LEE- Kontrol ve Otomasyon Mühendisliği Lisansüstü Programı

Bu topluluk için Kalıcı Uri

http://hdl.handle.net/11527/19359

Gözat

2-step indoor localization for "smart AGVs"

(Graduate School, 2022-06-17) Yılmaz, Abdurrahman ; Temeltaş, Hakan ; 504142101 ; Control and Automation Engineering

With the fourth industrial revolution, in other words, Industry 4.0 (I4.0), the transition from traditional mass production to personalized production started in factories. One of the components of the next-generation factories compatible with I4.0 is cyber-physical systems (CPSs). Smart manufacturing islands, smart warehouses, and smart material-handling vehicles are examples of CPSs. The material handling vehicles employed in today's factories, such as automated guided vehicles (AGVs), are not ready for use in smart factories, as the digital transformation has not been completed and the vehicles are not equipped with software to perform fully autonomous operations. In smart factories, it is aimed that the new generation AGVs will do all the planning themselves while performing a given task. Thus smart AGVs will be able to use the whole free space in the factory instead of being restricted to the routes reserved for them. With this development, it will be possible to increase flexibility and efficiency in production. There may be no physical difference between the traditional and smart AGVs, but thanks to the capabilities of the embedded software, smart AGVs will be able to operate autonomously. One challenging problem to be overcome for smart AGVs to effectively realize an assigned logistic task is localization. Although localization is an extensively studied topic for both indoor and outdoor environments, there are still open problems. Considering the logistics problem, the localization problem can be divided into three in the general sense. The first is global localization, which means determining where the smart AGV is in the environment at the time the vehicle wakes up. The second problem is position tracking, which means updating the pose information depending on the movements of the robot, while the instantaneous pose of the robot is known. The third and last problem is the kidnapped robot problem, which occurs when the robot is moved from one place to another without informing. Cases that reduce the reliability of the calculated pose, such as instantaneous skidding, slipping, and crashing an object, can also be addressed under this problem. The localization approach to be utilized in smart factories is supposed to overcome these three sub-problems. There are two main tasks in a logistic operation. The first is the docking stage, which covers the cases of taking a load to the smart AGV or dropping the load of the smart AGV. At this stage, the aim is to reach the target (destination) where the load will be taken or left with industrial standards. With I4.0, reaching the target with sub-centimeter precision has become a goal. Therefore, estimating the pose with high accuracy and precision is expected from the docking localization algorithm. The second is the delivery stage, which covers carrying the load to the destination in the fastest and safest way in the parts outside the docking region. It is not essential to follow the planned route exactly in this stage, so rather than the high accuracy of the localization approach, showing similar positioning performance in the entire operating field is more important. Within the scope of this thesis, different localization algorithms have been proposed for the delivery and docking stages. In addition, a probabilistic decision mechanism that determines the boundary between the delivery and docking stages is designed. A variant of the particle filter-based Monte Carlo Localization (MCL) approach, Self-Adaptive MCL (SA-MCL), is taken as the basis localization method for the delivery stage. The main reason for choosing SA-MCL is that it can solve all aforementioned sub-problems of localization. While performing the traditional SA-MCL global localization task, it uses energy maps and assumes that all range sensors are uniformly placed on the robot in energy map generation. However, this assumption is not valid for many real applications, such as AGVs with two-dimensional (2D) laser scanners front and rear. Moreover, three-dimensional (3D) sensing technology is developing day by day with the widespread use of autonomous vehicle technology. With the ellipse-based energy model proposed in this thesis, the energy map-generating part of the traditional SA-MCL has been updated to overcome both of these constraints. The pose estimation accuracy of the SA-MCL approach performs more or less the same across the entire environment, making it suitable for the delivery stage. However, since the pose estimation accuracy level is proportional to the grid dimensions of the occupancy map, it may not be possible to reach the expected sub-centimeter precision within the docking region in large areas such as factories. Therefore, it was decided to use a scan matching-based precise localization algorithm in the docking region, and for this purpose, the affine iterative closest point (ICP) algorithm was adapted to the localization problem. To make the developed method robust against factors such as noises, disturbances, and/or outliers, the correntropy criterion was utilized while constructing the cost function of affine ICP. As a result, an updated SA-MCL method with an ellipse-based energy model is proposed for the solution of global localization, position tracking, and kidnapped robot problems in the delivery stage. On the other hand, an affine ICP-based precise localization approach is presented for position tracking in the docking stage. However, the boundary between the delivery stage and the docking stage may not be clear. For example, limiting the docking stage to a zone very close to the target may require extra maneuvers to tolerate positioning errors during the delivery stage due to the physical constraints of smart AGVs. If a larger area is specified as a docking stage, it may not meet the expectations since the performance of the precise localization approach may decrease further away from the target. For this reason, there is a need for a switching mechanism that can be adapted specifically to the application and decides whether to switch from the delivery stage to the docking stage. Since the pose estimation performance of the SA-MCL-based localization approach is roughly similar on the entire map, the deciding factor in the transition to the docking stage is the performance of the precise localization method used in the docking stage. In the literature, it is emphasized that the amount of overlap between matched point sets is supposed to be above 50% for the scan-matching-based methods to yield successful results. Within the scope of the thesis, a correntropy-based similarity rate definition, which gives better results than the overlap ratio calculation methods in the literature, is presented and utilized as the decision parameter of the switching approach. To avoid instabilities, a gap is left according to Hysteresis curve behavior while switching from the delivery stage to the docking stage or vice versa. Within the scope of the thesis, the two-stage localization method developed for the next-generation AGVs to be used in smart factories has been experimentally tested on a differential drive mobile robot. First, the ellipse-based energy model addition to the SA-MCL method has been verified by field tests, and its superiority in global localization has been demonstrated. Then, the affine ICP-based localization method used in the docking stage has been tested over nine separate real-world scenarios and it has been shown that it is possible to compute pose with sub-centimeter precision and reach the target at industrial standards. In addition, an affine ICP method, which is not available in the literature, was proposed, and the point set matching performance was demonstrated over synthetic point sets. After validating its performance in point set registration, it was also used for precise localization. Finally, the whole system was tested together. The delivery was carried out with improved SA-MCL, and the switching point from delivery to the docking stage was determined by the decision mechanism. As seen through three different scenarios, it is possible to complete the localization tasks in the delivery and docking stages in the smart factories by using the proposed methods.
A comparative study of nonlinear model predictive control and reinforcement learning for path tracking

(Graduate School, 2022) Türkmen, Gamze ; Bogosyan, Ovsanna Seta ; 812314 ; Control and Automation Engineering Programme

One of the most financially significant industries is the automotive industry because of the benefits as well as the fact that it is always evolving and changing. Discoveries in computing and sensing hardware contributed to the evolution of this industry and led to the development of autonomous driving technology. Besides that, they offer several potentials for improving transportation safety, energy and fuel efficiency, as well as traffic congestion. These benefits and increasing attention to autonomous vehicles encourage the development of advanced driving systems. In this thesis, the path tracking problem of autonomous vehicles is investigated and a comparative analysis of two path tracking methods is presented. One of the selected methods is model predictive control and the other is a reinforcement learning algorithm soft actor-critic method. The model predictive controller is applied in a wide variety of path tracking problems due to its high performance and benefits over other control methods. The benefits of MPC are the ability to handle multi-input multi-output systems, optimize multiple objectives, work with nonlinear models, incorporate future steps into the optimization problem, overcome disturbances, and deal with constraints on the inputs, outputs, and states. Basically, MPC determines optimal control inputs for a given prediction horizon by minimizing the cost function while taking the system constraints and objectives into account. The system model is used to obtain future state predictions and these future state predictions are included in the cost function that determines the desired behaviour of the system. The optimization problem is solved for the current time step and system state, resulting in the generation of optimal control input sequences. Then, only the first input of the resulting optimal sequence is given to the system. This procedure is performed for each time step. In this thesis, the problem will be handled as a nonlinear model predictive control problem since a nonlinear vehicle model is used. NMPC problems are expressed as optimal control problems (OCP) and the multiple shooting method is used to transform the OCP into a nonlinear optimization problem (NLP) which is addressed by utilizing the optimization software package IPOPT. A vehicle model is one of the main things that MPC requires, and a vehicle model may be modelled with varying degrees of complexity depending on the problem and performance needs. There are several of different way to model vehicles such as a kinematic model which consists solely of a mathematical description of vehicle motion taken into account geometrically and ignoring the forces acting on the vehicle and a dynamic model which includes the forces affecting motion. Additionally, vehicle models can be described differently with various tire models. Basically, the kinematic model shows poor performance at high speeds due to lateral forces, whereas dynamical model shows high performance at high speeds but cannot be used in stop-and-go situations due to tire models becoming singular at low speeds. Additionally, the system identification process is easier for kinematic model since the kinematic model has only two parameters. Furthermore, one of the objectives of the thesis is to show that vehicles can be controlled with the minimum knowledge of the vehicle model. Therefore, a kinematic model is employed as it requires only distances from center of mass to axles. Control methods require parameters to be tuned manually or by optimization algorithms, and these approaches are not always capable of generalizing to new conditions, but intelligent methods arise with their ability to generalize to new conditions. In addition, while the vehicle model is needed for the controller, it is not always needed for intelligent methods. Intelligent methods like deep and machine learning have been included in autonomous driving studies to automate the driving task. These methods enable researchers to specify the desired behavior, teach the system to perform the desired behavior, and generalize their behaviors. Reinforcement learning has been selected as the method of choice to achieve automating the driving task. A learner agent interacts with the environment and collects experiences. Also, the environment gives feedback with reward signals. Because the agent is motivated to maximize positive reward signals and learns what to do as a result of its own experiences without specific instructions. However, the reinforcement learning problem becomes intractable as the states of the agent increase. The solution to this was found by combining deep learning and reinforcement learning and as a result, deep reinforcement learning has emerged. Deep reinforcement learning problems can be classified according to whether they have an environmental model or the way they optimize policy or whether they use different policies in training. Among many types, the soft actor-critic learning method is chosen for this thesis because it shows outperforming performance regarding both efficiency and stability compared to many other powerful methods. The soft actor-critic is an off-policy method that combines actor-critic and maximum entropy reinforcement learning methods. In order to generate stochastic policies with more exploration abilities, the entropy element is introduced to the objective function in this algorithm. As a result, the agent achieves learning by maximizing both expected reward and entropy rather than only maximizing expected reward as in other standard reinforcement algorithms. One of the important key parts of training reinforcement learning agents is that they require a lot of data and take a long time to learn. However, experience replays, which are mechanisms that allow using past experiences, are employed and it is observed that the learning is stabilized and the amount of experience required is decreased. In this thesis, SAC with different buffers are implemented and their efficiencies are examined. During parameter updates, experiences in the buffer are sampled uniformly in the vanilla experience replay. Prioritized experience replay (PER) is one of the experience replay methods used in this thesis, and it basically samples high important experiences more frequently. Emphasizing recent experience (ERE) is another strategy that samples more aggressively from recent experiences to emphasize the importance of the recently observed experience. These methods were chosen because PER has been shown to be effective in numerous studies, and ERE outperforms PER in some applications in terms of efficiency. However, the performance of ERE in the path tracking problem has not been compared with the PER and one of the aims of this thesis is to examine their efficiency in vehicle driving task. The simulation environment is chosen as CARLA simulator, which aims to be as realistic as possible in terms of control and visual elements. Several towns are available in CARLA, and two different ones have been chosen for this thesis. Also, it is necessary to establish the reference values that will be followed by the vehicle. For this purpose, paths were created for the selected towns and waypoints were produced for the vehicle to follow. Then, the cubic spline interpolation method was used as an optimization method for the waypoints because it is desired that the reference waypoints should be smooth and continuous. As a result of these operations, reference yaw angle and x and y positions were obtained. In addition, the speed reference is given in different values as a fixed reference. NMPC and SAC are responsible for both lateral and longitudinal control to follow the given path. As a longitudinal controller, they control the acceleration in order to achieve the target speed, and as a lateral controller, they change the steering wheel to track the reference path. This means that both have two action outputs which are steering angle and acceleration command. The states in NMPC are the states of the kinematic bicycle model, and the parameters of a Tesla Model 3 vehicle provided by CARLA are used. The states in SAC are chosen similar to the NMPC states and consist of steering and acceleration commands, target speed and reference tracking errors up to 10 steps ahead to reflect horizon information. A cost function consisting of tracking errors is constructed to minimize the error between the reference and followed paths for NMPC. The best weight coefficients of cost function are found after several experiments. Furthermore, steering angle and acceleration constraints are defined to participate in the optimization problem. Then, a symbolic framework CASADI is used to formulate this NMPC and provides an interface to IPOPT solver for solving the optimization problem. On the other side, for the SAC agent to follow the path, an appropriate reward function is prepared after many trials, which the agent will maximize according to its actions. Also, terminal conditions are created where the simulation ends if the agent goes out of lane, moves too slowly, and hits something. The network to be used in the training of the SAC agent consists of an actor network that decides on the actions and a critic network that measures how well the actions are. These networks are implemented with PyTorch library and hyperparameters for networks and buffers are taken from the original papers of the methods. The SAC agent is trained in CARLA on 10 and 5 different paths over 2000 episodes and it is observed that the agent trained on 10 different paths converged faster, so the training with other buffers are done on 10 different paths. After training with buffers, SAC+PER and SAC+ERE converged faster than SAC with vanilla buffer. It shows that the advanced buffer implementations enhance sampling efficiency. These trainings are done with random target velocities of 5 and 6 m/s, then for the SAC+PER agent, which is the fastest converging agent, the training is continued for the target velocities with 5 to 8 m/s. Simulations are carried out on 5 different paths to investigate path tracking performance. The results are discussed for each method and it is shown that the vehicle can follow the reference trajectory with a small margin of error for all approaches. This demonstrates that SAC agents have the ability to generalize since they performed well on unseen tracks. Although the performances of NMPC and SAC agents are very close to each other, SAC agents outperform NMPC in target velocity tracking and NMPC has better performance in yaw angle tracking. Also, as expected, the NMPC with the kinematic model performed worse as the speed increased. Furthermore, it is also observed that SAC+ERE and SAC+PER increase sample efficiency without reducing the performance.
A stable, energy and time efficient biped locomotion

(Lisansüstü Eğitim Enstitüsü, 2021) Yılmaz, Sabri ; Gökaşan, Metin ; 725780 ; Kontrol ve Otomasyon Mühendisliği

This thesis presents two different walking strategies for biped robots while ensuring energy efficiency. The first strategy is a closed-loop walking controller based on the most used 3-Dimensional (3D) Linear Inverted Pendulum Model (LIPM) which is used to calculate the Zero Moment Point (ZMP) approximately. The closed-loop Proportional Integral (PI) controller's coefficients are searched by the Genetic Algorithm (GA), which is developed to overcome the 3D LIPM's dynamical insufficiency. Because of its ease of modeling, the key concept is to continue to use the 3D LIPM with a closed-loop controller. For this purpose, the biped is modeled using the 3D LIPM, which is one of the most well-known modeling approaches for humanoid robots due to its ease of use and quick computations during trajectory planning. Model Predictive Control (MPC) is applied to the 3D LIPM once the simple model is obtained to search the reference trajectories for the biped while meeting the ZMP criteria. The second strategy is to express the ZMP in a detailed model instead of an approximate model. For this purpose, the biped is modeled with the conventional robot modeling methods and the detailed expression of the ZMP is obtained. Then the problem is redefined as a Nonlinear MPC problem. The highly complicated biped model is implemented in Matlab with the use of CasADi Library which is a symbolic library and used on large symbolic solutions. The optimal control problem is solved with the Interior Point Optimizer (IPOPT), which is an optimization solver for large equations. With the solution of the optimal control problem, reference trajectories are found for the biped while satisfying the ZMP criteria. Both strategies suggested in this thesis are studied and implemented on a biped robot which means the robot has no upper body elements. The main idea is that if the dynamic flaws are suppressed without any upper body elements, this study will open a way to work on more modular robots. After obtaining two different walking strategies, the energy-efficient trajectory for the swing leg is searched to have longer working durations on the field. The Big Bang Big Crunch with Local Search (BBBC-LS) global optimization algorithm is used for energy efficiency. With the newly defined trajectory there became nearly 10% energy consumption reduction compared to the sinusoidal trajectory. To implement the algorithms to the real biped, a new communication library is written to meet the desired communication speed. But with the increased speed in communication, there became random packet losses on the feedback from the motors. These packet losses are examined and it is observed that these random packet losses may make the system unstable, so to suppress the effects of packet losses the problem is redefined as a time delay problem. With the redefinition of the problem, the well-known Smith Predictor method is used to overcome the packet losses and from the results, it can be seen that with this redefinition the instability risk because of the packet losses has disappeared. In a short summary, a two-legged robot has been modeled using conventional methods in the literature. First, the dynamic defects of the simple model are eliminated with a conventional controller. Secondly, a more detailed dynamic model is obtained. Walking planning is done with both methods and comparisons are made with the method commonly used in the literature. The success of the proposed methods has been demonstrated in both simulations and experimental results. With the two methods proposed in this thesis, the oscillation problem encountered by one of the most widely used walking models in the literature has been resolved. After obtaining stable walking, energy optimization is studied so that the robot could work longer in the outdoor environment and trajectory improvement is made to reduce energy consumption during the robot's movement. Finally, a faster communication library is written to apply the designed algorithms to the real system and to solve the problems caused by communication speeds, the problem is redefined with a different approach and the traditional method, Smith Predictor, is used. Packet losses that are random thanks to the communication interfaces prepared for the mechanism; become predictable and the effects of packet losses are eliminated with Smith Predictor. Finally, all these control methods are applied to the system and used in experimental studies.
Active slam with informative path planning for heterogeneous robot teams

(Fen Bilimleri Enstitüsü, 2020) Akay, Mehmet Caner ; Temeltaş, Hakan ; İnsansız Hava Aracı'nı (İHA'yı) ve İnsansız Kara Aracı'nı (İKA'yı) bünyesinde bulunduran heterojen yapılı robot takımları, günümüzde gözetleme, takip, keşif, vb. farklı görevlerde kullanılmaktadır. Çevrenin haritalanmasını gerektiren keşif görevlerinde, heterojen robot takımlarının ortamı daha iyi anlayabilmesi adına, ortak bir haritaya ihtiyaç duyulmaktadır. Bu doğrultuda özel yaklaşımlarla, Lidar Odometre ve Haritalama (LOH) ile zorlayıcı yapıların bulunduğu ortamda, araçların kooperatif bir şekilde benzerlik metriklerini kullanarak ortak harita çıkarması sağlanmaktadır. Bunun yanı sıra, sınırları belirli bir alanın, heterojen robot takımları ile keşfini sağlamak adına sürekli olarak toplanan bilgiyi arttırıcı kontrolcü tasarımı kullanılmaktadır. Farklı tipte hareket denklemlerine ya da dinamik modellere ve/veya farklı sensör yapılarına sahip robotlardan oluşan robot takımlara heterojen yapılı robot takımları denmektedir. Diğer taraftan robot takımlarının eş zamanlı konumlama ve haritalama problemi ile bu takımdaki robotların yol planlamalarının eş zamanlı gerçeklemesi ise Aktif eş zamanlı konumlama ve haritalama (EZKH) problemi olarak adlandırılmaktadır. Buradaki eş zamanlı gerçeklemedeki amaç otonom robot araçları için planlanan yolların aynı zamanda EZKH'deki belirsizliği de minimize edecek şekilde gerçekleştirilmesidir. Diğer bir deyişle otonom robot araçları için bilgilendirici yol planlarının oluşturulmasıdır. Bu çalışmanın temel amacı heterojen yapılı robot grupları için bilgilendirici yol planlamaya dayalı bir Aktif-EZKH sistemi tasarlamaktır. Robot takımlarının farklı dinamik ve sensörlere sahip olması diğer bir deyişle heterojen yapıda olmaları, bu robot takımlarına avantajlar getirmektedir. Örneğin; hava robotları hızlı hareket edebilir, kara robotları daha ağır faydalı yükler taşıyabilir ve hedef nokta ile doğrudan etkileşime girebilirler. Karma bir araçlı bir yapı içerisinde yer alan İHA ile İKA oluşan bir robot grubu keşif, arama veya güvenlik amaçlı sınırları belirlene bir bölge içinde iş birliği yaparak ortam içindeki görevlerini insandan bağımsız bir şekilde otonom olarak gerçekleyebilir. Burada İHA ve İKA'ların birbirleri ile yer istasyonu aracılığı ile veri paylaşımında olduğu varsayılmaktadır. Komşuluk alanları içerisinde haberleşme ile harita paylaşımı ya da araç durum vektörü paylaşımı yapabilen robot birimleri kooperatif robotlar olarak gösterilmektedir. Bu çalışmada dış ortam sensörü olarak 360° ortam taraması yapabilen ve saniyede 300.000 adet noktanın mesafesini ölçebilen 3B LIDAR sistemi kullanılmıştır. Yüksek çözünürlüklü ölçüm avantajının yanı sıra bu kadar büyük miktardaki veriden optimum miktarda ve hızlı bir şekilde anlamlı veri üretip bunları robot konumlama, planlama ve koordinasyonunda kullanım da ayrı bir zorluk ortaya koymaktadır. Temel olarak, hareketli olan bir araçtan elde edilen nokta bulutunun coğrafik olarak yerleştirilmesi gerekmektedir. Bu işlem sadece Lidar sensörü kullanılarak da; farklı sensörlerin verilerinin ortak bir şekilde kullanılması aracılığıyla da yapılabilir. SadeceLidar ile toplanmış verilerin işlenerek nokta bulutunun coğrafik olarak yerleştirilmesi ve gözlem sırasında sensörün hareketinin elde edilmesi, bu çalışmada LOH ile sağlanmaktadır. Bu sayede; GPS ve IMU olmaksızın EZKH yapılabilmektedir. Buna ek olarak, sensörlere binen gürültülerden dolayı oluşabilecek kaymalar ve yanlış veri elde edilmesi engellenebilmektedir. Buna karşılık, GPS, enkoder ve IMU verileri ile Lidar verileri birleştirilerek Genişletilmiş Kalman Filtresi (GKF) konumlaması da sağlanabilmektedir. Burda sensör verilerinin olasılıksal yaklaşımlarla işlenmesi ile robotun konumu elde edilmektedir ve bu konum ile Lidar verilerinin coğrafik yerleştirme yapılması sonucunda da belirli bir orijine sabitlenmiş nokta bulutu çıktısı alınmaktadır. Sonrasında da bu nokta bulutu ile istenilen yöntem ile elde edilen odometre ve nokta bulutu verisi farklı haritalama yöntemleri kullanılarak ayarlanabilir özel görsel çıktılar sağlanabilmektedir. Bunlardan biri, sekizli ağaç yapıları kullanılarak elde edilen OctoMap olmaktadır. OctoMap yöntemi, tez çalışmasında kullanılmasının temel sebepleri olan, çözünürlük ayarlaması, doluluk olasılığı üst ve alt sınırları belirlenmesi ve 3B olarak sağlanabilmesi açısından faydalı bir araç olmaktadır. Bu yöntem ile, ortamın uyarlanabilir şekilde, ortamın 3B haritasının çıkarılması sağlanmaktadır. Lidar sensörlerinin havadan alınan nokta bulutları ile karadan alınan nokta bulutları farklı geometrik özellikler taşımaktadır. Ancak, hava ve kara Lidar görüntülemesinin birbirlerini tamamlaması bakımından oldukça büyük avantajları da mevcuttur. Hava aracı ve kara aracı tarafından yapılan ve birilerinin göremedikleri bölgelerin görüntülenebilmesi sağlanılmaktadır. Bu avantajı kullanabilmek adına farklı açılardan lokal olarak görüntülenen ortamın ortak bir haritada birleştirilmesi gerekmektedir. Harita birleştirme adımını gerçekleştirmek adına her iki robotun elde ettiği verilerden ortak olanını belirlemek gerekmektedir. Kuş bakışı veya yatay olması fark etmeksizin bir nesnenin yere göre yüksekliği; hem havadan hem karadan yapılan gözlemlerde sensörlerin görüş açısı sınırları içerisinde aynı olacaktır. Bu doğrultuda, yükseklik verileri üzerinden benzerlik metrikleri kullanılarak haritaların birleştirilmesi sağlanabilmektedir. Bu tez çalışmasında, İHA ve İKA tarafından elde edilen nokta bulutu ızgara haritasına benzer bir yapıda olan yükselti haritaları kullanılmıştır. Izgaralar ile bölünmüş hücrelerdeki en yüksek noktanın verisinin kullanılması ile 2.5D harita elde edilmesi sayesinde yükselti haritaları oluşturulmaktadır. Benzerlik metrikleri aracılığıyla ise bu haritadaki yükseklik bilgilerinin birbirine oturmasını sağlayacak konum ve yönelim farkı belirlenmektedir. Çalışmanın sonraki aşamalarında entropi teorisi kullanılması sebebiyle entropi temelli benzerlik metrikleri ile harita birleştirme yapılmıştır. Yedi farklı tipteki entropi metriği ile yapılan benzerlik karşılaştırması sonucunda "Jensen Divergence" entropi tanımının en az hata ile haritalar arasında dönme ve öteleme farkının belirlenmesini sağladığı, deneyler ile doğrulanmıştır. Ayrıca; haritanın dikey eksende katmanlara ayrılması ve bu katmanlar üzerinden yapılan yükseklik benzerlikleri hesaplaması ile optimum konum ve yönelim ( veya dönme ve öteleme) farklarının belirlenmesinin; katmanlara ayırma metodunun kullanılmasına göre daha avantajlı olduğu da gösterilmiştir. Her bir otonom araç "Harita Birleştirme" süreci sonrasında bu harita Aktif-EZKH süreci için kullanılarak hem harita bilgileri daha hassas hale getirilir hem de robotun gitmesi gereken yeni konumu tespit edilmiş olur. Yol planlaması, görevin etkin bir şekilde icrası için gerekli olan kritik adımlardan biridir. Enerji tüketim, elde edilen sonucun gerçekleşme süresi ve kalitesi uygulamanın ana kriterleridir. Bu nedenle, yol planlama algoritmaları etkin sistemler oluşturmak üzere kullanılmaktadır. Yol planlama algoritmaları farklı türde olabilir ama özelliklehedef işaretleme ve bilgi maksimizasyonuna dayalı yöntemler diğer yol planlama yöntemlerine göre belirgin üstün özelliklere sahip olanlarıdır. Hedef odaklı yol planlama algoritmalarında, birimlerin belirli bir hedefe ulaşabilmesi adına oluşturduğu kontrol eylemleri bulunmaktadır. Bilgi maksimizasyonu yaklaşımı; ortam, nesnenin diğer nesneler veya bir hedef hakkında daha fazla bilgi almak için bir doğrultu boyunca hareket etmesi olarak tarif edilebilir. Burada bağıl entropi teorisi, bilgi maksimizasyonu yaklaşımı olarak sunulmuştur. İlaveten, bağıl entropi, karşılıklı bilgi ile çevresel durum entropisiyle arasındaki farktır. Bağıl entropi kullanılarak, bilgi metrik olarak ifade edilebilmektedir. Çevresel durumlar ile gözlemler ile elde edilen durumlar arasındaki bağıl entropi üzerinden yaratılan amaç fonksiyonunun optimal çözümü sonucunda elde edilen hedef nokta, o bölgedeki bilginin belirlenen kriterlere göre istenilen seviyeye çekilmesini sağlamaktadır. Bu, EZKH ile etkileşimli çalışan yol planlaması temelli bir optimal kontrol yöntemidir. Bu yöntem çerçevesinde Bilgi Teorisinden faydalanılarak belirsizlik terimleri ile entropi terimleri arasında ilişki kuran bir Karşılıklı Bilgi terimi tanımlanır. Kulback-Liebler Mesafesi olarak da tanımlanan bu Karşılık Bilgi terimi maksimum değerine ulaştığında belirsizleri temsil eden entropi terimleri de minimize olurlar. Bu sebeple Karşılık Bilgi terimine dayalı bir amaç fonksiyonu oluşturularak bu fonksiyonu maksimize yapacak robot konum ve hareket vektörleri optimal kontrol yaklaşımı ile elde edilir. Bu elde edilen terimler heterojen robot takımında yer alan otonom robotlara uygulanarak onların hareketleri planlanmış olur. Amaç fonksiyonunu Lyapunov kararlı yapan bu noktalar ise bir hacimsel bölgenin merkezidir ve bu hacimsel bölgedeki bilgiyi maksimize etmek üzere belirlenmiştir. Bu noktaya ulaşmak için, robotlar belirlenen kurallar çerçevesinde hareket etmektedir. Bu kurallar ise İHA veya İKA'nın hedef noktaya hareketinin seçimi ve hedef noktaya ulaşım için engellerden kaçınmayı içermektedir. Bu yöntemin; özellikle farklı boyutlarda nokta bulutu ölçümü yapabilen hava be kara araçlı robot takımındaki uygulamaları literatürde mevcut değildir. Bu teorik çalışmaları ön plana alan çalışmaların çıktılarının özellikle arama-kurtarma, keşif ve güvenlik gibi robot takımı uygulamaları için büyük önem taşıyacağı değerlendirilmektedir. Önerilen yöntemde, ortamdan yapılan ölçümler ile araç hareketlerinde oluşabilecek belirsizliklerini etkilerini en aza indiren kara ve hava robotlarından oluşan heterojen yapılı robot takımlarının keşif amaçlı yol planlama algoritmalarının geliştirilmesi ve performanslarının test edilmesi hedeflenmiştir. Aynı zamanda, bu görevleri icra edebilmek adına belirli harita birleştirmenin de gerçekleştirilmesi gerekmektedir. Öncelikle; harita birleştirilmesi yönteminin doğrulanması adına üniversite kampüsünde belirli bir bölgede kara aracı olarak Clearpath Husky A200, hava aracı olarak ise DJI Matrice 600Pro ve bu araçlar üzerinde bulunan Lidar sensörü kullanılmıştır. Sonuç olarak; teorik çalışmalarda verilen benzerlik metriklerinden en optimum olanı deneyler aracılığıyla belirlenmiştir. Sonrasında; bilgilendirici yol planlama yönteminin doğrulanması amacıyla Robot İşletim Sistemi ("ROS") ve Gazebo temelli, karmaşık ancak günlük yaşantıda karşılaşılabilinen bir simülasyon ortamı kurulmuştur. Bu simülasyon ortamında altı farklı durum yaratılarak heterojen robot takımları için bilgilendirici yol planlamalı Aktif EZKH gösterilmiş ve parametre ayarlamaları ile uygulamaya göre değiştirilebilir bir yapı sağlanmıştır. ; 650277 ; Kontrol ve Otomasyon Mühendisliği Ana Bilim Dalı

Recently, heterogeneous teams consisting of unmanned ground vehicles and unmanned aerial vehicles are being used for different types of missions such as surveillance, tracking, and exploration, etc. Exploration missions with heterogeneous robot teams should acquire a common map for understanding the surroundings better. The unique approach presented in this dissertation with cooperative use of agents provides a well-detailed observation over the environment where challenging details and complex structures are involved. Also, the presented method is suitable for real-time applications and autonomous path planning for exploration. Lidar Odometry and Mapping with various similarity metrics such as Shannon Entropy, Kullback-Liebler Divergence, Jeffrey Divergence, K Divergence, Topsoe Divergence, Jensen-Shannon Divergence and Jensen Divergence are used to construct a common height map of the environment. Furthermore, the given layering method that provides more accuracy and a better understanding of the common map. All of the given similarity metrics are compared, and the advantage of utilizing the layering method is shown. The best similarity metric for constructing a heterogeneous robot team common map of the experimental area was obtained by using the Jensen Divergence similarity metric and layering method. Moreover, Extended Kalman Filter localization and OctoMap techniques are utilized to create an adaptive simultaneous localization and mapping infrastructure for informative path planning. Optimal parameter tuning for the specified simulation environment provides adjustable memory allocation and exploration performance, such as; duration, collected information and effort. The information seeking controller obtained with the use of relative entropy ensures exploration of the given area to minimize the uncertainty between observed states and environmental states. Robots move to the volumetric spaces' center under given rules and collect measurements by proprioceptive and exteroceptive sensors. With the use of heterogeneous robot teams, the measurements collected by the Lidar provide an advantage in perceiving complex details that can not be done by homogeneous robot teams. Constructing common map part of the theoretical approaches in this thesis are experimentally validated. In addition, the complete demonstration of this dissertation is done with six different cases by simulation studies. The theoretical background of active simultaneous localization and mapping with informative path planning for heterogeneous robot teams are validated, and the advantages of this study are remarked.
An online adjustment mechanism for membership functions of single input interval type-2 fuzzy PID controller

(Lisansüstü Eğitim Enstitüsü, 2023-05-25) Aldreiei, Oqba ; Güzelkaya, Müjde ; 504191149 ; Control and Automation Engineering

The characteristics of the footprint of uncertainty (FOU) in interval type-2 membership functions (IT2-MFs) are crucial for the performance and robustness of interval type-2 fuzzy controllers (IT2 FCs). However, existing IT2-FC designs mostly use fixed FOU structures. This study proposes an online adjustment mechanism for membership functions of single input interval type-2 fuzzy PID controller (SIT2-FPID) by adjusting the footprint of uncertainty (FOU) and the weights of the antecedent and consequent membership functions (MFs) respectively to achieve high performance and robustness. The proposed online adjustment mechanism consists of two main parts: relative rate observer (RRO) and adjustment mechanism which has two inputs "error" and "normalized acceleration (Rv)", whereas the "normalized acceleration" provides relative information about the fastness or slowness of the system response. Meta-rules for the modification of the output of online adjustment mechanism (γ) are derived according to the error value and the relative information on the fastness or slowness of the system response and by analyzing the transient phase of the unit step response of the closed-loop system. The output of online adjustment mechanism (γ) in the proposed online tuning method is used as a tuning variable for the footprint of uncertainty (FOU) of the antecedent interval type-2 membership functions and the weights of the consequent crisp membership functions. This provides a dynamic membership functions (MFs) structure, where the heights of the Lower MFs (LMFs) or Upper MFs (UMFs) of each IT2 fuzzy set and the weights of the crisp output are defined as functions of the output of online adjustment mechanism (γ). By doing so, the method accomplishes the task of an online adjustment of the FOU and the weights of the antecedent and consequent membership functions respectively. The single input interval type-2 fuzzy PID controller (SIT2-FPID) with the proposed membership function adjustment mechanism was compared with the conventional PID controller and single input interval type-2 fuzzy PID controller with fixed membership functions through simulations. Throughout the simulation studies seven different performance measures are considered, three of them classical transient system response criteria: settling time (Ts), overshoot (%OS), and rise time (Tr) and the other performance measures are considered as: Integral Absolute Error (IAE), Integral Square Error (ISE), Integral Time Squared Error (ITSE) and Integral Time Absolute Error (ITAE). In addition, a step input and output disturbances have been employed to observe the disturbance rejection performance of the proposed method. The proposed online adjustment mechanism for membership functions method is demonstrated to be effective in linear and non-linear systems through simulations, and to be efficient in compensation of input and output disturbances in a short period of time.
Analysis and design of general type-2 fuzzy logic controllers

(Fen Bilimleri Enstitüsü, 2020) Sakallı, Ahmet ; Kumbasar, Tufan ; 656903 ; Kontrol ve Otomasyon Mühendisliği Bilim Dalı

This thesis presents new interpretations on the design parameters of the general type-2 fuzzy logic controllers by investigating their internal structures, proposes novel systematic design approaches for the general type-2 fuzzy logic controllers based on comprehensive and comparative analyses, and validates theoretical findings as well as proposed tuning methods via simulation and real-time experiments. The fuzzy systems have been successfully realized in a wide variety of engineering areas such as controls, image processing, data processing, decision making, estimation, modeling, and robotics. The fuzzy logic systems provide complex mappings from inputs to outputs, and this benefit usually results in better performances in comparison to non-fuzzy counterparts. Due to this, the fuzzy logic controllers have been applied to numerous challenging control problems for decades. Nowadays, more attention has been given to a new research direction of the fuzzy sets and systems, the general type-2 fuzzy logic controllers, which is the main motivation of this thesis. The internal structures of a class of Takagi-Sugeno-Kang type fuzzy logic controllers are first examined in detail. In this context, three fuzzy logic controller types (type-1, interval type-2, and general type 2) and two kinds of controller configurations (single-input and double-input) are considered. The baseline controllers, i.e. type-1 and interval type-2 fuzzy logic controllers, are presented in the preliminaries section. The fuzzy sets, fuzzy relations, fuzzy rules, fuzzy operators, and PID forms of these fuzzy logic controllers are explained in detail. The design assumptions and design parameters are given, also the most common design approaches are listed. Afterward, the general type-2 fuzzy sets and the general type-2 fuzzy logic controllers are presented. The general type-2 fuzzy logic controllers are described with α-plane associated horizontal slices because the α-plane representation provides useful advantages on the handling of the secondary membership function of the general type-2 fuzzy sets and the calculation of the general type-2 fuzzy logic controller output. It is shown that the α-plane based general type-2 fuzzy logic controller output calculation is accomplished through the well-known interval type-2 fuzzy logic computations. The secondary membership functions are further detailed in terms of their mathematical definitions and design options. The structure analysis on the general type-2 fuzzy sets shows the interactions between non-fuzzy, type-1 fuzzy, interval type-2 fuzzy, and general type-2 fuzzy sets happen in the secondary membership function. It is shown that the general type-2 fuzzy logic controller can easily transform into interval type-2 fuzzy, or type-1 fuzzy counterparts based on the secondary membership function definitions. As an outcome of this structural analysis, a new representation of the trapezoid secondary membership function is proposed based on a novel parameterization of the parameters that form the trapezoid shape. It is shown that the parameterized trapezoid secondary membership function is capable to construct trapezoid, triangle, interval, and singleton shapes so that the general type-2 fuzzy logic controllers are further capable to transform into interval type-2 fuzzy, or type-1 fuzzy counterparts. It is also shown that the proposed parameterization of the trapezoid secondary membership functions allows designing the control curves/surfaces of the general type-2 fuzzy logic controllers with a single tuning parameter. Moreover, the structural design suggestions are presented not only to construct fuzzy controllers in a straightforward manner but also to ease the design of the controllers with few design parameters. The design parameters of the general type-2 fuzzy logic controllers are grouped as the shape and the sensitivity design parameters with respect to their effects on the accuracy and the shape of the resulting fuzzy mapping. Accordingly, the tuning parameter of the secondary membership functions and the total number of α-planes are interpreted and as the sensitivity and shape design parameters, respectively. The shape analyses of the general type-2 fuzzy logic controllers show the effects of the proposed shape design parameter on the control curves/surfaces. In this context, the resulting fuzzy mappings of single input and double input general type-2 fuzzy logic controller structures are compared for various design settings of the shape design parameter. The comparative analyses provide interpretable and practical explanations on the potential advances of the shape design parameter. Based on the shape analyses, novel design approaches are proposed to tune the shape design parameter in a systematic way. In this context, it is suggested constructing the general type-2 fuzzy logic controllers over their type-1 and interval type-2 baselines and tuning them via the shape design parameter by providing a tunable tradeoff between robustness and performance. Therefore, it is aimed to combine benefits of baseline type-1 (relatively more aggressive control curves/surfaces better performance measures) and interval type 2 (relatively smoother control curves/surfaces, better robustness measures) fuzzy logic controllers. To enhance the control performance, two scheduling mechanisms are also proposed for online-tuning of the shape design parameter with respect to the steady-state operating points as well as transient-state dynamics. The sensitivity analyses of the general type-2 fuzzy logic controllers show the effects of the proposed sensitivity design parameter on the accuracy of the control curves/ surfaces. In this context, the resulting fuzzy mappings of single input and double input general type-2 fuzzy logic controller structures are also compared for various design settings of the sensitivity design parameter. The comparative sensitivity analyses show interpretable and practical explanations of the sensitivity design parameter in terms of calculation accuracy and computation burden. Therefore, it is suggested tuning the sensitivity design parameter by considering the limitations of hardware components such as resolution and processing speed. To accomplish the design in accordance with a tradeoff between sensitivity and computational time, a novel iterative algorithm is proposed to tune the sensitivity design parameter. The simulation and real-time experimental control studies validate the proposed design recommendations, systematic design approaches, and tuning methods for the general type-2 fuzzy logic controllers on benchmark control systems. In these control studies, the general type-2 fuzzy logic controllers are designed based on the proposed design methods. In order to show the performance improvements on the control systems, the general type-2 fuzzy logic controllers (tuned either online or offline) are compared with type-1 fuzzy and interval type-2 fuzzy counterparts. The performance measures clearly show that the online-tuned general type-2 fuzzy logic controllers outperform all general type-2, interval type-2, and type-1 counterparts on account of the proposed scheduling mechanisms over the proposed systematic design rules. The results also show that the systematic design of the general type-2 fuzzy logic controllers is simply accomplished by following the proposed tuning steps of the shape and sensitivity design parameters.
Analysis and design of robust disturbance observers

(Graduate School, 2023-09-04) Akyol, İsa Eray ; Söylemez, Mehmet Turan ; 504162104 ; Control and Automation Engineering

Robustness has been one of the most defining features of control systems since the classical control period. In the early days, the robustness of the control system was expressed using concepts like phase margin and gain margin, adapted from telecommunications engineering, and this terminology was faithfully used during the period when the significant achievements of modern control theory were demonstrated. However, by the end of the 70s, two separate developments marked the beginning of the golden age of robust control theory. The first of the developments that heralded this new era is Kharitonov's theorem, which established a new field of research for examining the stability of systems with parametric uncertainty. The other is John Doyle's demonstration that even in a single-input, single-output system, the LQG regulator does not have any guaranteed robustness margin, unlike the LQ regulator. While the first formed the basis of the research field known as the parametric approach, the other was one of the precursors of the $H_{\infty}$ theory. Since then, robust control has been seen as an independent sub-branch of control theory. Both approaches reached their peak with both theoretical and practical applications throughout the 1980s and 1990s. On the other hand, it has been shown that more robust closed-loop systems can be developed by changing the structure of the controller. One of the prominent methods is the approach known in the literature as the disturbance-observer (DOB). This approach, which enables the prediction and cancellation of disturbances and uncertainties that impact the system at its input, has been widely implemented, particularly in practical applications. On the other hand, the theoretical limits of the method, its analysis under uncertainty, and its design with newly developed robust control methods have lagged behind practical applications. Although theoretical studies have been carried out especially with the $H_{\infty}$ approach since the 2000s, DOB design and analysis under parametric uncertainties have not attracted the attention of researchers sufficiently. The main purpose of this thesis is to develop new approaches for both the analysis and design of disturbance observers under parametric uncertainties. In the analysis of systems with parametric uncertainty, how the uncertainties are modeled is the factor that directly affects the analysis method. In Kharitonov's paradigm, the parametric uncertainty bounding set is usually expressed as a box, which corresponds to the $l_{\infty}$ representation of the parameter box. However, the $l_{2}$ analog of the same representation is also possible. In fact, this representation is more suitable for the situation where the mathematical model is obtained by linear or nonlinear regression methods under system identification approach. Based on this, in the first part of the thesis, the answer to the question of "How much uncertainty can be tolerated with the DOB structure?", has been sought. Although approaches in the frequency domain produce effective results for DOB analysis, new challenges arise when the problem is expressed in the state space. Two approaches have come to the fore for examining parametric uncertainties in the state space. The first of these is to move the problem to the frequency domain where there are theorems and mathematical tools mature enough to examine parametric uncertainties. However, when this method is utilized, even the simplest interval system matrices show themselves as a affine-linear or more complex polynomial when expressed as a polynomial. Therefore, design in state space was seen as a "hard nut to crack" problem, in Yedevalli's words, and pushed control theorists to different research directions. The other method is to consider the problem directly in the state space. Although similar difficulties exist in this approach, when designing directly in the state space, the use of proven state space methods is also possible. Although new solutions are proposed, especially under the concept of quadratic stability, the nature of the problem condemns control theorists to use conservative approaches. In addition, a suitable Lyapunov function has not yet been proposed in the case where the design regions used to limit the parametric uncertainties are disjoint. The second contribution put forward within the scope of the thesis is the guardian-map approach, which offers less conservative disturbance observer design. Thanks to the method, robustness criteria can be assigned for each nominal eigenvalue separately and the disturbance observer is designed to meet this criterion. In this way, the inherent trade-off between robustness of the disturbance observer and the disturbance observer bandwidth is decided according to whether the closed-loop system satisfies the previously determined eigenvalue spread criterion. Advantages of considering the problem in state space include the possibility to use LMI tools and the incorporation of useful methods such as eigenstructure assignment into the solution of the problem. Many control problems can be expressed in LMI form, and these LMIs can be formulated as appropriate convex optimization problems. The LMI framework is particularly useful for expressing parametric uncertainties and constraining eigenvalue spread. However, when the dominant methods in the literature are examined, the design regions defined by the LMI approach are not defined separately for each eigenvalue, but a combined LMI design region is defined for all eigenvalues. This situation complicates the eigenvalue assignment problem and does not allow defining different robustness criteria between the eigenvalues in the non-dominant region, which is less important for the design, and the dominant region eigenvalues, which determine the behavior of the system. In addition, when the eigenstructure assignment methods are considered, the methods for minimizing the sensitivity of the system dominate the literature, instead of expressing the parametric uncertainties directly. Although robust eigenstructure assignment methods based on $H_{\infty}$-based approaches have been proposed, eigenstructure assignment methods have not been sufficiently studied in direct parametric uncertainty system design. In the eigenstructure assignment methods, since the eigenvalues are assigned strictly at the beginning of the design, the vector space to which the eigenvectors can be assigned in the rest of the design is also limited. In order to overcome this, although methods such as regional assignment, partial eigenvalue assignment and loose eigenstructure assignment are suggested in the literature, suppressing the effect of parametric uncertainties has not been the primary design criterion in these approaches. In order to fill these gaps in the literature, a new design method has been proposed, and in this approach, the robustness of the system to parametric uncertainties has been made the primary criterion of the design, and a novel disturbance observer design method has been proposed by using eigenstructure assignment and LMI approaches together for this purpose. The approach does not require any heuristic algorithms or global optimization methods, as well as allowing the solution of the robust root clustering problem for disjoint design regions. As a result, the method inevitably suffers from conservatism. However, the design reduces the problem of finding robust eigenvectors to finding the appropriate one among a finite number of eigenvectors. As a conclusion, within the scope of this thesis, a method is proposed to examine the robustness of the disturbance observer under parametric uncertainties, and two new design methods are proposed to limit the eigenvalue spread in the state space within the disjoint design regions determined for each nominal eigenvalue. By using the obtained results, a disturbance observer in the state space is designed for systems with parametric uncertainty and the results are shared.
Asenkron motorun farklı kontrol yöntemleri ile hız kontrolü ve raylı sistemlere uygulanması

(Lisansüstü Eğitim Enstitüsü, 2023-02-09) Çalıcıoğlu, Alp Eren ; Söylemez, Mehmet Turan ; 504181130 ; Kontrol ve Otomasyon Mühendisligi

Hareketin olduğu tüm alanlarda motorlara da ihtiyaç vardır. Başta üretim, ulaşım, enerji gibi genel sektörler olmak üzere gündelik hayatımızda karşımıza çıkan küçük ev aletleri, beyaz eşyalar ve akla gelen çoğu alanda motorlar kullanılmaktadır. Artan dünya nüfusu ve modernizasyon ile birlikte motorlara olan ihtiyaç gün geçtikçe artmaktadır. Motor, kaba bir tabirle kullandığı enerjiyi hareket enerjisine çeviren makinelerdir. Kullanılan enerji katı yakıt, sıvı yakıt ve elektrik gibi çeşitli türlerde olabilir, bu yakıtları kullanan motorların farklı kullanım alanları vardır. Bu motorların birbirlerine göre avantajları ve dezavantajları bulunmaktadır. Çevre kirliliği günümüzde oldukça artmıştır ve gün geçtikçe de artmaya devam etmektedir, bu sebeple her alanda karşımıza çıkan ve çok yaygın şekilde kullanılan motorların çevre kirliliği açısından zararsız olması oldukça önemlidir. Elektrik motorları, yüksek verimleri, geniş tork ve hız karakteristikleri ve çevre dostu olmaları sebebiyle geniş bir kullanım alanı bulmaktadırlar. Farklı sınıflandırmalara göre çeşitli tipte elektrik motorları bulunmaktadır ve bu elektrik motorlarının farklı kullanım alanları, avantajları ve dezavantajları bulunmaktadır. Tez kapsamında simülasyonu yapılacak olan asenkron motorlar çok basit yapılıdırlar, bu sebeple oldukça ucuz, küçük boyutlu ve dayanıklı bir elektrik motoru türüdür. Benzer şekilde yapılarında fırça ve komütatör olmadığı için kıvılcım gibi güvenlik sorunları da oluşturmazlar ve bakım gereksinimleri yoktur veya çok kısıtlıdır. Asenkron motorlar, ulaşım ve üretim sektörü başta olmak üzere endüstride çok yaygındır. Asenkron motorlar, çalışma mantıkları gereği tek bir alternatif akım ile beslenirler. Statorun beslendiği bu akım yardımıyla rotorda akım endüklenir ve hareket oluşur, bu sebepten dolayı indüksiyon motoru ismiyle de isimlendirilirler. Basit çalışma mantığının getirdiği avantajlarının yanı sıra bazı dezavantajları da bulunmaktadır. Bunların başında DC motorlar gibi ayrı akımlar kullanılarak tork ve akı kontrolünün yapılamadığı gelmektedir, bu sebeple asenkron motorların kontrol yapıları ayrı akım ile sürülen elektrik motorlarına göre zordur. Ayrıca asenkron motorların doğrusal olmayan yapıları kontrol edilmelerini zorlaştırmaktadır. Asenkron motorların farklı kontrol yöntemleri mevcuttur, bunların başında skaler ve vektörel kontrol gelmektedir. Belirtilen iki yöntemin kullanım amaçları ve avantajları farklıdır. Bu çalışma kapsamında daha hassas kontrol sonuçları verebilen vektörel kontrol çalışılmıştır. Vektörel kontrol de kendi içerisinde doğrudan ve dolaylı vektörel kontrol olmak üzere ikiye ayrılmaktadır, çalışma kapsamında akı değerine ve pozisyonuna doğrudan ihtiyaç duyulmayan dolaylı vektörel kontrol yöntemi tercih edilmiştir. Vektörel kontrol ile birlikte asenkron motor bir DC motor gibi iki ayrı akım ile birlikte kontrol edilir ve bu sebeple yapılan kontrol işlemi nispeten basit bir hale getirilmiş olur. Ulaşım sektöründeki araç sayısı gün geçtikçe artmaktadır, bu sebeple ulaşım sektöründe kullanılan motorların çevreci ve yüksek verimli olması oldukça önemlidir. Demiryolu ulaşım araçları düşünüldüğünde yüksek çalışma saatleri, uzun süreli kullanım ömürleri ön plandadır, dolayısıyla itki sisteminin en önemli parçası olan motorun verimi çok önemlidir. Mıknatıslı elektrik motorları, verimin yüksek olduğu tüm alanlarda iyi bir alternatif olmaktadır, fakat yaşanan mıknatıs temini problemleri sebebiyle mıknatıslı elektrik motorlarındaki yaygın kullanım gün geçtikçe azalmaktadır. Metrolar, büyük şehirler için iyi bir ulaşım aracı alternatifidir, çünkü demiryollarını kullandıkları ve yer altından gittikleri için ek bir kara yolu şeridi işgal etmezler. Benzer sebeple insan yoğunluğunun fazla olduğu büyük şehirlerde, trafiksiz bir çözüm sundukları için kullanımları gün geçtikçe yaygınlaşmaktadır. Çalışma kapsamında MATLAB Simulink ortamında modellenen asenkron motor modeli bir metro aracında kullanılacak şekilde tasarlanmıştır. Metrolar çalışma prensipleri gereği genelde şehir içlerinde çalıştıkları için emniyet sebebiyle belirli bir hızın üstünde çalışmaları istenmez, ayrıca yolcu konforu ve emniyeti sebebiyle de belirli bir ivme üstüne çıkmaları engellenir. Bu limitler modelleme yapılırken dikkate alınmıştır, ayrıca asenkron motorun yapısı gereği oluşturulan modelin maksimum gerilim, maksimum tork ve maksimum güç üstüne çıkması engellenmiştir. Asenkron motor kontrolü düşünüldüğünde yukarıda bahsedilen emniyet ve konfor sebebiyle ivme kontrol altında tutulmalıdır, hız ve konum ise hassas bir şekilde kontrol edilmelidir, çünkü metrolardan belirlenen konumlarda ve çok küçük hata payı içerisinde durmaları beklenir. Ayrıca hız ve konum kontrolü için aşım istenen bir durum değildir. Bu performans kriterleri oluşturulan kontrol yapıları için göz önüne alınmıştır. Asenkron motorlar, diğer elektrik motorları gibi çalışırken ısınırlar, bu sebeple motor parametrelerinde ısınma sonucu değişimler oluşur. Ayrıca yukarıda bahsedildiği gibi asenkron motorların doğrusal olmayan yapılarından dolayı oluşturulan modelde belli kabuller yapılmıştır. Tüm bu model kaynaklı bilinmezlikler ve parametrik değişimlere ek olarak, metronun hareketini sürdürdüğü yoldan kaynaklı bilinmezlikler ve değişimler ve metro içerisine binen yolculardan dolayı oluşan toplam ağırlık değişimi yapılan kontrol yapısının dayanıklı olmasını gerektirir. Bu sebeple tasarlanan kontrol yapısının dayanıklı olması ve sistemi farklı koşullarda da başarılı bir şekilde kontrol edebilmesi de bir performans kriteri olarak göz önüne alınmıştır. Asenkron motor kontrolünde PID, PI-PD, bulanık kontrol, kayan kipli kontrol ve doğrusal olmayan dinamik tersleme yöntemleri kullanılmıştır. Bu kontrol yöntemleri asenkron motorun hız kontrolünü yapabilmek için tasarlanmıştır. Tasarımları yapılan kontrol yapıları istenen performans kriterlerine göre kıyaslanmıştır. Kullanılan kontrol yöntemlerinde tasarım yapılırken Osman Kaan Erol ve İbrahim Eksin tarafından ortaya atılan büyük patlama büyük çöküş optimizasyon yönteminden faydalanılmıştır. Çalışmada son olarak yapılan tasarımların karşılaştırmalı sonuçları yer almaktadır.
Bi-fractional order reference model based control system design

(Graduate School, 2022) Keçeci, Ertuğrul ; Güzelkaya, Müjde ; 732343 ; Kontrol ve Otomasyon Mühendisliği Ana Bilim Dalı

The emergence of fractional calculus arose from a correspondence between Leibniz and L'Hopital. In this letter written in 1695, L'Hopital asked Leibniz what the result would be if \emph{n} is chosen as 0.5 in the n-order derivative expression. It is known that Leibniz, in response to this question, said: \emph{"one day in the future, the answer to this question will bring useful results"}. Since this date, contributions have been made on fractional calculus by mathematicians at first and by engineers since the middle of the $20^{th}$ century. Today, the most well-known fractional order operator definitions are presented by Riemann-Liouville, Grünwald-Letnikov and Caputo. Riemann-Liouville and Caputo generalized the integer-order integral operator with subject certain constraints, while Grünwald-Letnikov generalized the integer-order derivative expression to express a non-integer-order derivative. It is not possible to obtain the time domain response of fractional-order derivative and integral operators by using classical calculus. Thus, the factorial and exponential functions used in classical calculus are generalized for fractional calculus. The responses of the fractional derivative and integral operators in the time domain can be obtained with the help of this generalizations. On the other hand, the frequency domain allows the effects of fractional-order derivative and integral operators to be obtained in a much more convenient way. In classical calculus, the $n^{th}$ order derivative or $n$-fold integral frequency has a $\pm20ndB/dec$ effect on the gain margin in the definition region, while it takes the phase margin to $\pm90n$ degrees. Similarly, a $\gamma$-order fractional order derivative or a $\gamma$-fold fractional order integral has a $\pm20\gamma dB/dec$ effect on the gain margin and leads the phase margin to $\pm90\gamma$ degrees. The reality that some behaviors in nature can be modeled with fractional calculus has increased the interest of the control field on this subject. Fractional order modeling has been performed in many applications such as viscoelasticity, heat transfer, energy transmission lines, diffusion. However, the fractional-order calculation is exactly included in the field of control engineering at 1961. After that, the first fractional order controller method is introduced and it is showed that the fractional controller outperforms integer order PID controller. At the end of the twentieth century, the fractional order PID controller is introduced by making a generalization of the integer order PID controller. Closed-loop system transfer functions that demonstrate the desired dynamics are often called a reference model.
Bir metro hattının anahtarlamalı sistem olarak modellenmesi

(Graduate School, 2023-08-15) Birol, Berkin ; Ergenç, Ali Fuat ; 504102109 ; Kontrol ve Otomasyon Mühendisliği

Özellikle büyük şehirlerde yaşanan nüfus artışları insanların bir yerden bir yere ulaşma ihtiyaçlarını arttırmaktadır. Ulaşım için bireysel araçların kullanımı trafik sıkışıklığına neden olmaktadır, bu nedenle trafik sıkışıklıklarını azaltıp konforlu ve etkin bir ulaşım sağlamak için bireysel araçlarla ulaşım yerine toplu taşıma tercih edilmelidir. Toplu taşımanın cazip hale getirilmesi için toplumun ihtiyaçlarını karşılayacak şekilde kurgulanması, ihtiyaç duyulan sefer sıklığını konforlu bir yolculuk ile sunması gerekmektedir. Bir ulaşım sisteminde bulunan istasyon ve araçlardaki yolcu sayıları ile sefer aralıkları arasında doğrusal bir ilişki bulunmaktadır. Sefer aralıklarını azaltmak yolcu konforunu arttırsa da, işletme maliyetlerini arttırmaktadır. Bu nedenle iyi ayarlanmış bir sefer aralığı hem işletmeci hem de yolcular açısından önem kazanmaktadır. Sefer aralığının sağlıklı şekilde ayarlanması için iyi kurgulanmış bir modele ihtiyaç duyulmaktadır. Bu model, hem araçların ve istasyonların konumlarını içermeli, hem de yoğunluğu takip edebilmek için yolcu sayılarını dikkate almalıdır. Sefer aralığının güncellenmesi araçların sistemde bir bölgede toplanmasını engellemek için ilk istasyondan başlatılmalıdır, bu da diğer istasyonlardaki sefer aralıklarının belirli bir zaman gecikmesi ile güncellenmesine neden olmaktadır. Anahtarlamalı sistemler, birden çok sistemin birbirleri arasında bir kurala bağlı olarak geçiş yaptığı sistemler olarak tanımlanmaktadırlar. Bir toplu taşıma ağındaki yolcu sayılarının davranışı bir aracın bir durağa yanaşıp yanaşmamasına göre değişkenlik gösterdiği için, bu sistemler anahtarlamalı sistem olarak ele alınabilirler. Bu nedenle, bu tez çalışmasında, bir metro hattındaki yolcu sayıları anahtarlamalı sistem olarak modellenmiştir. Sistemin matematiksel modeli oluşturulduktan sonra, dinamik model MATLAB Simulink® yazılımında gerçeklenmiştir. Modelin doğruluğunu sınamak için, sistem bir ayrık olay benzetim yazılımı olan Rockwell Arena®'da da gerçeklenmiştir. Her iki modelleme yazılımında yapılan benzetimlerde Metro İstanbul'dan M2 hattı için alınan gerçek yolcu verileri kullanılmıştır. Bu benzetimler sonucunda elde edilen yolcu grafikleri dışarı alınıp karşılaştırılmıştır ve dinamik modelin sonuçlarının ayrık olay benzetimi ile oluşturulan model ile aynı olduğu doğrulanmıştır. Buna ek olarak, dinamik model ve modeli oluşturmaya olanak sağlayan MATLAB Simulink® yazılımının, ayrık olay benzetimi ile modellemeyi sağlayan Rockwell Arena® yazılımına göre benzetimi daha hızlı koşturduğu ortaya konmuştur. Dinamik modelin geçerliliği doğrulandıktan sonra, sistemin kararlılık analizi yapılmıştır. Kararlılık analizi için anahtarlamalı sistemlerin kararlılık analizinde kabul gören iki farklı yöntem seçilmiştir. Sistemde bozucunun olmadığı durumlar için 'ortak Lyapunov', bozucunun olmadığı durumlar için de 'girişten duruma kararlılık analizi' yöntemleri ile analizi yapılmıştır. MATLAB Simulink®'te oluşturulan modelde bozuculu durumlar için sınır koşullarında Metro İstanbul'dan alınan M2 hattı verileri ile koşturulan benzetimlerin sonuçlarıyla kararlılık analiz sonuçları doğrulanmıştır. Dinamik modelin davranışının iyileştirilmesi için yolcu transferlerinin daha dinamik olduğu bir model de kurgulanmıştır ve MATLAB Simulink®'te oluşturulan model bu yaklaşıma göre güncellenip daha gerçekçi bir yolcu davranışı elde edilmiştir. Bu tez çalışmasında kurulan model, literatürdeki yolcu sayılarının dinamik olarak modellenmesindeki boşluğu doldurmuş olup, kurulan modelin, bu tez çalışması sonrasında geliştirilmesi planlanan, istasyon ve trenlerdeki aktif yolcu sayıları ve işletme maliyetlerini dikkate alarak dinamik olarak sefer aralığını güncelleyecek bir kontrolör tasarımını doğrulamak için kullanılması hedeflenmektedir.
Bulanık PID kontrolörlerinin çıkış üyelik fonksiyonlarını çevrimiçi ayarlanma yöntemi

(Lisansüstü Eğitim Enstitüsü, 2022-06-10) Delibaş, Mehmet ; Güzelkaya, Müjde ; 504191119 ; Kontrol ve Otomasyon Mühendisliği

Lotfi Zadeh 1965 yılında bulanık küme mantığını geliştirmiştir. Bulanık küme teorisi klasik mantığa belirsizlik katmaktadır. Böylece hayatta karşımıza çıkan birçok belirsizlik içeren problemin çözümünü de kolaylaştırmaktadır. Bulanık küme mantığı kontrol alanına ilk olarak 1975 yılında uygulanmıştır. Daha sonraki yıllarda araştırmacılar tarafından oldukça önemli bir çalışma alanı haline gelmiş ve endüstride bulanık kontrolörlerin kullanımı arttırmıştır. Geleneksel PID kontrolör tekniklerinin doğrusal sistemlere karşı başarılı bir şekilde uygulanmasına rağmen karmaşık ve belirsiz sistemler üzerindeki etkisinin yetersizliğinden dolayı bulanık kontrolörler oldukça cazip bir hale gelmiştir. Literatürde geleneksel bulanık PID kontrolörlerin başarımını geliştirmek amacıyla çeşitli yöntemler önerilmiştir. Bu yöntemler kontrolör parametrelerini çevrimiçi ayarlamaya dayalı yöntemlerdir. Ayar parametreleri olarak giriş ve çıkış ölçekleme katsayıları, bulanık kurallar, üyelik fonksiyonlarının parametreleri ve bulanık kural ağırlıkları kullanılmaktadır. Bu tez çalışmasında, ilk olarak, Karasakal ve diğ. (2011) tarafından önerilen hata tabanlı çevrimiçi bulanık kural ağırlıklandırma yöntemi ele alınmıştır. Bu yöntemde, hatanın pozitif büyük ve hatanın değişiminin negatif olduğu bölgede kullanılan sabit bir katsayı serbest parametre olarak seçilmiş ve çeşitli değerler verilerek analizi yapılmıştır. Daha sonra Xu ve Shin (2005) tarafından önerilen bulanık kontrolörün çıkış üyelik fonksiyonlarının merkezini ayarlayan yöntem ele alınmıştır. Bu yöntemde, çıkış üyelik fonksiyonlarının merkezini ayarlamak amacıyla bulanık yapıda bir ayar mekanizması bulunmaktadır. Bu ayar mekanizmasının kendi giriş ve çıkış üyelik fonksiyonları ve kural tablosu bulunmaktadır. Çalışmamızda ikinci olarak bu çıkış ayarlama mekanizması kural tablosunda bulunan bazı parametreler serbest parametre olarak değerlendirilmiş ve bu parametrelerin analizi yapılmıştır. Son olarak hata tabanlı çevrimiçi bulanık kural ağırlıklandırma yöntemi ile bulanık kontrolörün çıkış üyelik fonksiyonlarının merkezini ayarlayan yöntem birleştirilmiştir. Birleştirilmiş yöntemin etkinliği geleneksel bulanık PID kontrolör yöntemi, hata tabanlı çevrimiçi bulanık kural ağırlıklandırma yöntemi ve bulanık kontrolörün çıkış üyelik fonksiyonlarının merkezini ayarlayan yöntem ile karşılaştırılmıştır. Yapılan analizler MATLAB/SIMULINK ortamında doğrusal ve doğrusal olmayan sistemler üzerinde yapılmış ve irdelenmiştir.
Centralized task allocation for multiple quadrupeds

(Graduate School, 2023-06-22) Sarı Çevik, Handan ; Temeltaş, Hakan ; 504191115 ; Control and Automation Engineering

The thesis focuses on analyzing different centralized task allocation methods for multiple quadruped systems. The goal is to assign tasks to agents in a way that minimizes power consumption, completes the mission in the shortest possible time, and maximizes task completion ratio. The power consumption and cost-of-transmission for cheetah-type quadruped are analyzed, and the power consumption is extrapolated for speeds between (0,1) m/s using the results from the literature. The methods are analyzed and simulated using MATLAB and its Global Optimization toolbox. Moreover, A* path planning algorithm is used to decide paths that agents take. Three different task assignment problems are explored where there are fewer tasks than agents, task and agent count are equal, and there are more tasks than agents. The resulting task assignments and metrics are analyzed. A greedy algorithm that aims to assign tasks according to the shortest distances between the agent quadrupeds is proposed and analyzed. However, since this algorithm does not consider power consumption and task completion ratio, it underperforms in some cases. The Genetic Algorithm and Particle Swarm Optimization methods are used by utilizing custom optimization (fitness) function. The optimization function is a geometric combination of total energy consumption, mission completion time, and task completion ratio. As a result, the resulting task assignments generally consume more power while reducing mission completion time tremendously. The growing trend of automation in various fields, leading to less error, more accurate results, and time-saving. The thesis also explains the concept of task allocation for autonomous systems and the different methods used for it. The methods can be decentralized or centralized, depending on whether there is a predefined decision-maker or not. In conclusion, the thesis provides valuable insights into the centralized task allocation process for multiple quadruped systems. The different methods and algorithms analyzed show that a combination of power consumption, mission completion time, and task completion ratio can result in a more efficient and effective task allocation process compared to shortest distance based allocations. The findings can contribute to the development of more advanced and autonomous systems in various fields, leading to increased productivity, accuracy, and efficiency.
Controller design methodologies for fractional order system models

(Graduate School, 2022-01-25) Yumuk, Erhan ; Güzelkaya, Müjde ; 504152101 ; Control and Automation Engineering

Fractional order calculation deals with cases where the derivative and integral order is non-integer. Although the notion of fractional order was introduced at the end of the 17th century, this concept in engineering was employed after the first quarter of the 19th century. Its first application to control engineering areas was made after the second quarter of the 20th century. Since fractional calculus is a generalized version of integer order calculus, it provides great flexibility in system modeling and controller design. In other words, fractional calculus offers three different combinations in terms of the controller and system types: Fractional order control for integer order system, Fractional order control for fractional order system, and Integer order control for fractional order system. In this respect, fractional calculus is an excellent tool to describe a control system compared to integer order calculus. Besides the flexibility, the notion brings more complexity to system modeling and controller tuning. Therefore, many studies over the last half-century have been trying to overcome these difficulties. Numerous real-time systems have nonlinear characteristics and high-order system dynamics. In literature, simple integer-order models, i.e. the first and second order with or without time delay, are used to represent system dynamics.
Deep reinforcement learning for partially observable markov decision processes

(Graduate School, 2022-07-19) Haklıdır, Mehmet ; Temeltaş, Hakan ; 504102110 ; Control and Automation Engineering

Deep reinforcement learning has recently gained popularity owing to its many successful real-world applications in robotics and games. Conventional reinforcement learning faces a substantial challenge in developing effective algorithms for high-dimensional environments. The use of deep learning as a function approximator in reinforcement learning is a viable solution to overcome this challenge. Furthermore, in deep reinforcement learning, the environment is often thought to be fully observable, meaning that the agent can perceive the true state of the environment and so act appropriately in the current state. Most real-world problems are partially observable and the environmental models are unknown. Therefore, there is a significant need for reinforcement learning approaches to solve these problems, in which the agent perceives the state of the environment partially and noisily. Guided reinforcement learning methods solve this issue by providing additional state knowledge to reinforcement learning algorithms during the learning process, thereby allowing them to solve a partially observable Markov decision process (POMDP) more effectively. However, these guided approaches are relatively rare in the literature, and most existing approaches are model-based, which means that they require learning an appropriate model of the environment first. In this thesis, we present a novel model-free approach that combines the soft actor-critic method and supervised learning concept to solve real-world problems, formulating them as POMDPs. We evaluated our approach using modified partially observable MuJoCo tasks. In experiments performed on OpenAI Gym, an open-source simulation platform, our guided soft actor-critic approach outperformed other baseline algorithms, gaining 7∼20% more maximum average return on five partially observable tasks constructed based on continuous control problems and simulated in MuJoCo. To solve the autonomous driving problem, we focused on decision making under uncertainty, as a partially observable Markov decision process, using our guided soft actor-critic approach. A self-driving car was trained in a simulation environment, created using MATLAB/SIMULINK, for a scenario in which it encountered a pedestrian crossing the road. Experiments demonstrate that the agent exhibits desirable control behavior and performs close to the fully observable state under various uncertainty situations.
Design and deployment of deep learning based fuzzy logicsystems

(Graduate School, 2023-08-29) Beke, Aykut ; Kumbasar, Tufan ; 504182102 ; Control and Automation Engineering

In the past decade, significant progress has been made in the field of Deep Learning (DL), driven by innovative learning methods, novel layer structures, and the use of graphics cards for enhanced processing power. This progress has led to the training of neural network models with numerous hidden layers and neurons, resulting in breakthroughs in various domains such as semantic segmentation, object detection, and classification. Deep Neural Networks (DNNs) have proven to be highly effective in machine learning and artificial intelligence applications. DNNs offer advantages over traditional machine learning techniques, including the ability to learn features at multiple layers, which allows them to capture complex features of input data. Through forward pass and backpropagation, DNNs extract meaningful features and outperform other methods in many tasks. As a result, DNNs have gained popularity and are widely used in commercial and industrial applications, contributing to advancements in machine learning. Fuzzy Logic Systems (FLSs) have been employed to various fields and applications over the last years. FLSs use linguistic Fuzzy Sets (FSs) and fuzzy rules, enabling the modeling of human-like reasoning and decision-making processes. This has led to advancements in the development of intelligent control systems capable of effectively handling nonlinear and uncertain dynamics. Besides, FLSs have been applied in image processing, leveraging the FSs to represent uncertain data. FLSs provide robust image analysis, pattern recognition, and image understanding, contributing to advancements in computer vision and image processing applications. Overall, FLSs have been extensively utilized in modeling various systems and phenomena. Their ability to handle uncertainty provides a flexible and interpretable modeling approach, capturing complex relationships and uncertainties in real-world systems. Conventional FLSs, known as Type-1 FLSs (T1-FLSs), have limitations in representing uncertainty. To address this, Type-2 Fuzzy Sets (T2-FSs) have been introduced as an alternative, offering a more flexible representation. T2-FSs can better handle nonlinear and uncertain systems, and T2-Fuzzy Logic Systems (T2-FLSs) have the potential to handle complex problems. However, learning T2-FLSs presents challenges due to their design complexity and the need to learn the parameters associated with fuzzy sets. Different approaches have been proposed, including adapting pre-trained T1-FLSs to T2-FLSs and employing evolutionary algorithms or Neural Network (NN) approaches to optimize the parameters of Interval T2-FLSs (IT2-FLSs). These approaches aim to simplify the design complexity and improve the performance of T2-FLSs. Despite advancements, integrating neural networks and evolutionary algorithms with T2-FLSs faces challenges when applied to extensive datasets. The curse of dimensionality and the increasing number of parameters in T2-FLSs brings some difficulties that is not possible to solve with the current approaches. Recent research has focused on combining FLSs and deep neural networks to overcome these challenges, leading to the development of hybrid models that leverage the strengths of both generalization capabilities of the DNNs and the power of the mini-batch sampled optimization algorithms. In this thesis study, a novel approach is proposed to learn the parameters of T2-FLSs using deep learning-based parameter learning methods. The proposed approach aims to handle extensive datasets and construct models with both a good prediction accuracy and the ability to handle the uncertainties. In the scope of this thesis, specifically, three studies are conducted: the first study (i) is titled with "Learning with Type-2 Fuzzy Activation Functions to Enhance the Performance of Deep Neural Networks", in the second study (ii), we propose a framework which is titled with "More Than Accuracy: A Composite Learning Framework for Interval Type-2 Fuzzy Logic Systems" and in the (iii) last study, we propose reliable uncertainty quantification for GT2-FLSs named as "Towards Reliable Uncertainty Quantification and High Precision with General Type-2 Fuzzy Systems". In the first study (i), we introduce a new method called IT2 Fuzzy Activation Layer (IT2-FAL) that aims to enhance the learning performance of DNNs. The IT2-FAL consists of Single Input IT2 (SIT2) Fuzzy Rectifying Units (FRUs) which used as activation units within the DNN structure to improve learning capabilities. We construct a closed-form representation of the SIT2-FRU structure, and an analysis is conducted to understand how the parameters of this structure influence the generation of input-output mappings. The research findings demonstrate that these mappings can be regarded either as hyperparameters to be set or as parameters to be learned. We provide a learning algorithm to these hyperparameters using DL based frameworks. To evaluate the effectiveness of the proposed IT2-FAL, a comparison is made against existing activation units like ReLU, PReLU, and ELU. The novel SIT2-FRU not only addresses the vanishing gradient problem but also exhibits a fast convergence rate. It achieves this by pushing the mean activation close to zero through the processing of inputs defined in the negative quadrant. This property of SIT2-FRU enables DNNs to exhibit improved learning behavior. The experiments conducted using the selected benchmark datasets show the efficiency and superiority of the IT2-FAL approach. By incorporating the IT2-FAL and its activation units (SIT2-FRU components), DNNs can enhance their learning capabilities and benefit from a more robust and flexible network structure. The proposed approach has the potential to improve the performance of DNNs as the experimental results revealed and it also gives opportunity to enhance the learning capabilities of DNNs. The second study (ii) introduces a novel composite learning approach that utilizes type-reduced sets of Interval Type-2 Fuzzy Logic Systems (IT2-FLSs) to capture uncertainty and establish Prediction Intervals (PIs). Unlike mainstream training approaches that primarily focus on accuracy, the objective of this new approach is to not only achieve high prediction accuracy but also effectively address and capture uncertainty by exploiting the type-reduced sets of IT2-FLSs. In order to achieve such a goal, we identify three main challenges in this context: (1) the capability to handle uncertainty, (2) the construction of a composite loss function, and (3) the development of a learning algorithm that addresses the training complexity while considering the definitions of IT2-FLSs. In (1), to address these challenges, the proposed approach exploits the type-reduced set of IT2-FLSs by combining quantile regression and DL parameter learning methods with IT2-FLSs. The ability of IT2-FLSs to process uncertainty depends on the methods employed for calculating the center-of-sets, while their representation capability is determined by the structure of their antecedent and consequent membership functions. In the scope of thesis, we introduce various parametric IT2-FLSs and defines the learnable parameters for all IT2-FLSs, along with their constraints that need to be satisfied during the training process. In (2), the construction of the loss function is defined which involves construction of a multi-objective loss that is subsequently converted into a constrained composite loss. This composite loss comprises the log-cosh loss component, which aims to optimize accuracy, and a tilted loss component that focuses on the representation of uncertainty. Notably, the tilted loss explicitly utilizes the type-reduced set. In (3), a DL approach is presented for training IT2-FLSs using unconstrained optimizers. The study also introduces parameterization techniques to convert the constrained optimization problem of IT2-FLSs into an unconstrained one without violating the definitions of fuzzy sets. In order to evaluate the effectiveness of the proposed approach, comprehensive comparative results are provided. In the thesis, we provide a hyperparameter sensitivity analysis and inter/intra-model comparisons conducted on various benchmark datasets. These evaluations shed light on the performance and robustness of the proposed novel approach in handling uncertainty and achieving high prediction accuracy for regression problems. In the third study (iii), we present a new learning approach for 𝛼-plane based General Type-2 Fuzzy Logic Systems (GT2-FLSs) to improve pointwise prediction accuracy and generate reliable Prediction Intervals (PIs). The approach focuses on exploiting the shape and size of the Secondary Membership Functions (SMFs) through a novel composite loss function. The novel composite loss function consists of two main components: an uncertainty quantification-focused loss and an accuracy-focused term. Within the uncertainty-focused loss, only the type-reduced set of IT2-FLS associated with the 𝛼0=0 plane, known as the FOU, is explicitly utilized. This allows the SMF size parameters of the GT2-FLS to quantify uncertainty and learn PIs. For the accuracy-focused part, two alternative loss terms are provided. In one approach, the aggregated output of the GT2-FLSs is used directly, while in the other approach, only the output associated with the 𝛼𝐾=1 level is utilized. In both cases, the SMF shape parameters of the GT2-FLS are enforced to enable pointwise prediction with high precision. Thus, different roles are assigned to the IT2-FLS associated with 𝛼-planes within the proposed loss function. Since the output of the 𝛼0=0 plane does not contribute to the output calculation of the GT2-FLS, a partially independent learning of the GT2-FSs becomes possible, allowing for capturing uncertainty while maintaining high accuracy. We present a DL based parameter learning approach for GT2-FLSs to facilitate efficient learning to be able to handle the complex parameter learning problem of the GT2-FLSs and also in the presence of high-dimensional and complex data. This is achieved by defining an unconstrained learning problem. We also proposed novel parameterization tricks such that the definitions of GT2-FSs are not violated. We also provide statistical comparative analyses using benchmark datasets in order to demonstrate the superiority of the proposed learning approach. The results of these analyses show the potential of learning GT2-FLS with the proposed DL based approach as a promising solution for reliable uncertainty quantification with high precision in real-world applications.
Determination of system architectures based on RAMS analysis

(Graduate School, 2024-06-10) Can, Hazel ; Söylemez, Mehmet Turan ; 504201116 ; Control and Automation Engineering

Rail systems engineering is seen as a crucial transportation alternative in today's world, especially for developed and developing countries. The construction of high-speed trains and the development of these systems have therefore become a focal point for many nations around the world. One of the fundamental reasons for this focus is the ability to achieve safe, uninterrupted transportation at minimal cost within a short time frame. On the other hand, with advancing technology, air and automotive transportation have become top preferences for individuals and logistics companies. This has also necessitated the advancement and acceleration of rail systems technologies. These advancements are aimed at elevating usability and safety to the highest levels. Steps towards reliability, usability, maintainability, and safety are crucial for the development of rail transportation and its increasing prominence in the sector. However, achieving these concepts can lead to significant costs. Therefore, there has arisen a necessity to integrate cost optimization with the conducted studies. Reliability studies should be carried out with a specific engineering perspective to prevent unexpected errors and outcomes before, during, and after system operations. The reliability of a system is made possible by detailed probabilistic calculations related to the system. Therefore, system reliability is a measure of the probabilistic calculations of the system. With the increasing needs and developing systems of railway transportation, the creation of safe and uninterrupted transportation traffic has become even more important. For this reason, focusing on RAMS (Reliability, Availability, Maintainability, and Safety) analysis by rail systems engineers can provide solutions to many focal points, thereby shedding light on the answers provided by probabilistic calculations. Answers to questions such as the criticality of errors, when they will occur, and how frequently they will occur can only be obtained through probabilistic calculations. The predictions made from these calculations guide the measures to be taken and the system engineering perspective. RAMS is an important engineering principle that examines and guides these probabilistic answers from many perspectives. Many studies have been conducted to minimize errors and enhance safety in railway systems. However, as railway transportation is also widely used for passenger transport, research has generally focused on specific areas. Studies have been conducted with a holistic approach to prevent any fault that could lead to accidents, aiming to minimize harm to society and the environment. However, there is a lack of studies that directly target usability and determine the cost requirements related to system architecture from a RAMS perspective. This study is prepared as a report to guide future studies with an engineering perspective that aims for uninterrupted transportation and calculations on how to achieve high usability rates. In this research, RAMS and rail systems infrastructure concepts are primarily focused on, providing a summarized literature review related to these concepts, and methods to optimally increase availability at minimal cost are discussed. Redundant system architectures among these methods are examined in detail and evaluated from multiple perspectives with a holistic approach. An infrastructure has also been created for various modeling analyses such as the Reliability Block Diagram and Fault Tree Analysis related to these architectures. As a result, sample studies on potential interruption costs of these redundant system architectures have been conducted and compared with suitable architectures. The architectures aimed at uninterrupted transportation are implemented according to the BS IEC 61508 safety standard. While this study aims to increase availability from a RAMS perspective while ensuring uninterrupted transportation, it also allows for cost analysis of various redundant architectures. This research will focus on reliability (safety) as it will focus only on processes over hazard failure rates. It is important to emphasize that this study will focus on minimizing errors that can cause significant harm to the system, humans, and the environment, considering that even non-hazardous error rates can have the potential to stop the system. This perspective has been used since the analyses on redundant systems will be conducted for rail system transportation. In railway systems, the most important criteria are always focused on preventing errors that can cause significant harm to humans, the environment, or the system itself. One of the primary objectives of this research is to provide a general perspective on system requirements and cost analyses along with appropriate architectural selection. Therefore, necessary calculations will be made to minimize downtime costs by reducing the downtime of a system (increasing its operational time). Subsequently, calculations related to the operational cost and initial investment cost of the system will be carried out along with assumptions. One of the critical focus points of this thesis is to analyze the initial investment cost while minimizing error frequency and downtime costs. The most suitable architectural selection can only be possible by taking all cost analyses into account. Therefore, analyses have been conducted not only on how much the system downtime is reduced but also on whether the initial investment cost is suitable for all these system architecture developments. The selection of the final and most optimal architecture can vary for each system and each project. Architectures where less critical systems or components are backed up at a lower cost might be the ideal choice for the operation of that system. However, for systems where errors can lead to significant failures and consequences, architectural selections with higher initial investment costs might be appropriate. This research provides examples and studies on the redundancy of the signaling system, which is extremely critical and important for rail systems. Therefore, analyses and comments will be made considering the criticality of this redundant system in the architectural selection. This study aims to be adaptable to necessary systems or components and enable the most suitable selection among architectures due to cost constraints. Therefore, it is supportive and contributive to the literature. This research is intended as a guide aiming for uninterrupted transportation with balanced financial conditions throughout all operational periods from the design and development stages of a rail system project. Future studies will aim to provide a more comprehensive and integrated response with a safety perspective approach to analyses on high usability and financial balance.
Development of certification-compliant safety-critical flight control software using a model-based design approach

(Graduate School, 2024-07-17) Ballı, Hakan ; Yalçın, Yaprak ; 504201136 ; Control and Automation Engineering

With the rapid pace of technological advancements, software is becoming increasingly complex and is being used in safety-critical areas such as aircraft. This situation further emphasizes the importance of software safety levels. The development of safety-critical software not only increases the complexity of implementation due to the critical nature of the operational environments of aircraft but also faces increasing challenges due to customer expectations for shorter product development cycles and demands for lower production costs. This situation necessitates that software developers meet high safety standards while also providing solutions optimized for efficiency and cost-effectiveness. In this context, avionics and flight control software in aircraft must fully perform the functions expected of them in the operational environment and must not adversely affect other functions while executing their tasks. These two factors clearly highlight the need for engineering methods aimed at reducing development complexities and supporting certification efforts. International aviation certification authorities have defined these two fundamental rules in their aviation regulations and have published the DO-178C software guidance document to ensure compliance of aviation software with these rules. Additionally, by referencing the DO-331 supplement, which explains the model-based design method used in software development processes, they aim to ensure the safe development of safety-critical software. The advancement of software, directives from authorities, and the competitive environment among manufacturers have increased the variety of products and services in the aviation sector. This situation has enabled software development processes under the DO-178C/DO-331 guidance documents using the model-based design method, allowing for software development with superior aspects such as shorter product development cycles and cost advantages. In this study, the processes followed throughout the software development lifecycle, the activities that need to be completed, and the outcome that need to be created and delivered during the development of a flight control software using the model-based design method are examined in detail. Additionally, the certification process for flight control software is thoroughly analyzed. In this study, MathWorks' MATLAB/Simulink model-based design tool was used in a software development project for the F-16 fighter aircraft. The aircraft and its components together with the flight control system were modeled rigorously within the Simulink tool. The flight control algorithm was constructed using the nonlinear dynamic inversion method, and source code for the flight control software was generated from the flight control algorithm model created using the model-based design approach. Additionally, this approach was applied throughout the software development process using the DO-331 guidance document. During the flight control software development process, system requirements allocated to the software (SRAT) were defined corresponding to the software lifecycle procedures, and from these, high-level requirements (HLR) were derived. Bidirectional traceability links between SRATS and HLR were established using the MATLAB development tool, adhering to software lifecycle procedures. After the HLR were established, the flight control system model, which represents the low-level requirements, was developed using the model-based design approach. Prior to generating source code, requirement-based functional tests were performed on the model, considering the DO-331 model simulation activity, to detect any errors. Additionally, model coverage analyses were conducted alongside these tests. Performance metrics were obtained based on the results of both the requirement-based tests and the model coverage analyses. Similarly, a static standards compliance test conducted on the model was evaluated as a performance metric, leading to the source code generation phase. It is generated using the MATLAB development tool, reviewed using MATLAB's tools, and performance metrics were gathered. Subsequently, the executable object code was created, and the performance metrics were evaluated through in-loop software simulation testing. Finally, throughout the software development process, relevant process reports were generated at each step from requirements to executable object code, configuration tracking was conducted, and the software quality assurance and certification processes were prepared for submission to the authority. As a result, a flight control software compliant with the certification requirements under the DO-178C/DO-331 guidance documents were successfully developed.
Differential flatness-based fuzzy controller design for aggressive maneuvering of quadcopters

(Graduate School, 2023-05-04) Güzay, Çağrı ; Kumbasar, Tufan ; 504142105 ; Control and Automation Engineering

This study presents a new differential flatness-based single input fuzzy logic controller structure for aggressive maneuvering control alongside its real-world application on a nano quadcopter. We propose both type-1 and interval type-2 single input fuzzy logic controllers as the primary controllers in the flight control system, which are built on the concept of differential flatness. Today, quadcopters are used for a wide variety of applications and purposes such as aerial photography, search and rescue operations, surveying and mapping, inspection, agriculture, and emergency response. Quadcopters are getting more and more well-liked in the commercial and consumer markets as a result of the rising demand for their usage areas. Additionally, the dimensions of quadcopters have significantly changed along with the rapid development in contemporary technology. As a result, we can discuss quadcopter types such as mini, micro, or nano. Nano quadcopters, the smallest ones, are lightweight, more portable, and easier to operate and maneuver with high agility since they are constructed with small-scale rotors and frames.
Discrete-time adaptive control of port controlled hamiltonian systems

(Fen Bilimleri Enstitüsü, 2021) Alkrunz, Mohammed ; Yalçın, Yaprak ; 657354 ; Kontrol ve Otomasyon Mühendisliği Ana Bilim Dalı

In control theory, the design of the adaptive controllers in the discrete-time setting for nonlinear systems has been an interesting area of research. The adaptive controller deals with the problem of finding an appropriate and efficient control structure with an adaptation mechanism to preserve stability and an acceptable closed-loop performance in the existence of a considerable amount of uncertainties or time-varying parameters. It is well known that nonlinear systems are sensitive to disturbances, unknown noises, and parameter perturbations. For these kinds of perturbed systems, adaptive control theory is a powerful tool to establish compensation procedures in an effective way that automatically updates the controller to improve the performance of the controlled systems. This thesis study considers adaptive control of an important class of nonlinear systems so-called Port-controlled Hamiltonian systems (PCH) with uncertainty in their energy function and proposes adaptive discrete-time controllers with novel construction of parameter estimators for the multiplicative uncertainty case, the linearly parametrized case, and the nonlinearly parameterized case. The proposed method adopts the Interconnection and Damping Assignment Passivity-based control (IDA-PBC) as the control design method and the Immersion and Invariance (I&I) for parameter(s) estimation. Therefore, the two approaches, namely, the IDA-PBC and I&I techniques, are combined in a discrete-time framework such that all the trajectories of the closed-loop system are bounded, and system states successfully converge to the stable desired equilibrium points, namely the minimum of the desired energy function. As mentioned previously, the Immersion and Invariance (I&I) approach is considered to develop an automatic tuning mechanism for the adaptive IDA-PBC controller. To comply with I&I conditions, for each case, the estimation error dynamic is defined such that it includes a free design function of the system states, and then the parameter estimator is constructed by establishing a parameter update rule and by presenting a novel function for the mentioned free design function such that Lyapunov stability of the estimator error dynamics is ensured. This novel design function includes some parameters, that can vary in a determined range, to provide the ability to assign desired dynamics to the estimator error system. By replacing the uncertain terms with the values obtained by the I&I estimator, the closed-loop system is immersed in the desired closed-loop system which would be obtained with the IDA-PBC controller with true parameters. In the multiplicative uncertainty case, and as an initial formulation of this study, the uncertainties in energy function appear as multiplicative uncertainties to the gradient of the Hamiltonian function. Unlike the other two formulation cases, no specific perturbation is considered in the system parameters and instead, a general multiplicative uncertainty is presented to the gradient of the Hamiltonian function and thus the adaptive IDA-PBC controller is constructed considering this multiplicative uncertainty formulation. The I&I based estimator is designed by selecting an update rule and presenting a general structure for the free design function such that the estimator error dynamics are Lyapunov asymptotically stable. The proposed general structure includes a free parameter that enables to assign different desired dynamics to the estimator. By including the proposed estimator in the constructed adaptive IDA-PBC controller, the local asymptotic stability of the obtained closed-loop system is shown in a sufficiently large set. One underactuated Hamiltonian system example is considered. In the linear parameterized case, the uncertainties of system parameters appear linearly in the energy function and thus the uncertain system dynamics are formulated such that these uncertainties appear in linearly parameterized form in the gradient of the Hamiltonian function. By considering this formulation of the linear parameterization of the uncertain system parameters, the adaptive IDA-PBC controller is constructed. Since PCH is linearly parameterized in the proposed formulation, the gradient of the Hamiltonian function could be factorized in two terms such as one of the terms becomes a matrix that includes all the known terms of system states and system parameters while the other term is a vector of unknown parameters. The mentioned matrix can be a full column rank or not. In the case where this matrix is full rank, the Lyapunov asymptotic stability of the estimator is proved while the Lyapunov stability of the estimator is shown for the case when it is not full rank. It is also shown that, for the case of having not full rank matrix, the term representing the effect of uncertainties in the closed-loop system dynamics obtained with the IDA-PBC controller that uses the estimated parameters approaches to zero. Furthermore, the Lyapunov asymptotic stability of the obtained closed-loop system is shown in a sufficiently large local set either the matrix is full rank or not. For the I&I based estimator design, a general structure for the free design function that includes some free parameters is presented that makes the estimator error dynamics Lyapunov stable where these free parameters are in a determined specific range. So that, by selecting different values for these free parameters in the determined range, different desired dynamics can be assigned to the estimation of each unknown parameter. Three linearly parameterized examples are considered; two fully actuated systems (One has a formulation with a full rank matrix while the other has a formulation with a not full rank matrix), and one underactuated system. In the nonlinear parametrized case, the parameter uncertainties that appear nonlinearly in the energy function are considered. A proper formulation for uncertain system dynamics is presented such that the uncertainties appear in non-linearly parameterized form in the gradient of the Hamiltonian function and the adaptive IDA-PBC controller is constructed considering this formulation. The conditions on the Lyapunov asymptotic stability of the estimator dynamics are derived. Namely, it is proved that if these conditions are satisfied, the estimator error dynamics become asymptotically stable. Assuming these conditions are satisfied, local asymptotic stability of the closed-loop system, which is obtained when the proposed estimator is used with the adaptive IDA-PBC controller, in a sufficiently large set is proved. For the I&I based estimator design, a structure for the free design function of the estimator is proposed including some other free design functions to satisfy these conditions however it is seen that it is not easy to give general suggestions for these last free functions. It is concluded that for each example, a special selection of these functions is needed. Two nonlinearly parameterized examples are considered and proper selections of the free design functions in the proposed structure is performed. One of the example is a fully actuated mechanical system while the other one is under-actuated. The simulation results for each of the previously mentioned systems illustrated the effectiveness of the proposed adaptive controller in comparison to the non-adaptive controller for the same test conditions. The estimator successfully estimates the uncertain parameters and the adaptive IDA-PBC controller that utilizing these parameters stabilizes the closed-loop system and preserves the performance of the stable desired Hamiltonian systems.
Doğrusal olmayan sistemler için model öngörülü kontrol yöntemine ters optimal kontrol yapısının katılması

(Lisansüstü Eğitim Enstitüsü, 2021-08-02) Ulusoy, Lütfi ; Güzelkaya, Müjde ; 504122103 ; Kontrol ve Otomasyon Mühendisliği

Optimal kontrol probleminin amacı, bazı kontrol ve durum kısıtlamalarını sağlayacak ve bir başarım kriterini optimize edecek şekilde bir kontrol giriş fonksiyonu veya kontrol kuralı elde etmektir. Buna rağmen, optimal kontrol kuralı, kısıtsız ve doğrusal durumlarda bile oldukça kolay ve analitik olarak bulunamaz. Optimal kontrol kuralının çözümünün Hamilton-Jacobi-Bellman (HJB) denklemini çözmeyi gerektirdiği iyi bilinen bir gerçektir ki bu son derece zordur. Dahası, doğrusal olmayan sistemlerin çoğu için analitik bir HJB çözümü mevcut değildir. Sistem doğrusal olduğunda ve başarım kriteri ikinci dereceden olduğunda, HJB, belirli durumlarda analitik olarak çözülmesi zor olabilen bir Riccati denklemi olarak ortaya çıkar. Bu zorlukların üstesinden gelmek amacıyla önceden belirlenmiş bir sonlu ufuk için mevcut sistem durumunu, başlangıç durumu olarak atayarak, sistem modeli yardımıyla optimal kontrol problemini tekrar tekrar ve ardışıl olarak çözmek düşünülmüştür. Bu stratejiyi kullanan kontrol yaklaşımları, Model Öngörülü Kontrol (MÖK) olarak adlandırılır. Bu yaklaşımda, sistemin gelecekteki davranışı, sistem modeli kullanılarak tahmin edilir ve kontrol işareti, anlık sistem durumlarına göre her kontrol ufku için tekrar tekrar yenilenir. Öte yandan, HJB problemini çözmek yerine bize farklı bir bakış açısı sağlayan bir başka yaklaşım ise Ters Optimal Kontrol (TOK) teorisidir. TOK, HJB denklemini çözmenin zahmetli görevinden kaçınarak, doğrusal olmayan optimal kontrol problemini çözmek için alternatif bir yaklaşımdır. Son yıllarda, birçok gerçek zamanlı uygulamada doğrusal olmayan optimal kontrol problemlerini çözmek için ters optimizasyon yaklaşımı giderek daha fazla kullanılmaktadır. Tezde, ilk olarak model öngörülü kontrol yaklaşımının optimal kontrol problemini ele alış biçimi anlatılmıştır. Önerilecek yöntem ile karşılaştırabilmek amacıyla, klasik model öngörülü yaklaşımlarından, doğrusal sistem modelini kullanan gradyant tabanlı MÖK ve doğrusal olmayan sistem modeli Runge-Kutta tabanlı MÖK (RKMÖK) yaklaşımları verilmiştir. Daha sonra ters optimal kontrol (TOK) yaklaşımları incelenmiş ve ayrık-zamanlı girişte-afin doğrusal olmayan sistemler için TOK problemini Kontrol Lyapunov Fonksiyonu (KLF) bulma problemine dönüştürerek çözen TOK yaklaşımı anlatılmıştır. TOK yaklaşımı için takip probleminde karşılaşılabilecek sorunlar üzerinde durulmuştur. Bu tezde ilk olarak, takip problemi sorunlarını çözebilmek amacıyla kontrol işareti ağırlık matrisinin her bir elemanı için sistem durum değişkenlerine bağlı bir sigmoid fonksiyon önerilmiştir. Önerilen yaklaşımın başarımını gösterebilmek için klasik TOK yaklaşımıyla karşılaştırma yapılmıştır. Bu tez çalışmasında, ayrıca girişte-afin doğrusal olmayan sistemler için MÖK ve TOK yaklaşımları birleştirilerek yeni bir optimal kontrol yöntemi önerilmektedir. Gerçek hayatta ve literatürde karşılaşılan doğrusal olmayan sistemlerin ve sistem modellerinin çoğu, bazı doğrusal olmayan azaltma yöntemleri ile girişte-afin biçime dönüştürülebilir. Önerilen yöntemin temel özelliği, her kayan ufuk ve sonuç olarak yeni bir başlangıç koşulu için çözülmesi gereken MÖK optimizasyon problemini TOK problemi olarak ele alıp, bu TOK problemini tekrar tekrar çözmesidir. Bu yaklaşımda, sistemin gelecekteki davranışının tahminini elde etmek için sistem modeli kullanılır ve önceden belirlenmiş bir kontrol ufku için TOK yönteminden elde edilen kontrol işareti sisteme uygulanır. TOK probleminin çözümü aşamasında, belirlenmesi gereken aday kontrol Lyapunov fonksiyon matrisinin parametreleri, evrimsel Büyük Patlama-Büyük Çöküş (BP-BÇ) optimizasyon arama algoritması kullanılarak çevrim içi bir şekilde tahmin edilir. Önerilen kontrol yapısında, MÖK yaklaşımında her kontrol ufku için uygun bir KLF matrisinin aranması ile optimal kontrol problemi çözülmektedir. Diğer bir bakış açısından ise, MÖK yapısı TOK problemine dahil edilerek TOK problemi, her kayan ufkun başlangıcındaki farklı başlangıç koşulları kullanılarak tekrar tekrar çözülmekte ve böylece, TOK için çevrim içi bir düzeltme mekanizması elde edilmektedir. Bu yaklaşım ve literatürdeki diğer yöntemler kullanılarak top ve çubuk kontrol sistemi üzerinde benzetim çalışmaları ve gerçek zamanlı uygulama yapılmıştır. Elde edilen sonuçlar bazı kontrol başarım ölçütlerine karşılaştırılmış ve önerilen yaklaşımın başarımı değerlendirilmiştir.

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