طراحی قانون هدایت پیش‌بین در یک مساله هدایت دو بعدی با وجود محدودیت در شتاب ورودی

نوع مقاله: مقاله پژوهشی

نویسنده

عضو هیات علمی / گروه مهندسی برق، دانشکده مهندسی، دانشگاه خلیج فارس

چکیده

در این مقاله، به منظور طراحی قانون هدایت پیش‌بین، یک روش مبتنی بر نامساوی ماتریسی خطی LMI پیشنهاد می‌گردد. برای رسیدن به این هدف، ابتدا با نوشتن معادله‌های حاکم بر حرکت جسم و هدف در دستگاه مختصات دو بعدی، مساله هدایت و قانون هدایت پیش‌بین فرموله می‌شود. در قانون هدایت پیش‌بین، با استفاده از یک مدل دینامیکی رفتار سیستم هدایت می‌تواند پیش‌بینی شود. سپس در هر لحظه دلخواه از زمان، یک سیگنال فرمان به گونه‌ای محاسبه می‌گردد تا یک تابع هزینه مینیمم شود. در این مطالعه برای طراحی قانون هدایت پیش‌بین، یک قانون هدایت متناسب با تغییرات زاویه خط دید، با بهره متغیر (نامعلوم) انتخاب می‌گردد. با استفاده از مفاهیم و تعاریف LMI، مساله طراحی قانون هدایت پیش‌بین به حل یک مساله دیگر مینیمم‌یابی تبدیل می‌گردد. در هر لحظه از زمان، چنین مساله بهینه‌یابی مبتنی بر LMI می‌تواند به صورت عددی حل شود. سپس با توجه به جواب بدست آمده، بهره قانون هدایت پیشنهادی بروز‌‌رسانی شود. الگوریتم هدایت پیشنهادی در یک سیستم هدایت دو بعدی شبیه‌سازی می‌گردد. نتایج شبیه‌سازی بیانگر اثر بخشی و کارآیی روش هدایت پیشنهادی در مقایسه با روش هدایت موجود می باشد.

کلیدواژه‌ها


عنوان مقاله [English]

Model Predictive Guidance Law Design in a Two-Dimensional Guidance Problem in Presence of Input Constraint

نویسنده [English]

  • Valiollah Ghaffari
Assistant Professor / Department of Electrical Engineering, School of Enginnering, Persian Gulf University
چکیده [English]

In this paper, an LMI based algorithm is mainly addressed to design a model predictive guidance law in presence of the input acceleration constraint. For achieving this purpose, firstly, the model predictive guidance issue is mathematically formulated in a two-dimensional problem. In the proposed algorithm, the future behavior of the guidance problem can be predicted by using of a dynamical model. The commanded acceleration would be determined, at each certain time instant, while a quadratic cost function is minimized. In this study, an acceleration command proportional to the line-of-sight (LOS) rate is considered as the predictive guidance policy with unknown variable gain. Then the model predictive guidance issue would be translated into another minimization problem subjected to some linear matrix inequalities (LMI). Hence, at each known time instant, such an optimization problem can be numerically solved in the real-time applications. Then the gain of the proposed guidance algorithm can be automatically updated. The proposed method will be used in a typical two-dimensional guidance example. The simulation results will show the effectiveness of the suggested method in comparing with the existing guidance algorithms.

کلیدواژه‌ها [English]

  • Linear matrix inequality
  • model predictive guidance law
  • guidance law
  • constrained system
[1] G. M. Siouris, Missile guidance and control systems: Springer Science Business Media, 2004.

[2] P. Zarchan, Tactical and strategic missile guidance: American Institute of Aeronautics and Astronautics, 2012.

[3] N. F. Palumbo, R. A. Blauwkamp, and J. M. Lloyd, Basic principles of homing guidance, Johns Hopkins APL Technical Digest, vol. 29, pp. 25-41, 2010.

[4] C. Y. Li and W. X. Jing, Geometric approach to capture analysis of PN guidance law, Aerospace Science and Technology, vol. 12, pp. 177-18, 2008.

[5] J. Heyrani Nobari, New insight in the pursue-escape geometry by the inspiration of PN guidance, Journal of Control, vol. 4, pp. 29-35, 2010. (in Persian)

[6] H. K. Khalil, Noninear systems. New Jersey: Prentice-Hall, 1996.

[7] D. Chwa and J. Y. Choi, Adaptive nonlinear guidance law considering control loop dynamics, IEEE Transactions on Aerospace and Electronic Systems, vol. 39, pp. 1134-1143, 2003.

[8] A. Saleem and A. Ratnoo, Lyapunov-based guidance for impact time control and simultaneous arrival, Journal of Guidance, Control and Dynamics, vol. 39, pp. 164-173, 2015.

[9] D. Cho, H. J. Kim, and M. J. Tahk, Nonsingular sliding-mode guidance for impact time control, Journal of Guidance, Control, and Dynamics, vol. 39, pp. 61-68, 2015.

[10] J. Moon, K. Kim, and Y. Kim, Design of missile guidance law via variable structure control, Journal of Guidance, Control, and Dynamics, vol. 24, pp. 659-664, 2001.

[11] V. Behnam Gol, I. Mohammad Zaman, A. Vali, and N. A. Ghahramani, Guidance law design using finite time second order sliding-mode control, Journal of Control, vol. 5, pp. 36-44, 2011. (in Persian)

[12] V. Behnamgol, A. Vali, and A. Mohammadi, A new backstepping sliding-mode guidance law considering control loop dynamics, Journal of Space Science and Technology, vol. 8, pp. 9-17, 2016. (in Persian)

[13] S. S. Moosapour, G. Alizadeh, and S. Khanmohammadi, Three-dimensional optimal robust guidance law design for missile using sliding-mode control and SDRE, Journal of Control, vol. 6, pp. 55-64, 2012. (in Persian)

[14] D. Chwa, Robust nonlinear disturbance observer-based adaptive guidance law against uncertainties in missile dynamics and target maneuver, IEEE Transactions on Aerospace and Electronic Systems, vol. 54, pp. 1739-1749, 2018.

[15] D. Zhou, C. Mu, and W. Xu, Adaptive sliding-mode guidance of a homing missile, Journal of guidance, control, and dynamics, vol. 22, pp. 589-594, 1999.

[16] Binazadeh, M. H. Shafiei, and E. Bazregarzadeh, New approach in guidance law design based on finite-time partial stability theorem, Journal of Space Science and Technology, vol. 8, pp. 1-7, 2015. (in Persian)

[17] D. Zhou, S. Sun, and K. L. Teo, Guidance laws with finite time convergence, Journal of guidance, control and dynamics, vol. 32, pp. 1838-1846, 2009.

[18] V. Ghaffari and P. Karimaghaee, Performance and stability investigation of a line of sight based guidance system in the presence of measurement noise, Journal of Space Science and Technology, vol. 11, pp. 31-40, 2018. (in Persian)

[19] S. A. H. Tabatabaei, A. Yousefi Koma, S. M. Ayati, and S. S. Mohtasebi, Design and simulation of a fuzzy-supervisory control system and an optimized three-dimensional fuzzy carrot-chasing guidance algorithm for a fixed-wing MAV, Modares Mechanical Engineering, vol. 16, pp. 10-20, 2016. (in Persian)

[20] M. Mirzaei and M. M. Alishahi, Performance investigation of control and guidance system for a spinning flight vehicle with dithering canard, Modares Mechanical Engineering, vol. 14, pp. 169-175, 2014. (in Persian)

[21] E. Jomehzadeh and F. Tavakoli, A closed-loop sub-optimal guidance design for sub-orbital flying system, Modares Mechanical Engineering, vol. 17, pp. 97-106, 2017. (in Persian)

[22] A. R. Basohbat Novinzadeh and M. Asadi Matak, Design of stable nonlinear guidance of an underwater vehicle in the ship wake via estimated path by particle filter, Modares Mechanical Engineering, vol. 17, pp. 260-266, 2017. (in Persian)

[23] A. R. Babaei and S. M. R. Setayandeh, Design of nonlinear optimal guidance law for high maneuver targets based on state dependent Riccati equation, Aerospace Knowledge and Technology Journal, vol. 6, pp. 93-107, 2017. (in Persian)

[24] T. Shima and O. M. Golan, Head pursuit guidance, Journal of Guidance, Control, and Dynamics, vol. 30, pp. 1437-1444, 2007.

[25] M. Weiss and T. Shima, Minimum effort pursuit evasion guidance with specified miss distance, Journal of Guidance, Control, and Dynamics, vol. 39, pp. 1069-1079, 2016.

[26] E. F. Camacho and C. B. Alba, Model predictive control: Springer Science Business Media, 2013.

[27] J. M. Maciejowski, Predictive control: with constraints: Pearson education, 2002.

[28] V. Ghaffari, A robust control system scheme based on model predictive controller (MPC) for continuous‐time systems, Optimal Control Applications and Methods, vol. 38, pp. 1032-1041, 2017.

[29] C. Scherer and S. Weiland, Linear matrix inequalities in control. Delft, Netherlands: Dutch Institute for Systems and Control, 2000.

[30] F. A. Cuzzola, J. C. Geromel, and M. Morari, An improved approach for constrained robust model predictive control, vol. 38, pp. 1183-1189, 2002.

[31] V. Ghaffari, S. V. Naghavi, and A. Safavi, Robust model predictive control of a class of uncertain nonlinear systems with application to typical CSTR problems, Journal of Process Control, vol. 23, pp. 493-499, 2013.

[32] K. Hoffman and R. Kunze, Linear Algebra. New Jersey: Englewood Cliffs, 1971.