i BIASED PROPORTIONAL NAVIGATION GUIDANCE FOR IMPACT ANGLE CONTROL WITH ...

196 Pages·2015·6.62 MB·English

by  Koray S. Erer

BIASED PROPORTIONAL NAVIGATION GUIDANCE
FOR IMPACT ANGLE CONTROL
WITH EXTENSION TO THREE-DIMENSIONAL ENGAGEMENTS

A THESIS SUBMITTED TO
THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
OF
MIDDLE EAST TECHNICAL UNIVERSITY

BY

KORAY SAVAŞ ERER

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR
THE DEGREE OF DOCTOR OF PHILOSOPHY
IN
MECHANICAL ENGINEERING

FEBRUARY 2015

i
ii
Approval of the thesis:

BIASED PROPORTIONAL NAVIGATION GUIDANCE
FOR IMPACT ANGLE CONTROL
WITH EXTENSION TO THREE-DIMENSIONAL ENGAGEMENTS

submitted by KORAY SAVAŞ ERER in partial fulfillment of the requirements for
the degree of Doctor of Philosophy in Mechanical Engineering Department,
Middle East Technical University by,

Prof. Dr. Gülbin Dural Ünver ______________
Dean, Graduate School of Natural and Applied Sciences

Prof. Dr. R. Tuna Balkan ______________
Head of Department, Mechanical Engineering

Prof. Dr. M. Kemal Özgören ______________
Supervisor, Mechanical Engineering Dept., METU

Dr. Osman Merttopçuoğlu ______________
Co-Supervisor, TMS-GCD Dept., Roketsan Missiles Inc.

Examining Committee Members:

Prof. Dr. Bülent E. Platin ______________
Mechanical Engineering Dept., METU

Prof. Dr. M. Kemal Özgören ______________
Mechanical Engineering Dept., METU

Prof. Dr. Ozan Tekinalp ______________
Aerospace Engineering Dept., METU

Prof. Dr. Kemal Leblebicioğlu ______________
Electrical and Electronics Engineering Dept., METU

Prof. Dr. Yücel Ercan ______________
Mechanical Engineering Dept., TOBB ETÜ

Date: 10.02.2015

iii
I hereby declare that all information in this document has been obtained and
presented in accordance with academic rules and ethical conduct. I also declare
that, as required by these rules and conduct, I have fully cited and referenced
all material results that are not original to this work.

Name, Last Name: Koray Savaş Erer

Signature:

iv
ABSTRACT

BIASED PROPORTIONAL NAVIGATION GUIDANCE
FOR IMPACT ANGLE CONTROL
WITH EXTENSION TO THREE-DIMENSIONAL ENGAGEMENTS

Koray Savaş Erer
Ph.D., Department of Mechanical Engineering
Supervisor: Prof. Dr. M. Kemal Özgören
Co-Supervisor: Dr. Osman Merttopçuoğlu

February 2015, 174 pages

This work shows that the impact angle can be controlled by means of bias addition to
pure proportional navigation guidance commands. After obtaining the closed-form
solution of the nonlinear differential equations governing the engagement kinematics
between a pursuer and a stationary target, it is shown that the proposed strategy
corresponds to the optimal solution in the linear domain. Three alternative guidance
laws that do not require the time to go are proposed. The first law constitutes a two-
phased approach, where the bias is removed after obtaining proper pursuit
conditions. The second law, which makes use of the range-to-go information, and the
third law, which leads to an exponentially decaying error profile, are single-phased
approaches that do not suffer from the open-loop nature of the first one in its second
phase. The framework of this study allows the treatment of both the look angle and
the acceleration constraints in such a way that the impact angle capacity
corresponding to any engagement geometry can be analyzed. In addition to a
complete but impractical formulation, a feasible constrained guidance solution is
presented. A single-gain range observer that addresses the observability issue in a
convenient manner is formulated to supplement the trajectory shaping effort. The

v
case of moving targets is dealt with by means of constructing the collision triangle.
Two different schemes are considered based on the rotations of the absolute and
relative velocity vectors. The plane-pursuit midcourse guidance method proposed to
confine a general engagement scenario to a single plane facilitates the extension to
three-dimensional engagements.

Keywords: Impact Angle, Proportional Navigation, Bias, Constrained Guidance,
Three-Dimensional Engagement

vi
ÖZ

EK TERİMLİ ORANSAL SEYRÜSEFER GÜDÜM İLE
ÇARPMA AÇISI KONTROLÜ
VE ÜÇ BOYUTLU EŞLEŞMELERE UYARLANMASI

Koray Savaş Erer
Doktora, Makina Mühendisliği Bölümü
Tez Yöneticisi: Prof. Dr. M. Kemal Özgören
Ortak Tez Yöneticisi: Dr. Osman Merttopçuoğlu

Şubat 2015, 174 sayfa

Bu çalışma, çarpma açısının, saf oransal seyrüsefer güdüm komutlarına ek terim
eklenmesiyle kontrol edilebileceğini göstermektedir. Takipçi ve sabit bir hedef
arasındaki eşleşme kinematiğini yöneten doğrusal olmayan diferansiyel denklemlerin
çözümünün elde edilmesinden sonra, önerilen yöntemin doğrusal ortamdaki en
uygun çözüme karşılık geldiği gösterilmektedir. Kalan süreye ihtiyaç duymayan üç
adet alternatif güdüm kanunu önerilmektedir. Birinci kanun, ek terimin uygun takip
koşullarının elde edilmesiyle kaldırıldığı iki fazlı bir yaklaşımdır. Kalan mesafe
bilgisini kullanan ikinci kanun ve hatanın üstel şekilde eritilmesini sağlayan üçüncü
kanun, tek fazlı yaklaşımlardır ve birincinin ikinci fazdaki açık döngü doğasının
benzerine maruz kalmazlar. Bu çalışmanın çatısı, bakış açısı ve ivme kısıtlarının
değerlendirmeye alınmasına izin vermektedir; herhangi bir eşleşme geometrisine ait
çarpma açısı kapasitesi analiz edilebilir. Eksiksiz fakat elverişsiz bir formülasyonun
yanı sıra, uygulanabilirliği olan bir kısıt altında güdüm çözümü sunulmaktadır.
Gözlemlenebilirlik sorununu uygun şekilde ele alan tek kazançlı bir menzil
gözlemcisi, yörünge şekillendirmeyi desteklemek adına kurgulanmıştır. Hareketli
hedeflere ilişkin durum, çarpışma üçgeninin kurulmasıyla çözülmektedir. Mutlak ve

vii
bağıl hız vektörlerinin dönüşlerine dayanan iki farklı yöntem değerlendirilmektedir.
Genel bir eşleşme senaryosunu tek bir düzleme hapsederek üç boyuta uyarlamayı
sağlaması için düzlem takip adı verilen bir arafaz güdüm yöntemi önerilmektedir.

Anahtar Kelimeler: Çarpma Açısı, Oransal Seyrüsefer, Ek Terim, Kısıt Altında
Güdüm, Üç Boyutlu Eşleşme

viii
to

my father

and to

my dearest one

ix
ACKNOWLEDGEMENTS

I would like to thank

my supervisor Prof. Dr. M. Kemal Özgören firstly for providing a free thinking
environment, then for his many useful suggestions and finally for bearing with
my not-so-very-systematic way of studying;

my co-supervisor Dr. Osman Merttopçuoğlu who took the trouble to answer my
petty questions without letting go of his unique sense of humor;

Raziye Tekin for her invaluable technical insight she generously shared with me
and for her selfless support throughout the whole process;

Paul Zarchan for the encouragement he provided;

Prof. Dr. M. Kemal Özgören once more and Prof. Dr. Bülent E. Platin for
teaching me “Advanced Dynamics” and “Dynamics of Nonlinear Systems”, the
graduate courses on which the foundations of this dissertation rest;

Roketsan for giving me the opportunity to combine my professional activities
with my academic interests;

my mother and brother for simply being there.

x