F-16 jet uçağı için açık model izleme tabanlı boylamsal kontrolör tasarımı ve hücum açısı kestirimi
Explicit model following based longitudinal controller design and angle of attack estimation for F-16 jet aircraft
Yazar: GÜLŞAH KESGİN ERTÜRK
Danışman: DOÇ. DR. İLKER ÜSTOĞLU
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Kontrol ve Otomasyon Mühendisliği Ana Bilim Dalı / Kontrol ve Otomasyon Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2023
Konu: Bilgisayar Mühendisliği Bilimleri-Bilgisayar ve Kontrol = Computer Engineering and Computer Science and Control
Dizin: Atmosfer modelleri = Atmospheric models ; Dinamik modelleme = Dynamic modelling ; Havacılık = Aviation ; Kontrol teorisi = Control theory

Özet:
F-16 jet uçağı matematiksel olarak modellenmiş ve Açık Model Takip tabanlı bir yaklaşım kullanılarak uçağın boylamsal dinamik kontrolörünün tasarımı anlatılmıştır. Tasarlanan kontrolör mimarisi ile uçağın kontrol performansı ve kararlılık sonuçları analiz edilmiştir. Ayrıca geri beslemede kullanılan hücum açısı verisinde hata olması durumunda Tamamlayıcı filtre ile hücum açısı kestirimi gerçekleştirilmiş ve sonuçlar tartışılarak değerlendirilmiştir. Bu tez kapsamında, Matlab/Simulink yazılımı kullanılarak F-16 jet savaş uçağının altı serbestlik dereceli (6-DOF) matematiksel modeli geliştirilmiştir. Hava aracının tüm alt sistemlerinin matematiksel modelleri ve hareket denklemleri ayrıntılı olarak ele alınmıştır. F-16 simülasyon modelinin aerodinamik veri tabanı, −20◦ ila 90◦ hücum açısı, ±30◦ yana kayma açısı ve Mach 0.6'dan düşük hava hızı gibi aerodinamik uçuş koşulları için oluşturulmuştur. Motor modeli Huo'nun çalışmasına dayanmaktadır ve 1 Mach'ın altındaki hava aracı hızları ve 15240 metrenin altındaki irtifalar için geçerlidir. Atmosfer modeli Uluslararası Standart Atmosfer (ISA) denklemleri kullanılarak oluşturulmuştur. Kontrol yüzeyleri ve ön-kenar kanat eyleyicisi birinci dereceden transfer fonksiyonları olarak modellenmiştir. Konum ve hız limitleri NASA tarafından yayınlanan teknik belgeye dayanmaktadır. Hareket denklemleri Newton-Euler yöntemi ile elde edilmiştir. Hareket denklemlerinin ve kinematiğin elde edilebilmesi için eksen takımı tanımlarına ve bu eksen takımlarının birbirlerine göre dönüşümlerine ihtiyaç vardır. Genel olarak hava araçları için yer eksen takımı, gövde eksen takımı, kararlılık eksen takımı ve rüzgar eksen takımı kullanılmaktadır. Kararlılık analizi ve kontrol sistemi tasarımında, doğrusal olmayan hava aracı dinamik denklemlerinin doğrusal olmayan modelleri kullanılır. Bu nedenle, hava aracının dinamik hareketlerini ve durumlarını içeren doğrusal olmayan hareket denklemleri, belirli statik denge noktaları etrafında doğrusallaştırılır. Bu doğrusal modeller, hava aracının doğrusal olmayan modelini statik denge noktası etrafındaki bir uçuş zarfında temsil edecek kadar yakınlaştırılır. Uçuş zarfına bağlı olarak belirlenen statik denge noktaları etrafında doğrusal olmayan hava aracı modelinin doğrusallaştırılması ile durum uzayı modelleri elde edilir. Bu çalışmada kullanılan açık model takip tabanlı boylamsal kontrol yapısı kontrol mimarisine dayanmaktadır. Kontrol mimarisinin sentez modeli girdileri ve kriter çıktıları arasında istenen frekans tepkilerini oluşturmak için inşa edilen bir modelidir. Bu çalışmada kullanılan sentez modeli ile Açık Model Takibine (EMF) dayalı mimari arasında benzerlikler bulunmaktadır. EMF mimarisinden farklı olarak, çıkış kriteri, gerçek model çıkışı ile istenen model çıkışı arasındaki fark olan hataya dayanmaktadır. Sentez yapısının mantığında, istenen sistem modelini elde etmek için açık döngü hava aracı modeline sıfırlar eklenir. Frekans bölgesi kriterleri kısa dönem cezası ve uzun dönem cezanın toplamı olarak tanımlanır. Açık döngü hava aracı modeline eklenen sıfırlar ilgili maliyet fonksiyonu cezalarını belirlemeyi amaçlamaktadır. LQRy algoritması toplam ceza kriterini minimize eder ve genel sentez modelindeki her bir durum için kazanç değerlerini hesaplar. Elde edilen kazanç katsayıları, kararlılık ve faz paylarını hesaplamak için analiz modelinde kullanılır. Analiz modeli filtreler, sensör gecikmeleri ve aktüatör modelleri gibi sistem gecikmelerinin daha doğru bir şekilde yansıtılmasını sağlar. Bu mimarinin amacı, uçuş zarfı boyunca ve ağırlık ve ağırlık merkezi aralığı boyunca hız ve manevra kararlılığı ile tutarlı ve kararlı uçuş özellikleri sağlamaktır. Bu kontrol mimarisinin en kritik noktalarından biri hücum açısı sinyalinin tahmin edilmesidir. Bu çalışmada, hücum açısı sensörünün arızalanması durumunda hücum açısı Tamamlayıcı bir filtre ile tahmin edilmektedir. Kestirim algoritmasında aerodinamik veri tabanından hesaplanan hücum açısı ve hücum açısının değişim oranı kullanılmaktadır. Aerodinamik veri tabanından hesaplanan hücum açısı verisi, verideki gürültü ve sapma nedeniyle doğrudan kullanılmamaktadır. Tamamlayıcı filtre ile verideki gürültü ve sapmalar düzeltilmektedir. Doğrusal olmayan modelde uçakta kullanılan tüm filtreler, sensör gecikmeleri, eyleyici modelleri gibi sistem gecikmelerinin gerçekçi bir biçimde dahil edildiği bir model oluşturulur. Doğrusal modelden elde edilen ve tüm uçuş zarfını kapsayan kazanç değerleri kazanç sıralama yöntemi ile doğrusal olmayan modele aktarılır. Doğrusal olmayan modelde kapalı çevrim kararlılık analizi için filtre ve tüm sistem gecikmeleri dahil edilerek sonuçlar analiz edilmiştir.

Abstract:
The F-16 jet aircraft is mathematically modeled and the design of the aircraft longitudinal dynamic controller using an Explicit Model Following based approach is explained. The aircraft's control performance and stability results with the designed controller architecture are analyzed. In addition, in case of an error in the angle of attack data used in the feedback, angle of attack estimation is performed with the Complementary filter and the results are discussed and evaluated. A mathematical model is necessary to observe the states of an aircraft during the real flight and to design the controller. For this purpose, the dynamic and kinematic equations of the aircraft are obtained by using Newton's laws of motion. The aircraft mathematical model consists of 12 equations, six dynamic equations, and six kinematic equations. To obtain the equations of motion, it is first assumed that the aircraft behaves like a rigid body. Based on this assumption, it is assumed that any mass on the plane does not move relative to any other mass. In this study, standard dynamic and kinematic equations are used and linear models are obtained from these equations. In the scope of this thesis, a six-degree-of-freedom (6-DOF) mathematical model of the F-16 jet fighter aircraft is developed using Matlab/Simulink software. Aircraft mathematical models of all subsystems and equations of motion are described in detail. The aerodynamic database of the F-16 simulation model is for aerodynamic flight conditions of −20◦ to 90◦ angle of attack, ±30◦ sideslip angle, and airspeed of less than Mach 0.6. The engine model is based on the work of Huo. The engine model is valid for aircraft speeds below 1 Mach and altitudes below 15240 meters. The atmosphere model is constructed using the International Standard Atmosphere (ISA) equations. The control surfaces and leading-edge wing actuators are modeled as first-order transfer functions. Position and rate limits are based on a technical document published by NASA. The equations of motion are obtained by the Newton-Euler method. In order to obtain the equations of motion and kinematics, reference frame definitions and the transformation of these frame definitions with respect to each other are required. Transformation matrices realize the relations between the equations. In general, earth frame, body frame, stability frame, and wind frame are utilized for the aircraft model. The definitions and transformations of these frames are described in detail in the relevant sections. The aerodynamic database is created using wind tunnel test results from NASA Langley and Ames Research Centre. This database includes values from −20◦ to 90◦ for angle of attack, ±30◦ for sideslip angle, and true airspeed less than Mach 0.6. The forces and moments on the aircraft are calculated using the dimensionless aerodynamic coefficients obtained from wind tunnel testing or CFD analysis. Therefore, a suitable model is needed to provide values for the dimensionless aerodynamic coefficients around the body axis of the aircraft. Using the coefficients in the aerodynamic database, the total forces and moments are calculated with respect to the aerodynamic center of the aircraft.  In the aerodynamic model, forces and moments are defined in dimensionless form. Aerodynamic coefficients for non-dimensional forces or moments are given in the relevant sections. The International Standard Atmosphere (ISA) equations and tables are used for atmosphere model. The atmosphere is modeled in a Simulink environment and dynamic and static pressures, Mach number, and atmospheric gravity outputs are obtained using true airspeed and altitude inputs. In physical systems, a mathematical model is required to investigate and analyze their dynamics. Mathematical models can be used to observe and analyze the situations that will occur during the flight with six-degrees-of-freedom (DOF) equations of motion. The mathematical modeling of nonlinear dynamical systems, especially of a flying aircraft, is highly complex. When the equations of motion of an aircraft are considered, some assumptions are used to simplify the equations. These assumptions are divided into 3 basic parts. The first assumption is that the aircraft behaves like a rigid body, i.e. the distance between any two points on the fuselage is assumed to be constant. Therefore, the center of gravity of the aircraft has no relative velocity with respect to the body axis. Secondly, the mass of the aircraft is assumed to be constant. And the last assumption is that the mass distribution of the aircraft is assumed to be constant with time. Therefore, the moment of inertia remains constant. The equation of motion of an aircraft is basically obtained in the frames of the earth frame and the body frame. The equations of motion are derived according to the Newton-Euler method. The total force and moment equations are defined in the body frame. Aerodynamic forces and moments are converted from the wind frame to the body frame. A total of twelve equations of motion, including six dynamic and six kinematic equations, can be solved by numerical methods. The aircraft consists of six dynamic equations of motion. The newton-Euler method is used to obtain the dynamic equations. In the equations of motion, the right-hand side of the equations contains the applied forces and moments, and the left-hand side of the equations contains the responses of the aircraft to these forces and moments.  All aerodynamic force and moment equations are defined in the body frame. In addition, all the avionic types of equipment and sensors on the aircraft produce data according to the body frame. For these reasons, it would be useful to convert the dynamic forces and moments on the aircraft to the body frame. In the aircraft, 6 dynamic equations as well as 6 equations of motion need to be defined. The kinematic equations are not included in the linear model of the aircraft but are used as supporting equations for the nonlinear aircraft model. In the stability analysis and control system design, nonlinear models of nonlinear aircraft dynamic equations are used. Therefore, the nonlinear equations of motion, which contain the dynamic motions and states of the aircraft, are linearized around certain static equilibrium points. These linear models are approximated closely enough to represent the nonlinear model of the aircraft in a flight envelope around the static equilibrium point. These specific points where the aircraft is linearized are the static equilibrium points. The linearization of the nonlinear mathematical model is performed around the specified static equilibrium points for stability analysis and design of linear controllers. The nonlinear mathematical model of the aircraft for different flight envelopes and different static equilibrium conditions is described. The obtained linear equations are then decomposed to represent the longitudinal and lateral modes of the motion of the aircraft. Based on the aerodynamic literature, an aircraft in equilibrium is described as being in static equilibrium (trim) condition. Mathematically, the definition of static equilibrium is that the total forces and moments on the aircraft are zero. Linear models are obtained around static equilibrium points and control systems are calculated and designed at points defined around static equilibrium conditions. Mathematically, the definition of the static equilibrium representation is that the total forces and moments on the aircraft are zero. Linear models are derived from static equilibrium points and control systems are calculated and designed at points defined around static equilibrium conditions. State space models are obtained by the linearization of the nonlinear aircraft model around the static equilibrium points determined depending on the flight envelope. In this thesis, the linearize command of the Matlab program is used to obtain linear models around the static equilibrium point. The linear longitudinal aircraft model is used for longitudinal performance analysis and for obtaining longitudinal controller gain coefficients. The aircraft is characterized by two different oscillation periods, the short period and the phugoid mode. The short period of the aircraft in the longitudinal axis includes the angle of attack and the rate of change of the pitch angle. The short-period mode of the aircraft in the longitudinal axis presents short oscillations around the aircraft's center of gravity. When the Root-Locus curves of the linearized state space equations of the aircraft around the static equilibrium are obtained, the short period has a complex conjugate. In the short-period mode, the altitude and airspeed are hardly constant. The phugoid mode of the aircraft in the longitudinal axis includes the airspeed and pitch angle . The long period mode (slightly damped) has a behavior that takes a long time to be damped, unlike the short-period mode. In the phugoid mode, the aircraft periodically maintains a constant angle of attack depending on the altitude and the airspeed (potential and kinetic energy) until the aircraft re-stabilizes. In this study, the explicit model following based longitudinal control structure used in this study is based on the control architecture. In the longitudinal control architecture, the design is realized using the four longitudinal states of the aircraft. The control architecture consists of two main parts. The first is the synthesis model, built to establish the desired frequency responses between the control inputs and the criterion outputs. There are similarities between the synthesis model used in this study and the architecture based on Explicit Model Tracking (EMF). Unlike the EMF architecture, the output criterion is based on the error, which is the difference between the actual model output and the desired model output. In the logic of the synthesis structure, three zeros are added to the open-loop system to obtain the desired system model. The desired zeros are determined according to the frequency and damping ratio of the short-period mode. The transfer function between the normal acceleration and the elevator command is calculated. The synthesis model is constructed to obtain the desired frequency responses between the control inputs and the criterion outputs. The frequency domain criteria are defined as the sum of two penalties. These two penalty criteria are divided into the short-period penalty and the long-period penalty. This structure aims to determine the relevant cost function penalties by adding three zeros to the open-loop aircraft model. The LQRy algorithm minimizes the total penalty criterion and calculates the gain values for each state in the overall synthesis model. The resultant gain coefficients are used in the analysis model to calculate the stability margin and phase margin. The analysis model provides a more accurate reflection of system delays such as filters, sensor delays, and actuator models. By manipulating the target zeros, different gain values are obtained for the desired stability margins and performance values in the analysis model. The aim of this architecture is to provide stable flight characteristics consistent with speed and maneuvering stability throughout the flight envelope and across the weight and center of gravity range. The feedback integral provides both the pitch force per g and the pitch force per knot, i.e. the stability of the airspeed. One of the most critical points of this control architecture is the estimation of the angle of attack signal. In this study, the angle of attack is estimated by a Complementary filter in case of a failure of the angle of attack sensor. The angle of attack calculated from the aerodynamic database and the rate of change of the angle of attack are used in the estimation algorithm. The angle of attack data calculated from the aerodynamic database is not used directly because of the noise and bias in the data. With the help of Complementary filter, the noise and biases in the data are corrected. The performance results of the longitudinal control architecture obtained in the linear domain for the F-16 jet aircraft nonlinear model are analyzed. In the nonlinear model, a model is created in which system delays such as all filters, sensor delays, and actuator models used in the aircraft are included to consider the real flight conditions. The gain values obtained from the linear model and covering the entire flight envelope are transferred to the nonlinear model by the gain scheduling method. For the closed-loop stability analysis in the nonlinear model, a delay of $80$ ms is transferred to the model by including the filter and all system delays.