IEEE/CAA Journal of Automatica Sinica
Citation:  Amit S. Chopade, Swapnil W. Khubalkar, A.S. Junghare, M.V. Aware and Shantanu Das, "Design and Implementation of Digital Fractional Order PID Controller Using Optimal PoleZero Approximation Method for Magnetic Levitation System," IEEE/CAA J. Autom. Sinica, vol. 5, no. 5, pp. 977989, Sept. 2018. doi: 10.1109/JAS.2016.7510181 
[1] 
C. M. Lin, M. H. Lin, and C. W. Chen, "SoPCbased adaptive PID control system design for magnetic levitation system, " IEEE Syst. J. , vol. 5, no. 2, pp. 278287, Jun. 2011. doi: 10.1109/JSYST.2011.2134530.

[2] 
H. K. Chiang, C. A. Chen, and M. Y. Li, "Integral variablestructure grey control for magnetic levitation system, " IEE Proc. Electric Power Appl. , vol. 153, no. 6, pp. 809814, Nov. 2006. doi: 10.1049/ipepa:20060056.

[3] 
Z. J. Yang, K. Kunitoshi, S. Kanae, and K. Wada, "Adaptive robust outputfeedback control of a magnetic levitation system by Kfilter approach, " IEEE Trans. Industr. Electron. , vol. 55, no. 1, pp. 390399, Jan. 2008. doi: 10.1109/TIE.2007.896488.

[4] 
R. Morales, V. Feliu, and H. SiraRamírez, "Nonlinear control for magnetic levitation systems based on fast online algebraic identification of the input gain, " IEEE Trans. Control Syst. Technol. , vol. 19, no. 4, pp. 757771, Jul. 2011. doi: 10.1109/TCST.2010.2057511.

[5] 
C. M. Lin, Y. L. Liu, and H. Y. Li, "SoPCbased functionlink cerebellar model articulation control system design for magnetic ball levitation systems, " IEEE Trans. Industr. Electron. , vol. 61, no. 8, pp. 42654273, Aug. 2014. doi: 10.1109/TIE.2013.2288201.

[6] 
A. El Hajjaji and M. Ouladsine, "Modeling and nonlinear control of magnetic levitation systems, " IEEE Trans. Industr. Electron. , vol. 48, no. 4, pp. 831838, Aug. 2001. doi: 10.1109/41.937416.

[7] 
C. A. Kluever, Dynamic Systems: Modeling, Simulation, and Control. Hoboken, NJ, USA: John Wiley and Sons, 2015.

[8] 
G. F. Franklin, J. D. Powell, and A. EmamiNaeni, Feedback Control of Dynamic Systems, 3rd ed., Reading, MA, USA: AddisonWesley, 1994.

[9] 
T. H. Wong, "Design of a magnetic levitation control system: an undergraduate project, " IEEE Trans. Educ. , vol. E29, no. 4, pp. 196200, Nov. 1986. doi: 10.1109/TE.1986.5570565.

[10] 
R. Sinha and M. L. Nagurka, "Analog and labviewbased control of a maglev system with NIELVIS, " in Proc. ASME Int. Mechanical Engineering Congr. Expo. , Orlando, Florida, USA, 2005, pp. 741746.

[11] 
S. Saha, S. Das, R. Ghosh, B. Goswami, R. Balasubramanian, A. K. Chandra, and A. Gupta, "Design of a fractional order phase shaper for Isodamped control of a PHWR under stepback condition, " IEEE Trans. Nucl. Sci. , vol. 57, no. 3, pp. 16021612, Jun. 2010. doi: 10.1109/TNS.2010.2047405.

[12] 
S. Das, S. Das, and A. Gupta, "Fractional order modeling of a PHWR under stepback condition and control of its global power with a robust PI^{λ}D^{μ} controller, " IEEE Trans. Nucl. Sci. , vol. 58, no. 5, pp. 24312441, Oct. 2011. doi: 10.1109/TNS.2011.2164422.

[13] 
S. Saha, S. Das, R. Ghosh, B. Goswami, R. Balasubramanian, A. K. Chandra, S. Das, and A. Gupta, "Fractional order phase shaper design with Bodeś integral for isodamped control system, " ISA Trans. , vol. 49, no. 2, pp. 196206, Apr. 2010. doi: 10.1016/j.isatra.2009.12.001.

[14] 
S. Das, "Fuel efficient nuclear reactor control, " in Proc. Int. Conf. Nuclear Engineering, Beijing, China, 2005.

[15] 
K. J. Aström and T. Hägglund, PID Controllers: Theory, Design and Tuning, 2nd ed. Triangle Park, NC, USA: Instrument Society of America, 1995.

[16] 
I. Podlubny, Fractional Differential Equations, New York, NY, USA: Academic Press, 1999.

[17] 
S. Das, Functional Fractional Calculus for System Identification and Controls, Berlin, Heidelberg, Germany: Springer Science and Business Media, 2008. doi: 10.1007/9783540727033.

[18] 
I. Podlubny, "Fractionalorder systems and PI^{λ}D^{μ} controllers, " IEEE Trans. Automat. Control, vol. 44, no. 1, pp. 208214, Jan. 1999. doi: 10.1109/9.739144.

[19] 
A. Charef, H. H. Sun, Y. Y. Tsao, and B. Onaral, "Fractal system as represented by singularity function, " IEEE Trans. Automat. Control, vol. 37, no. 9, pp. 14651470, Sep. 1992. doi: 10.1109/9.159595.

[20] 
A. Oustaloup, F. Levron, B. Mathieu, and F. M. Nanot, "Frequencyband complex noninteger differentiator: characterization and synthesis, " IEEE Trans. Circuits Syst. I Fundam. Theory Appl. , vol. 47, no. 1, pp. 2539, Jan. 2000. doi: 10.1109/81.817385.

[21] 
Feedback Instruments Ltd., "Magnetic levitation control experiments, " East Susses, UK, Feedback Part No. 116033942S, 2006.

[22] 
R. Pintelon and J. Schoukens, System Identification: A Frequency Domain Approach, New York, NY, USA: WileyIEEE Press, 2012.

[23] 
C. Yeroglu and N. Tan, "Note on fractionalorder proportionalintegraldifferential controller design, " IET Control Theory Appl. , vol. 5, no. 17, pp. 19781989, Nov. 2011. doi: 10.1049/ietcta.2010.0746.

[24] 
D. Valerio and J. S. da Costa, "Introduction to singleinput, singleoutput fractional control, " IET Control Theory Appl. , vol. 5, no. 8, pp. 10331057, May 2011. doi: 10.1049/ietcta.2010.0332.

[25] 
D. L. Chen, Y. Q. Chen, and D. Y. Xue, "Digital fractional order SavitzkyGolay differentiator, " IEEE Trans. Circuits Syst. Ⅱ Express Briefs, vol. 58, no. 11, pp. 758762, Nov. 2011. doi: 10.1109/TCSⅡ.2011.2168022.

[26] 
M. Ö. Efe, "Fractional order systems in industrial automation: a survey, " IEEE Trans. Industr. Inf. , vol. 7, no. 4, pp. 582591, Nov. 2011. doi: 10.1109/TⅡ.2011.2166775.

[27] 
J. A. T. Machado, "Discretetime fractionalorder controllers, " Fract. Calc. Appl. Anal. , vol. 4, no. 1, pp. 4766, Jan. 2001.

[28] 
A. S. Dhabale, R. Dive, M. V. Aware, and S. Das, "A new method for getting rational approximation for fractional order differintegrals, " Asian J. Control, vol. 17, no. 6, pp. 21432152, Nov. 2015. doi: 10.1002/asjc.1148.

[29] 
Y. Q. Chen and K. L. Moore, "Discretization schemes for fractionalorder differentiators and integrators, " IEEE Trans. Circuits Syst. I Fundam. Theory Appl. , vol. 49, no. 3, pp. 363367, Mar. 2002. doi: 10.1109/81.989172.

[30] 
I. Pan and S. Das, "Gain and order scheduling for fractional order controllers, " in Intelligent Fractional Order Systems and Control, I. Pan and S. Das, Eds. Berlin, Heidelberg, Germany: Springer, 2013, pp. 147157. doi: 10.1007/97836423154976.

[31] 
I. Petráš, "Fractionalorder feedback control of a DC motor, " J. Electr. Eng. , vol. 60, no. 3, pp. 117128, Mar. 2009.

[32] 
S. Cuoghi and L. Ntogramatzidis, "Direct and exact methods for the synthesis of discretetime proportionalintegralderivative controllers, " IET Control Theory Appl. , vol. 7, no. 18, pp. 21642171, Dec. 2013. doi: 10.1049/ietcta.2013.0064.

[33] 
Y. Q. Chen, I. Petras, and D. Y. Xue, "Fractional order controla tutorial, " in Proc. American Control Conf. , St. Louis, MO, USA, 2009, pp. 13971411. doi: 10.1109/ACC.2009.5160719.

[34] 
Y. Jin, Y. Q. Chen, and D. Xue, "Timeconstant robust analysis of a fractional order[proportional derivative] controller, " IET Control Theory Appl. , vol. 5, no. 1, pp. 164172, Jan. 2011. doi: 10.1049/ietcta.2009.0543.

[35] 
C. A. Monje, B. M. Vinagre, V. Feliu, and Y. Q. Chen, "Tuning and autotuning of fractional order controllers for industry applications, " Control Eng. Pract. , vol. 16, no. 7, pp. 798812, Jul. 2008. doi: 10.1016/j.conengprac.2007.08.006.

[36] 
J. P. Zhong and L. C. Li, "Tuning fractionalorder PI^{λ}D^{μ} controllers for a solidcore magnetic bearing system, " IEEE Trans. Control Syst. Technol. , vol. 23, no. 4, pp. 16481656, Jul. 2015. doi: 10.1109/TCST.2014.2382642.

[37] 
F. Padula and A. Visioli, "Optimal tuning rules for proportionalintegralderivative and fractionalorder proportionalintegralderivative controllers for integral and unstable processes, " IET Control Theory Appl. , vol. 6, no. 6, pp. 776786, Apr. 2012. doi: 10.1049/ietcta.2011.0419.

[38] 
S. Das, S. Saha, S. Das, and A. Gupta, "On the selection of tuning methodology of FOPID controllers for the control of higher order processes, " ISA Trans. , vol. 50, no. 3, pp. 376388, Jul. 2011. doi: 10.1016/j.isatra.2011.02.003.

[39] 
S. Das, I. Pan, S. Das, and A. Gupta, "A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices, " Eng. Appl. Artif. Intell. , vol. 25, no. 2, pp. 430442, Mar. 2012. doi: 10.1016/j.engappai.2011.10.004.

[40] 
S. Das, I. Pan, S. Das, and A. Gupta, "Improved model reduction and tuning of fractionalorder PI^{λ}D^{μ} controllers for analytical rule extraction with genetic programming, " ISA Trans. , vol. 51, no. 2, pp. 237261, Mar. 2012. doi: 10.1016/j.isatra.2011.10.004.

[41] 
S. Das, I. Pan, K. Halder, S. Das, and A. Gupta, "LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index, " Appl. Math. Model. , vol. 37, no. 6, pp. 42534268, Mar. 2013. doi: 10.1016/j.apm.2012.09.022.

[42] 
S. Das, I. Pan, and S. Das, "Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time, " ISA Trans. , vol. 52, no. 4, pp. 550566, Jul. 2013. doi: 10.1016/j.isatra.2013.03.004.

[43] 
S. Das, I. Pan, S. Das, and A. Gupta, "Masterslave chaos synchronization via optimal fractional order PI^{λ}D^{μ} controller with bacterial foraging algorithm, " Nonlinear Dyn. , vol. 69, no. 4, pp. 21932206, Sep. 2012. doi: 10.1007/s110710120419x.

[44] 
S. Saha, S. Das, S. Das, and A. Gupta, "A conformal mapping based fractional order approach for suboptimal tuning of PID controllers with guaranteed dominant pole placement, " Commun. Nonlinear Sci. Numer. Simul. , vol. 17, no. 9, pp. 36283642, Sep. 2012. doi: 10.1016/j.cnsns.2012.01.007.

[45] 
S. Das, I. Pan, K. Halder, S. Das, and A. Gupta, "Impact of fractional order integral performance indices in LQR based PID controller design via optimum selection of weighting matrices, " in Proc. 2012 IEEE Int. Conf. Computer Communication and Informatics, Coimbatore, India, 2012, pp. 16. doi: 10.1109/ICCCI.2012.6158892.

[46] 
S. Das, I. Pan, S. Das, and A. Gupta, "Genetic algorithm based improved suboptimal model reduction in nyquist plane for optimal tuning rule extraction of PID and PI^{λ}D^{μ} controllers via genetic programming, " in Proc. 2011 IEEE Int. Conf. Process Automation, Control and Computing, Coimbatore, India, 2011, pp. 16. doi: 10.1109/PACC.2011.5978962.

[47] 
A. Rajasekhar, S. Das, and A. Abraham, "Fractional order PID controller design for speed control of chopper fed DC motor drive using artificial bee colony algorithm, " in Proc. 2013 World Congr. Nature and Biologically Inspired Computing, Fargo, ND, USA, 2013, pp. 269266. doi: 10.1109/NaBIC.2013.6617873.

[48] 
R. R. Song and Z. L. Chen, "Design of PID controller for maglev system based on an improved PSO with mixed inertia weight, " J. Netw. , vol. 9, no. 6, pp. 15091517, Jan. 2014. doi: 10.4304/jnw.9.6.15091517.

[49] 
A. Q. H. Badar, B. S. Umre, and A. S. Junghare, "Reactive power control using dynamic particle swarm optimization for real power loss minimization, " Int. J. Electr. Power Energy Syst. , vol. 41, no. 1, pp. 133136, Oct. 2012. doi: 10.1016/j.ijepes.2012.03.030.
