Abstract
A new design method of a robust fractional order PI controller for uncertain First Order Plus Dead Time systems is proposed in this paper. The proposed design method uses a numerical optimization algorithm to determine the unknown controller parameters. The main objective of the proposed design method is improving the robustness in degree of stability to gain variations and the stability robustness to the other parameters variations that affect the phase by imposing a constant phase margin to the corrected open loop system in a pre-specified frequency band. Several simulation examples are presented to design the robust fractional PI controller and test the robustness for different forms of uncertainty.
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References
Amairi, M., Aoun, M., Saidi, B.: Design of robust fractional order pi for fopdt systems via set inversion. In: 2014 IEEE Conference on Control Applications (CCA), pp. 1166–1171. IEEE (2014)
Annal, A.W.P., Kanthalakshmi, S.: An adaptive pid control algorithm for nonlinear process with uncertain dynamics. Int. J. Automation Control 11(3), 262–273 (2017)
Ben Hmed, A., Amairi, M., Aoun, M.: Robust stabilization and control using fractional order integrator. Trans. Inst. Meas. Control 39(10), 1559–1576 (2017)
Bouyedda, H., Ladaci, S., Sedraoui, M., Lashab, M.: Identification and control design for a class of non-minimum phase dead-time systems based on fractional-order smith predictor and genetic algorithm technique. Int. J. Dyn. Control 7(3), 914–925 (2019)
Das, S., Saha, S., Das, S., Gupta, A.: On the selection of tuning methodology of FOPID controllers for the control of higher order processes. ISA Trans. 50(3), 376–388 (2011)
Feliu-Batlle, V., Rivas, R., Castillo, F.: Fractional order controller robust to time delay variations for water distribution in an irrigation main canal pool. Comput. Electronics Agric. 69, 185–197 (2009)
Guo, J., Dong, L.: Robust load frequency control for uncertain nonlinear interconnected power systems. Int. J. Automation Control 11(3), 239–261 (2017)
Kannan, G., Saravanakumar, G., Saraswathi, M.: Two-degree of freedom pid controller in time delay system using hybrid controller model. Int. J. Automation Control 12(3), 399–426 (2018)
Liang, T., Chen, J., Lei, C.: Algorithm of robust stability region for interval plant with time delay using fractional order \(PI^\lambda D^\nu \) contoller. Commun. Nonlineair Sci. Numer. Simulat. 17, 979–991 (2011)
Lu, D., Tang, J.: Particle swarm optimisation algorithm for a time-delay system with piece-wise linearity. Int. J. Automation Control 11(3), 290–297 (2017)
Boudana, Marwa, Ladaci, S.J.J.L.: Fractional order pi \(^\lambda \) and pi\(^\mu \) d \(^\lambda \) control design for a class of fractional order time-delay systems. Int. J. Cyber-Phys. Syst. (IJCPS) 1(2), 1–18 (2019)
Mercader, P., Banos, A., Vilanova, R.: Robust proportional-integral-derivative design for processes with interval parametric uncertainty. IET Control Theor. Appl. 11(7), 1016–1023 (2017)
Monje, C., Chen, Y., Vinagre, B., Xue, D., Feliu, V.: Fractional-Order Systems and Controls: Fundamentals and Applications. Springer (2010)
Neçaibia, A., Ladaci, S.: Self-tuning fractional order pi \(^\lambda \) d \(^\mu \) controller based on extremum seeking approach. Int. J. Automation Control 8(2), 99–121 (2014)
Podlubny, I.: Fractional-order systems and \(\rm {P}I^\lambda D^\nu \) controller. IEEE Trans. Automatic Control 44, 208–214 (1999)
Pourhashemi, A., Ramezani, A., Siahi, M.: Designing dynamic fractional terminal sliding mode controller for a class of nonlinear system with uncertainties. Int. J. Automation Control 13(2), 197–225 (2019)
Rabah, K., Ladaci, S., Lashab, M.: Bifurcation-based fractional-order pi \(\lambda \) d \(\mu \) controller design approach for nonlinear chaotic systems. Front. Inf. Technol. Electronic Eng. 19(2), 180–191 (2018)
Saidi, B., Amairi, M., Najar, S., Aoun, M.: Bode shaping-based design methods of a fractional order pid controller for uncertain systems. Nonlinear Dyn. 80(4), 1817–1838 (2014)
Saidi, B., Amairi, M., Najar, S., Aoun, M.: Multi-objective optimization based design of fractional PID controller. In: 12th International Multi-Conference on Systems, Signals & Devices (SSD), pp. 1–6. IEEE (2015)
Saidi, B., Amairi, M., Najjar, S., Aoun, M.: Fractional pid min-max optimisation-based design using dominant pole placement. Int. J. Syst. Control Commun. 9(4), 277–305 (2018)
Saidi, B., Najar, S., Amairi, M., Abdelkrim, M.N.: Design of a robust fractional \(\rm {PID}\) controller for a second order plus dead time system. In: 10th International Multi-Conference on Systems, Signals & Devices (SSD), pp. 1–6. IEEE (2013)
Somasundaram, S., Benjanarasuth, T.: Cdm-based two degree of freedom pi controller tuning rules for stable and unstable foptd processes and pure integrating processes with time delay. Int. J. Automation Control 13(3), 263–281 (2019)
Toscano, R.: A simple robust \(\rm {PI}\)/\(\rm {PID}\) controller design via numerical optimization approach. J. Process Control 15, 81–89 (2005)
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This work was supported by the Ministry of the Higher Education and Scientific Research in Tunisia.
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Saidi, B., Yacoub, Z., Amairi, M., Aoun, M. (2022). Constant Phase Based Design of Robust Fractional PI Controller for Uncertain First Order Plus Dead Time Systems. In: Naifar, O., Ben Makhlouf, A. (eds) Fractional Order Systems—Control Theory and Applications. Studies in Systems, Decision and Control, vol 364. Springer, Cham. https://doi.org/10.1007/978-3-030-71446-8_9
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