İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Uçak ve Uzay Mühendisliği Anabilim Dalı / Havacılık ve Uzay Mühendisliği Bilim Dalı
A4 uçağı için geliştirilmiş otopilot tasarımı
Autopilot design for A4 aircraft
İbrahim Can Karagöz
İnsansız savaş uçaklarının görev zorunlulukları ve ihtiyaçları nedeniyle hareket manevralarının planlanması ve otonomlaştırılması zorunlu bir hal almıştır. Bu amaçla, çalışmada insansız savaş uçaklarının hareket manevralarının aktüatör girişleri ile etkileşimi incelenmiş, hareket modlarının bu eyleyici girişleri ile kontrol edilebilmesi için PID, LQR, kök yerleştirme ve iç-dış çevrim kontrolcüleri tasarlanmış, uçuşta karşılaşılabilecek bozuntuların giderilmesine çalışılmış ve uçuşun otonomlaştırılması amaçlanmıştır. Bu amaçlara yönelik olarak, uçak doğrusal ve doğrusal olmayan hareket denklemleri geliştirilmiş, her iki tip hareket denklemi için eyleyicilerin uçak durum değişkenlerine etkisi gözlemlenmiştir. Bu gözlemlerden hareketle, öngörüldüğü gibi, doğrusal olmayan hareket denklemlerinden belirli varsayımlar ile türetilen doğrusal durum denklemlerinin belirli bir hataya sebebiyet verdiği belirlenmiş ve bu hata miktarı ortaya konulmuştur. Çalışmanın devamında, uzunlamasına ve yanlamasına hareket için LQR, PID ve iç-dış çevrim, durum geri besleme kontrolcüleri ile referans girişe karşılık gelen cevap gözlenmiş, karşılaştırılmış ve gerekli eyleyici girişleri, maksimum ve minimum limitleri göz önüne alınmış ve uçuş otonomlaştırılmıştır.Bu bölüme kadar uçuşun belirli bir kondisyonda gerçekleştirildiği varsayımı ile hareket edilmiştir. Gerçekleştirilen tasarımlar da nominal ölçütlerde düşünülmüştür. Ancak uçak kararlılık türevlerinin uçuş kondisyonuna bağlı olarak değiştiği bilinmektedir. Gerçekleştirilen simülasyonlarla da bu kararlılık türevlerinin uçağı kararsızlaştırabilecek etkilerde bulunabileceği gözlemlenmiştir. Buradan hareketle dayanıklı (robust) bir kontrolcü tasarımı gereksinimi saptanmıştır. Kayma kipli kontrolcü ve dayanıklı PID kontrolcü tasarımları gerçekleştirilmiştir. Bu tasarımların parametrik belirsizliklere ve bozuntulara rağmen kararlı davranış sergilediği görülmüştür.
In the last decades, making unmanned air vehicle autonomous has gained highly importance in the point of controlling flight modes especially for fighter aircrafts. From this point, observing and developing of flight maneuver abilities necessity have emerged. On the other hand, precision and effectiveness of developed techniques is very important. In this regard, response of flight modes to actuator inputs for both non-linear and linearized flight equations is a valuable research subject which is worked on in the thesis. The validity of linearized equations is discussed and presented the area which can be accepted to lead these linearized equations.Other important subject is to achieve maneuver abilities in the form of desired input. Controller design which would provide possible maneuver tasks to the fighter aircrafts on the time of mission is an inevitable necessity. The purpose of maneuver planning and making autonomous unmanned combat air vehicles (UCAV?s) because of flight missions and requirements is in dense in the thesis.All the referred tasks cause some analysis on the field of control engineering. Effects of actuator inputs on flight modes of UCAV?s have been examined and designed PID, Inner loop-Outer loop, Pole Placement and LQR controller techniques. For this sequence, at the beginning, aircraft?s six degree of freedom non-linear dynamic equations have been created. Once non-linear equations, the linearized model is derived from non-linear equations with some assumptions. Defined actuator inputs have effects on state variable of the aircraft. Both non-linear and linear equations bring solution to actuator inputs. From the simulations results, although the same reference input manage the system, linear equations lead some error for the certain flight conditions. On the next step, linearized model is divided by two separated flight which named longitudinal and lateral flights. With the control designs PID, Inner loop-Outer loop, Pole Placement and LQR, response to reference input (desired output) is obtained for the both longitudinal and lateral flights with the allowance of physical limits of actuator mechanisms. Linear model is said to be derived by some assumption. These assumptions include constant stability derivative. But in real flight, stability derivatives are variable parameters and change of at least one state variable would change other derivative values. This fact requires robust stability analysis within the limits of stability derivatives and a robust controller design is an obligation to guarantee stability of aircraft.Main forces which have effects on flight dynamics are classified as aerodynamic forces, thrust force and aircraft weight. By taking consideration of these forces and with the regard of Newton law, we obtain six degree of freedom non-linear equations of aircraft. From this point for the linearization purpose of equations, state variables are classified into longitudinal and lateral flight. So, effects of state variables on eachothers are cancel out and two separated flights are proceeded. The other assumption is that flight is around a certain trim point and deviations from trim point are not that important to change flight condition and stability derivatives. The other assumption is separating elevator and thrust effects as longitudinal flight inputs and aileron and rudder effects as lateral flight inputs. This means that both linearized systems have multiple inputs. Subsequent assumption is to set beginning rotational rates to zero. So pitch, roll and yaw rates are zero origins. Additionally, roll and yaw angle are zeros as well. Further assumption is the small degree and high perturbations.With all the assumption and defined flight conditions linear model has constructed. The work should be done after that step is to carry out the linear equations to state space model. The aim of this model is to construct a first order differential equation with A system matrix, B input matrix, C output matrix and D feed through matrix. The state space model will help to transition to transfer functions of input-to-output with the Cramer rule and ease the simulation modeling. System variables are chosen among the energy absorbing variables. After eigenvalue investigation and simulation results, it is decided that, in longitudinal flight, all the poles are at the left side of s-plane, so system is stable but there are two poles very close to origin which are needed to be damped faster. 1 degree deflection of elevator input is observed and its causes are negative pitch moment and increment in speed for the steady flight. Thrust increment causes augmentation for speed in short term but in long term its effect is pitch up moment. Simulation results have proved that the aircraft has short term and long term oscillation which must be controlled. In lateral flight 4 roots represent 3 different flight modes. 2 complex conjugate roots represent dutch-roll mode which is defined by the action both rolling and yawing modes, third root represents rolling mode and finally fourth root represents spiral mode. Aileron deflection changes lift forces of two wings in different directions and generate roll moment and additionally it has yawing moment contribution. So dutch-roll mode appears by the side effects. Rudder deflection causes mostly yawing moment but also generates roll moment because of the location of the rudder. The results from analysis and simulations are the needs of a controller design for the stabilization of unstable modes and fast response.Governing the non-linear equations is quite different apart from the linear one. Since the change in control surfaces and state variable situations would change the stability derivative, system may be destabilized. Stability derivatives are defined as functions of high and mach number, so a more complex stability analysis will be required.Comparison of non-linear and linear equations solution includes some basic methods. One is to keep the control surfaces deflected quite short time and small values. By this way stability derivatives will not change highly and response will be very close to linear solution. The other one is the contrarily deflection and response will be very different. This kind of solution would show the validity limits of linear solution.Controller need has been fulfilled by different methods. For the constant parameters using linear model optimal control, modern control and a control theory which is common in aeronautic field named inner loop-outer loop control have been conducted. Linear model which has variable stability derivatives need robust control. Robust stability analysis is also worked on.PID controller which is frequently used for the dynamical systems control and has a wide application area is known its easy design and proper response to systems needs. Direct output feedback and calculated or estimated proportional, integral and derivative constants are sufficient simulation requirements to design this system.Inner loop-outer loop controller is a little bit more complicated than PID controller.Manipulation of longitudinal flight modes with inner loop-outer loop controller design, two flight?s modes will be examined as SISO systems and defined feedback and feed-forward constants. After stabilization the modes system will be converted to MIMO system and output states will be stable and equal to reference input. For the pitch angle, firstly pitch rate is defined as output state. Gyroscope coefficient can be sought by observing root locus as elevator to be input. Pitch rate is now stabilized, next step would be seeking feedback constant of outer loop which will converge the pitch angle to reference input.Loop for speed is provided by throttle input, feedback function is chosen by derivative and proportional constants and loop is completed. Moreover, a feed-forward amplifier using decrements overshoot and shortens peak and settling time. Inner loop-outer loop design gives satisfactory response for longitudinal flight.In inner loop-outer loop control design of lateral flight, yaw angle would be tried to be equal to reference input. For this purpose, firstly steady state value of yaw rate would be equal to zero. Nextly, sliding angle would be minimized by feedback of the mode. Lastly, Aileron input is represented as inner and outer loop feedback of yaw and roll rates.Simulation results shows that such a design worked on achieve to keep pitch angle and speed at desired output. In lateral flight, by inner loop yaw rate is set to zero and by outer loop sliging angle is set to desired output. Additionally, roll rate is set to zero for the stabilization purpose of roll angle. All the required feedback and feed-forward coefficients are found from root locus graphs.Linear Quadratic Regulator (LQR) is a controller to guarantee asymptotic stability. Riccati equation solution would define state feedback matrix. In order to find proper feedback matrix which provide asymptotic stability some rules must be followed like choice of Q and R matrix. The choice of Q and R matrices would directly affect output matrices, so weight of every element of these matrices should be carefully examined.Pole placement technique is a subject of modern control theory which require to be fully controllable and observable systems to apply the theory. In the case of unobservable system, control system needs an observer to estimate unmeasurable modes of flight. The main purpose of this design is to place the roots to desired points at the s-plane by using state feedback to the input device. That is why all the states need to be known or estimated. In the case of observer use, observer dynamics must be faster than aircraft dynamics, in other words observer roots must be placed to the left side of system roots to estimate the state variables faster than the dynamic system.Until this part of the thesis, it is assumed that the flight is operated in a certain condition. The realized desings is thought in nominal cases. But, it is a fact that stability derivatives are changeable depending on flight condition. Simulations that are presented is showing that these stability derivatives can destabilize the aircraft. The lack of stability forces us to the design of a robust controller. Subsequently, sliding mode controller and robust PID controller designs are realized. Although parameter uncertainties and disturbances, the aircraft behaves as a stable characteristic.