طراحی کنترل‌کننده و تحلیل پایداری مجانبی مبدل باک با ساختار کنترلی آبشاری و استفاده از نظریه آشفتگی منفرد
محورهای موضوعی : مهندسی برق و کامپیوترسجاد آذراستمال 1 , محمد هجری 2 *
1 - دانشگاه صنعتی سهند تبریز
2 - دانشگاه صنعتی سهند
کلید واژه: پایداری مجانبی کنترل آبشاریکنترل مد لغزشیمبدل باک DC-DCنظریه آشفتگی منفرد,
چکیده مقاله :
این مقاله، اثبات نظری پایداری مجانبی حلقه بسته مبدل باک DC-DC را بر مبنای نظریه آشفتگی منفرد ارائه می‌دهد. به دلیل ماهیت ساختار دو مقیاس زمانی با دینامیک‌های تند و کند در این مبدل، برای کنترل آن از ساختار کنترلی آبشاری استفاده شده است. این کنترل‌کننده دارای دو حلقه کنترلی می‌باشد: یک حلقه بیرونی برای کنترل ولتاژ خروجی بر مبنای کنترل تناسبی- انتگرالی و یک حلقه درونی برای کنترل جریان سلف بر مبنای کنترل مد لغزشی. کنترل‌کننده‌های مربوط به هر کدام از حلقه‌ها بر مبنای نظریه آشفتگی طوری طراحی می‌شوند که محدودیت‌های در نظر گرفته شده برای مبدل را برآورده کرده و پایداری مجانبی حلقه بسته را در گستره وسیعی از شرایط اولیه مبدل، تضمین کنند. جهت اعتبارسنجی، روش پیشنهادی برای یک مبدل باک نوعی در محیط Matlab-Simulink شبیه‌سازی شده است. نتایج شبیه‌سازی نشان می‌دهد که با انتخاب مناسب ضرایب کنترل‌کننده PI حلقه بیرونی، مطلوبات مسئله برآورده شده و سیستم پایدار مجانبی می‌شود. همچنین مقاومت سیستم در برابر نامعینی بار و اغتشاشات ورودی و نیز نحوه ردیابی مرجع ولتاژ مورد ارزیابی قرار گرفته و ساختار پیشنهادی با ساختار PI-PI مقایسه شده است.
This paper presents the theoretical proof for the closed-loop asymptotic stability of a DC-DC buck converter based on singular perturbation theory. Due to the two-time scales structure of this converter with fast and slow dynamics, a cascade control structure is used to control it. This controller has two control loops: an outer loop to control the output voltage based on the proportional-integral control and an inner loop to control the inductor current based on the sliding mode control. The controllers in the loops are designed based on perturbation theory to meet the constraints of the converter and ensure the asymptotic stability of the closed-loop system over a wide range of initial conditions. For validation, the proposed control design method is simulated for a typical buck converter in the MATLAB-SIMULINK environment. The simulation results show that by properly selecting the PI controller coefficients in the outer loop, the problem requirements are met, and the asymptotic stability of the closed-loop system is guaranteed in a wide range of the converter initial conditions. Furthermore, the system robustness against load uncertainty and input disturbances as well as the voltage reference tracking are evaluated, and the proposed structure is compared with a PI-PI structure.
[1] M. H. Rashid, M. Kumar, and A. R. Kulkarni, Power Electronics Circuits, Devices and Applications, Pearson, 2014.
[2] R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, Kluwer Academic, 2004.
[3] F. L. Luo and H. Ye, Advanced DC/DC Converters, CRC Press, 2017.
[4] K. M. Tsang and W. L. Chan, "Cascade controller for DC/DC buck converter," IEE Proc.-Electr. Power Appl., vol. 152, no. 4, pp. 827-831, Jul. 2005.
[5] V. Utkin, J. Guldner, and J. Shi, Sliding Mode Control in Electro-Mechanical Systems, CRC Press, 2009.
[6] A. B. Corripio, Tuning of Industrial Control Systems, 2nd Edition, ISA, 2001.
[7] Y. Zhong and Y. Luo, "Comparative study of single-loop control and cascade control of third-order object," Procedia Engineering, vol. 15, pp. 783-787, 2011.
[8] S. Garai, R. Maity, S. Das, S. Chakraborty, and S. Ghosh, "A review of tuning method for cascade control," International J. of Engineering and Management Research, vol. 6, no. 5, pp. 61-69, Sep./Oct. 2016.
[9] Y. I. Son, I. H. Kim, D. S. Choi, and H. Shim, "Robust cascade control of electric motor drives using dual reduced-order PI observer," IEEE Trans. Industrial Electronic, vol. 62, no. 6, pp. 3672- 3682, Jun. 2015.
[10] L. V. Bellinaso, H. H. Figueira, M. F. Basquera Jr., R. P. Vieira, H. A. Grundling, and L. Michels, "Cascade control with adaptive voltage controller applied to photovoltaic boost converters," IEEE Trans. Industrial Electronic, vol. 55, no. 2, pp. 1903-1912, Mar./Apr. 2019.
[11] C. Guo, Q. Song, and W. Cai, "A neural network assisted cascade control system for air handling unit," IEEE Trans. Industrial Electronic, vol. 54, no. 1, pp. 620-628, Feb. 2007.
[12] S. Rees, "New cascaded control system for current-source rectifiers," IEEE Trans. Industrial Electronic, vol. 52, no. 3, pp. 774-784, Jun. 2005.
[13] A. R. Cukla, R. C. Izquierdo, F. A. Borges, E. A. Perondi, and F. J. Lorini, "Optimum cascade control tuning of a hydraulic actuator based on firefly metaheuristic algorithm," IEEE Latin America Trans., vol. 16, no. 2, pp. 384-390, Feb. 2018.
[14] M. A. Mahar and A. S. Larik, "Performance assessment of buck converter using single and cascade control loops," in Proc. of the Int. Conf. on Industrial Engineering and Operations Management, pp. 948-954, Pilsen, Czech Republic, 23-26 Jul. 2019.
[15] K. M. Tsang and W. L. Chan, "Non-linear cascade controller of DC/DC buck converter," Electric Power Components and Systems, vol. 36, no. 9, pp. 977-989, Aug. 2008.
[16] O. Rabiaa, B. H. Mouna, S. Lassaad, F. Aymen, and A. Aicha, "Cascade control loop of DC-DC boost converter using PI controller," in Proc. Int. Symp. on Advanced Electrical and Communication Technologies, ISAECT'18, 5 pp., Rabat, Morocco, 21-23 Nov. 2018.
[17] V. D. Yurkevich, "PWM controller design based on singular perturbation technique: a case study of buck-boost converter," in Proc. 18th IFAC World Congress, pp. 9739-9744, Milano, Italy, 28 Aug.-2 Sep. 2011.
[18] E. A. Aksenov and V. D. Yurkevich, "Cascaded control system design for a Cuk converter via singular perturbation approach," in Proc. 16th Int. Conf. on Micro/Nanotechnologies and Electron Devices EDM, pp. 534-54, Erlagol, Russia ,29 Jun.-3 Jul. 2015.
[19] Z. Wu, J. Zhao, and J. Zhang, "Cascaded PID control of buck-boost-type DC/DC power converter," in Proc. 6th World Congress on Intelligent Control and Automation, pp. 8467-8471, Dalian, China, 21-23 Jun. 2006.
[20] M. Hejri and H. Mokhtari, "Hybrid predictive control of a DC-DC boost converter in both continuous and discontinuous current modes of operation," Optim. Control Appl. Meth., vol. 32, no. 3, pp. 270-284, Jan. 2010.
[21] م. هجری، "مدل‌سازی و کنترل هیبرید سرتاسری مبدل DC-DC باک- بوست به وسیله سیستم‌های دینامیکی- منطقی مخلوط،" نشریه مهندسی برق و مهندسی کامپیوتر ایران، شماره 1، سال 17، صص. 1-12، بهار 1398.
[22] V. S. C. Raviraj and P. C. Sen, "Comparative study of proportional-integral, sliding mode, and fuzzy logic controllers for power converters," IEEE Trans. Industry App., vol. 33, no. 2, pp. 518-524, Mar./Apr. 1997.
[23] C. Asma, A. Zaidi, and Z. Nadia, "Dual loop control of DC-DC boost converter based cascade sliding mode control," in Proc. G Int. Conf. on Green Energy Conversion Systems, GECS’17, 6 pp., Hammamet, Tunisia, 23-25 Mar. 2017.
[24] B. M. David and K. K. Sreeja, "PID and sliding mode control of buck power converter as a smooth starter for DC motor," International J. of Innovative Research in Science, Engineering and Technology, vol. 4, no. 8, pp. 7108-7115, Aug. 2015.
[25] H. Guldemir, "Sliding mode control of DC-DC boost converter," J. of Applied Sciences, vol. 5, no. 3, pp. 588-592, Mar. 2005.
[26] L. Ahmethodzic, N. Hadzimejlic, and A. Ahmethodzic, "Cascade SMC control of Cuk converter for telecommunication systems power supply," in Proc. Int. Symp. on Telecommunication, 5 pp., Sarajevo, Bosnia and Herzegovina, 27-29 Oct. 2014.
[27] Z. Chen, W. Gao, J. Hu, and X. Ye, "Closed-loop analysis and cascade control of a nonminimum phase boost converter," IEEE Trans. Power Electron., vol. 26, no. 4, pp. 1237-1252, Apr. 2011.
[28] Z. Chen, "PI and sliding mode control of a Cuk converter," IEEE Trans. Power Electron., vol. 27, no. 8, pp. 3695-3703, Aug. 2012.
[29] F. Ahmad, A. Rasool, E. E. Ozsoy, A. Sabanovic, and M. Elitas, "A robust cascaded controller for DC-DC boost and Cuk converters," World J. of Engineering, vol. 14, no. 5, pp. 459-466, Oct. 2017.
[30] N. Genc, H. Uzmus, and I. Iskender, "Dynamic behavior of DC-DC boost converter controlled with cascade PI-ASC," in Proc. Electronics, Computer and Artificial Intelligence, ECAI'16, 4 pp., Ploiesti, Romania, 30 Jun.- 2 Jul. 2016.
[31] E. A. Aksenov and V. D. Yurkevich, "Sliding mode and time-scales in control system design for a Cuk converter," in Proc. 17th Int. Conf. on Micro/Nanotechnologies and Electron Devices EDM, pp.401-406, 30 Jun.- 4 Jul. 2016.
[32] E. A. Aksenov and V. D. Yurkevich, "Control system design based on sliding mode control and singular perturbation technique for a Cuk converter," in Proc. 13th Int. Scientific-Technical Conf. on Actual Problems of Electronics Instrument Engineering, APEIE'16, vol. 3, pp. 77-82, 3-6 Oct. 2016.
[33] K. Al-Hosani, A. Malinin, and V. I. Utkin, "Sliding mode PID control of buck converters," in Proc. European Control Conf., pp. 2740-2744, Budapest, Hungary, 23-26 Aug. 2009.
[34] H. Li and X. Ye, "Sliding-mode PID control of DC-DC converter," in Proc. 5th IEEE Conf. on Industrial Electronics and Applications, pp. 730-734, Taichung, Taiwan, 15-17 Jun. 2010.
[35] H. K. Khalil, Nonlinear Systems, Prentice Hall, 2002.
[36] P. Kokotovic, H. K. Khalil, and J. O'Reilly, Singular Perturbation Methods in Control: Analysis and Design, Philadelphia, PA: SIAM, 1999.
[37] M. A. Khosravi and H. D. Thaghirad, "Dynamic modeling and control of parallel robots with elastic cables: singular perturbation approach," IEEE Trans. Robotics, vol. 30, no. 3, pp. 694-704, Jun. 2014.
[38] G. Cimatti, "A singular perturbation problem in magnetohydrodynamics," IMA J. of Applied Mathematics, vol. 75, no. 2, pp. 240-245, Apr. 2010.
[39] M. Kiani Oshtorjani, A. Mikkola, and P. Jalali, "Numerical treatment of singularity in hydraulic circuits using singular perturbation theory," IEEE/ASME Trans. Mechatronics, vol. 24, no. 1, pp. 144-153, Feb. 2019.
[40] M. Kamenski, P. Nistri, and M. Quincampoix, "Sliding mode control of uncertain systems: a singular perturbation approach," IMA J. of Mathematical Control and Information, vol. 19, no. 4, pp. 377-398, Dec. 2002.
[41] A. J. Forsyth and S. V. Mollov, "Modeling and control of DC-DC converters," Power Engineering J., vol. 12, no. 5, pp. 229-236, Oct. 1998.
[42] J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, 1991. J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, 1991.