An overview of FOPID controller design in v-domain: design methodologies and robust controller performance

References

• Alagoz, B. B. (2016). A note on robust stability analysis of fractional order interval systems by minimum argument vertex and edge polynomials. IEEE/CAA Journal of Automatica Sinica, 3(4), 411–421. https://doi.org/10.1109/JAS.2016.7510088
   Google Scholar
• Alagoz, B. B. (2017). Hurwitz stability analysis of fractional order LTI systems according to principal characteristic equations. ISA Transactions, 70, 7–15. https://doi.org/10.1016/j.isatra.2017.06.005
   PubMed Web of Science ®Google Scholar
• Alagoz, B. B. (2018). Fractional order linear time invariant system stabilization by brute-force search. Transactions of the Institute of Measurement and Control, 40(5), 1447–1456. https://doi.org/10.1177/0142331216685391
   Web of Science ®Google Scholar
• Alagoz, B. B., Tan, N., Deniz, F. N., & Keles, C. (2015a). Implicit disturbance rejection performance analysis of closed loop control systems according to communication channel limitations. IET Control Theory & Applications, 9(17), 2522–2531. https://doi.org/10.1049/iet-cta.2015.0175
   Web of Science ®Google Scholar
• Alagoz, B. B., Yeroglu, C., Senol, B., & Ates, A. (2015b). Probabilistic robust stabilization of fractional order systems with interval uncertainty. ISA Transactions, 57, 101–110. https://doi.org/10.1016/j.isatra.2015.01.003
   PubMed Web of Science ®Google Scholar
• Bode, H. W. (1945). Network analysis and feedback amplifier design. D. Van Nostrand Company.
   Google Scholar
• Byeon, J., Kim, J. S., Sung, S. W., & Lee, J. (2011). Fractional order integrator for the relay feedback identification of a process Nyquist point in the third quadrant. Korean Journal of Chemical Engineering, 28(12), 2227–2229. https://doi.org/10.1007/s11814-011-0118-1
   Web of Science ®Google Scholar
• Chen, H., Li, C., Mafarja, M., Heidari, A. A., Chen, Y., & Cai, Z. (2023). Slime mould algorithm: A comprehensive review of recent variants and applications. International Journal of Systems Science, 54(1), 204–235. https://doi.org/10.1080/00207721.2022.2153635
   Web of Science ®Google Scholar
• Chen, L., He, Y., Wu, R., Chai, Y., & Yin, L. (2014). Robust finite time stability of fractional-order linear delayed systems with nonlinear perturbations. International Journal of Control, Automation and Systems, 12(3), 697–702. https://doi.org/10.1007/s12555-013-0436-7
   Web of Science ®Google Scholar
• Chen, Y., Petras, I., & Xue, D. (2009). . Fractional order control – A tutorial. 2009 American Control Conference. https://doi.org/10.1109/ACC.2009.5160719.
   Google Scholar
• Chen, Y. Q., Bhaskaran, T., & Xue, D. (2008). Practical tuning rule development for fractional order proportional and integral controllers. Journal of Computational and Nonlinear Dynamics, 3(2), 021403. https://doi.org/10.1115/1.2833934
   Web of Science ®Google Scholar
• Chen, Z., Yuan, X., Ji, B., Wang, P., & Tian, H. (2014). Design of a fractional order PID controller for hydraulic turbine regulating system using chaotic non-dominated sorting genetic algorithm II. Energy Conversion and Management, 84, 390–404. https://doi.org/10.1016/j.enconman.2014.04.052
   Web of Science ®Google Scholar
• Cheng, Y., & Hwang, C. (2006). Stabilization of unstable first-order time-delay systems using fractional-order PD controllers. Journal of the Chinese Institute of Engineers, 29(2), 241–249. https://doi.org/10.1080/02533839.2006.9671121
   Web of Science ®Google Scholar
• Colín-Cervantes, J. D., Sánchez-López, C., Ochoa-Montiel, R., Torres-Muñoz, D., Hernández-Mejía, C. M., Sánchez-Gaspariano, L. A., & González-Hernández, H. G. (2021). Rational approximations of arbitrary order: A survey. Fractal and Fractional, 5(4), 267. https://doi.org/10.3390/fractalfract5040267
   Web of Science ®Google Scholar
• Dastjerdi, A. A., Vinagre, B. M., Chen, Y. Q., & HosseinNia, S. H. (2019). Linear fractional order controllers; A survey in the frequency domain. Annual Reviews in Control, 47, 51–70. Elsevier Ltd. https://doi.org/10.1016/j.arcontrol.2019.03.008
   Web of Science ®Google Scholar
• Demiroğlu, U., & Şenol, B. (2021). Frequency frame approach on tuning FOPI controller for TOPTD thermal processes. ISA Transactions, 108, 96–105. https://doi.org/10.1016/j.isatra.2020.08.029
   PubMed Web of Science ®Google Scholar
• Deniz, F. N. (2022). An effective Smith predictor based fractional-order PID controller design methodology for preservation of design optimality and robust control performance in practice. International Journal of Systems Science, 53(14), 2948–2966. https://doi.org/10.1080/00207721.2022.2067366
   Web of Science ®Google Scholar
• Deniz, F. N., Keles, C., Alagoz, B. B., & Tan, N. (2014, June 23–25). Design of fractional-order PI controllers for disturbance rejection using RDR measure. 2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014. https://doi.org/10.1109/ICFDA.2014.6967446
   Google Scholar
• Domański, P. D. (2019). Control quality assessment using fractal persistence measures. ISA Transactions, 90, 226–234. https://doi.org/10.1016/j.isatra.2019.01.008
   PubMed Web of Science ®Google Scholar
• Flores-Estrella, R. A., Alcaraz-González, V., García-Sandoval, J. P., & González-Álvarez, V. (2019). Robust output disturbance rejection control for anaerobic digestion processes. Journal of Process Control, 75, 15–23. https://doi.org/10.1016/j.jprocont.2018.12.012
   Web of Science ®Google Scholar
• Hartley, T. T., & Lorenzo, C. F. (2002). Dynamics and control of initialized fractional-order systems. Nonlinear Dynamics, 29(1–4), 201–233. https://doi.org/10.1023/A:1016534921583
   Web of Science ®Google Scholar
• Imik, O., & Alagoz, B. B. (2017, October 30). Discretization of fractional order transfer functions by weighted multi-objective particle swarm optimization method. IDAP 2017 - International Artificial Intelligence and Data Processing Symposium. https://doi.org/10.1109/IDAP.2017.8090162
   Google Scholar
• Kavuran, G., Ates, A., Alagoz, B. B., & Yeroglu, C. (2017). An experimental study on model reference adaptive control of TRMS by error-modified fractional order MIT rule. Control Engineering and Applied Informatics, 19(4), 101–111.
   Web of Science ®Google Scholar
• Kim, B. S., Kim, T. Y., Park, T. C., & Yeo, Y. K. (2018). A model predictive functional control based on proportional-integral-derivative (PID) and proportional-integral-proportional-derivative (PIPD) using extended non-minimal state space: Application to a molten carbonate fuel cell process. Korean Journal of Chemical Engineering, 35(8), 1601–1610. https://doi.org/10.1007/s11814-018-0068-y
   Web of Science ®Google Scholar
• Komathi, C., & Umamaheswari, M. G. (2020). Design of Gray Wolf optimizer algorithm-based fractional order PI controller for power factor correction in SMPS applications. IEEE Transactions on Power Electronics, 35(2), 2100–2118. https://doi.org/10.1109/TPEL.2019.2920971
   Web of Science ®Google Scholar
• Koseoglu, M., Deniz, F. N., Alagoz, B. B., Yuce, A., & Tan, N. (2021). An experimental analog circuit realization of Matsuda’s approximate fractional-order integral operators for industrial electronics. Engineering Research Express, 3(4), 1–15. Article ID: 045041. https://doi.org/10.1088/2631-8695/ac3e11.
   Google Scholar
• Lee, J., & Edgar, T. F. (2016). Globally stable control systems for processes with input multiplicities. Korean Journal of Chemical Engineering, 33(2), 416–422. https://doi.org/10.1007/s11814-015-0153-4
   Web of Science ®Google Scholar
• Li, X., & Gao, L. (2021). Robust fractional-order PID tuning method for a plant with an uncertain parameter. International Journal of Control, Automation and Systems, 19(3), 1302–1310. https://doi.org/10.1007/s12555-019-0866-y
   Web of Science ®Google Scholar
• Liang, S., Peng, C., Liao, Z., & Wang, Y. (2015). Robust analysis and synthesis for a class of fractional order systems with coupling uncertainties. International Journal of Control, Automation and Systems, 13(2), 494–500. https://doi.org/10.1007/s12555-013-0123-8
   Web of Science ®Google Scholar
• Liu, L., & Zhang, S. (2018). Robust fractional-order PID controller tuning based on Bode’s optimal loop shaping. Complexity, 2018, 1–14. Article ID: 6570560. https://doi.org/10.1155/2018/6570560.
   Web of Science ®Google Scholar
• Mandić, P. D., Šekara, T. B., Lazarević, M. P., & Bošković, M. (2017). Dominant pole placement with fractional order PID controllers: D-decomposition approach. ISA Transactions, 67, 76–86. https://doi.org/10.1016/j.isatra.2016.11.013
   PubMed Web of Science ®Google Scholar
• Monje, C. A., Vinagre, B. M., Feliu, V., & Chen, Y. Q. (2008). Tuning and auto-tuning of fractional order controllers for industry applications. Control Engineering Practice, 16(7), 798–812. https://doi.org/10.1016/j.conengprac.2007.08.006
   Web of Science ®Google Scholar
• Nikita, S., & Lee, M. (2019). Control of a wastewater treatment plant using relay auto-tuning. Korean Journal of Chemical Engineering, 36(4), 505–512. https://doi.org/10.1007/s11814-019-0225-y
   Web of Science ®Google Scholar
• Oustaloup, A., Levron, F., Mathieu, B., & Nanot, F. M. (2000). Frequency-band complex noninteger differentiator: Characterization and synthesis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(1), 25–39. https://doi.org/10.1109/81.817385
   Web of Science ®Google Scholar
• Padula, F., & Visioli, A. (2011). Tuning rules for optimal PID and fractional-order PID controllers. Journal of Process Control, 21(1), 69–81. https://doi.org/10.1016/j.jprocont.2010.10.006
   Web of Science ®Google Scholar
• Pan, I., & Das, S. (2013). Frequency domain design of fractional order PID controller for AVR system using chaotic multi-objective optimization. International Journal of Electrical Power & Energy Systems, 51, 106–118. https://doi.org/10.1016/j.ijepes.2013.02.021
   Web of Science ®Google Scholar
• Petras, I. (2008). Stability of Fractional-Order Systems with Rational Orders. http://arxiv.org/abs/0811.4102.
   Google Scholar
• Pisano, A., Rapaić, M. R., Jeličić, Z. D., & Usai, E. (2010). Sliding mode control approaches to the robust regulation of linear multivariable fractional-order dynamics. International Journal of Robust and Nonlinear Control, 20(18), 2045–2056. https://doi.org/10.1002/rnc.1565
   Web of Science ®Google Scholar
• Radwan, A. G., Soliman, A. M., Elwakil, A. S., & Sedeek, A. (2009). On the stability of linear systems with fractional-order elements. Chaos, Solitons & Fractals, 40(5), 2317–2328. https://doi.org/10.1016/j.chaos.2007.10.033
   Web of Science ®Google Scholar
• Rodríguez-Guerrero, L., Cuvas-Castillo, C., Santos-Sánchez, O.-J., Ordaz-Oliver, J.-P., & García-Samperio, C.-A. (2019). Robust guaranteed cost control for a class of perturbed systems with multiple distributed time delays. Journal of Process Control, 80, 127–142. https://doi.org/10.1016/j.jprocont.2019.04.015
   Web of Science ®Google Scholar
• Saha, S., Das, S., Das, S., & Gupta, A. (2012). A conformal mapping based fractional order approach for sub-optimal tuning of PID controllers with guaranteed dominant pole placement. Communications in Nonlinear Science and Numerical Simulation, 17(9), 3628–3642. https://doi.org/10.1016/j.cnsns.2012.01.007
   Web of Science ®Google Scholar
• Sayyaf, N. (2023). Analytical design of robust FO-PID controller for diffusion processes despite of uncertainty on all model parameters. International Journal of Systems Science, 54(6), 1344–1359. https://doi.org/10.1080/00207721.2023.2177900
   Web of Science ®Google Scholar
• Senol, B., Ates, A., BaykantAlagoz, B., & Yeroglu, C. (2014). A numerical investigation for robust stability of fractional-order uncertain systems. ISA Transactions, 53(2), 189–198. https://doi.org/10.1016/j.isatra.2013.09.004
   PubMed Web of Science ®Google Scholar
• Tabatabaei, M., & Salehi, R. (2017). Fractional order PID controller design based on Laguerre orthogonal functions. International Journal of Dynamics and Control, 5(3), 542–550. https://doi.org/10.1007/s40435-016-0248-8
   Google Scholar
• Tufenkci, S., Senol, B., & Alagoz, B. B. (2019, January 21). Stabilization of fractional order PID controllers for time-delay fractional order plants by using genetic algorithm. 2018 International Conference on Artificial Intelligence and Data Processing, IDAP 2018. https://doi.org/10.1109/IDAP.2018.8620770
   Google Scholar
• Tufenkci, S., Senol, B., & AlagOz, B. B. (2019, September 1). Disturbance rejection fractional order PID controller design in v-domain by particle swarm optimization. 2019 International Conference on Artificial Intelligence and Data Processing Symposium, IDAP 2019. https://doi.org/10.1109/IDAP.2019.8875931
   Google Scholar
• Tüfenkçi, S., Şenol, B., & Alagöz, B. B. (2019). V-alanında Minimum Açılı Kutup Yerleşimi Yöntemine Göre Kesir Dereceli PI Denetçi Tasarımı ve Dayanıklı Kontrol Performansının İncelenmesi. Avrupa Bilim ve Teknoloji Dergisi, 17(17), 9–19. https://doi.org/10.31590/ejosat.599221.
   Google Scholar
• Tufenkci, S., Senol, B., Alagoz, B. B., & Matušů, R. (2020). Disturbance rejection FOPID controller design in v-domain. Journal of Advanced Research, 25, 171–180. https://doi.org/10.1016/j.jare.2020.03.002
   PubMed Web of Science ®Google Scholar
• Tufenkci, S., Senol, B., Matušů, R., & Alagoz, B. B. (2021). Optimal v-plane robust stabilization method for interval uncertain fractional order PID control systems. Fractal and Fractional, 5(1), 3–21. https://doi.org/10.3390/fractalfract5010003
   Web of Science ®Google Scholar
• Vinagre, B. M., Petráš, I., Podlubny, I., & Chen, Y. Q. (2002). Using fractional order adjustment rules and fractional order reference models in model-reference adaptive control. Nonlinear Dynamics, 29(1–4), 269–279. https://doi.org/10.1023/A:1016504620249
   Web of Science ®Google Scholar
• Vu, T. N. L., & Lee, M. (2014). Smith predictor based fractional-order PI control for time-delay processes. Korean Journal of Chemical Engineering, 31(8), 1321–1329. https://doi.org/10.1007/s11814-014-0076-5
   Web of Science ®Google Scholar
• Wen, S., Chen, X., Zhao, Y., Rad, A. B., Othman, K. M., & Zhang, E. (2014). The study of Fractional Order Controller with SLAM in the Humanoid Robot. Advances in Mathematical Physics, 2014, 1–8. https://doi.org/10.1155/2014/741351
   Web of Science ®Google Scholar
• Xue, D., Zhao, C., & Chen, Y. (2006, June 25-28). A modified approximation method of fractional order system. 2006 International Conference on Mechatronics and Automation. https://doi.org/10.1109/ICMA.2006.257769
   Google Scholar
• Zamani, M., Karimi-Ghartemani, M., Sadati, N., & Parniani, M. (2009). Design of a fractional order PID controller for an AVR using particle swarm optimization. Control Engineering Practice, 17(12), 1380–1387. https://doi.org/10.1016/j.conengprac.2009.07.005
   Web of Science ®Google Scholar
• Zhang, B., Pi, Y., & Luo, Y. (2012). Fractional order sliding-mode control based on parameters auto-tuning for velocity control of permanent magnet synchronous motor. ISA Transactions, 51(5), 649–656. https://doi.org/10.1016/j.isatra.2012.04.006
   PubMed Web of Science ®Google Scholar
• Zheng, W., Chen, Y. Q., Wang, X., Lin, M., & Guo, J. (2023). Robust fractional order PID controller synthesis for the first order plus integral system. Measurement and Control, 56(1–2), 202–214. https://doi.org/10.1177/00202940221095564
   Web of Science ®Google Scholar