, K., Vaidyanathan, S., Karthikeyan, A. et al. Dynamic analysis and chaos suppression in a fractional order brushless DC motor. Electr Eng 99, 721–733 (2017). https://doi.org/10.1007/s00202-016-0444-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00202-016-0444-8
Keywords
- Chaos Control
- BLDC motor
- Fractional order
- Sliding mode control
- Robust control
- Extended back-stepping control