Abstract
Advances in the use of fractional order calculus in control theory increasingly make their way into control applications such as in the process industry, electrical machines, mechatronics/robotics, albeit at a slower rate into control applications in automotive and railway systems. We present work on advances in high-speed rail vehicle tilt control design enabled by use of fractional order methods. Analytical problems in rail tilt control still exist especially on simplified tilt using non-precedent sensor information (rather than use of the more complex precedence (or preview) schemes). Challenges arise due to suspension dynamic interactions (due to strong coupling between roll and lateral dynamic modes) and the sensor measurement. We explore optimized PID-based non-precedent tilt control via both direct fractional-order PID design and via fractional-order based loop shaping that reduces effect of lags in the design model. The impact of fractional order design methods on tilt performance (track curve following vs ride quality) trade off is particularly emphasized. Simulation results illustrate superior benefit by utilizing fractional order-based tilt control design.
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K.J. Åström, T. Hägglund, Advanced PID Control. ISA - The Instrum., Systems, and Autom. Society, Res. Triangle Park, NC (2006).
A. Banos, J. Cervera, P. Lanusse, J. Sabatier, Bode optimal loop shaping with CRONE compensators. Journal of Vibration and Control 17, No 13 (2011), 1964–1974.
G.W. Bohannan, Analog fractional order controller in temperature and motor control applications. Journal of Vibration and Control 14, No 9–10 (2008), 1487–1498.
D. Boocock, B.L. King, The development of the prototype advanced passenger train. Proc. of the Institution of Mechanical Engineers 196, No 1 (1982), 35–46.
R. Caponetto, S. Graziani, V. Tomasello, A. Pisano, Identification and fractional super-twisting robust control of IPMC actuators. Fract. Calc. Appl. Anal. 18, No 6 (2015), 1358–1378; DOI: 10.1515/fca-2015-0079; https://www.degruyter.com/view/j/fca.2015.18.issue-6/issue-files/fca.2015.18.issue-6.xml.
Y. Chen, K.L. Moore, B.M. Vinagre, I. Podlubny, Robust PID controller autotuning with a phase shaper. In: 1st IFAC Workshop on Fractional Differentiation and its Applications 2004 (2004), 162–167.
E.F. Colombo, E. Di Gialleonardo, A. Facchinetti, S. Bruni, Active car-body roll control in railway vehicles using hydraulic actuation. Control Eng. Practice 31 (2014), 24–34.
K. Deliparaschos, K. Michail, A. Zolotas, S. Tzafestas, FPGA-based efficient hardware/software co-design for industrial systems with systematic sensor selection. Journal of Elec. Eng. 67, No 3 (2016), 150–159.
E. Gonzalez, L. Dorcak, C.A. Monje, J. Valsa, F. Caluyo, I. Petráš, Conceptual design of a selectable fractional-order differentiator for industrial applications. Fract. Calc. Appl. Anal. 17, No 3 (2014), 697–716; DOI: 10.2478/s13540-014-0195-z; https://www.degruyter.com/view/j/fca.2014.17.issue-3/issue-files/fca.2014.17.issue-3.xml.
F. Hassan, A.C. Zolotas, R. Margetts, Improved PID control for tilting trains. In: Students on Applied Engineering (ISCAE), International Conference for IEEE (2016), 269–274.
I.M. Horowitz, Quantitative Feedback Design Theory: (QFT), Vol. 1. Boulder, Colo., QFT Publications (1993).
A. Lamara, G. Colin, P. Lanusse, A. Charlet, D. Nelson-Gruel, Y. Chamaillard, Pollutant reduction of a turbocharged diesel engine using a decentralized MIMO CRONE controller. Fract. Calc. Appl. Anal. 18, No 2 (2015), 307–332; DOI: 10.1515/fca-2015-0021; https://www.degruyter.com/view/j/fca.2015.18.issue-2/issue-files/fca.2015.18.issue-2.xml.
P. Lanusse, J. Sabatier, and A. Oustaloup, Extension of PID to fractional orders controllers: a frequency-domain tutorial presentation. IFAC Proceedings 47, No 3 (2014), 7436–7442.
J.T. Machado, F. Mainardi, and V. Kiryakova, Fractional calculus: Quo Vadimus? (Where are we going?). Fract. Calc. Appl. Anal., 18, No 2 (2015), 201–218; DOI: 10.1515/fca-2015-0031; https://www.degruyter.com/view/j/fca.2015.18.issue-2/issue-files/fca.2015.18.issue-2.xml.
F. Merrikh-Bayat, Fractional-order unstable pole-zero cancellation in linear feedback systems. J. of Proc. Control 23, No 6 (2013), 817–825.
C.A. Monje, Y. Chen, B.M. Vinagre, D. Xue, V. Feliu-Batlle, Fractional-order Systems and Controls: Fundamentals and Applications. Springer Science & Business Media (2010).
C.A. Monje, B.M. Vinagre, V. Feliu-Batlle, Y. Chen, Tuning and auto-tuning of fractional order controllers for industry applications. Control Engineering Practice 16, No 7 (2008), 798–812.
C.A. Monje, B.M. Vinagre, A.J. Calderón, V. Feliu-Batlle, Y. Chen, Auto-tuning of fractional lead-lag compensators. IFAC Proceedings 38, No 1 (2005), 319–324.
K. Moskvitch, The trouble with trying to make trains go faster. In: BBC Future (2014), http://www.bbc.com/future/story/20140813-the-challenge-to-make-trains-fast.
G. Obinata, B.D.O. Anderson, Model Reduction for Control System Design. Springer Verlag, New York (2001).
A. Orvnäs, On active secondary suspension in rail vehicles to improve ride comfort. Doctoral Thesis, KTH, Sweden (2011).
A. Oustaloup, P. Melchior, P. Lanusse, O. Cois, F. Dancla, The CRONE toolbox for Matlab. In: Computer-Aided Control System Design (CACSD 2000), IEEE International Symposium (2000), 190–195.
A. Oustaloup, Fractional order sinusoidal oscillators: optimization and their use in highly linear FM modulation. IEEE Trans. on Circuits and Systems 28, No 10 (1981), 1007–1009.
J.T. Pearson,, R.M. Goodall, I. Pratt, Control system studies of an active anti-roll bar tilt system for railway vehicles. Proc. of the Institution of Mechanical Engineers, Part F: J. of Rail and Rapid Transit 212, No 1 (1998), 43–60.
I. Petráš, Tuning and implementation methods for fractional-order controllers. Fract. Calc. Appl. Anal. 15, No 2 (2012), 282–303; DOI: 10.2478/s13540-012-0021-4; https://www.degruyter.com/view/j/fca.2012.15.issue-2/issue-files/fca.2012.15.issue-2.xml.
M.S. Tavazoei, Time response analysis of fractional-order control systems: A survey on recent results. Fract. Calc. Appl. Anal. 17, No 2 (2014), 440–461; DOI: 10.2478/s13540-014-0179-z; https://www.degruyter.com/view/j/fca.2014.17.issue-2/issue-files/fca.2014.17.issue-2.xml.
I. Petráš, B. Vinagre, Practical application of digital fractional-order controller to temperature control. Acta Montanistica Slovaca 7, No 2 (2002), 131–137.
I. Petráš, The fractional-order controllers: Methods for their synthesis and application. arXiv Preprint Math/ 0004064 (2000).
I. Podlubny, Fractional-order systems and PIλDmu-controllers. IEEE Transaction on Automatic Control 44, No 1 (1999), 208–214.
I. Podlubny, Fractional Differential Equations. Academic Press, San Diego (1999).
I.E. Pratt, Active suspension applied to railway trains. PhD Dissertation, Loughborough University of Technology (1996).
S. Skogestad, I. Postlethwaite, Multivariable Feedback Control: Analysis and Design, 2. Wiley, New York (2007).
M.S. Tavazoei, M. Haeri, Chaos control via a simple fractional-order controller. Physics Letters A 372, No 6 (2008), 798–807.
R. Vilanova, A. Visioli, PID Control in the Third Millennium. Springer, London (2012).
B.M. Vinagre, I. Podlubny, A. Hernandez, V. Feliu, Some approximations of fractional order operators used in control theory and applications. Fract. Calc. Appl. Anal. 3, No 3 (2000), 231–248.
D. Xue, C. Zhao, Y. Chen, A modified approximation method of fractional order system. In: International Conference on Mechatronics and Automation, IEEE (2006), 1043–1048.
Z. Yang, J. Zhang, Z. Chen, B. Zhang, Semi-active control of high-speed trains based on fuzzy PID control. Procedia Engineering 15 (2011), 521–525.
R. Zhou, A. Zolotas, R. Goodall, Integrated tilt with active lateral secondary suspension control for high speed railway vehicles. Mechatronics 21 (2011), 1108–1122.
A.C. Zolotas, J. Wang, R.M. Goodall, Reduced-order robust tilt control design for high-speed railway vehicles. Vehicle System Dynamics 46, No S1 (2008), 995–1011.
A.C. Zolotas, R.M. Goodall, Advanced control strategies for tilting railway vehicles. UKACC Internat. Conference on Control, University of Cambridge (2000).
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Hassan, F., Zolotas, A. Impact of Fractional Order Methods on Optimized Tilt Control for Rail Vehicles. FCAA 20, 765–789 (2017). https://doi.org/10.1515/fca-2017-0039
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DOI: https://doi.org/10.1515/fca-2017-0039