حضور تأخیر محدود در سیگنال سوئیچ سیستم‌های سوئیچینگ خطی‌تبار
محورهای موضوعی : مهندسی برق و کامپیوترآرمان صحت نیا 1 , فرزاد هاشم‌زاده 2 * , مهدی برادران نیا 3
1 - دانشكده مهندسي برق و كامپيوتر، دانشگاه تبریز
2 - دانشكده مهندسي برق و كامپيوتر، دانشگاه تبریز
3 - دانشكده مهندسي برق و كامپيوتر، دانشگاه تبریز
کلید واژه: سیستم‌های سوئیچینگ خطی‌تبار, سیگنال سوئیچ‌زنی, تأخیر محدود, پایداری عملی لیاپانوف,
چکیده مقاله :
در این مقاله پیامد حضور تأخیر در سیگنال سوئیچ برای سیستم‌های سوئیچینگ خطی‌تبار بررسی می‌شود. ابتدا بر اساس اصول پایداری، روند استخراج سیگنال سوئیچ به‌عنوان تنها ورودی کنترلی بررسی شده و سپس با ارائه مبحث پایداری عملی برای سیستم‌های سوئیچ‌دار، دیدگاه واقع‌گرایانه‌تری نسبت به این سیستم‌ها مطرح می‌شود. تمرکز اصلی مقاله بر روی تأثیر تأخیر در انتقال اطلاعات سیگنال سوئیچ خواهد بود. حضور تأخیر محدود در سیگنال سوئیچ معمولاً ناشی از حجم بالای محاسبات قانون سوئیچ‌زنی و یا هر گونه حمله سایبری است. در این مقاله نتایج پایداری عملی لیاپانوف مربوط به حالات قبل و بعد از حضور تأخیر در سیگنال برای یک سیستم سوئیچینگ خطی‌تبار به صورت تحلیلی و شبیه‌سازی مقایسه می‌شوند. نتایج مقایسه این حالت‌ها نشان‌دهنده آن است که با افزایش تأخیر محدود در سیگنال سوئیچ، کران غایی سیستم هم بزرگ‌تر می‌شود و این به معنی کاهش همگرایی حالت‌های سیستم است. در این راستا نتایج به‌دست‌آمده برای یک مبدل قدرت DC-DC پیاده‌سازی و مقایسه‌های لازم در فصل آخر ارائه می‌شود.
In this article, the consequence of the presence of delay in the switch signal for switched affine systems is investigated. First, based on the principles of stability, the process of extracting the switch law as the only control input is examined, then by presenting the practical stability issue for switched systems, more realistic view of these systems is proposed. The main focus of the article will be on the effect of delay in the transmission of switching signal information. The presence of limited delay in switching signal is usually caused by high volume of switching law calculations or any cyber attacks. In this paper, the practical Lyapunov stability results related to the states before and after the presence of delay in switching signal for a linear switched affine system are compared analytically and simulated. The results of the comparison of these modes show that when the value of delay in switching signal increases, the ultimate limit of the error for system states becomes larger, and this means a decrease in the convergence of the system states. In this regard, the results implemented for a DC-DC power converter and the necessary comparisons are presented in the last chapter.
[1] E. Feron, Quadratic Stabilizability of Switched Systems via State and Output Feedback, Center for Intelligent Control Systems, 13 pp., 1996.
[2] Y. Chang, G. Zhai, L. Xiong, and B. Fu, "Global quadratic stabilization in probability for switched linear stochastic systems," IEEE Access, vol. 8, pp. 103610-103618, 2020.
[3] C. Peng and H. Sun, "Switching-like event-triggered control for networked control systems under malicious denial of service attacks," IEEE Trans. on Automatic Control, vol. 65, no. 9, pp. 3943-3949, Sept. 2020.
[4] M. Hejri, "Practical stability analysis and switching controller synthesis for discrete-time switched affine systems via linear matrix inequalities," Scientia Iranica, Articles in Press, 2022.
[5] A. Shams, M. Rehan, M. A. Razaq, and M. Tufail, "A new approach using multiple Lyapunov functions for bipartite consensus of multi-agents over directed switching signed graphs," Nonlinear Analysis: Hybrid Systems, vol. 44, Article ID: 101143, May 2022.
[6] X. Zhang and Z. Wang, "Stability and robust stabilization of uncertain switched fractional order systems," ISA Trans., vol. 103, 9 pp., Aug. 2020.
[7] Y. Ma, Z. Li, and J. Zhao, "H∞ control for switched systems based on dynamic event-triggered strategy and quantization under state-dependent switching," IEEE Trans. on Circuits and Systems I: Regular Papers, vol. 67, no. 9, pp. 3175-3186, Sept. 2020.
[8] N. K. Son and L. Van Ngoc, "On robust stability of switched linear systems," IET Control Theory & Applications, vol. 14, no. 1, pp. 19-29, Jan. 2020.
[9] K. Zhu, J. Hu, Y. Liu, N. D. Alotaibi, and F. E. Alsaadi, "On ℓ2–ℓ∞ output-feedback control scheduled by stochastic communication protocol for two-dimensional switched systems," International J. of Systems Science, vol. 52, no. 14, pp. 2961-2976, 2021.
[10] G. O. Berger and R. M. Jungers, "Quantized stabilization of continuous-time switched linear systems," IEEE Control Systems Letters, vol. 5, no. 1, pp. 319-324, Jan. 2020.
[11] Y. Shi and X. M. Sun, "Bumpless transfer control for switched linear systems and its application to aero-engines," IEEE Trans. on Circuits and Systems I: Regular Papers, vol. 68, no. 5, pp. 2171-2182, May 2021.
[12] F. A. Faria, et al., "Robust switched state feedback design for linear uncertain systems subject to disturbances," in Proc. 16th Int. Workshop on Variable Structure Systems, VSS'2022, pp. 22-28, Rio de Janeiro, Brazil, 11-14 Sept. 2022.
[13] D. Llorente‐Vidrio, M. Mera, I. Salgado, and I. Chairez, "Robust control for state constrained systems based on composite barrier Lyapunov functions," International J. of Robust and Nonlinear Control, vol. 30, no. 17, pp. 7238-7254, 25 Nov. 2020.
[14] Y. Xie and W. Wang, "Hybrid control strategy of DC-DC converters based on admissible edge-dependent average dwell time," in Proc. 4th Int Conf. on Intelligent Green Building and Smart Grid, IGBSG'19, pp. 401-404, Hubei, China, 6-9 Sept. 2019.
[15] L. I. Allerhand and U. Shaked, "Robust state-dependent switching of linear systems with dwell time," IEEE Trans. on Automatic Control, vol. 58, no. 4, pp. 994-1001, Apr. 2012.
[16] D. Yang and J. Zhao, "Feedback passification for switched LPV systems via a state and parameter-triggered switching with dwell time constraints," Nonlinear Analysis: Hybrid Systems, vol. 29, pp. 147-164, Aug. 2018.
[17] T. Sun, T. Liu, and X. M. Sun, "Stability analysis of cyclic switched linear systems: an average cycle dwell time approach," Information Sciences, vol. 544, pp. 227-237, 12 Jan. 2021.
[18] Q. Liu and L. Long, "State‐dependent switching law design with guaranteed dwell time for switched nonlinear systems," International J. of Robust and Nonlinear Control, vol. 30, no. 8, pp. 3314-3331, 25 May. 2020.
[19] P. Bolzern and W. Spinelli, "Quadratic stabilization of a switched affine system about a nonequilibrium point," in Proc. of the American Control Conf., vol. 5, pp. 3890-3895, Boston, MA, USA, 30 Jun.- 2 Jul. 2004.
[20] X. Xu, G. Zhai, and S. He, "On practical asymptotic stabilizability of switched affine systems," Nonlinear Analysis: Hybrid Systems, vol. 2, no. 1, pp. 196-208, Mar. 2008.
[21] X. Yan, Z. Shu, and S. M. Sharkh, "Prediction-based sampled-data control for DC-DC buck converters," in Proc. 1st Workshop on Smart Grid and Renewable Energy, SGRE'15, 6 pp., Doha, Qatar, 22-23 Mar. 2015.
[22] L. Hetel and E. Fridman, "Robust sampled-data control of switched affine systems," IEEE Trans. on Automatic Control, vol. 58, no. 11, pp. 2922-2928, Nov. 2013.
[23] F. Wu, X. Qu, C. Li, J. Lian, and L. Xu, "Multi-rate sampled-data control of switched affine systems," IET Control Theory & Applications, vol. 14, no. 11, pp. 1524-1530, 23 Jul. 2020.
[24] H. Yang, P. Li, M. Xing, and B. Zhang, "Robust sampled-data control for direct_current-to-direct_current converters via switched affine description and error tracking strategy," Proc. of the Institution of Mechanical Engineers, Part I: J. of Systems and Control Engineering, vol. 236, no. 1, pp. 169-181, 2022.