روابط تقریبی فاصلة خطای هدایت تناسبی ناشی از تأخیر زمانی خالص مبتنی بر تحلیل بدترین شرایط

نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری / دانشکدة مهندسی مکانیک، دانشگاه تربیت مدرس

2 عضو هیات علمی / دانشکدة مهندسی مکانیک، دانشگاه تربیت مدرس

چکیده

در این مقاله، تأثیر تأخیر زمانی خالص سیستم بر فاصلة خطای قانون هدایت تناسبی برای سیستم هدایت و کنترل با تابع تبدیل دوجمله­ای مرتبه بالا بررسی شده است. برای این منظور از مدل خطی یک‌بعدی استفاده شده است. فاصلة خطای بی­بعد ناشی از خطای سمت اولیه، مانورهای ثابت، خطی و سهمی هدف و نویز جستجوگر با استفاده از روش الحاقی محاسبه شده است. برای جستجوگر نویزهای تابش، مستقل از فاصله، وابسته به فاصلة سیستم فعال و نیمه­فعال در نظر گرفته شده و نتایج با روش مستقیم اعتبارسنجی شده است. همچنین، اثر تأخیر زمانی خالص سیستم، ثابت زمانی سیستم، ضریب ناوبری مؤثر و افزایش مرتبة سیستم تا 30، بر فاصلة خطای ناوبری تناسبی بررسی شده است. در ادامه، ضریب ناوبری اکسترمم برای حداقل‌کردن فاصلة خطای بدترین حالت با توجه به زمان نهایی استخراج شده است. سپس، روابط تقریبی فاصلة خطا براساس تحلیل بدترین حالت در زمان نهایی با توجه به منابع خطای ذکر شده و با استفاده از برازش منحنی ارائه شده است. در نهایت، روابط تقریبی ضرایب بی­بعد پایای فاصلة خطا ناشی از نویز برحسب ضریب ناوبری مؤثر، به‌طور نمونه به ازای سیستم هدایت و کنترل مرتبة پنجم و دهم ارائه شده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Approximate miss distance formulas of proportional navigation due to time delay based on worst case analysis

نویسندگان [English]

  • Ali Arabian Arani 1
  • Seyed Hamid Jalali Naini 2
چکیده [English]

In this paper, the effect of system time delay on the miss distance of proportional navigation guidance law is studied for high-order binomial guidance and control systems. For this purpose, a linearized model is utilized in one dimension. The normalized miss distance due to heading error (HE), step, ramp, and parabolic target maneuvers, and seeker noise is computed using normalized adjoint equations. The glint, range-independent, and (semi-) active range-dependent noises are considered for the seeker, and the results are verified by straight-forward method. Moreover, the effects of system time lag, system time constant, effective navigation ratio, system order up to 30 in proportional navigation miss distance are also investigated. An extremum effective navigation ratio is also obtained to minimize the worst case miss distance with respect to the final time. Furthermore, approximate miss distance formulas are presented based on worst case analysis on final time using curve fitting for mentioned miss distance sources. Finally, the approximate formulas of steady state nondimensional coefficients due to seeker noise in terms of effective navigation coefficient, for example for system orders of 5 and 10, are obtained.

کلیدواژه‌ها [English]

  • proportional navigation
  • time delay
  • extremum navigation ratio
  • normalized miss distance

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