Frequency Loop-Shaping and IMC-Based Integer-Order Robust PID Controller Design for Fractional-Order Processes with Time-Delay

References

• Y. A. Rossikhin, and M. V. Shitikova, “Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems,” Acta Mech., Vol. 120, no. 1-4, pp. 109–125, 1997. DOI: 10.1007/BF01174319
   Web of Science ®Google Scholar
• H. Özbay, C. Bonnet, and A. R. Fioravanti, “PID controller design for fractional-order systems with time delays,” Syst. Control Lett., Vol. 61, no. 1, pp. 18–23, 2012. DOI: 10.1016/j.sysconle.2011.09.011
   Web of Science ®Google Scholar
• Z. Gao, M. Yan, and J. Wei, “Robust stabilizing regions of fractional-order PD μ controllers of time-delay fractional-order systems,” J. Process. Control, Vol. 24, no. 1, pp. 37–47, 2014. DOI: 10.1016/j.jprocont.2013.10.008
   Web of Science ®Google Scholar
• A. Yüce, N. Tan, and D. P. Atherton, “Fractional order PI controller design for time delay systems,” IFAC-PapersOnLine, Vol. 49, no. 10, pp. 94–99, 2016. DOI: 10.1016/j.ifacol.2016.07.487
   Google Scholar
• F. Padula, and A. Visioli, “Tuning rules for optimal PID and fractional-order PID controllers,” J. Process Control, Vol. 21, no. 1, pp. 69–81, 2011. DOI: 10.1016/j.jprocont.2010.10.006
   Web of Science ®Google Scholar
• Y. Luo, Y. Q. Chen, C. Y. Wang, and Y. G. Pi, “Tuning fractional order proportional integral controllers for fractional order systems,” J. Process Control, Vol. 20, no. 7, pp. 823–831, 2010. DOI: 10.1016/j.jprocont.2010.04.011
   Web of Science ®Google Scholar
• P. Swethamarai, and P. Lakshmi, “Adaptive-fuzzy fractional order pid controller-based active suspension for vibration control,” IETE J. Res., Vol. 68, no. 5, pp. 1–16, 2020.
   Web of Science ®Google Scholar
• M. D. Patil, K. Vadirajacharya, and S. W. Khubalkar, “Design and tuning of digital fractional-order PID controller for permanent magnet DC motor,” IETE J. Res., Vol. 69, no. 7, pp. 1–11, 2021.
   Web of Science ®Google Scholar
• D. Matignon, “Stability results for fractional differential equations with applications to control processing,” in Computational Engineering in Systems Applications, Vol. 2. IEEE-SMC Lille, France: IMACS, 1996, pp. 963–968.
   Google Scholar
• C. Bonnet, and J. R. Partington, “Coprime factorizations and stability of fractional differential systems,” Syst. Control Lett., Vol. 41, no. 3, pp. 167–174, 2000. DOI: 10.1016/S0167-6911(00)00050-5
   Web of Science ®Google Scholar
• M. S. Tavazoei, and M. Haeri, “A note on the stability of fractional order systems,” Math. Comput. Simul., Vol. 79, no. 5, pp. 1566–1576, 2009. DOI: 10.1016/j.matcom.2008.07.003
   Web of Science ®Google Scholar
• M. Bettayeb, and S. Djennoune, “New results on the controllability and observability of fractional dynamical systems,” J. Vibration Control, Vol. 14, no. 9-10, pp. 1531–1541, 2008. DOI: 10.1177/1077546307087432
   Web of Science ®Google Scholar
• Z. Qingshan, C. Guangyi, and Z. Xinjian, “Research on controllability for a class of fractional-order linear control systems,” J. Syst. Eng. Electron., Vol. 16, no. 2, pp. 376–381, 2005.
   Google Scholar
• M. Aoun, R. Malti, F. Levron, and A. Oustaloup, “Synthesis of fractional Laguerre basis for system approximation,” Automatica, Vol. 43, no. 9, pp. 1640–1648, 2007. DOI: 10.1016/j.automatica.2007.02.013
   Web of Science ®Google Scholar
• T. Djamah, R. Mansouri, S. Djennoune, and M. Bettayeb, “Optimal low order model identification of fractional dynamic systems,” Appl. Math. Comput., Vol. 206, no. 2, pp. 543–554, 2008. DOI: 10.1016/j.amc.2008.05.109
   Web of Science ®Google Scholar
• M. S. Tavazoei, and M. Haeri, “Rational approximations in the simulation and implementation of fractional-order dynamics: A descriptor system approach,” Automatica, Vol. 46, no. 1, pp. 94–100, 2010. DOI: 10.1016/j.automatica.2009.09.016
   Web of Science ®Google Scholar
• M. S. Tavazoei, and M. Haeri, “A proof for non existence of periodic solutions in time invariant fractional order systems,” Automatica, Vol. 45, no. 8, pp. 1886–1890, 2009. DOI: 10.1016/j.automatica.2009.04.001
   Web of Science ®Google Scholar
• M. S. Tavazoei, M. Haeri, M. Attari, S. Bolouki, and M. Siami, “More details on analysis of fractional-order van der pol oscillator,” J. Vibration Control, Vol. 15, no. 6, pp. 803–819, 2009. DOI: 10.1177/1077546308096101
   Web of Science ®Google Scholar
• F. Merrikh-Bayat, “General rules for optimal tuning the PIλDμ controllers with application to first-order plus time delay processes,” Can. J. Chem. Eng., Vol. 90, no. 6, pp. 1400–1410, 2012. DOI: 10.1002/cjce.v90.6
   Web of Science ®Google Scholar
• F. Padula, and A. Visioli, “Optimal tuning rules for proportional-integral-derivative and fractional-order proportional-integral-derivative controllers for integral and unstable processes,” IET Control Theory Appl., Vol. 6, no. 6, pp. 776–786, 2012. DOI: 10.1049/iet-cta.2011.0419
   Web of Science ®Google Scholar
• R. El-Khazali, “Fractional-order PIλDμ controller design,” Comput. Math. Appl., Vol. 66, no. 5, pp. 639–646, 2013. DOI: 10.1016/j.camwa.2013.02.015
   Web of Science ®Google Scholar
• F. Merrikh-Bayat, and M. Karimi-Ghartemani, “Method for designing PIλDμ stabilisers for minimum-phase fractional-order systems,” IET Control Theory Appl., Vol. 4, no. 1, pp. 61–70, 2010. DOI: 10.1049/iet-cta.2008.0062
   Web of Science ®Google Scholar
• M. Bettayeb, R. Mansouri, U. Al-Saggaf, and I. M. Mehedi, “Smith predictor based fractional-order-filter PID controllers design for long time delay systems,” Asian J. Control, Vol. 19, no. 2, pp. 587–598, 2017. DOI: 10.1002/asjc.v19.2
   Web of Science ®Google Scholar
• R. Ranganayakulu, G. Uday Bhaskar Babu, and A. Seshagiri Rao, “Fractional filter IMC-PID controller design for second order plus time delay processes,” Cogent Eng., Vol. 4, no. 1, p. 1366888, 2017. DOI: 10.1080/23311916.2017.1366888
   Web of Science ®Google Scholar
• R. Desai, “Comparative analysis of integer and fractional order controller for time delay system,” in Proceedings of the International Conference on Data Engineering and Communication Technology, 2017, pp. 331–341. Lavasa City, Pune.
   Google Scholar
• S. Chakraborty, J. Singh, A. K. Naskar, and S. Ghosh, “A new analytical approach for set-point weighted 2DOF-PID controller design for integrating plus time-delay processes: An experimental study,” IETE J. Res., Vol. 69, no. 10, pp. 1–15, 2022.
   Web of Science ®Google Scholar
• M. Khanra, J. Pal, and K. Biswas, “Rational approximation of fractional operator–a comparative study,” in 2010 International Conference on Power, Control and Embedded Systems (ICPCES), 2010, pp. 1–5. Allahabad, India.
   Google Scholar
• A. Oustaloup, F. Levron, B. Mathieu, and F. M. Nanot, “Frequency-band complex noninteger differentiator: characterization and synthesis,” IEEE Trans. Circuits Syst. I: Fundamental Theory Appl., Vol. 47, no. 1, pp. 25–39, 2000. DOI: 10.1109/81.817385
   Web of Science ®Google Scholar
• H. Wade Bode, Network analysis and feedback amplifier design. Toronto, New York and London: D. Van Nostrand Company, Inc, 1945.
   Google Scholar
• R. S. Barbosa, J. A. T. Machado, and I. M. Ferreira, “Tuning of PID controllers based on Bode's ideal transfer function,” Nonlinear Dyn., Vol. 38, no. 1, pp. 305–321, 2004. DOI: 10.1007/s11071-004-3763-7
   Web of Science ®Google Scholar
• E. Grassi, K. S. Tsakalis, S. Dash, S. V. Gaikwad, W. MacArthur, and G. Stein, “Integrated system identification and PID controller tuning by frequency loop-shaping,” IEEE Trans. Control Syst. Technol., Vol. 9, no. 2, pp. 285–294, 2001. DOI: 10.1109/87.911380
   Web of Science ®Google Scholar
• V. M. Alfaro, and R. Vilanova, “Robust tuning and performance analysis of 2DoF PI controllers for integrating controlled processes,” Ind. Eng. Chem. Res., Vol. 51, no. 40, pp. 13182–13194, 2012. DOI: 10.1021/ie300605w
   Web of Science ®Google Scholar
• S. Boyd, and L. Vandenberghe, Convex optimization. New York: Cambridge University Press, 2004.
   Google Scholar
• D. P. Bertsekas, Nonlinear programming. Belmont, MA: Athena scientific Belmont, 1999.
   Google Scholar
• M. Li, P. Zhou, Z. Zhao, and J. Zhang, “Two-degree-of-freedom fractional order-PID controllers design for fractional order processes with dead-time,” ISA Trans., Vol. 61, pp. 147–154, 2016. DOI: 10.1016/j.isatra.2015.12.007
   PubMed Web of Science ®Google Scholar
• B. Maâmar, and M. Rachid, “IMC-PID-fractional-order-filter controllers design for integer order systems,” ISA Trans., Vol. 53, no. 5, pp. 1620–1628, 2014. DOI: 10.1016/j.isatra.2014.05.007
   PubMed Web of Science ®Google Scholar
• D. Valério, and J. S. Da Costa, “Tuning of fractional PID controllers with Ziegler–Nichols-type rules,” Signal Processing, Vol. 86, no. 10, pp. 2771–2784, 2006. DOI: 10.1016/j.sigpro.2006.02.020
   Web of Science ®Google Scholar