ارائه یک روش جدید به منظور تخمین برخط تأخیر زمانی در سیستم‌های SISO-LTI با تأخیر زمانی متغیر با زمان و نامعلوم در ورودی کنترلی
محورهای موضوعی : مهندسی برق و کامپیوترهادی چهکندی نژاد 1 * , محسن فرشاد 2 , رمضان هاونگی 3
1 - دانشگاه آزاد اسلامی واحد بیرجند
2 - دانشگاه بیرجند
3 - دانشگاه بیرجند
کلید واژه: فیلتر کالمن سیستم‌های L.T.I. تأخیر زمانی متغیر در ورودیعدم قطعیتتخمینگر تأخیر,
چکیده مقاله :
در این مقاله یک تخمینگر نوین برای تخمین بلادرنگ تأخیر زمانی در سیستم‌های L.T.I. تک‌ورودی- تک‌خروجی، با تأخیر متغیر با زمان و نامعلوم در ورودی کنترلی ارائه شده است. واضح است که تابع تبديل لاپلاس یک سیستم تأخیردار، شامل یک عامل تأخیر زمانی (عامل نمایی و غیر گویا) است. در این مقاله فرض بر این است که تنها پارامتر نامعلوم و متغیر با زمان در سیستم، پارامتر تأخیر زمانی سیستم است. در راستای طراحی تخمینگر پیشنهادی، ابتدا بایستی به منظور گویاکردن تابع تبديل سیستم، از یک تقریب پده (Pade) برای عامل نمایی تأخیر زمانی استفاده شود. لذا تابع تبديل جدید که تقریبی از تابع تبديل اصلی سیستم است، شامل یک پارامتر (متغیر با زمان) تأخیر زمانی خواهد بود. پس از نوشتن یک تحقق فضای حالت، از تابع تبديل مذکور و در نظر گرفتن پارامتر تأخیر زمانی به عنوان یک متغیر حالت اضافی، یک سیستم با معادلات حالت غیر خطی تولید خواهد شد. نهایتاً با استفاده از یک فیلتر کالمن (خطی و توسعه‌یافته برای معادلات حالت خطی‌سازی شده و غیر خطی) حالت‌های این سیستم، از جمله تأخیر زمانی سیستم، پیش‌بینی می‌شوند. در پایان، نتایج شبیه‌سازی‌ها، عملکرد نسبتاً مطلوب تخمینگر پیشنهادی در مواجهه با تأخیرهای متغیر با زمان و نامعلوم را نشان می‌دهند.
In this paper, a novel observer is designed for online time delay estimation, in SISO linear systems, with variable and unknown time-delay in control input. It is clear that Laplace transfer function of a delayed system includes a time-delay operator (exponential and non-rational). In this article, it is assumed that the only unknown and variable parameter in the system is the system’s time-delay. For designing the proposed observer, first, a Pade approximation is used for exponential operator of time delay to rationalize the system transfer function. Therefore, the new transfer function, which is an approximation of the main transfer function of the system, will include a time-variant delay parameter. After rewriting a state space realization of the mentioned transfer function and considering time delay parameter as an extra state variable, a system with nonlinear state equations will be formed. Eventually, using a Kalman filter, the systems states, such as system time-delay, are estimated. Finally, simulations results show rather desirable performance of the proposed estimator in dealing with unknown and variable time-delays.
[1] J. E. Normey-Rico and E. F. Camacho, Control of Dead-Time Processes, Springer-Verlag, London, UK, 2007.
[2] Q. C. Zhong, Robust Control of Time-Delay Systems, Springer-Verlag, London, UK, 2006.
[3] M. Wu, Y. He, and J. H. She, Stability Analysis and Robust Control of Time-Delay Systems, Science Press Beijing and Springer-Verlag Berlin Heidelberg, 2010.
[4] S. Bjorklund and L. Ljung, "A review of time-delay estimation techniques," in Proc. 42nd IEEE Int. Conf. on Decision and Control, vol. 3, pp. 2502-2507, Maui, HI, USA, 9-12 Dec. 2003.
[5] A. O. Dwyer and R. Gao, "Comparison of two B-polynomial methods application to the identification of time delayed processes," in Proc. of the Irish Signals and Systems Conf., pp. 105-111, NUI Maynooth, Ireland, Jun. 2001.
[6] J. Roe, R. Gao, and A. Dwyer, "Identification of a time-delayed process model using an overparameterization method," in Proc. of the China-Ireland Int. Conf. on Information and Communications Technologies, CIICT'07, 10 pp., DCU, Aug. 2007.
[7] K. Taarita, L. Belkoura, M. Ksouri, and J. P. Richard, "A fast identification algorithm for systems with delayed inputs," Int. J. Syst. Sci., vol. 42, no. 3, pp. 449-456, Mar. 2011.
[8] A. O'Dwyer and J. V. Ringwood, "Model parameter and time delay estimation using gradient methods," in Proc. of the Irish Colloquium on DSP and Control, pp. 211-218, Dublin, Ireland, Jul. 1994.
[9] L. Belkoura, J. P. Richard, and M. Fliess, "On-line identification of systems with delayed inputs," in Proc. 17th Symp. on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, Jul. 2006.
[10] D. Etter and S. Stearns, "Adaptive estimation of time delays in sampled data systems," IEEE. Trans. Acoust., vol. 29, no. 3, pp. 582-587, Jun. 1981.
[11] S. Ahmed, B. Huang, and S. L. Shah, "Parameter and delay estimation of continuous-time models using a linear filter," J. Process. Control, vol. 16, no. 4, pp. 323-331, Apr. 2006.
[12] Z. Sun and Z. Yang, "System identification for nonlinear FOPDT model with input-dependent dead-time," in Proc. 15th Int. Conf. on System Theory, Control and Computing, 6 pp., Sinaia, Romania, 11-14 Oct. 2011.
[13] J. Kozłowski and Z. Kowalczuk, "On-line parameter and delay estimation of continuous-time dynamic systems," Int. J. Appl. Math. Comput. Sci., vol. 25, no. 2, pp. 223-232, Jun. 2015.
[14] V. Lechappe, E. Moulay, and F. Plestan, "Dynamic observation-prediction for LTI systems with a time-varying delay in the input," in Proc. IEEE 55th Conf. on Decision and Control, CDC'16, pp. 2302-2307, Las Vegas, NV, USA, 12-14 Dec. 2016.
[15] C. Lai and P. Hsu, "Design the remote control system with the time-delay estimator and the adaptive smith predictor," IEEE. Trans. Industr. Inform., vol. 6, no. 1, pp. 73-80, Feb. 2010.
[16] R. M. C. De Keyser, "Adaptive dead-time estimation," in Proc. 2nd IFAC Workshop on Adaptive Systems in Control and Signal Processing, Lund, Sweden, vol. 20, no. 2, pp. 385-389, Jul. 1986.
[17] J. Tuch, A. Feuer, and Z. J. Palmor, "Time delay estimation in continuous linear time-invariant systems," IEEE. Trans. Automat. Contr., vol. 39, no. 4, pp. 823-827, Apr. 1994.
[18] V. Lechappe, J. De Leon, E. Moulay, F. Plestan, and A. Glumineau, "Delay and state observer for SISO LTI systems," in Proc. American Control Conf., ACC'15, pp. 4585-4590, Chicago, IL, USA, 1-3 Jul. 2015.
[19] X. Hong and Q. Zhu, "An on-line algorithm of uncertain time delay estimation in a continuous system," in Proc. Int.l Conf. on Networking, Sensing and Control, pp. 498-501, Okayama, Japan, 26-29 Mar. 2009.
[20] M. Krstic, "Lyapunov stability of linear predictor feedback for time-varying input delay," IEEE Trans. Automat. Contr., vol. 55, no. 2, pp. 554-559, Feb. 2010.
[21] N. Nguyen and E. Summers, "On time delay margin estimation for adaptive control and robust modification adaptive laws," in Proc. AIAA Guidance, Navigation, and Control Conf., Guidance, Navigation, and Control and Co-located Conf., pp. 1-26, Portland, ON, USA, 8-11 Aug. 2011.
[22] Y. Liu, L. S. Hu, and P. Shi, "A novel approach on stabilization for linear systems with time-varying input delay," Appl. Math. Comput., vol. 218, no. 10, pp. 5937-5947, Jan. 2012.
[23] F. Cacace, F. Conte, and A. Germani, "State feedback stabilization of linear systems with unknown input time delay," IFAC-PapersOnLine, vol. 50, no. 1, pp. 1245-1250, Jul. 2017.
[24] Y. Wei and Z. Lin, "A delay-independent output feedback for linear systems with time-varying input delay," Int J. Robust Nonlinear Control., vol. 28, no. 8, pp. 1245-1250, Feb. 2018.
[25] D. Yue and Q. L. Han, "Delayed feedback control of uncertain systems with time-varying input delay," Automatica, vol. 41, no. 2, pp. 233-240, Feb. 2005.
[26] C. Y. Kao and B. Lincoln, "Simple stability criteria for systems with time-varying delays," Automatica, vol. 40, no. 8, pp. 1429-1434, Aug. 2004.
[27] W. A. Zhang and L. Yu, "A robust control approach to stabilization of networked control systems with time-varying delays," Automatica, vol. 45, no. 10, pp. 2440-2445, Oct. 2009.
[28] A. Polyakov, A. Poznyak, and J. Richard, "Robust output stabilization of time-varying input delay systems using attractive ellipsoid method," in Proc. 52nd IEEE Conf. on Decision and Control, pp. 934-939, Florence, Italy, 10-13 Dec. 2013.
[29] C. Yuan and F. Wu, "ℋ∞ state-feedback control of linear systems with time-varying input delays," in Proc. IEEE 55th Conf. on Decision and Control, CDC'16, pp. 586-591, Las Vegas, NV, USA, 12-14 Dec. 2016.
[30] D. B. Pietri, F. Mazenc, and N. Petit, "Robust compensation of a chattering time-varying input delay with jumps," Automatica, vol. 92, pp. 225-234, Jun. 2018.
[31] S. Roy and I. N. Kar, "Robust control of uncertain Uuler Lagrange systems with time-varying input delay," in Proc. of the ACM Advances in Robotics, AIR'17, New York, NY, USA, Article No.: 16, 6 pp., Jun. 2017.
[32] R. Matusu and R. Prokop, "Control of systems with time-varying delay: a comparison study," in Proc. 12th WSEAS Int. Conf. on Automatic Control, Modelling and Simulation, pp. 125-130, May 2010.
[33] J. G. Dawson, "Fuzzy logic control of linear systems with variable time delay," in Proc. of 9th IEEE Inte. Symp. on Intelligent Control, pp. 5-10, Columbus, OH, USA, 16-18 Aug. 1994.
[34] D. Srinivasagupta, H. Schattler, and B. Joseph, "Time-stamped model predictive control: an algorithm for control of processes with random delays," Comput. Chem. Eng., vol. 28, no. 8, pp. 1337-1346, Jul. 2004.
[35] S. Y. Yoon and Z. Lin, "Truncated predictor feedback control for exponentially unstable linear systems with time-varying input delay," Syst. Control. Lett., vol. 62, no. 10, pp. 837-844, Oct. 2013.
[36] F. Cacace, A. Germani, and C. Manes, "Predictor-based control of linear systems with large and variable measurement delays," Int. J. Control., vol. 87, no. 4, pp. 704-714, Apr. 2014.
[37] V. Lechappe, E. Moulay, and F. Plestan, "Prediction-based control for LTI systems with uncertain time-varying delays and partial state knowledge," Int. J. Control., vol. 91, no. 6, pp. 1403-1414, Jun. 2018.
[38] X. Han, E. Fridman, and S. K. Spurgeon, "Sliding mode control in the presence of input delay: a singular perturbation approach," Automatica, vol. 48, no. 8, pp. 1904-1912, Aug. 2012.
[39] Y. Farid and N. Bigdeli, "Robust adaptive intelligent sliding model control for a class of uncertain chaotic systems with unknown time-delay," Nonlinear. Dyn., vol. 67, no. 3, pp. 2225-2240, Feb. 2012.
[40] F. Carravetta, P. Palumbo, and P. Pepe, "Quadratic optimal control of linear systems with time-varying input delay," in Proc. 49th IEEE Conf. on Decision and Control, CDC'10, pp. 4996-5000, Atlanta, GA, USA, 15-17 Dec. 2010.
[41] F. Cacace, F. Conte, and A. Germani, "Memoryless approach to the LQ and LQG problems with variable input delay," IEEE Trans. Automat. Contr., vol. 61, no. 1, pp. 216-221, Jan. 2016.
[42] F. Cacace, F. Conte, A. Germani, and G. Palombo, "Optimal control of linear systems with large and variable input delays," Syst. Control. Lett., vol. 89, pp. 1-7, Mar. 2016.
[43] J. K. Pieper, B. W. Surgenor, and J. Z. Liu, "On self-tuning control of processes with time varying dead time," in Proc. American Control Conf., pp. 2166-2171 Boston, MA, USA, Jun. 1991.
[44] H. Kurzt and W. Goedecke, "Digital parameter-adaptive control of processes with unknown dead time," Automatica, vol. 17, no. 1, pp. 245-252, Jan. 1981.
[45] G. A. Dumont, A. Elnaggar, and A. Elshafelt, "Adaptive predictive control of systems with time-varying time delay," Int. J. Adapt. Control. Signal. Process., vol. 7, no. 2, pp. 91-101, Mar. 1993.
[46] C. Chandra Prasad, V. Hahn, H. Unbehauen, and U. Keuchel, "Adaptive control of a variable dead time process with an integrator," IFAC-Papers OnLine, vol. 18, no. 15, pp. 71-75, Oct. 1985.
[47] J. P. Nelson and M. J. Balas, "Direct model reference adaptive control of linear systems with input/output delays," Nume. Algebra. Control. Optim., vol. 3, no. 3, pp. 445-462, Sept. 2013.
[48] M. T. Nihtila, "Adaptive control of a continuous-time system with time-varying input delay," Syst. Control. Lett., vol. 12, no. 4, pp. 357-364, May 1989.
[49] P. S. Agachi, Z. K. Nagy, M. V. Cristea, and A. L. Imre-Lucaci, Model Based Control, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2006.
[50] N. B. Liberis and M. Krstic, "Nonlinear control under nonconstant delays," in Advances in Design and Control, Society for Industrial and Applied Mathematics, SIAM-Society for Industrial and Applied Mathematics, 2013.
[51] C. K. Chui and G. Chen, Kalman Filtering with Real-Time Applications, Springer-Verlag, 5th Ed, Berlin Heidelberg, Germany, 2009.