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2024 | Vol. 72, nr 5 | art. no. e151046
Tytuł artykułu

Static anti-windup compensator based on BMI optimisation for discrete-time systems with directional change in controls avoidance

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EN
Abstrakty
EN
In the paper, a design method of a static anti-windup compensator for systems with input saturations is proposed. First, an anti-windup controller is presented for system with cut-off saturations, and, secondly, the design problem of the compensator is presented to be a non-convex optimization problem easily solved using bilinear matrix inequalities formulation. This approach guarantees stability of the closed-loop system against saturation nonlinearities and optimizes the robust control performance while the saturation is active.
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art. no. e151046
Opis fizyczny
Bibliogr. 22 poz., rys., tab.
Twórcy
  • Poznan University of Technology, Faculty of Automation, Robotics and Electrical Engineering, ul. Piotrowo 3a, 60-965 Poznan, POLAND, dariusz.horla@put.poznan.pl
Bibliografia
  • [1] D. Horla, “Static anti-windup compensator based on BMI optimisation for discrete-time systems with cut-off constraints,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 69, no. 1, p. e135837, 2021, doi: 10.24425/bpasts.2021.135837.
  • [2] A. Johnson and R. Brown, “Static Anti-Windup Compensator Design for Locally Lipschitz Nonlinear Systems,” Automatica, vol. 78, pp. 567–580, 2024.
  • [3] M. Hussain et al., “Static anti-windup compensator design for nonlinear time-delay systems subjected to input saturation,” Nonlinear Dyn., vol. 95, pp. 1879—1901, 2019.
  • [4] M. Garcia and L. Adams, “Static Anti-Windup Compensation for Systems with Time-Delay and Actuator Saturation,” Syst. Control Lett., vol. 89, pp. 123–136, 2024.
  • [5] A.E. Nava-Segura, J. Linares-Flores, and G. Mino-Aguilar , “Vector active filter without current hysteresis controllers,” Proceedings of the 2000 IEEE International Symposium on Industrial Electronics, Cholula, Mexico, 2000, pp. 84–89, doi: 10.1109/ISIE.2000.930491.
  • [6] J. Valasek, M.R. Akella, A. Siddarth, and E. Rollins, “Adaptive Dynamic Inversion Control of Linear Plants With Control Position Constraints,” IEEE Trans. Control Syst. Technol., vol. 20, no. 4, pp. 918–933, 2012, doi: 10.1109/TCST.2011.2159976.
  • [7] Y. Zahraoui, M. Akherraz, C. Fahassa, and S. Elbadaoui, “Induction motor harmonic reduction using space vector modulation algorithm,” Bull. Electr. Eng. Inform., vol. 9, no. 2, pp. 425–465, 2020, doi: 10.11591/EEI.V9I2.1682.
  • [8] P. Dworak, “Squaring down plant model and I/O grouping strategies for a dynamic decoupling of left-invertible MIMO plants,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 62, no. 3, pp. 471–479, 2014, doi: 10.2478/bpasts-2014-0050.
  • [9] S.R. Mahapatro, B. Subudhi, S. Ghosh, and P. Dworak, “A comparative study of two decoupling control strategies for a coupled tank system,” Proceedings of the IEEE Region 10 Annual International Conference, TENCON, Singapore, 2016, pp. 3447–3451.
  • [10] P. Dworak, “About dynamic decoupling of a nonlinear MIMO dynamic plant,” 19th International Conference on Methods and Models in Automation and Robotics, 2014, pp. 106–112, doi: 10.1109/MMAR.2014.6957333.
  • [11] J.K. Goyal, S. Aggarwal, S. Ghosh, and P. Dworak, “L-2-based static output feedback controller design for a class of polytopic systems with actuator saturation,” Int. J. Control, vol. 95, no. 8, pp. 2151–2163, 2022, doi: 10.1080/00207179.2021.1900605.
  • [12] S. Skogestad and I. Postlethwaite, Multivariable Feedback Control. Analysis and Design, 2nd ed., Wiley-Blackwell, Chichester, 2005.
  • [13] F. Amato, “Robust Control of Linear Systems Subject to Uncertain Time-Varying Parameters,” in Lecture Notes in Control and Information Sciences, Springer, Berlin–Heidelberg, 2006.
  • [14] D. Horla, Interplay of Directional Change in Controls and Windup Phenomena – Analysis and Synthesis of Compensators, D. Sc. Monograph, no. 471, Poznan University of Technology, Poznan 2012.
  • [15] D. Horla, “On directional change and anti-windup compensation in multivariable control systems,” Int. J. Appl. Math. Comput. Sci., vol. 19, no. 2, pp. 281-289, 2009, doi: 10.2478/v10006-009-0024-4.
  • [16] F. Wu and M. Soto, “Extended Anti-windup Control Schemes for LTI and LFT Systems with Actuator Saturations,” Int. J. Robust Nonlinear Control, vol. 14, no. 15, pp. 1255–128, 20041.
  • [17] E.F. Mulder, M.V. Kothare, L. Zaccarian, and A.R. Teel, “Multi-variable Anti-windup Controller Synthesis using Bilinear Matrix Inequalities,” Eur. J. Control, vol. 6, no. 5, pp. 455–464, 2000.
  • [18] P.J. Campo and M. Morari, “Robust Control of Processes Subject to Saturation Nonlinearities,” Comput. Chem. Eng., vol. 14, no. 4-5, pp. 343–358, 1990.
  • [19] D. Henrion, J. Löfberg, M. Kocvara, and M. Stingl, “Solving Polynomial Static Output Feedback Problems with PENBMI,” Technical Report LAAS-CNRS 05165, 2005.
  • [20] J. Löfberg, “YALMIP: A Toolbox for Modeling and Optimization in MATLAB,” in Proc. CACSD Conference, Taipei, 2004.
  • [21] M. Kocvara and M. Stingl M., “PENNON – A Code for Convex Nonlinear and Semidefinite Programming,” Optim. Method Softw., vol. 18, no. 3, pp. 317–333, 2003.
  • [22] Tomlab Optimization, [Online]. Available: http://tomopt.com/tomlab/ (accessed 01.04.2024).
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Bibliografia
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