Bir uçağın yatış açısı kontrolü için farklı tip denetleyici karşılaştırmaları

Abstract

Kapalı çevrim kontrol sistemleri, kontrol edilen çıkış değişkeninin ölçülüp geri beslenerek arzu edilen giriş değişkeni ile karşılaştırıldığı sistemlerdir. Sistemin çıkışı, arzu edilen çıkış değerini sağlayacak biçimde giriş büyüklüğü ile ayarlanır. Negatif geri beslemede daima giriş ile çıkışın bir farkı alınır. Kontrol elemanına bir hata girişi olarak iletilen bu fark, çıkışın istenilen değere getirilmesini ve bu değerde sabit tutulmasını sağlar. Kapalı çevrim kontrol sistemlerinde denetleyicinin amacı, hata değerinin yapısına ve kendi denetim etkisine bağlı olarak uygun bir kumanda denetim sinyali üretmektir. Sistem yapısına bağlı olarak bir takım ayarlamalar ile P, PI, PD ve PID denetleyiciler, bu amaçla sıklıkla kullanılan geleneksel denetleyicilerdir. Klasik denetleyicilerin yetersiz kaldığı durumlarda, bulanık denetleyiciler de bu amaçla kullanılabilir olup, burada da üyelik fonksiyonları ve kuralların seçimi önem kazanmaktadır. Bu çalışmada, bir uçağın uçuş kontrol sisteminde önem arzeden yatış açısı kontrolü için klasik denetleyicilerden P, PD, PI tip denetleyiciler ile küme ve kuralları deneme yoluyla oluşturulmuş bulanık denetleyicinin karşılaştırmaları yapılmaktadır. Klasik denetleyicilerde kazanç ayarlamalarıyla, bulanık denetleyicide ise üyelik fonksiyonlarının ve kurallarının seçilmesi ile elde edilen çıktılar karşılaştırıldıklarında, eğer yatışkın duruma daha çabuk ulaşılmak isteniyor ve belli bir kararlılık hata tolerans değeri söz konusuysa P veya PD denetleyicili sistem, yatışkın duruma gelme zamanından daha çok kararlılık hatası değerinin minimum olması hedefse PI denetleyicili sistem ya da bunların kesişimi şeklinde bir çözüm aranıyorsa bulanık denetleyicili sistem kullanım yoluna gidilebilir sonucuna ulaşılmıştır.

Basic automatic control system consists of controller, actuator, sensor and plant. In a closed loop control system, the difference between the input and feedback is fed to the controller so as to reduce the error and bring the output of the system to a desired value. The actuator is a power device that produces the input to the plant according to the control signal so that the output will approach the reference input. The sensor converts the output variable into another suitable variable. An advantage of this system is the fact that the use of feedback makes the system response relatively insensitive to external disturbances and internal variations. The aim of the controller of the closed loop control systems is to produce an output following the input. P, PD, PI and PID controllers are widely used for this aim with some variations according to the system structure. These controllers have advantages and disadvantages. P type controller’s main advantage is its simplicity. The advantage is I controller is that the output is proportional to the accumulated error. Thus, error can be eliminated by using it. The advantage is D controller is that the controller will provide large connections before the error becomes large. P type controller’s main disadvantage is that there may be fix steady state error. The disadvantage is I controller is that the system less stable if adding the pole at the origin. The disadvantage is D controller is that if the error is constant it will not produce a control output. While designing the control system with classical controllers, the root locus technique allows the designer to examine the movement of the closed loop poles of the control system as a function design variables .Classical controller is based on mathematical model. In many cases, the mathematical model of the control process may not exist, or may be too "expensive" in terms of computer processing power and memory, and a system based on empirical rules may be more effective. If the model is known less, or not got, the control reaction is not produced. In this situation, the fuzzy logic, neural network and genetic algorithm based on developing controller algorithms are also used. The fuzzy logic controllers can be used for this aim, for which the membership functions and the choice of the rules are essential. A fuzzy control system is a control system based on fuzzy logic. A mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of either 0 and 1 (true and false). The input variables in a fuzzy control system are in general mapped into by sets of membership functions similar to this, known as "fuzzy sets". The process of converting a crisp input value to a fuzzy value is called "fuzzification". Given "mappings" of input variables into membership functions and truth values, the microcontroller then makes decisions for what action to take based on a set of "rules". Rules can be solved in parallel in hardware, or sequentially in software. The results of all the rules that have fired are "defuzzified" to a crisp value by one of several methods. Although genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases, fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, so that their experience can be used in the design of the controller. This makes it easier to mechanize tasks that are already successfully performed by humans. In this study, the comparison of the P, PD, PI and fuzzy controllers are realized by utilizing the roll control system of an airplane. The system is composed of a comparator, actuator and aircraft equation of motion. Sensor is considered to be perfect device and represented as a unity feedback. The P type controller is designed from root locus plot at the crossover point. The PD type controller is get from desired stability errors using time domain. The PI type controller is designed using Routh- Hurwitz stability criterion. In classical controllers, the outputs having the preferred performance can be obtained by adjusting the gain; whereas, for the fuzzy controllers better values can be obtained by increasing the number of input and output functions and the number of the rules.