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Data-driven anti-windup compensator synthesis for unknown linear systems with time delay. (English) Zbl 1483.93179

Summary: Delay and actuator saturation are inevitable in practical control engineering, which may lead to system performance degradation, or even divergence of controlled variables. Combination of Smith predictor (SP) and model recovery anti-windup method is an effective solution to anti-windup synthesis for linear delayed systems, but model-dependent property brings obstacles for the application and promotion. To overcome such a difficulty, a few-shot data-driven approach has been proposed in this paper, and operating data are collected to simultaneously tune feedback controller parameters and estimate internal model applied in SP. Subsequently, the anti-windup compensator is constructed with the estimated model and compensator gain is calculated by using the Lyapunov equation. Finally, the effectiveness of the proposed method is verified through simulations that implemented three typical processes in engineering.

MSC:

93B50 Synthesis problems
93C05 Linear systems in control theory
93C80 Frequency-response methods in control theory
93C43 Delay control/observation systems
Full Text: DOI

References:

[1] Campi, M. C.; Lecchini, A.; Savaresi, S. M., Virtual reference feedback tuning: A direct method for the design of feedback controllers, Automatica, 38, 8, 1337-1346 (2002) · Zbl 1008.93037 · doi:10.1016/S0005-1098(02)00032-8
[2] Cao, Y. Y.; Lin, Z.; Ward, D. G., An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation, IEEE Transactions on Automatic Control, 47, 1, 140-145 (2002) · Zbl 1364.93612 · doi:10.1109/9.981734
[3] Cristofaro, A.; Galeani, S.; Onori, S.; Zaccarian, L., A switched and scheduled design for model recovery anti-windup of linear plants, European Journal of Control, 46, 23-35 (2019) · Zbl 1412.93041 · doi:10.1016/j.ejcon.2018.04.002
[4] Ding, X.; Cui, B., Adaptive control for mismatch Smith predictor with disturbance, Computer Engineering and Applications, 53, 6, 223-226 (2017)
[5] Forni, F.; Galeani, S.; Zaccarian, L., Model recovery anti-windup for continuous-time rate and magnitude saturated linear plants, Automatica, 48, 8, 1502-1513 (2012) · Zbl 1267.93045 · doi:10.1016/j.automatica.2012.05.019
[6] Grimm, G.; Teel, A. R.; Zaccarian, L., The l2 anti-windup problem for discrete-time linear systems: Definition and solutions, Systems & Control Letters, 57, 4, 356-364 (2008) · Zbl 1133.93039 · doi:10.1016/j.sysconle.2007.09.014
[7] Herrmann, G.; Turner, M. C.; Postlethwaite, I., Discrete-time and sampled-data anti-windup synthesis: Stability and performance, International Journal of Systems Science, 37, 2, 91-113 (2006) · Zbl 1126.93048 · doi:10.1080/00207720500444074
[8] Hu, T.; Lin, Z., Control systems with actuator saturation: Analysis and design (2001), Springer Science & Business Media · Zbl 1061.93003
[9] Hu, T.; Lin, Z., Composite quadratic Lyapunov functions for constrained control systems, IEEE Transactions on Automatic Control, 48, 3, 440-450 (2003) · Zbl 1364.93108 · doi:10.1109/TAC.2003.809149
[10] Hu, T.; Teel, A. R.; Zaccarian, L., Anti-windup synthesis for linear control systems with input saturation: Achieving regional, nonlinear performance, Automatica, 44, 2, 512-519 (2008) · Zbl 1283.93120 · doi:10.1016/j.automatica.2007.06.003
[11] Kaneko, O.; Miyachi, M.; Fujii, T., Simultaneous updating of model and controller based on fictitious reference iterative tuning, SICE Journal of Control, Measurement, and System Integration, 4, 1, 63-70 (2011) · doi:10.9746/jcmsi.4.63
[12] Kaneko, O.; Yamamoto, S.; Wadagaki, Y., Simultaneous attainment of model and controller for linear time delay systems with the data driven Smith compensator, IFAC Proceedings Volumes, 44, 1, 7684-7689 (2011) · doi:10.3182/20110828-6-IT-1002.02792
[13] Lennart, L., System identification: Theory for the user, 1-14 (1999), PTR Prentice Hall
[14] Lima, T. A.; de Almeida Filho, M. P.; Torrico, B. C.; Nogueira, F. G.; Correia, W. B., A practical solution for the control of time-delayed and delay-free systems with saturating actuators, European Journal of Control, 51, 53-64 (2020) · Zbl 1429.93268 · doi:10.1016/j.ejcon.2019.06.012
[15] Peng, X.; Jia, S.; Zhang, B., An anti-saturation method for a class of nonlinear systems with actuator saturation, Acta Automatica Sinica, 42, 5, 798-804 (2016) · Zbl 1363.93114 · doi:10.16383/j.aas.2016.c150104
[16] Ran, M.; Wang, Q.; Dong, C., Anti-windup design for uncertain nonlinear systems subject to actuator saturation and external disturbance, International Journal of Robust and Nonlinear Control, 26, 15, 3421-3438 (2016) · Zbl 1350.93036 · doi:10.1002/rnc.v26.15
[17] Ran, M.; Wang, Q.; Dong, C., Stabilization of a class of nonlinear systems with actuator saturation via active disturbance rejection control, Automatica, 63, 302-310 (2016) · Zbl 1329.93121 · doi:10.1016/j.automatica.2015.10.010
[18] Rizvi, S. A. A.; Lin, Z., Adaptive dynamic programming for model-free global stabilization of control constrained continuous-time systems, IEEE Transactions on Cybernetics, 1-13 (2020) · doi:10.1109/tcyb.2020.2989419
[19] Sofrony, J.; Turner, M. C.; Postlethwaite, I., Anti-windup synthesis using Riccati equations, International Journal of Control, 80, 1, 112-128 (2007) · Zbl 1115.93031 · doi:10.1080/00207170600944229
[20] Soma, S.; Kaneko, O.; Fujii, T., A new method of controller parameter tuning based on input-output data—fictitious reference iterative tuning (FRIT), IFAC Proceedings Volumes, 37, 12, 789-794 (2004) · doi:10.1016/S1474-6670(17)31566-5
[21] Sutikno, J. P.; Hidayah, N.; Handogo, R., Maximum peak-gain margin (Mp-GM) tuning method for two degree of freedom PID controller, PID Control for Industrial Processes, 21-42 (2018) · doi:10.5772/intechopen.74293
[22] Syaichu-Rohman, A.; Middleton, R. H.; Seron, M. M., A multivariable nonlinear algebraic loop as a QP with applications to MPC (2003)
[23] Tang, X.; Wang, D.; Wang, Y.; Jiang, W., Internal model control method based on virtual reference feedback tuning, Journal of South China University of Technology, 41, 5, 15-21 (2016) · doi:10.3969/j.issn.1000-565X.2016.05.010
[24] Tian, Y.; Yan, H.; Zhang, H.; Yang, S. X.; Li, Z., Observed-based finite-time control of nonlinear semi-Markovian jump systems with saturation constraint, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 1-11 (2020) · doi:10.1109/TSMC.2019.2962318
[25] Wu, M.; Cheng, J.; Lu, C.; Chen, L.; Chen, X.; Cao, W.; Lai, X., Disturbance estimator and Smith predictor-based active rejection of stick-slip vibrations in drill-string systems, International Journal of Systems Science, 51, 5, 826-838 (2020) · Zbl 1483.93635 · doi:10.1080/00207721.2020.1744046
[26] Wu, X.; Lin, Z., Dynamic anti-windup design in anticipation of actuator saturation, International Journal of Robust and Nonlinear Control, 24, 2, 295-312 (2014) · Zbl 1279.93053 · doi:10.1002/rnc.v24.2
[27] Yang, S. K., A new anti-windup strategy for PID controllers with derivative filters, Asian Journal of Control, 14, 2, 564-571 (2012) · Zbl 1286.93073 · doi:10.1002/asjc.293
[28] Yuan, Y.; Wang, Z.; Yu, Y.; Guo, L.; Yang, H., Active disturbance rejection control for a pneumatic motion platform subject to actuator saturation: An extended state observer approach, Automatica, 107, 353-361 (2019) · Zbl 1429.93086 · doi:10.1016/j.automatica.2019.05.056
[29] Zaccarian, L.; Nešić, D.; Teel, A. R., L2 anti-windup for linear dead-time systems, Systems & Control Letters, 54, 12, 1205-1217 (2005) · Zbl 1129.93394 · doi:10.1016/j.sysconle.2005.04.009
[30] Zhai, D.; Zhang, Q. L.; Liu, G. Y., Data-driven criteria synthesis of system with two-degree-of-freedom controller, International Journal of Systems Science, 45, 11, 2275-2281 (2014) · Zbl 1317.93110 · doi:10.1080/00207721.2013.768306
[31] Zhang, W.; Xu, X., Analytical design and analysis of mismatched Smith predictor, ISA Transactions, 40, 2, 133-138 (2001) · doi:10.1016/S0019-0578(00)00045-8
[32] Zhou, B.; Lin, Z., Parametric Lyapunov equation approach to stabilization of discrete-time systems with input delay and saturation, IEEE Transactions on Circuits and Systems I: Regular Papers, 58, 11, 2741-2754 (2011) · Zbl 1468.93143 · doi:10.1109/TCSI.2011.2143170
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