A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Advanced Search

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 18.3, Top 1 (SCI Q1)
    CiteScore: 28.2, Top 1% (Q1)
    Google Scholar h5-index: 95， TOP 5
Turn off MathJax
Article Contents
Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2026  > In Press, Accepted Manuscript
M. D. Mihai, R. D. Keyser, I. R. Birs, C. M. Ionescu, and C. I. Muresan, “A novel fractional-order PID autotuning method with robustness to time constant variations,” IEEE/CAA J. Autom. Sinica, early access, 2026. doi: 10.1109/JAS.2026.126236
Citation: M. D. Mihai, R. D. Keyser, I. R. Birs, C. M. Ionescu, and C. I. Muresan, “A novel fractional-order PID autotuning method with robustness to time constant variations,” IEEE/CAA J. Autom. Sinica, early access, 2026. doi: 10.1109/JAS.2026.126236
shu

A Novel Fractional-Order PID Autotuning Method With Robustness to Time Constant Variations

doi: 10.1109/JAS.2026.126236
Funds:  This work was supported by a grant of the Romanian Ministry of Research, Innovation and Digitization, (PNRR-III-C9-2022-I8, 760068/23.05.2023). This work was also supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS-UEFISCDI (PN-IV-P2-2.1-TE-2023-0831), within PNCDI IV. I. R. Birs acknowledges the support of Flanders Research Foundation, Postdoc (1203224N, 2023-2026). The work of Clara M. Ionescu was supported by Flanders Research Foundation through the GOPID Research Project (G060126N)
More Information
    Abstract
  • Fractional-order PID controllers have received considerable attention due to their enhanced flexibility and potential improvements in disturbance rejection, performance and robustness. This paper introduces a model-free fractional-order Proportional Integrative Derivative (FO-PID) autotuning framework that explicitly targets robustness to dominant time constant variations, a robustness aspect that is largely unaddressed by current fractional-order autotuners. The process is locally parametrised using a single sine test, which provides the frequency-response point and slope information required for tuning. Based on these data, the process is assigned to a low-order or high-order family, and a corresponding target open-loop slope $dL$ is selected from a nominal guideline table. The controller is then tuned by adjusting the fractional-orders (via Levenberg--Marquardt optimisation or a simple grid search) to match the target $dL$, while the remaining controller gains and time constants are computed directly from the tuning equations. Fractional operators are implemented through Oustaloup’s recursive approximation. Extensive numerical studies on representative process families show that the resulting FO-PID controllers preserve phase margin and overshoot over wide dominant time constant changes, thereby yielding near-invariant closed-loop behaviour. Overall, the main contribution is a practical, experimentally driven autotuning method that transfers time constant-robustness concepts into the fractional-order PID setting without requiring a parametric plant model, providing a basis for extensions toward delay-robust, adaptive, and multi-objective variants.

     

    • FullText(HTML)
  • loading
    • References(53)
  • [1]
    I. Petráš, “Fractional-order control: New control techniques,” in Emerging Methodologies and Applications in Modelling, Cambridge: Academic Press, 2022, pp. 71−106.
    [2]
    A. Tepljakov, B. B. Alagoz, C. Yeroglu, E. A. Gonzalez, S. H. Hosseinnia, E. Petlenkov, A. Ates, and M. Cech, “Towards industrialization of FOPID controllers: A survey on milestones of fractional-order control and pathways for future developments,” IEEE Access, vol. 9, pp. 21016–21042, Jan. 2021. doi: 10.1109/ACCESS.2021.3055117
    [3]
    X. Li and L. Gao, “Robust fractional-order PID tuning method for a plant with an uncertain parameter,” Int. J. Control, Autom. Syst., vol. 19, no. 3, pp. 1302–1310, Mar. 2021. doi: 10.1007/s12555-019-0866-y
    [4]
    I. Birs, C. Muresan, I. Nascu, and C. Ionescu, “A survey of recent advances in fractional order control for time delay systems,” IEEE Access, vol. 7, pp. 30951–30965, Mar. 2019. doi: 10.1109/ACCESS.2019.2902567
    [5]
    A. A. Dastjerdi, B. M. Vinagre, Y. Q. Chen, and S. H. HosseinNia, “Linear fractional order controllers; A survey in the frequency domain,” Annu. Rev. Control, vol. 47, pp. 51–70, Apr. 2019. doi: 10.1016/j.arcontrol.2019.03.008
    [6]
    A. Apte, U. Thakar, and V. Joshi, “Disturbance observer based speed control of PMSM using fractional order PI controller,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 316–326, Jan. 2019. doi: 10.1109/jas.2019.1911354
    [7]
    J. Viola, L. Angel, and J. M. Sebastian, “Design and robust performance evaluation of a fractional order PID controller applied to a DC motor,” IEEE/CAA J. Autom. Sinica, vol. 4, no. 2, pp. 304–314, Apr. 2017. doi: 10.1109/jas.2017.7510535
    [8]
    P. Chen, Y. Luo, Y. Peng, and Y. Chen, “Optimal robust fractional order PIλD controller synthesis for first order plus time delay systems,” ISA Trans., vol. 114, pp. 136–149, Aug. 2021. doi: 10.1016/j.isatra.2020.12.043
    [9]
    S. Saxena and Y. V. Hote, “Design of robust fractional-order controller using the bode ideal transfer function approach in IMC paradigm,” Nonlinear Dyn., vol. 107, no. 1, pp. 983–1001, Jan. 2022. doi: 10.1007/s11071-021-07003-z
    [10]
    G. Singh, D. Kumar, P. Aryan, T. R. Chelliah, and G. L. Raja, “Robust and unified fractional order AGC-AVR scheme for hydropower plant,” IEEE Trans. Ind. Appl., 2026, DOI: 10.1109/TIA.2026.3675039.
    [11]
    A. K. Deep, G. L. Raja, and G. D. Meena, “Robust single-parameter frequency controller tuned with Artificial intelligence-driven hybrid optimization for modern power systems amid cyber threats and latency,” Comput. Electr. Eng., vol. 131, Art. no. 110920, Mar. 2026. doi: 10.1016/j.compeleceng.2025.110920
    [12]
    D. Kumar, G. L. Raja, M. Alkhatib, and U. R. Muduli, “Maximum sensitivity based robust latency compensator for frequency regulation in microgrid with SMES,” in Proc. IEEE Industry Applications Society Annual Meeting, Taipei, China, 2025, pp. 1−6.
    [13]
    P. Aryan, G. L. Raja, U. Mehta, T. R. Chelliah, and U. R. Muduli, “A resilient tri-parametric fractional frequency control for cybersecurity threats amid latency,” IEEE Trans. Ind. Appl., vol. 61, no. 4, pp. 5597–5611, Jul.-Aug. 2025. doi: 10.1109/TIA.2025.3546173
    [14]
    S. Dudhe, D. K. Dheer, and G. L. Raja, “A portable meconium aspirator with fractional augmented pressure control system,” IEEE Trans. Circuits Syst. II: Express Briefs, vol. 72, no. 5, pp. 733–737, May 2025. doi: 10.1109/TCSII.2024.3378312
    [15]
    C. Kumar, G. L. Raja, and D. K. Dheer, “Robust fractional controller for closed-loop chemotherapy dose scheduling,” AEU – Int. J. Electron. Commun., vol. 203, Art. no. 156090, Jan. 2026. doi: 10.1016/j.aeue.2025.156090
    [16]
    C. A. Monje, A. J. Calderon, B. M. Vinagre, Y. Chen, and V. Feliu, “On fractional PIλ controllers: Some tuning rules for robustness to plant uncertainties,” Nonlinear Dyn., vol. 38, no. 1, pp. 369–381, Dec. 2004.
    [17]
    Z. Wu, D. Li, Y. Xue, T. He, and S. Zheng, “Tuning for fractional order PID controller based on probabilistic robustness,” IFAC-PapersOnLine, vol. 51, no. 4, pp. 675–680, Jan. 2018. doi: 10.1016/j.ifacol.2018.06.179
    [18]
    B. B. Alagoz, C. Yeroglu, B. Senol, and A. Ates, “Probabilistic robust stabilization of fractional order systems with interval uncertainty,” ISA Trans., vol. 57, pp. 101–110, Jul. 2015. doi: 10.1016/j.isatra.2015.01.003
    [19]
    M. C. Martins-Gomes, F. A. de C. Ayres Junior, C. T. da Costa Junior, I. V. de Bessa, N. J. da S. Farias, R. L. P. de Medeiros, L. E. S. Silva, and V. F. de Lucena Júnior, “Fractional-order robust control design under parametric uncertain approach,” ISA Trans., vol. 153, pp. 420–432, Oct. 2024. doi: 10.1016/j.isatra.2024.07.023
    [20]
    Z. Gao, “Robust stabilization criterion of fractional-order controllers for interval fractional-order plants,” Automatica, vol. 61, pp. 9–17, Nov. 2015. doi: 10.1016/j.automatica.2015.07.021
    [21]
    V. Mihaly, M. ŠSušcǎ, E. H. Dulf, D. Morar, and P. Dobra, “Fractional order robust controller for fractional-order interval plants,” IFAC-PapersOnLine, vol. 55, no. 25, pp. 151–156, Oct. 2022. doi: 10.1016/j.ifacol.2022.09.339
    [22]
    A. Rhouma, S. Hafsi, and K. Laabidi, “Stabilizing and robust fractional PID controller synthesis for uncertain first-order plus time-delay systems,” Math. Probl. Eng., vol. 2021, no. 1, Art. no. 9940634, May 2021.
    [23]
    M. Beschi, F. Padula, and A. Visioli, “The generalised isodamping approach for robust fractional PID controllers design,” Int. J. Control, vol. 90, no. 6, pp. 1157–1164, Jun. 2017. doi: 10.1080/00207179.2015.1099076
    [24]
    Y. Jin, Y.-Q. Chen, and D. Xue, “Time-constant robust analysis of a fractional order [proportional derivative],” IET Control Theory Appl., vol. 5, no. 1, pp. 164–172, Jan. 2011. doi: 10.1049/iet-cta.2009.0543
    [25]
    V. Badri and M. S. Tavazoei, “On time-constant robust tuning of fractional order proportional derivative controllers,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1179–1186, Sep. 2019. doi: 10.1109/jas.2017.7510667
    [26]
    C. I. Muresan, M. D. Mihai, E. T. Hegedus, N. Badau, I. R. Birs, and R. De Keyser, “A robust fractional order PI controller for time constant variations,” Fract. Calculus Appl. Anal., vol. 29, no. 2, pp. 980–1005, Apr. 2026. doi: 10.1007/s13540-026-00488-8
    [27]
    C. Yeroglu, C. Onat, and N. Tan, “A new tuning method for PIλDµ controller,” in Proc. Int. Conf. Electrical and Electronics Engineering, Bursa, Turkey, 2009, pp. 312−316.
    [28]
    J. J. Gude and E. Kahoraho, “Modified Ziegler-Nichols method for fractional PI controllers,” in Proc. 15th Conf. Emerging Technologies & Factory Automation, Bilbao, Spain, 2010, pp. 1−5.
    [29]
    M. Tajjudin, S. F. Tahir, M. H. F. Rahiman, N. M. Arshad, and R. Adnan, “Fractional-order PI controller with relay auto-tuning method,” in Proc. 4th Control and System Graduate Research Colloquium, Shah Alam, Malaysia, 2013, pp. 121−126.
    [30]
    C. I. Muresan and R. De Keyser, “Revisiting Ziegler-Nichols. A fractional order approach,” ISA Trans., vol. 129, pp. 287–296, Oct. 2022.
    [31]
    D. Valério and J. Sá da Costa, “Tuning-rules for fractional PID controllers,” IFAC Proc. Volumes, vol. 39, no. 11, pp. 28–33, Jan. 2006.
    [32]
    C. A. Monje, B. M. Vinagre, G. E. Santamaría, and I. Tejado, “Auto-tuning of fractional order PI·D· controllers using a PLC,” in Proc. IEEE Conf. Emerging Technologies & Factory Automation, Palma de Mallorca, Spain, 2009, pp. 1−7.
    [33]
    G. E. Santamaria, I. Tejado, B. M. Vinagre, and C. A. Monje, “Fully automated tuning and implementation of fractional PID controllers,” in Proc. Int. Design Engineering Technical Conferences and Computers and Information in Engineering Conf., San Diego, USA, 2009, pp. 1275−1283.
    [34]
    R. Caponetto, G. Dongola, F. L. Pappalardo, and V. Tomasello, “Autotuning method for PIλDμ controllers design,” Int. J. Innovative Comput., Inf. Control, vol. 9, no. 10, pp. 4043–4055, Jan. 2013.
    [35]
    R. Trivedi and P. K. Padhy, “Fractional order automatic tuning of PIλD controller for stable processes,” ISA Trans., vol. 99, pp. 351–360, Apr. 2020. doi: 10.1016/j.isatra.2019.09.011
    [36]
    R. De Keyser, C. I. Muresan, and C. M. Ionescu, “A novel auto-tuning method for fractional order PI/PD controllers,” ISA Trans., vol. 62, pp. 268–275, May 2016. doi: 10.1016/j.isatra.2016.01.021
    [37]
    R. De Keyser, C. I. Muresan, and C. M. Ionescu, “Autotuning of a robust fractional order PID controller,” IFAC-PapersOnLine, vol. 51, no. 25, pp. 466–471, Jan. 2018. doi: 10.1016/j.ifacol.2018.11.181
    [38]
    C. I. Muresan, I. Birs, C. Ionescu, E. H. Dulf, and R. De Keyser, “A review of recent developments in autotuning methods for fractional-order controllers,” Fractal Fract., vol. 6, no. 1, Art. no. 37, Jan. 2022.
    [39]
    M. Ben Hariz, F. Bouani, and M. Ksouri, “Robust controller for uncertain parameters systems,” ISA Trans., vol. 51, no. 5, pp. 632–640, Sep. 2012. doi: 10.1016/j.isatra.2012.04.007
    [40]
    A. O’Dwyer, Handbook of PI and PID Controller Tuning Rules. 3rd ed. London, UK: Imperial College Press, 2009.
    [41]
    D. E. Seborg, T. F. Edgar, D. A. Mellichamp, and F. J. Doyle Ⅲ, Process Dynamics and Control. 4th ed. New York: John Wiley & Sons, 2016.
    [42]
    R. Grygiel, R. Bieda, and M. Blachuta, “On significance of second-order dynamics for coupled tanks systems,” in Proc. 21st Int. Conf. Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, 2016, pp. 1016−1021.
    [43]
    J. Na, Y. Huang, Q. Pei, X. Wu, G. Gao, and G. Li, “Active suspension control of full-car systems without function approximation,” IEEE/ASME Trans. Mechatron., vol. 25, no. 2, pp. 779–791, Apr. 2020. doi: 10.1109/TMECH.2019.2962602
    [44]
    B. Wahlberg and H. Sandberg, “Cascade structural model approximation of identified state space models,” in Proc. 47th IEEE Conf. Decision and Control, Cancun, Mexico, 2008, pp. 4198−4203.
    [45]
    J. J. Moré, “The Levenberg-Marquardt algorithm: Implementation and theory,” in Numerical Analysis, G. A. Watson, Ed. Berlin, Heidelberg, Germany: Springer, 1978, pp. 105−116.
    [46]
    Y. Dimitrov, S. Georgiev, and V. Todorov, “Approximation of Caputo fractional derivative and numerical solutions of fractional differential equations,” Fractal Fract., vol. 7, no. 10, p. 750, Oct. 2023. doi: 10.3390/fractalfract7100750
    [47]
    R. Scherer, S. L. Kalla, Y. Tang, and J. Huang, “The Grünwald-Letnikov method for fractional differential equations,” Comput. Math. Appl., vol. 62, no. 3, pp. 902–917, Aug. 2011. doi: 10.1016/j.camwa.2011.03.054
    [48]
    F. Merrikh-Bayat, “Rules for selecting the parameters of Oustaloup recursive approximation for the simulation of linear feedback systems containing PIλDμ controller,” Commun. Nonlinear Sci. Numer. Simul., vol. 17, no. 4, pp. 1852–1861, Apr. 2012. doi: 10.1016/j.cnsns.2011.08.042
    [49]
    C. A. Monje, Y. Q. Chen, B. M. Vinagre, D. Xue, and V. Feliu, Fractional-Order Systems and Controls: Fundamentals and Applications. London, UK: Springer, 2010, pp. 231−258.
    [50]
    R. De Keyser, C. I. Muresan, and C. M. Ionescu, “An efficient algorithm for low-order direct discrete-time implementation of fractional order transfer functions,” ISA Trans., vol. 74, pp. 229–238, Mar. 2018. doi: 10.1016/j.isatra.2018.01.026
    [51]
    R. De Keyser, I. R. Birs, C. I. Muresan, and C. M. Ionescu, “Revisiting the impulse response creates an improved PID autotuner,” Sci. Rep., vol. 15, no. 1, Art. no. 36203, Oct. 2025.
    [52]
    K. J. Åström and T. Hägglund, PID Controllers, Theory, Design and Tuning, 2nd ed. Research Triangle Park, USA: Instrument Society of America, 1995.
    [53]
    M. Ghorbani, M. Tavakoli-Kakhki, A. Tepljakov, and E. Petlenkov, “Robust stability analysis of smith predictor based interval fractional-order control systems: A case study in level control process,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 3, pp. 762–780, Mar. 2023. doi: 10.1109/JAS.2022.105986
    • Related Articles
    • Supplements(0)

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(19)  / Tables(2)

    Get Citation
    PDF
    XML

    Article Metrics

    Article views (27) PDF downloads(6) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return