Yapay sinir ağları ve genetik algoritmaların uçuş kontrol sistemlerine uygulanması

Abstract

Bu çalışmada uçağın dinamik denklemlerine kısaca değinilerek sistem ve kontrol dizaynı problemi tartışılmıştır. Klasik kontrol yöntemleri kıyaslama açısından baz oluşturabilmek için kısaca anlatılmıştır. Sistemin lineerliğin dışına çıkması durumunda klasik kontrolörün yetersiz kalacağı açık ve sistemin matematik modelinin elde edilmesi zor, bazı durumlarda imkansızdır. Çalışma konusu olan sistem bu gibi klasik kontrol yöntemlerinin yetersiz kaldığı durumlarda, gelişmekte olan bir daim : yapay sinir ağlarının, uygulanabilirliğini ve üstünlüğünü ortaya koymaktadır. Çalışmada uçuş kontrol sistemlerinin sürekli gelişmesi göz önünde bulundurularak Yapay Sinir Ağlan ve Genetik Algoritmaların uçuş kontrol sistemlerine uygulanmasına çalışılmıştır. Ayrıca geliştirilmekte olan bir Kontrol ve Animasyon yazılımından kısaca söz edilmiş ve bazı görsel malzemeler sunulmuştur. Bu çalışmada elde edilen sonuçlar, yapay sinir ağlarının ve genetik algoritmaların gelecek açısından büyük vaadler taşıdığını göstermektedir.

In this work the aircraft is considered as a rigid body moving in an inertial reference frame which is the ambient atmosphere. Thus any atmospheric acceleration due to winds, earth rotation, movement of earth around the sun, etc. are neglected. In three dimensional space the aircraft will have three translational degrees of freedom and three rotational degrees of freedom [5]. The vehicle is acted on by gravity, aerodynamic, and propulsive forces. In order to proceed to a derivation of the scalar equations of motion leading to the airframe transfer operators, several axis systems have been defined. Of which the most important one is the Flight-Path axis system, becuse of the convinience of representing the translational equations of motions of the airframe. Before writing the vector equations of motion in terms of scalar components, the general formula for expressing the time rate of change of a vector as viewed from an observer in an inertial frame in terms of the time rate of change of the vector as viewed by an observer in a rotating frame of referance is reviewed. Following this, the translational equations of motion of the aircraft have been written in body axes. Similarly, the rotational equations of motion of the aircraft have been written in body axis too. In general, the aerodynamic force components acting on the airframe are represented as the product of the dynamic pressure times the characteristic area times a dimensionless aerodynamic coefficient. In this work various aerodynamic coefficients are considered as a function of angle of attack and Mach number. In the same manner as above, the aerodynamic moment components acting on the airframe are represented as the product of dynamic pressure times characteristic area times characteristic length times dimensionless aerodynamic coefficient. VI The gravity force is represented as the product of the aircraft mass times the acceleration due to gravity and is assumed to be fixed. Following this, the Euler angle rates have been used in transformations between the various axis systems defined. After all these the six degrees of freedom of the aircraft equations have been written as linear perturbation equations with respect to equilibrium symetric flight. Only the longitudinal equations of motion have been used in derivation of the longitudinal transfer operator. Actually two different transfer operators have been developed [5]. The first one is the exact transfer operator relating the input -elevator displacement- to the output -pitch position- and the second is the transfer operator derived using the short period and phugoid approximation. In the third chapter the basic concepts of conventional control methods have been outlined. In a general automatic control system a compensator circuit is always attached to the system. The task of the compensator is to minimize the difference between the input and output of the system and to make it stable. Different types of such systems have been explained in this chapter. The study of linear systems is based on the examination of the response of the system in the time and frequency domain after applying a step, impulse or sinusoidal input. These domains are related to each other by the Laplace and Fourier transformations. Someone could ask the following question: "What is the reason of forming different types of criterias in different domains?". There are two reasons: first, it is likely to select such criterias that handle measurable quantities and the second is that for mathematical point of view, it is easier to handle such systems in the frequency domain. In the same direction, the quantities belonging to the temporary state of the time domain are basic quantities. However, although there is a one to one relation between these two domains, it is impossible to develop a general rule which includes both domains. The criterias of the time domain have been examined in detail and three most frequently used systems heve been explained. Compensation techniques using the time domain criterias have been explained. The most commonly used techniques are the root locus and state feedback. However both of them are related with sliding the closed loop roots. In addition, compensation techniques using the frequency domain criterias have been explained either. The response of a control system in the frequency domain can be characterised with the phase angle and the amplitude. Because the most commonly used control systems are minimum phased systems, knowing the change rate of the amplitude according to frequency is sufficient to identify the system. vu In practice control systems behave as low pass filters. In the method described above the main objective is: a)- To increase the band amplitude b)- To increase the gain and the phase rates. In order the output of the system to follow the input at all frequencies, the ratio of the output to the input must be equal to 1.0. That means that the band amplitude will be infinite. On the other hand if the ratio mentioned above is not too small at high frequencies the system will be affected by noise, easily. In the fourth chapter neural networks, genetic algorithms and their applications in control systems have been explained [11]. Since the generalized delta rule, or backpropagation scheme, was presented, attempts at applying perceptron-like neural networks to various problems have been increasing. The advantages of neural networks are two fold: learning ability and versatile mapping capabilities from input to output. Expectations for applying the network to controllers are also associated with these advantages. The versatile mapping capabilities should provide a means of controlling non-linear plants which can not be carried out well with conventional linear feedback controllers. The learning ability can reduce human effort in designing controllers and it even suggests a potential for discovering better control schemes than presently known. No general optimal design principles for highly nonlinear plants have been established so far. In addition, causes of optimal design difficulties do not necessarily lie in the plant dynamics, but may also be in the specifications required. The modelling uncertainty also gives rise to a difficult problem with regard to robustness. Learning by experiments on an actual plant could skip the modelling process and avoid the uncertainty. Two types of control system architectures including the network are possible. The first type is a self-tuning configuration, where the neural network adjusts the parameters of a convetional controller. The second type is a much simpler configuration, in which the network serves as a direct controller. Since the self-tuning type does not actually control the plant, it's performance is subject to the conventional controller limitations. So we focused on the direct type. vm Dispite the simlicity of the configuration, we have to overcome an important problem : "Who can teach the controller and how ?". Although evaluation of the plant response is quite easy, it is very difficult to show the right answer at each time step of a transient process. If the evaluation can be made on an instantaneous basis we can tell whether the output of this moment is approriate or not. Most dynamic systems, unlike static systems, do not guarantee the success of this local, instantaneous judgement. The evaluation should be made based on a global basis where the appropriateness of the control at each time is judged in a total response curve which spans the time from initial to the settling. In this work, at first a standard form of the genetic algorithm is summarized, which is a general purpose stochastic optimization method for search problems. The data processed by the algorithm are a set (population) of strings which represent multiple points in a search space. The string is a binary figure with a finite length where each bit is called an allele and is decoded by an evaluator to obtain the objective function value of an individual point in a search space. This function value, which should be maximized by this algorithm, is then converted to a fittness value, which determines the probability of the individual undergoing transitional operators. The transitional operators change the population of the strings to that of offspring : a next generation. The total number of strings included in a population is kept unchanged through generations. The operators are analogous to the biological terms of cross-over and mutation. Before applying these operators, a pair of strings is selected among the population with probabilities proportional to their fitness values. The version mentioned above, as told before, is a standart one [10] and is quite different from the one used in this work. Becuse of applying the genetic algorithms to neural networks some alterations have been made to this classical approach. These alterations are explained in detail in this chapter. In addition three neural network architectures which are used in this work are mentioned either. We have seen that a simple architecture in which a neural network takes over the conventional feedback controller has promising capabilities. One distinguishing feature is its self-learning ability. Since the evolutional scheme proposed here does not need any teacher to show teaching patterns, this suggests prospects for freeing us from design routines, and even for discovering control schemes beyond our imagination. Its versatility to accept arbitrary objective functions also facilitates creating a controller which meets various user preferences that may also include environmental conditions such as noise, parameter changes and non-linearities. IX Although the learning presented here has been based on simulations, experiment- based approaches should be possible. This is left for future study. In the fifth chapter a comparison between the PID, PI, P techniques and the Neural Network control techniques takes place for the transfer functions introduced in the second chapter. As it will be seen later, the best results by controlling a system ( in this case the longitudinal behaviour of an airplane ) with neural networks were obtained with the first linear neural net explained in the fourth chapter. Among the other neural nets the results obtained by this net were the closest if compared with PID control. In addition, the derivation of the parameters used by PID, PI and P control methods is discussed in detail by the documentation given in the references part of this work [6], [7] and [8], in this chapter only the results were used in order to make a comparison. A very important poin for linear neural networks that should be mentioned here is the following : "It is enough to train a linear net only for one situation. After the training it can give accurate results for other cases, too." This point of view gives us an alternative way for controlling linear plants or plants that can be linearized using different methods. Beside these it should not be forgotten that the training of the neural nets explained in this work were done with a 486 DX 2-50 and only for 800 steps. If the training time and hardware speed were increased better results shoul be expected. Finally in this work a Control and Graphics Animation Program is introduced. This program is devloped in our department as a final undergraduate project and according to the inputs given by the users it tries to optimize the connection weigths of a neural network to control a given system (airplane). It uses the same algorithm developed in this work. Furthermore it simulates and animates the airplane. The main objective in developing such a project is to fill the gap between the theory and the practice in such an expensive subject.