طراحی جبران‌سازهای دینامیکی و استاتیکی رفع انباشتگی برای یک خودخلبان سه‌حلقه‌ای

نوع مقاله : مقاله پژوهشی

نویسنده

کارشناس / سازمان صنایع هوافضا

چکیده

وجود تابع غیرخطی اشباع عملگر در یک خودخلبان سه‌حلقه‌ای وسیله پرنده منجر به افت عملکرد ناشی از پدیده انباشتگی می‌شود. در این مقاله، یک جبران‌ساز دینامیکی و یک جبران‌ساز استاتیکی برای رفع انباشتگی (AW) پیشنهاد می‌شود. جبران‌ساز دینامیکی موجود در بعضی از مراجع برای سیستم‌های با پس‌خور از خروجی سیستم به‌گونه‌ای طراحی شده‌است که حالت‌های کنترل‌کننده سیستم اشباع‌شده نزدیک به حالت‌های کنترل‌کننده سیستم اشباع‌نشده ‌شود. در این مقاله، این جبران‌ساز برای کنترل‌کننده‌هایی مشابه خودخلبان سه حلقه‌ای وسایل پرنده که در آن فرمان کنترلی، علاوه بر پس‌خور از خروجی، پس‌خور از حالت‌های سیستم نیز است، توسعه و استفاده ‌شده‌است. به‌منظور مقایسه با جبران‌ساز دینامیکی، یک جبران‌ساز استاتیکی نیز با یک رویکرد جدید به این‌گونه‌ طراحی شده که خروجی کنترل‌کننده، خروجی تابع اشباع را تعقیب کند. با این معیار انتظار می‌رود که انباشتگی ایجاد نشود. بر مبنای این خواسته، بهره‌ مناسب جبران‌ساز استاتیکی بر اساس تحلیل حساسیت عددی به‌دست آمده است. این دو جبران‌ساز بر روی یک خودخلبان سه حلقه‌ای وسیله پرنده آیرودینامیکی دم-کنترل اعمال شده و در دو شرایط پایدار و ناپایدار عملکرد این جبران‌سازها به لحاظ کنترلی با هم مقایسه شده‌اند. نتایج نشان دهنده عملکرد بهتر جبران‌ساز استاتیکی در مقابل جبران‌ساز دینامیکی در تعقیب فرمان مطلوب در هر دو شرایط کاری است. همچنین با شبیه‌سازی سیستم هدایت وسیله پرنده، نشان داده می‌شود که استفاده از کنترل‌کننده با جبران‌ساز رفع انباشتگی منجر به کاهش خطای برخورد می‌شود. به خصوص استفاده از جبران‌ساز استاتیکی منجر به کاهش خطای برخورد در حدود 50% در شرایط ناپایدار نسبت به استفاده از جبران‌ساز دینامیکی می‌شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Design of dynamic and static antiwindup compensators for a three-loop autopilot

نویسنده [English]

  • mahdi nikusokhan lame
Aerospace science industry
چکیده [English]

The presence of the actuator saturation in a three-loop autopilot of a flying vehicle arising from the windup phenomena leads to the performance degradation. In this paper, a dynamic anti-windup and a static anti-windup compensators are proposed. The dynamic compensator, available in some references for systems with output feedback is designed to make the controller states of the saturated system arbitrarily close to the controller states of the unsaturated system. In this paper, this compensator is developed for controllers similar to three-loop autopilot of a flying vehicle, in which, the controller is a feedback of both plant output and plant states. In order to compare with the dynamic compensator, a static compensator is also designed with a new approach in such a way that the controller output tracks the output of saturation function. With this requirement, it is expected that no windup will occur. These two compensators have been applied on the autopilot of an aerodynamic tail-controlled flying vehicle in two stable and unstable conditions and their performances have been compared to each other in terms of control performance. The results show the better performance of the static compensator compared to the dynamic compensator in tracking the desired command in both operating conditions. Moreover, through simulation of flying vehicle guidance system, it is shown that using anti-windup leads to the less miss distances. Especially, using the static compensator leads to reduction of the miss distance by about 50% in unstable conditions compared to the use of the dynamic compensator.

کلیدواژه‌ها [English]

  • input saturation
  • anti windup
  • dynamic and static compensators
  • autopilot
 [1] I.E. Kose and F. Jabbari., “Scheduled Controllers for Linear Systems with Bounded Actuators”, Automatica, vol. 39, pp. 1377-1387, Aug. 2003.
[2] F. Jabbari. And I.E. Kose, “Rate and Magnitude-Bounded Actuators: Scheduled Output Feedbcak Design”, Int. J. Robust and Nonlinear Control, vol. 14, pp. 1169-1184, Sep. 2004.
[3] S. Tarbouriech and M. Turner. “Anti-windup design: an overview of some recent advances and open problems” IET Control Theory Appl., vol. 3, no. 1, pp. 1-19, Jan. 2009.
[4] R. Chai, A. Tsourdos, H. Gao, Y. Xia, and S. Chai, “Dual-loop tube-based robust model predictive attitude tracking control for spacecraft with system constraints and additive disturbances”, IEEE Transactions on Industrial Electronics, vol. 69, no. 4, pp. 4022-4033, 2021.
[5] Y. Yaguang, “Attitude Model Predictive Control with Actuator Saturation Using an Arc-Search Interior-Point Method”, Journal of Guidance, Control and Dynamics, vol. 46, no. 4, pp. 726-733, April. 2023.
[6] P. Hippe., “Windup in Control: Its Effects and Their Prevention”, first edition, Springer, 2006.
[7] L. Zaccarian. and A. R. Teel, “Modern Anti-windup Synthesis: Control Augmentation for Actuator Saturation”, Princeton University Press, 2011.
[8] E. F. Mulder, M. V. Kothare, and M. Morari,  “Multivariable Anti-Windup Controller Synthesis Using Bilinear Matrix Inequlities”, European Journal of Control, vol. 6, pp. 455-464, Nov. 2000.
[9] E.F. Mulder, M.V. Kothare and M. Morari, “Multivariable Anti-windup Controller Synthesis Using Linear Matrix Inequalities”, Automatica, vol. 37, pp. 1407-1416, Sep. 2001.
[10] G. Grimm., J. Hatfield., I. Postethwatie., A. R. Teel., M. C. Turner., and L. Zaccarian; “Anti-windup for stable linear systems with input saturation: an LMI based synthesis”, IEEE Transaction on automatic control, vol. 48, no. 9, pp. 1025-1067, Sep. 2003.
[11] G. Grimm, A.R. Teel and L. Zaccarian, “Results on Linear LMI-Based External Anti-windup Design”, IEEE Trans. on Automatic Control, vol. 48, no. 9, Sep. 2003.
[12] S. S. Kia, and F. Jabbari, “Modified Anti-windup Compensators for Stable Plants: Dynamic Anti-windup Case”, IEEE Trans. on Automatic Control, vol. 54, no. 8, pp. 1934-1939, Aug. 2009.
[13] S. S. Kia, and F. Jabbari, “Multi-stage Anti-Windup Compensation for Open-loop Stable Plants”, IEEE Trans. on Automatic Control, vol. 56, no. 9, pp. 2166-2172, Sep. 2011.
[14] J.K. Park, and C.H. Choi, “Dynamic compensation method for multivariable control systems with saturating actuators”, IEEE Transctions on Automatic Control, vol. 40, no. 9, pp. 1635-1640 , Sep. 1995.
[15] J.K. Park, and C.H. Choi “Dynamical Anti-Reset Windup Method for Discrete-Time Saturating Systems”, Automatica, vol. 33, pp. 1055-1072, Dec. 1997.
[16] A. Park, C.H. Choi, and H. Choo, “Dynamic anti-windup method for a class of time-delay control systems with input saturation”, International Journal of Robust and Nonlinear Control, vol. 10, no. 6, pp. 457-488 , May. 2000.
[17] J.K., Park, and H.Y. Youn, “Dynamic anti-windup based control method for state constrained systems”, Automatica, vol. 39, no. 11, pp. 1915-1922 , Nov. 2003.
[18] V. Bohlouri , “Satellite Attitude Control Using Modified PID Controller in the presence of Uncertainty ”, Journal of Aeronautical Engineering, vol. 23, no. 2, pp. 80-91, 2021 (in Persian).
[19] M. C. Turner, and C. M. Richards, “Constrained Rigid Body Attitude Stabilization: An Anti-Windup Approach”, IEEE Control Systems Letters, vol. 5, no. 5, pp. 1663-1668, Nov. 2021.
[20] R. Sun, Z. Zhou, and X. Zhu, “Flight quality characteristics and observer-based anti-windup finite-time terminal sliding mode attitude control of aileron-free full-wing configuration UAV”, Aerospace Science and Technology, vol. 112, pp. 1-33, May. 2021.
[21] G. Avanzini, and S. Galeani, “Robust Antiwindup for Manual Flight Control of an Unstable Aircraft”, Journal of Guidance, Control and Dynamics, vol. 28, no. 6, pp. 1275-1282, Nov. 2005.
[22] S. S. Kia, A. F. Gabernet. and F. Jabbari, “Scheduled Anti-windup Controllers for Application to Aircraft in Unstable Operating Conditions”, in AIAA Guidance, Navigation, and Control Conference and Exhibit, Hilton Head, South Carolina, 2007, pp. 1-12.
[23] M. Vavabi, and H. Ghafari, “Unstable Aircraft Flight Control Based on Linear Matrix Inequality with Consideration of Control and Saturation Constraints”, Amirkabir Journal of Mechanical Engineering, vol. 53, no. 2, pp. 979-992, 2021 (in Persian).
[24] O. Brieger, M. Kerr, I. Postlethwaite, M. C. Turner, and J. Sofrony, “Pilot-Involved-Oscillation Suppression Using Low-Order Antiwindup: Flight-Test Evaluation”, Journal of Guidance, Control and Dynamics, vol. 35, no. 2, pp. 471-483, March. 2012.
[25] D. Ge, G. Sun, and H. R. Karimi, “Robust Anti-Windup Control Considering Multiple Design Objectives”, Mathematical Problems in Engineering, vol. 2012, pp. 1-13, Sep. 2012.
[26] S. Thai, S. Theodoulis, C. Roos, J. M. Biannic, and M. Proff, “Gain-Scheduled Autopilot Design with Anti-Windup Compensator for a Dual-Spin Canard-Guided Projectile”, in IEEE Conference on Control Technology and Applications, Montreal, Canada, 2020.
[27] P. Hippe, and C. Wurmthaler, “Comments on “Dynamic Compensation Method for Multivariable Control Systems with Saturating Actuators”, IEEE Transctions on Automatic Control, vol. 41, no. 10, pp. 1549-1550 , Oct. 1996.
[28] P. Zarchan., “Tactical and strategic missile guidance”, Fourth edition, AIAA series, 2002.