تحلیل جبری پایداری و بررسی امکان وجود کنترل‌کننده تناسبی جهت پایدارسازی: وجود نقطه عطف بحرانی در دیاگرام فاز
محورهای موضوعی : مهندسی برق و کامپیوترخشایار نشاط 1 , محمد صالح تواضعی 2 *
1 - دانشگاه صنعتی شریف
2 - دانشگاه صنعتی شریف
کلید واژه: روش‌های جبری در تحلیل پایداریپایدارسازی تناسبیپاسخ فرکانسی,
چکیده مقاله :
این مقاله به مسأله تحلیل جبری پایداری و بررسی امکان وجود کنترل‌کننده تناسبی جهت پایدارسازی بر اساس اطلاعات پاسخ فرکانسی می‌پردازد. در ابتدا نشان داده خواهد شد که استفاده از نتایج موجود در این زمینه در حالت خاصی که دیاگرام فاز سیستم حلقه باز در مسأله تحلیل جبری پایداری یا دیاگرام فاز پروسه در مسأله پایدارسازی به کمک کنترل‌کننده‌های تناسبی دارای نقطه عطف بحرانی است، می‌توانند منجر به برداشت‌هایی ناسازگار شود. سپس برای حل مشکل ناسازگاری ذکرشده، اصلاحاتی پیشنهاد خواهد شد. در نهایت نیز به صورت تحلیلی شرایطی برای وجود نقطه عطف بحرانی در دیاگرام فاز یک سیستم دینامیکی استخراج می‌شود.
This paper deals with algebraic stability analysis and investigating the existence of proportional stabilizing controllers on the basis of frequency response data. Firstly, it is shown that using the available results in this subject may yield in inconsistent subsequences in the cases that there is a critical inflection point in phase diagram of the open-loop/process transfer function. Then, to solve this inconsistency problem some modifications are proposed. Finally, conditions for ensuring the existence of critical inflection point in phase diagram of a dynamical system are analytically found.
[1] N. Sayyaf and M. S. Tavazoei, "Robust fractional-order compensation in the presence of uncertainty in a pole/zero of the plant," IEEE Trans. on Control Systems Technology, vol. 26, no. 3, pp. 797-812, May 2018.
[2] Q. G. Wang, Z. Ye, and C. C. Hang, "Tuning of phase-lead compensators for exact gain and phase margins," Automatica, vol. 42, no. 2, pp. 349-352, Feb. 2006.
[3] N. Sayyaf and M. S. Tavazoei, "Desirably adjusting gain margin, phase margin, and corresponding crossover frequencies based on frequency data," IEEE Trans. on Industrial Informatics, vol. 13, no. 5, pp. 2311-2321, Oct. 2017.
[4] F. Y. Wang, "The exact and unique solution for phase-lead and phase-lag compensation," IEEE Trans. on Education, vol. 46, no. 2, pp. 258-262, May 2003.
[5] M. S. Tavazoei and M. Tavakoli-Kakhki, "Compensation by fractional-order phase-lead/lag compensators," IET Control Theory and Appl., vol. 8, no. 5, pp. 319-329, 20 Mar. 2014.
[6] L. H. Keel and S. P. Bhattacharyya, "Controller synthesis free of analytical models: three term controllers," IEEE Trans. on Automatic Control, vol. 53, no. 6, pp. 1353-1369, Jul. 2008.
[7] B. Fang, "Computation of stabilizing PID gain regions based on the inverse Nyquist plot," J. Process Control, vol. 20, no. 10, pp. 1183-1187, Dec. 2010.
[8] B. Fang, "Design of PID controllers for interval plants with time delay," J. Process Control, vol. 24, no. 10, pp. 1570-1578, Oct. 2014.
[9] D. J. Wang, "A PID controller set of guaranteeing stability and gain and phase margins for time-delay systems," J. Process Control, vol. 22, no. 7, pp. 1298-1306, Jun. 2012.
[10] L. H. Keel and S. P. Bhattacharyya, "Phase properties of Hurwitz and Schur polynomial," IEEE Trans. Automatic Control, vol. 41, no. 5, pp. 733-735, May 1996.
[11] S. Khadraoui, H. Nounou, M. Nounou, A. Datta, and S. P. Bhattacharyya, "A control design method for unknown systems using frequency domain data," in Proc. 9th Asian Control Conf. ,ASCC'13, 6 pp., Istanbul, Turkey, 23-26 Jun. 2013.
[12] L. H. Keel and S. P. Bhattacharyya, "A bode plot characterization of all stabilizing controllers," IEEE Trans. on Automatic Control, vol. 55, no. 11, pp. 2650-2654, Nov. 2010.
[13] N. Mohsenizadeh, S. Darbha, L. H. Keel, and S. P. Bhattacharyya, "Model-free synthesis of fixed structure stabilizing controllers using the rate of change of phase," IFAC Proceedings Volumes, vol. 45, no. 3, pp. 745-750, Mar. 2012.
[14] E. Almodaresi and M. Bozorg, "kp-stable regions in the space of PID controller coefficients," IET Control Theory & Applications, vol. 11, no. 10, pp. 1642-1647, 23 Jun. 2017.
[15] E. Almodaresi and M. Bozorg, "kp-stable regions in the space of time delay and PI controller coefficients," International J. of Control, vol. 88, no. 3, pp. 653-662, Mar. 2015.
[16] S. Khadraoui, H. N. Nounou, M. N. Nounou, A. Datta, and S. P. Bhattacharyya, "A measurement‐based approach for designing fixed‐order controllers for unknown closed‐loop architecture," Asian J. of Control, vol. 18, no. 2, pp. 686-698, Mar. 2016.
[17] M. A. Fnaiech, et al., "A measurement-based approach for speed control of induction machines," IEEE J. of Emerging and Selected Topics in Power Electronics, vol. 2, no. 2, pp. 308-318, Jun. 2014.
[18] S. Khadraoui, H. Nounou, M. Nounou, A. Datta, and S. P. Bhattacharyya, "A model-free design of reduced-order controllers and application to a DC servomotor," Automatica, vol. 50, no. 8, pp. 2142-2149, Aug. 2014.
[19] S. Khadraoui, H. N. Nounou, M. N. Nounou, A. Datta, and S. P. Bhattacharyya, "A nonparametric approach to design robust controllers for uncertain systems: Application to an air flow heating system," Journal of Process Control, vol. 36, no. 1, pp. 1-10, Dec. 2015.