Hava aracı modeli ve uçuş kontrol sistemi tasarımı

Abstract

Uçuş kontrol sistemleri ve uçuş konfigürasyonları Orville-Wilbur Wright kardeşlerin ilk motorlu insanlı uçuşu gerçekleştirdiği 1900'lerin başından itibaren büyük değişim geçirmiştir. İnsaoğlunun hep daha iyiye ulaşma isteği bu değişimin başlıca sebepleri arasında gösterilebilmektedir. Özellikle savaş zamanlarında, hava araçlarına sahip olunmasının kazandırdığı avantajın farkına varılması yaşanan gelişmelerde büyük rol oynamıştır. Hava araçlarıyla hedef imha edilmesi, saldırı ve savunma gibi çeşitli görevlerin gerçekleştirilme ihtiyacı sebebiyle, ayrıca uçuş zarfının sürekli büyümesiyle hava araçlarının dinamikleri değişim göstermiştir. Bu gelişmeler beraberinde hava araçlarının uçuş kontrol sistemlerinin değişmesine ve gelişmesine sebep olmuştur. Özellikle hava araçlarının dinamiklerinde karşılaşılan bu değişimler uçuş kontrol sistemlerinin kullanılmasını zorunlu kılmıştır. Hava araçlarının kararlılığının sağlanması, manevra yeteneğinin artırılması ve hava aracının pilot tarafından daha kolay kontrol edilebilir olmasının sağlanması, uçuş kontrol sistemlerinin esas görevleri arasında yer almaktadır. Bunların doğrultusunda hava araçları için kararlılık ve kontrol konuları büyük öneme sahip olmuştur. Bu tez çalışması kapsamında General Dynamics tarafından geliştirilen F-16 savaş uçağının benzetim modeli oluşturulmuş, hava araçlarının dinamik-statik kararlılığı kavramları açıklanmış ve geleneksel dinamik kararlılık modları irdelenmiştir. Ardından klasik uçuş kontrol sistemi tasarlanmış ve bu sistemlerin uçuş dinamikleri üzerindeki etkisi gözlemlenmiştir. Bu kapsamda tezin ilk bölümünde havacılığın gelişimi tarihsel olarak anlatılmıştır. Literatürde mevcut olan F-16 savaş uçağı modelleri incelenmiştir. Tezin ikinci kısmında hava araçları için bilinmesi gereken temel kavramlar anlatılmıştır. Bu doğrultuda uçuş eksenleri, kontrol yüzeyleri, uçağa etkiyen moment ve kuvvetlerden bahsedilmiştir. Ayrıca F-16 savaş uçağı hakkında genel bilgiler ve özellikler verilmiştir. Üçüncü bölümde hava aracının benzetim modeli Matlab-Simulink kullanılarak oluşturulmuştur. Aerodinamik modeli NASA Langley Research Center'ın yayınladığı rüzgar tüneli testlerinden elde edilen kararlılık ve kontrol katsayıları kullanılarak oluşturulmuştur. Toplam kuvvet ve momentler elde edildikten sonra doğrusal olmayan hareket denklemleri türetilmiştir. Motor, eyleyici ve atmosfer modelinin oluşturulmasıyla hava aracının doğrusal olmayan matematiksel modeli elde edilmiştir. Hava aracı modelinin belirli koşullar için denge noktası bulunmuş ve küçük pertürbasyon teorisi kullanılarak bu doğrusal olmayan modelden cebirsel olarak doğrusal denklemler elde edilmiştir. Ardından bu hareket denklemleri, boylamsal ve yanal-dikey eksen olarak ikiye ayrılmıştır. Ayrıca bu bölümde hava araçları için kritik öneme sahip olan dinamik kararlılık modları boylamsal ve yanal-dikey hareket içerisinde ayrıntılı bir şekilde anlatılmıştır. Boylamsal hareket, kısa dönem ve phugoid modu olarak iki alt grupta, yanal hareket ise dutch roll, yuvarlanma ve spiral modları olarak üç alt grup içerisinde incelenmiştir. Ardından mod yaklaşımları ve kararlılık türevleri arasındaki ilişkiler kurulmuştur. Son bölümde ise uçuş kontrol sisteminin öneminden bahsedilmiştir. Bu sistemlerin uçak dinamikleri üzerindeki etkisi anlatılmıştır. Doğrusallaştırılmış hareket denklemleri kullanılarak belirli uçuş koşulları için kararlılık ve kontrol arttırma sistemi tasarımı yapılmıştır.

Flight control systems and aircraft configurations have undergone significant changes since the early 1900s when the Orville-Wilbur Wright brothers achieved the first motor-operated manned flight. The autopilot Sperry Stabilizer was developed by the Sperry Gyroscope Company. While the first planes flew at relatively low speeds and low altitudes over the past hundred years, these borders expanded over time. The human being always tries to aim better in any circumstances. For this reason, the change is inevitable. Particularly in times of war, the realization of the advantage of having an aircraft played a major role in the developments. The dynamics of aircraft have undergone many changes due to the need to perform various tasks such as target destruction, attack and defense by aircraft, and with the continuous expansion of the flight envelope. These developments also caused the changing and development of flight control systems of aircraft. These changes, especially in the dynamics of aircraft, made it necessary to use flight control systems. Ensuring the stability of aircraft, increasing the maneuverability, and making that the aircraft can be controlled more easily by the pilot, is among the main mission of flight control systems. For all these reasons, stability and control issues are of great importance for aircraft. Within the scope of the thesis, the simulation model of F-16 fighter aircraft that developed by General Dynamics was created. In this context, aerodynamic model, equation of motion, motor, actuator, and environment model were designed. The aircraft was trimmed in a desired flight condition and then linearized state equations were obtained. Then the concepts of dynamic and static stability of aircraft were explained and traditional dynamic stability modes are examined. After that, the classic flight control system was designed and the effect of these systems on flight dynamics was observed. In the introduction part of the study, the developments in aircraft and flight control systems were investigated historically. In the following section of the study, basic concept about aircraft was explained. Besides, axes of the flight, primary and secondary control surfaces, moments and forces affecting the aircraft was mentioned. Control and stability definition was given and the concept of Relaxed Static Stability is explained. The effects on aircraft stability of Relaxed Static Stability was described. In addition to general information about the F-16 fighter aircraft, the mass and geometric features of this aircraft are also given in this section. In the third part of the study, the simulation model of F-16 fighter aircraft was created by using Matlab-Simulink software. All parts of the simulation model were explained in detail. The mathematical model of the aircraft was created by combining many subsystems such as aerodynamic model, equation of motion, actuator model, sensor model, and engine model. The stability and control coefficients describe both static and dynamic behavior characteristics of the aircraft. For this reason, it is remarkably important to create an accurate aerodynamic model using these coefficients. In this context, the stability and control coefficients obtained from wind tunnel tests published by NASA Langley Research Center in 1979 were used to form the basis of the aerodynamic model. For the purpose of creating the aerodynamic model, these coefficients were used to obtain aerodynamic force and moment coefficients through the lookup tables in Matlab – Simulink software. After obtaining the total forces and moments affecting the aircraft, nonlinear 6 DOF equations of motion were derived according to kinematic relations and Newton's second law. These nonlinear aircraft equations of motion were modeled using the body axis coordinate system. In order to obtain the future possible states, the other coordinates systems which are wind and stability axes were used. Therefore, transition matrix was given for these coordinate systems. The thrust force was selected from the two-dimensional lookup tables that vary with altitude and Mach number, after the thrust response was derived within the engine model according to these tables and the applied throttle command. After creating the actuator model and the atmosphere model in which the environment in which the aircraft is located, the non-linear model of the aircraft was completed. The nonlinear aircraft model was solved using the fourth order Runge Kutta method with a sampling frequency of 100 Hz. Subsequently, the trim conditions were found for given conditions and algebraic linear equations were obtained by using the small perturbation theory from the nonlinear equations. In addition, dynamic stability modes, which have critical importance for the aircraft, are described in detail in longitudinal and lateral-directional motion. Longitudinal motion was analyzed in two subgroups as short period and phugoid mode, and lateral-directional motion was analyzed in three subgroups as Dutch roll, roll and spiral modes. In the short period mode of longitudinal motion, the angle of attack and pitch rate states are effective. In phugoid mode, true airspeed and flight path angle were seen to be effective. Similarly, for the Dutch roll mode, sideslip angle is important. In the other modes of lateral-directional motions, roll-spiral, roll angle and sideslip is critical states. Considering the variables that the modes have, it is seen that both the stability axis and the wind axis state variables were used. After that, the relationships between mode approaches and stability derivatives were established. Although separation between longitudinal motion modes were provided, lateral directional motions modes were not separated due to the coupling in these modes. The main purpose of the approaches is to provide basic understanding of the interpretation of these factors aerodynamic stability and dynamic behavior for each flight modes. In the final part, the flight control system is examined and the general procedure is mentioned. Using the linearized equations of motion of the F-16 fighter aircraft, a stability and control augmentation system was designed for given flight conditions. In this section, the method of classical control theory to design flight control system was explained. The one loop at one-time approach is used. In this way, the aircraft dynamic response is observed within the scope of loop changes and its effects. With the classical control theory, each gain was selected individually for each loop, and the effect of these gains were visualized using the Root locus technique to help understand the change of flight dynamics. Implementation of stability and control augmentation systems were mentioned in detail. The importance of aileron-rudder interconnection gain was briefly explained and the effect of the designed flight control systems on aircraft dynamic stability was examined.