Proportional Navigation Guidance with Variable Navigation Ratio in terms of the angle of relative velocity with respect to Line-of-Sight and its Rate

Jalali-Naini, S. Hamid; Arabian Arani, Ali

doi:10.30699/jsst.2020.1180

Proportional Navigation Guidance with Variable Navigation Ratio in terms of the angle of relative velocity with respect to Line-of-Sight and its Rate

Document Type : Original Research Paper

Authors

S. Hamid Jalali-Naini ¹

Ali Arabian Arani ²

¹ Associate Professor, Faculty of Mechanical Engineering Tarbiat Modares University.Tehran.IRAN

² Dept of Mechanical Engineering, Tarbiat Modares University.Tehran.IRAN

10.30699/jsst.2020.1180

Abstract

In the present work, the performance of True Proportional Navigation (TPN) with different profiles for effective navigation ratio in terms of the relative velocity angle with respect to line-of-sight is investigated due to initial heading errors and target maneuvers. Since an appropriate profile of effective navigation ratio for heading error is almost in contrary with the appropriate profile for maneuvering targets, a variable effective navigation ratio in terms of the relative velocity angle and its rate is introduced. In this way, the miss distance (MD) for the first two peaks of the normalized MD graph versus normalized final time, for example under an effective navigation ratio of 4, is reduced together. The analysis is carried out using normalized equations in polar coordinates for perfect and binomial fifth-order control systems without acceleration limit. Due to practical consideration, the effective navigation ratio is tuned and limited between 3 and 5.

Keywords

proportional navigation

variable navigation ratio

miss distance

20.1001.1.20084560.1399.13.2.1.3

Subjects

Space subsystems design: (navigation, control, structure and…)

Article Title Persian

هدایت تناسبی با ضریب ناوبری متغیر بر حسب زاویه بردار سرعت نسبی با خط دید و نرخ آن

Authors Persian

سید حمید جلالی نائینی ¹

علی عربیان آرانی ²

¹ دانشیار، دانشکده مهندسی مکانیک دانشگاه تربیت مدرس، تهران، ایران

² دانشکده مکانیک، دانشگاه تربیت مدرس، تهران، ایران

Abstract Persian

در تحقیق حاضر، عملکرد قانون هدایت تناسبی حقیقی با پروفیل‌های مختلف ضریب ناوبری متغیر برحسب زاویه بین بردار سرعت نسبی و خط‌‌دید در حالت خطای سمت اولیه و هدف با مانور ثابت بررسی شده‌است. از آنجایی که انتخاب پروفیل مناسب در حالت خطای سمت اولیه و مانور ثابت هدف، تقریباً عکس یکدیگر شده-است، یک ضریب ناوبری متغیر تابعی از دو پارامتر زاویة مذکور و نرخ آن ارائه شده‌است. به این طریق فاصله خطا، بطور نمونه برای ضریب ناوبری 4، برای دو قله نخست نمودار فاصله خطای بی‌بعد برحسب زمان بی‌بعد کاهش می‌یابد. تحلیل حاضر با استفاده از معادلات بی‌بعد در مختصات قطبی برای دو سیستم کنترل ایده‌ال و دوجمله‌ای مرتبه 5 بدون شتاب اشباع انجام شده‌است. به لحاظ کاربردی، نتایج به ازای ضرایب ناوبری 3 تا 5 تنظیم شده‌است.

Keywords Persian

هدایت تناسبی حقیقی

ضریب ناوبری متغیر

زاویه سرعت نسبی

فاصله خطا

[1] Zarchan, P., Tactical and Strategic Missile Guidance, Sixth ed., Progress in Astronautics and Aeronautics, Vol. 239, AIAA, 2012.

[2] Ben-Asher, J.Z., Yaesh, I., Advances in Missile Guidance Theory, Progress in Astronautics and Aeronautics, 180, American Institute of Astronautics Aeronautics, Inc., Washington, DC, 1998.

[3] Shneydor, N.A., Missile Guidance and Pursuit: Kinematics, Dynamics, and Control, 1^st Edition, Horwood Series in Engineering Science, 1998.

[4] Fleeman, E.L., Missile Design and System Engineering, second edition, AIAA Education Series, 2012.

[5] Balakrishnan, S.N., Tsourdos, A. and White, B.A., Advances in Missile Guidance, Control, and Estimation, Taylor & Francis Group, 2013.

[6] Jalali-Naini, S.H., “Generalized Solution for Proportional Navigation Guidance,” 10^th Annual (Intenational) Mechanic Engineering Conference, ISME2002, Tehran, May 2002.

[7] Maklouf, O., Saleh Basha, Eljubrani, A., “Performance Evaluation of Proportional Navigation Homing Guidance Law,” 5th Intenational Conference on Control Engineering&Information Technology, Vol. 33, 2017, pp. 14-18.

[8] Boord, W.J., Hoffman, J.B, Air and Missile Defense Systems Engineering, CRC Press, Taylor & Francis Group, Boca Raton, 2016.

[9] Biggers, E.L., “Air-to-Air Missile Guidance and Control,” Unpublished Technical Memorandumce, 1996.

[10] Jalali-Naini, S. H., A New Guidance Law for Homing Missiles, MS Thesis, Faculty of Engineering, University of Tehran, Aug. 1996 (in Persian)

[11] Yanushevsky, R.T., and Boord, W.J., “New Approach to Guidance Law Design,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 28, No. 1, 2005, pp. 162-166.

[12] Yanushevsky, R., Modern Missile Guidance, CRC Press, Taylor & Francis Group, Boca Raton, 2008.

[13] Yanushevsky, R.T., “Concerning Lyapunov-based guidance,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 29, No. 2, 2006, pp. 509-511.

[14] Jalali-Naini, S.H., “Miss Distance Analysis of Proportional Navigation Using Normalized Equations with Radome Effect, Saturation, and Body Rate Feedback,” Journal of Aeronautical Engineering, Vol. 14, No 1, 2012, pp. 1-11 (in Persian).

[15] Yuan, P.-J., Chern, J.-S., “Solutions of True Proportional Navigation for Maneuvering and Nonmaneuvering Targets,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 15, No. 1, 1992, pp. 268-271.