Sabit kanatlı insansız hava aracının daldırma ve değişmezlik yöntemiyle doğrusal olmayan uçuş kontrolü
Nonlinear flight control of fixed wing unmanned aerial vehicle via immersion and invariance methodology
Yazar: FIRAT ASLAN
Danışman: DOÇ. DR. YAPRAK YALÇIN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Mekatronik Mühendisliği Ana Bilim Dalı / Mekatronik Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2019
Konu: Mekatronik Mühendisliği = Mechatronics Engineering

Özet:
Bu tez çalışmasında, sabit kanatlı insansız hava aracı için daldırma ve değişmezlik yöntemiyle doğrusal olmayan uçuş kontrolörü tasarımı önerilmiştir. Kontrolör temel olarak gövde eksen takımında yuvarlanma, yunuslama ve yönelim açısal hızlarının istenilen değerlerde ayarlanmasını sağlamaktadır. Daldırma ve değişmezlik yönteminin seçilmesindeki en önemli neden, sistemin doğrusallaştırılmaya ihtiyaç duyulmadan kullanılabilmesidir. Çapraz terimlerin etkileri indirgenmektedir. 
İnsansız hava araçları diğer otonom sistemler gibi önemi gittikçe artan bir çalışma konusudur. İnsan faktöründen bağımsız olarak yeterince yüksek doğrulukta çalışması beklenen bu sistemlerin, bir kontrol sisteminden bağımsız olarak çalışması mümkün değildir. Gerçek sistem modeline uygun kontrol tasarımı yapılabilmesi için doğrusal olmayan durum denklemlerinin çözülmesi gerekir. 
Birinci bölümde tezin amacından bahsedilerek literatür araştırmasına geçilmiştir. Literatürde daldırma ve değişmezlik yönteminin kullanıldığı çalışmalardan ve havacılık konusundaki örneklerinden bahsedilmiştir.
İkinci bölümde farklı eksen takımları tanıtılarak bir insansız hava aracının kontrolü için gerekli olan çok serbestlik dereceli doğrusal olmayan uçuş dinamiğine ait denklemler nasıl elde edildiği anlatılmıştır. Katı cisim hareket denklemleri, atalet kuvvetleri ve momentleri, aerodinamik, yerçekimi ve itki kuvvetleri çözülmüştür. Kartezyen ve kutupsal koordinatlarda denklemlerin ifadeleri elde edilmiştir. Bu denklemler geleneksel yapıdaki diğer sabit kanatlı hava araçları için de geçerlidir.
Üçüncü bölümde daldırma ve değişmezlik yöntemi anlatılmış ve bir kontrolör tasarlanırken gerçekleştirilmesi gereken koşullar belirtilmiştir. 
Dördüncü bölümde uçuş denklemlerine uygulabilecek daldırma ve değişmezlik yönteminin kullanıldığı bir kontrolör önerilmiştir. Kararlı durum uçuş şartlarının geçerliği olduğu kabul edilmiştir. Kullanılan insansız hava aracının yapısından bahsedilmiş ve uçuş dinamiğinde gerekli olan parametre ve katsayılar belirtilmiştir. Kontrol yüzeyleri kanatçık, yükseliş dümeni ve yön dümeni olmak üzere gövde eksen takımında yuvarlanma, yunuslama ve yönelim açısal hız kontrolü yapılmıştır. Daldırma ve değişmezlik özelliğine ait koşullar sisteme uygun bir şekilde gerçekleştirilmiştir. Bunun için bir hedef sistem dinamiği belirlenmiş ve hedef dinamiklerle çakışan bir manifold oluşturularak sistem dinamiklerinin kısıtlanması sağlanmıştır. Tüm sistem yörüngelerini sınırlayan ve manifoldun çekim özelliğine sahip olmasını sağlayan bir kontrol kuralı tasarlanmıştır. Daha sonra kontrol edilmek istenilen bilgisayar ortamında simülasyon yapılmıştır.

Abstract:
In this thesis, nonlinear flight controller design is proposed via immersion and invariance methodology for a fixed wing unmanned aerial vehicle. The controller basically adjusts the pitch, roll and yaw angular velocities in the body axes frame to the desired values. One of the reasons for choosing immersion and invariance methodology is that the mathematical model of the system can be used without the need for linearization.
Unmanned aerial vehicles are matters of increasing importance as other autonomous systems. It is not possible for these systems to operate independent from a control system, which are expected to operate with high accuracy regardless of the human factor. 
Unmanned aerial vehicles today have applications in many different areas. Detection of natural disasters such as forest fires and landslides, monitoring of power lines and pipelines, search and rescue, prevention of crime and military applications are the most needed areas. Their importance increases especially in situations where the danger is high and human access or skills are limited.
Problems encountered in aviation were encouraging the development and implementation of control methods. Even the first aircraft designs based on the control of the wings that change the aerodynamic forces and moments using human feedback. Later, the development of jet engines, navigation devices, sensors and other actuators in the aircraft design show the necessity of control systems. The nonlinear state equations must be solved in order to make the control design suitable for the real system model.
In the first chapter, the aim of the thesis was discussed and literature research was done. In literature, the use of immersion and invariance methodology in aviation was mentioned.
In the second chapter, different axes were introduced. Multi-degree of freedom nonlinear flight equations and coefficients required to control unmanned aerial vehicles were explained. Equations of rigid body, inertial forces and moments, aerodynamics, gravity forces and propulsion forces were resolved. In the cartesian and the polar coordinates, expressions of equations were obtained. These equations also apply to other conventional fixed wing aircrafts.
In the third chapter, the method of immersion and invariance was explained and the conditions to be performed when designing a controller were shown. These conditions are defining a target system, immersion condition, implicit manifold and manifold attractivity and trajectory boundedness.
In the fourth chapter, a controller which uses the immersion and invariance methodology to apply to flight equations was proposed. All steps to design a controller were applied for fixed wing unmanned aerial vehicle. 
While designing the controller, steady state flight conditions were considered valid. The basic structure of the unmanned aerial vehicle was mentioned and the parameters and coefficients required in flight dynamics were given. 
The conditions for immersion and invariance were carried out in accordance with the system. For this purpose, a target system dynamics was determined. System dynamics were bounded by creating a manifold that coincided with the target dynamics. A stabilizing control rule that bounds all system trajectories and makes the manifold attractive was designed. 
Aileron, elevator and rudder were chosen as control inputs. Controls of roll, pitch and yaw angular velocities were performed and system responses were observed.
When meaningful reference inputs are applied, this control method provides accurate results before the control surfaces reach their limit values. When improper reference inputs are applied, the control surfaces reached the limit values and the system remained at the stable limit values. 
In the case of unstable flight conditions, e.g. when two or three different angular velocity references were applied, angular velocities remained at the desired reference but Euler angles did not changed as intended.
There are singularities due to the nature of flight equations when the pitch angle is 90˚ and also side-slip angle is 90˚. More suitable controller was designed by changing the mapping selections leading to these values. The expression between the off-the-manifold dynamics and off-the-manifold coordinate were edited and the overshoot of the system response was improved.
In body axes frame, speed in the x axis was fixed to 24 m/s. Speeds in the other axes were neglected. The controller operates meaningfully as long as the value of the air vehicle is constant at different air velocities which does not cause stall. When the angular velocities of roll, pitch and yaw were zero, trim control was also performed.
Process of designing controller was done in Matlab and Simulink. For every different angular velocity, controller blocks were defined with off-the-manifold coordinates and off-the-manifold dynamics. Control surface limits were also defined as saturation. 
To find proper mappings, different attempts were made. Mappings of roll, pitch and yaw angular velocities were obtained. After obtaining the off-the-manifold coordinates, derivation of the results were off-the-manifold dynamics. From off-the-manifold dynamics expressions, control input terms were obtained. Also control inputs are dependent to eachother. In the Simulink model, output of controller blocks were connected to the other controllers as feedbacks.
Simulations were performed where roll, pitch and yaw angular velocities equal to π/9 rad/s. And also these simulations were extended in case of π/18 rad/s step disturbance,(π/36)sin(t/2) rad/s sinusodial disturbance and white noise disturbance.
An unmanned aerial vehicle with a stabilizing controller designed via immersion and invariance methodology may operate independently in situations where it is desired to follow an angular trajectory and also, when trim control is required or there is wind as disturbance in level flight. It can be an example for other complex physical systems that include nonlinear equations.