Theses supervised by Prof. Dr. Mehmet Turan Söylemez
10 theses · İstanbul Technical University
Modelling and control of the Qball X4 quadrotor system based on pid and fuzzy logic structure
Multirotors have gained a high level of popularity during the last decade both in civilian, military and engineering applications because of the recent advances in sensing, communication, computing and control technologies. Quadcopters, one of the multirotors, are small aerial vehicles propelled by four rotors. This thesis focuses on a quadrocopter model, which is Qball X4. This quadrocopter model was developed by Quanser. In this work both linear and nonlinear models are described for use in to develop a controller. Axes of the Qball-X4 are denoted by x,y,z and these are defined with respect to the vehicle which is shown in Figure 1. Roll, pitch and yaw are defined as the angles of rotation about the x, y and z axes. First, the actuator dynamics, then respectively roll/pitch model, height model, x-y position model and yaw model are described. After the description of the models, a controller design method has been proposed. First, conventional PID control technique is presented. This technique has already been applied by the Quanser. The control gains for the PID are found using the LQR method. PID controller has been applied to both nonlinear and linear models of the Qball X4. Simulation results are shown for the position controls along x,y,z axis and roll, pitch yaw angles. Second, as an extension of the conventional PID control theory, a different fuzzy controller structure is applied. The proposed fuzzy controller structure is based on fuzzy logic. Fuzzy logic is a logic, in which the truth variables can take any real number between 0 and 1. It is different than the boolean logic, because in boolean structure, the truth variables can be in the only 0 or 1. Fuzzy logic has been extended to handle the concept of partial truth, so that the truth value can take range between completely true and comletely false. The name of the control structure is PID type fuzzy controller. Classical fuzzy PID controller requires three inputs and its rule base has three dimensions. On the other hand, the fuzzy type PID controller has just two inputs and its rule base has two dimensions. A PID type fuzzy controller structure includes both PD and PI type fuzzy controllers. Again PID type fuzzy controller has been applied to both nonlinear and linear model of the Qball X4. Simulation results are shown for the position controls along x,y,z axis and roll, pitch, yaw angles. Last, a different method which tunes the scaling factors of the PID type fuzzy controller is proposed. In this method, we cannot change the fuzzy rules and scaling factors, we can only set the membership function to improve the steady state response of the PID type fuzzy controller. Again, PID type fuzzy controller with self-scaling factors has been applied to both nonlinear and linear model of the Qball X4. Simulation results are shown for the position controls along x,y,z axis and roll, pitch, yaw angles, so that we can easily see the difference between the steady state response of the systems. As a result, in the simulation we can analyze six different cases.(3 cases belong to nonlinear, 3 cases belong to linear) These are both linear and nonlinear PID controller, both linear and nonlinear PID type fuzzy controllers and both linear and nonlinear PID type fuzzy controllers with self-scaling factors. The results are discussed in the last section.
Otomatik yarım bariyerli hemzemin geçit sisteminin kontrolü ve risk modelinin oluşturulması
Gelişmiş toplumlarda raylı ulaşım sistemleri önemli bir ulaşım alternatifi şeklinde kullanılmaktadır. Günümüzde raylı ulaşım sistemi araçları gerek yolcu taşımacılığında gerekse lojistik taşımacılığında önemli bir noktada bulunmaktadır. Diğer alternatif ulaşım araçlarına kıyasla daha güvenilir ve daha hızlı ulaşım imkanı sağlamaktadır. Demiryolu sistemlerinin gelişmesi ile beraber demiryolu sistemlerinde güvenlik önlemleri özel olarak önem kazanmıştır. Daha az maddi kayıp ve can kaybı işletmecilik açısından önemli olmaktadır. Demiryolu sistemleri bünyesinde bulunan hemzemin geçit sistemleri de bu güvenlik sistemlerinin önemli bir bölümünü oluşturmaktadır. Özellikle hemzemin geçit bölgesi karayolu ile demiryolunun kesişim noktasında olması sebebiyle can ve mal kaybının yüksek olduğu bir yerdir. Bu bölgede bulunan sistemlerin güvenlik önlemleri demiryolu sistemleri açısından özel önem taşımaktadır. Alınması gereken tedbirler ve hatada güvenli sistemlerin inşa edilmesi önemli bir yer oluşturmaktadır. Özellikle hemzemin geçit bölgesinde bulunan sistemlerin emniyet ve risk analizlerinin yapılması insan kaynaklı hataları minimuma indirecek hatta hiç olmamasını sağlayacaktır. Hemzemin geçit sistemleri özellikle ülkemizde bulunan demiryolu sisteminin önemli bir bileşenini oluşturmaktadır. Tez çalışmasında hemzemin geçit sistemleri genel olarak tanımlanmıştır. Çeşitleri hakkında bilgiler verilmiştir. Donanımsal ekipmanları hakkında tanımlamalar yapılmıştır. Karayolunda ve demiryolunda bulunması gereken işaret ve işaretçilerin önemi anlatılmıştır. Hemzemin geçit bölgesinde yapılması gereken risk analizinin nasıl yapılması gerektiği anlatılmıştır. RAMS yönteminin tanımı ve uygulaması örnekler verilerek anlatılmıştır. Risk analizinde kullanılması gereken teknikler ve metodlar üzerinde durulmuştur. Bu tez çalışmasında, otomatik yarım bariyerli hemzemin geçit sistemine ilişkin risk analizi yapılmıştır. Hemzemin geçit sisteminde risk indeksi belirlenmiştir. Risk analizi, FMEA ve FTA analizi yöntemleri kullanılarak hemzemin geçit sistemi için olası hata senaryoları tanımlanmış ve hata oranları belirlenmiştir. Özellikle yarım bariyerli hemzemin geçit sistemlerinde bulunan zigzag durumun engellenebilmesi için ne gibi tedbirlerin alınması gerektiği belirtilmiştir. 'V' modeli kullanılarak sistem yaşam döngüsünde bulunan her bir adım kontrol edilmiş ve hemzemin geçit sistemindeki hata oranları minimuma indirilmiştir. Hemzemin geçit bölgesinde SIL güvenlik sistemi analizi yapılmıştır. Otomatik yarım bariyerli hemzemin geçit sistemi için olması gereken sistem isterleri belirlenmiş ve otomatik yarım bariyerli hemzemin geçit sistemi tasarımı yapılmıştır.
Hybrid controller approach for an autonomous ground vehicle path tracking problem
Automotive industry is the one of the most important economic sectors according to its circulation. Starting from the last part of the 18th century, the industry keeps its up-to-dateness with the keep tracking the future technology very closely. According to these development, autonomous driving function is become hot topic when the range of the automotive industry is under consideration. Autonomous function is mainly based on driving without any labor which try to reduce faults cause by the humans. Thanks to this aim, safety, comfortable and effective transportation will offer by the future self-driver. Automated driving requires deep understanding and cooperation of many different disciplines and topics, such as sensor technologies, localization and mapping technologies, estimation and fusion algorithms, image processing algorithms, decision making and trajectory generation algorithms, vehicle controls theory and automotive engineering An ordinary driver just steers the steering wheel and apply brake or gas pedal to follow the lane and adjust the speed of the vehicle even without thinking. Nevertheless, this path following problem is under research for years as can be observed from the literature.. Path tracking methods can be divided into two main groups: Geometric and model based control methods. Geometric methods use only the geometrical relation between the path and the vehicle. In this thesis two geometric based selected Pure Pursuit and Stanley method. Then one model based method is selected as Steady State Cornering method which devoleped from linearized bicycled model. First two methods are based on the conception of an ordinary driver trying to track a given path. While the third approach is based on a simplified mathematical model of the vehicle that is trying to follow a given path. In that sense, it can be said that first two is more intuitive than the latter one, and it is obvious that each method has its own strengths and weaknesses. In contrast, Pure-Pursuit and Steady State Cornering methods look forward in order to maneuver. For that reason, the latter two methods can preview sudden changes on the path beforehand. But on a smooth path, these two methods cut corners and their performances are not as good as Stanley In order to use advantages of different methods at the same time, innovative approach that based on the combination of two method is proposed as hybrid controller. The proposed hybrid controller is using Pure-Pursuit and Stanley Method at the same time. A weight factor is adjusted depending on the smoothness of the path ahead. As the path gets smoother, the weight of the Stanley method is increased, if a sharp change is ahead the weight of the pure pursuit method is increased. To decide if the path is smooth or not, the look ahead strategy used in steady state method is implemented. After that, the proposed hybrid controller and three path tracking method performances are examined with three different path sceniros. These paths are 50 meter radius circle path, rectangular shaped path and mixed of rectangular and circle path. In comparisons, in order to see effect of speed changes on methods, simulations are done with three different speed such as 20 km/h 50km/h and 80 km/h. To sum up in this thesis, the first part will cover the literature survey on the wide range path following problem. Afterwards, the vehicle model that will be used on whole studies about the thesis will introduce at the Section-2. In Section-3, the tracking methodologies will be summarized with their mathematical backgrounds. The proposed hybrid methodology will present in Section-4. Accordingly, three different simulation studies and their comparisons will discuss in Section-5. Finally, the conclusion and planning future works on these topics will represent at the last part.
Designing, verification and validation of railway signaling systems using coloured petri nets
Every weekday just in United States of America, more than 7 million people use railways in their transportation. In the same time railway is used widely as reliable freight transportation solution. So in general, railway transportation can be considered as a very vital transportation mean, this importance emerges from the fact that railways are relatively cheap and environmental friendly. This enables them to be the main transportation system in many countries. Railways systems are exposed to accidents due to huge variety of reasons like signaling system failures, human errors …etc. As railways are used by a huge number of people, the safety of railways became very important issue. This led some governments to interfere by putting standards in order to organize the operations of railway systems. CENELEC is a safety reference name which states the necessary standards of railway sector and it is composed from the following standards EN 50126, EN 50128 and EN 50129. Based on these standards, Safety Integrity Levels (SILs) were built. Signalling systems are responsible for the operations of railway systems to ensure the safety of trains and their other components. Signalling ensures optimal control for traffic in order to avoid accidents. Formal methods have a very important role in software development. Formal methods are method use the discrete mathematic techniques and tools in software and hardware development process, where the mathematical notations are used in the design and the verification of software and hardware systems. The main purpose of using formal methods is to reduce the risky consequences that can occur due to serious specification and design errors by symbolically examine the entire state space of a design Formal methods help in presenting precise record of the created software that's why it is used widely in verification and validation processes To develop software using formal method, Formal Specifications are used to describe the behavior and properties using formal language and semantics. Formal Language is used to define Rules in a precise manner. Formal language describes the grammar rules and justifies the general algorithms to be used. Semantics provide an accurate mathematical meaning to every statement. These items together will provide a formal model for the system that enables the developers to state the expected properties and then formally verify it Petri net as the models of DES. Petri net graphs depict structural information about the simple and complex systems. Coloured Petri nets are a high-level Petri nets graphical language. It is based on normal PNs, but CTL is a branching time tree; the scenarios can be symbolized by hierarchical structure in a graphical form where different scenarios can be applied. CTL* (or ASK-CTL) is used to express the state and the transition properties of the models interviewed by the state space of the coluored Petri net In this research, a signalling system for a train yard is designed by CPN. The system was verified and validated using model checking which is considered as one of the formal methods. All the processes were performed according to CENELEC to achieve minimum SIL 3.
Demiryolu sinyalizasyonunda güvenilirlilik emre amadelik sürdürülebilirlik ve emniyet (RAMS) yönetimi ve FMEA - FTA analizi uygulaması
Raylı sistem taşımacılığı özellikle gelişmiş ve gelişmekte olan ülkelerde çok önemli bir ulaştırma alternatifi oluşturmaktadır. Avrupa ve Asya'da bulunan birçok ülke yüksek hızlı demiryolu yapımına son yıllarda özel önem göstermektedirler. Bu özel önemin ana sebebi hızlı demiryolu sistemleri inşa edilerek yolcu ve yük taşımacılığının daha kısa sürede, daha güvenli şekilde ve daha ucuz şekilde yapılmak istenmesinden kaynaklanmaktadır. Demiryolu teknolojisinin gelişmesiyle birlikte emniyet ve konfor kavramları daha da önem kazanmaya başlamıştır. Bu durum demiryolu sistem mühendisleri tarafından RAMS kavramının üzerinde durulmasına sebep olmuştur. Demiryolu sistemlerinde emniyet ve risk analizi konularında bugüne kadar birçok çalışma bulunmaktadır. Ancak ülkemizde ve bölgemizde hızla artan demiryolu altyapılarının teknik altyapıları ülkemizde herhangi bir sistem mühendisliği mevzuatı olmadığı için yeterince gelişememiştir. Bu çalışma, İstanbul Ulaşım AŞ Bünyesindeki bir demiryolu işletmesinin yerel olarak sinyalizasyonunun yapılması sırasında karşılaşılan risklerden örnekler alınarak hazırlanmış ve ileriki çalışmalar için bir rapor haline getirilmiştir. Bu çalışmada öncelikle RAMS ve sistem mühendisliği kavramları üzerinde durulmuş, bu kavramlar hakkında özet bir literatür bilgisi verildikten sonra risk analizleri ve önemli risklerin nicel olarak hesaplanabilmesi için kullanılan yöntemler ele alınmıştır. Bu yöntemler arasında FMEA ve FTA analiz yöntemleri tercih edilmiş ve birbirlerini bütünleyici analizler olarak kullanımları detaylı olarak incelenmiştir. Sonuç olarak, yukarıda bahsi geçen demiryolu işletmesinde örnek bir çalışma sunulmuştur. Bu çalışma bir raylı sistem projesinin planlanmasından başlayarak, tasarlanması, devreye alınması, işletilmesi, bakım yapılması ve nihayet sistemin sonlandırılmasına kadar bir başucu kaynağı olması gereken risk analizi yöntemlerini içermektedir. Daha sonra yapılacak olan çalışmalar, uluslararası sertifikasyon kuruluşları tarafından bir sistemin ne şekilde bu aşamalardan geçtiği ve uluslararası komisyonlarca yetkin bir sistemin nasıl elde edilmesi gerektiği sorusuna cevap bulmaya çalışmak olacaktır.
Simulation based tool for error propagation analysis of simulink models
Safety is a growing demand for all types of today's systems. Whether it is a nuclear or a transportation system, reliability and safety are the most urgent needs for the design of the entire system. Engineers have developed different standards and models to ensure the desired function of the system without any human life or material loss. All these safety and economy related issues make the topic "model-based error detection analysis" an important and interesting topic for different areas of engineering. This growing demand makes it compulsory for the companies in the industry to form dedicated departments just for the safety assessment and certification. Different types of methods and standards have been developed to calculate the reliability of such safety-critical systems. Various safety standards for various fields are also given by examples in the thesis. These methods can be qualitative or quantitative depending on the type of the system. Analyzes of these safety-critical systems require time and careful work by the designers and testers. As it is necessary to fulfill some criteria based on reliability, engineers developed methods such as fault tree analysis, failure mode and effect analysis, and hazard analysis. To validate the analytical results, a simulation-based approach is introduced in this thesis. After giving background information and mathematical models for the analytical approach, the benefits of a simulation-based approach and its difference from the analytical methods are explained. Simulation-based approach is developed for the environment of MATLAB Simulink, by implementing different types of faults and fault injection methods. These fault types are classified as the sub-elements of the general fault definitions such as sensor faults, hardware faults, and network faults. Every fault type can be injected by using a different method that consists the parameters of occurrence rates and the duration of the fault effect. The correct values that are used for the comparison by the tool are obtained through a fault-free run. The comparison of the faulty run values and the fault-free run values provides important information about the reliability and the performance of the system. In the next phase, the methodology to obtain these reliability and performance metrics are explained along with the features offered to the user by ErrorSim. How to use these features and how to interpret the results obtained by these features are introduced by explanatory examples. Apart from safety-related issues, the architecture of the developed tool is described. It gives the user an insight into the main algorithm which is behind fault injection and error detection. It is important for the user to know the listeners call-back functions and a few technical details for the correct usage of the tool. Results of the simulation are studied in different perspectives in order to show that the tool that is developed can also illustrate performance-related issues in control systems. Two different case studies are taken into consideration for the interpretation of the tool application results. In the conclusion section, the achievements and benefits of ErrorSim are discussed. The general usage of ErrorSim and its importance is explained. Possible improvements on ErrorSim and future works are also discussed.
Determination of parameter regions for diagonal dominance and stability of MIMO systems
Most of the industrial plants include more than one input and output variable. Compared to Single Input Single Output (SISO) systems, such systems include different structural properties. For instance, an output variable is effected by all input variables in general. On the other hand, in terms of controller structures, researchers have focused on two main approaches for such systems, which are "centralized" and "decentralized" controllers. However, it can be proposed that decentralized controllers are preferred more in practice due to various reasons like less number of tuning parameter, possibility to apply single loop controller design methods, ease of use for operators etc. Whereas, in general, performance and efficiency of such controllers reduce when there are significant interactions between different input-output pairs in a Multi Input Multi Output (MIMO) system. Reducing the interactions between different input-output pairs in MIMO systems is crucial in terms of decentralized controller design due to the previously mentioned reasons. Diagonal dominance which is a weaker condition compared to decoupling, is one of the approaches that can be used to reduce interactions in MIMO systems. One input variable is strongly related with one specific output variable in diagonal dominant systems. One of the main aims of this thesis is to determine controller parameter regions that achieve diagonal dominance conditions. Additionally, it is also aimed to determine stabilizing parameter spaces, since diagonal dominance does not indicate stability in general. As a result, controller parameter regions that achieve both diagonal dominance and stability conditions in closed loop are determined in this thesis as the first step of decentralized controller design. In literature, the diagonal dominance concept has gained attraction since the pioneering studies of Rosenbrock in early 1970s. However, in the meantime most of the researchers focused on determining a specific controller parameter pair that optimizes a predetermined condition. Such a case may restrict the designer in the next steps of the design process. Additionally, the number of studies are limited that investigates the diagonal dominance characteristics of the determined controller parameters in case uncertainties or checks how the system is close to the diagonal dominance boundaries. Two Input Two Output (TITO) systems are special subset of MIMO systems since in practice many MIMO systems can be treated as several TITO subsystems as proposed in literature. In terms of diagonal dominance, particularly, TITO systems and diagonal type controllers are discussed in detail, since it is aimed to determine necessary and sufficient conditions on diagonal dominance in terms of controller parameters. For such systems, exact conditions on the controller parameters in terms of both column and row diagonal dominance are derived at a given fixed frequency. Derived results are also valid for finite number of frequencies and practically applicable for a given frequency range. Moreover, weighting factors are added to the original definition of diagonal dominance in order to derive controller parameter regions that achieve better diagonal dominance ratios. Necessary and sufficient conditions on diagonal type controllers are also derived for the weighted diagonal dominance problem. Lastly, critical frequencies that may possibly change the interval characteristics of static diagonal controllers for the column diagonal dominance are derived. Effectiveness of the derived results in terms of diagonal dominance are demonstrated over several case studies using Gershgorin Disc plots and diagonal dominance ratio plots. On the other hand, a Lyapunov equation based stability mapping approach is proposed within the scope of this thesis to derive stabilizing controller parameter spaces of a given MIMO system. In the present approach, it is not necessary to calculate singular frequencies or apply frequency sweeping that most of the frequency based approaches require. From the Lyapunov point of view, positive definiteness of the Lyapunov matrix P(k) is necessary and sufficient for LTI systems. However, considering the numerators and denominators of the leading principal minors it is required to solve 2n parametric equation in order to determine positive definiteness of P(k). This number is reduced to n+1 at the first step. After that, Lyapunov matrix equation is reduced to the standard set of equation representation using the Kronecker products and vectorization operator. At this point, a new matrix M(k) is defined over the Kronecker products and it is shown that determinant of M(k) is the product of binary combinations of A(k). Using the relations between the system matrix A(k), Lyapunov matrix P(k) and M(k), it is shown that it is sufficient to solve at most 2 parametric equations which are |M(k)|=0 and |M(k)|->infinity. Determinant of M(k) includes redundant multiplications of binary combinations of eigenvalue pairs of A(k) due to the matrices P(k) and Q that are used in Lyapunov formulation are symmetric. In order to eliminate the redundant multiplications and reduce the computational complexity, elimination and duplication matrices are introduced as transformation matrices. In addition to MIMO systems, the proposed stability mapping approach is applicable to a broad range of systems, further system classes and sub problems where Lyapunov formulation is possible. In order to demonstrate these properties of the proposed approach, firstly, controller integrity problem of MIMO systems is discussed in detail. An approach is proposed to determine stabilizing controller parameter regions even in case of possible failures related with controller parameters. A benchmark case study is included and effectiveness of the proposed approach is shown over a comparative study with a currently existing approach. Additionally, discrete time systems is also discussed in detail to demonstrate the further application areas of the proposed Lyapunov equation based stability mapping approach. In this case, the structure of the Lyapunov equation varies slightly compared to the continuous time case. Another benefit of the proposed Lyapunov equation based approach is the opportunity to determine analytical expressions of stability boundaries. So that, it becomes possible to use Lyapunov equation based stability mapping approach in optimization based approaches by inserting the stability boundaries as constraints on such approaches. This case is also addressed through the robust Model Predictive Control (MPC) problem. Analytical stability boundaries which is derived in the off-line phase using the proposed stability mapping approach is inserted to the robust MPC problem formulation to achieve stability. In this way, robust MPC problem is transformed into the nominal MPC problem. The effectiveness of the proposed method is also demonstrated through a benchmark system that is frequently used in the literature. Diagonal dominance proposes weaker conditions compared to decoupling. As a result, it becomes possible to determine controller parameter regions that achieve diagonal dominance in case of parametric uncertainties. Within the scope of this thesis, two conservative approaches which are based on triangular inequality and griding are proposed for the systems that include interval type uncertainties in Transfer Function Matrix (TFM) elements. Using these approaches diagonal dominance problem of a parametric uncertain system is transferred to the weighted diagonal dominance problem of the nominal plant. After that, previously derived results are used to determine static diagonal controller parameter regions. Lastly, stability of parameter uncertain multivariable systems is discussed in order to determine robustly stabilizing parameter spaces. There are two main assumptions on uncertain parameters in literature. In the first assumption, there is no restriction on uncertain parameters and it is aimed to determine all uncertain parameter spaces that preserve stability of the closed loop system. In this case, proposed Lyapunov equation based stability mapping approach is directly applicable. Contrary to this approach, many methods that is currently available in the literature include the results obtained by making some assumptions on the number and the type of uncertain parameters. The validity of the Lyapunov equation based method has been demonstrated through different benchmark case studies. On the other hand, in some cases, it is assumed that upper and lower bounds of uncertain parameters are known. It is aimed to determine whether the whole polynomial family is stable in all cases where the uncertain parameters take any value between these known intervals. In some special cases, it was shown in literature that stability of finite number fixed polynomials guarantee the stability of whole uncertain polynomial family in case of SISO systems. However, the characteristic polynomial of MIMO systems includes the multiplication of free controller parameters and individual transfer functions even in the simplest cases. As a result, it can be proposed that compared to SISO systems, it is more difficult to determine the controller parameter areas that provide robust stability in such systems. In the discussed problem characteristic equation includes both uncertain parameters that have known upper and lower bounds and free controller parameters. In this thesis, an approach is presented to determine robustly stabilizing parameter spaces using the Kharitonov Theorem in accordance with the Lyapunov method by applying overbounding method on characteristic polynomial coefficients. The proposed method reduces the computational complexity significantly, since Kharitonov Theorem is used. However, it must also be noted that calculation of invariant controller parameter sub regions in terms of overbounding also introduces additional analysis steps. As a conclusion, in this thesis, it is mainly focused on determining controller parameter regions of the diagonal type controllers that make both nominal and parametric MIMO systems diagonal dominant and stable. The results are derived through TITO systems from the standpoint of diagonal dominance, since it is aimed to determine the necessary and sufficient conditions. On the other hand, there is no restriction on the system and controller type for the proposed stability mapping approach.
Birinci dereceden ölü zamanlı sistemler için kesirli dereceli PI kontrolör tasarımı
Bu çalışmada ilk olarak kesirli dereceli hesaplamaların tarihçesinden ve kesirli türev-integral kavramlarından bahsedilmektedir. Kesirli dereceli PI kontrolörün katsayılarının (kp, ki) esneklikleri, klasik PI kontrolör ile benzerlik göstermesine rağmen integral derecesi (λ) farklıdır ve iki yapı arasındaki farklılık buradan kaynaklanmaktadır. Kesirli dereceli kontrolör tasarlanırken dikkat edilmesi gereken en önemli nokta kontrolörün kapalı çevrim sistemi kararsız yapmamasıdır. Bu yüzden, öncelikle kontrolör katsayıları için sınırlı giriş – sınırlı çıkış (bounded input – bounded output) kararlılığından yararlanılarak katsayıların kararlılık bölgesini bulunur. İncelenen sistem ölü zaman içerdiğinde kontrolör katsayılarının kararlılık bölgesini araştırmak biraz daha karmaşık hale gelmektedir. Bu yüzden, karmaşıklığı gidermek için ölü zamanın farklı yaklaşımları ele alınır. İncelenen yaklaşımlardan en uygunu pade yaklaşımıdır. Bu yaklaşım ile elde edilecek olan ölü zamanın derecesi istenildiği gibi ayarlanabilmektedir. Derece ne kadar artarsa ölü zamana o kadar yaklaşmaktadır. Bu yaklaşımın kullanılmasıyla birlikte ölü zaman ve sistem birbirine seri bağlanmış iki sistem gibi ele alınabilmektedir. Bu durumda ölü zaman içeren sistem için tasarlanan kontrolörün katsayılarının kararlılık bölgesi daha kolay bir şekilde bulunmaktadır. Katsayıların kararlılık bölgesi bulunurken kesirli dereceli PI kontrolörün integral kısmının derecesi (λ) de önem kazanmaktadır. Katsayı parametrelerinin kararlılık bölgesi integral derecesinin değerine göre farklılık göstermektedir. Bu yüzden kontrolörün üç parametresiyle sınırlı olan kararlılık bölgesi bulunabilmektedir. Kararlılık bölgesi içerisinde katsayıların ve integralin derecesinin farklı değerlerine göre sistemin performansı değişmektedir. Kesirli dereceli sistemlerin simulasyonu MATLAB üzerinde doğrudan yapılamamaktadır. Bu yüzden kesirli dereceli sistemlerin simulasyonunu yapabilmek için gerekli MATLAB araç kutuları araştırılmış olup bu çalışmada gerekli olan fonksiyonlar tanıtılacaktır. Ayrıca bu fonksiyonlar MATLAB üzerinde simulasyon yapılırken kolayca ihtiyaç duyulduğu yerde kullanılabilmektedir. Bu aşamaya kadar yapılan araştırmalar sistemin istenilen performansı sağlayabilmesi için yol gösterici niteliktedir. Sistemin istenilen performansı sağlayabilmesi için gerekli olan parametreler Büyük Patlama Büyük Çöküş (Big Bang- Big Brunch) optimizasyon algoritmasıyla bulunacak ve elde edilen sonuçlar incelenecektir.
Multi agent intersection management considering energy consumption
Traffic congestion is one of the main reasons of increasing pollution and fuel consumption in the cities. According to recent urban mobility reports, traffic congestions cost up to $121 billion in USA every year due to productivity and time loss. Approximately 38-40 hours are spent by an average citizen in the traffic. Additionally, 25 billion kilograms of carbon dioxide is emitted due to congestions. Increasing number of vehicles on the urban roads leads congestions at the intersections. Traditional intersection management methods such as stop signs, traffic officer control and traffic lights, are getting insufficient. Traffic light timing depending on day time is a common application; however, it is not an adaptive method for changing traffic flow density. Traffic density can be measured by cameras, piezo and infrared sensors. Intelligent traffic light timing can be achieved using the traffic information gathered from the units integrated to the roads. Vehicle to vehicle and vehicle to infrastructure communication technologies allow us to gather information directly from vehicles, and analyze traffic congestion. Besides, vehicles can be informed about the traffic ahead or can be conditioned to reduce effect of congestions. Intersections can be managed by using information from the vehicles. One way to manage intersections is to integration of an intersection manager unit. Vehicles request reservation from intersection manager to pass the intersection. Another approach is interactive multi agent intersection management by the help of autonomous vehicles. Autonomous intersection management uses estimated trajectories provided by the vehicles to detect any possible crash at the intersection. Estimated position of a vehicle at a time can easily be simulated for a given velocity profile. Estimated position and time information of vehicles are compared and estimated collisions are detected. Possible collisions must be resolved before the vehicles arrive at the intersection. Most common approach is the first come – first served method, which allows the first vehicle that requests reservation first to pass the intersection, allocate the intersection. Other vehicles' trajectories must be adjusted to avoid the collision at the intersection. This adjustment is done by assigning delay to the arrival time of the vehicles at the intersection. Giving the priority to the vehicle that requests reservation first may not always be the most efficient decision in terms of total delay time. A method called look ahead intersection control policy is explained in the next sections. Look ahead intersection management policy assigns the priorities based on total delay time minimization. This method aims to reduce consecutive effect when the head vehicle of a convoy is delayed. In this study, we proposed an intersection management method searching the passing sequence from the collision point to minimize defined cost functions. First intersection model is explained to specify communication zone, velocity adjustment zone and grid structure at the center of intersection. Communication protocols are given for the communication zone. Crash detection and intersection management algorithm are executed in communication zone by all vehicles. Vehicles' estimated trajectories are transformed into time – space occupation at the intersection using grids to easily isolate possible collisions. Passing sequences of the vehicle, which are estimated to pass the collision point, are found. For each sequence, different vehicles' arrival are delayed by different amount of time. Therefore, each sequence results in different total delay time. Selection between possible passing sequences is done by minimizing total delay time. Another performance criterion is energy loss of the vehicle. Vehicle longitudinal dynamics are explained for energy loss calculation. Delay time is realized by deceleration and acceleration. Acceleration requires an increase in traction force, this leads energy loss compared to the nominal state. Since vehicle dynamics are different for different vehicles, the same velocity rate may result in different energy losses. Hence, each passing sequence has a different energy loss value associated with it. This difference is used to select the sequence with minimum energy loss. Energy loss and total delay based costs are then combined in one cost function using a rating parameter. After specifying cost functions, intersection management is simulated for different cases. A simulation framework is created in MATLAB. Vehicle kinematic bicycle model, which is used in the simulation environment, is explained. Vehicles with different masses and paths are simulated in different case studies. The case studies show that total delay based sequence selection distributes minimum delays to the vehicles only aiming to resolve estimated crashes. On the other hand, energy loss based method gives the priority to heavier vehicles to minimize energy loss. Thus, the total delay time increases in energy loss based method. The combined cost based selection method reduces energy loss of the total delay time based method. Similarly, it reduces total delay time of the energy loss based method. In this thesis, literature survey and motivation of the study is given. Then vehicle models are explained for further use in the thesis. The intersection model including communication protocols and crash detection are stated. Afterwards, the intersection management algorithm is explained. The total delay time, energy loss and combined cost functions are given. Finally, simulation environment is explained and results of case studies are discussed.
Slip-slide control system for railway vehicles
In railway transportation, braking and traction forces mainly depend on normal force and adhesion coefficient between wheel and rail. Regarding the restrictions on controlling normal force, maximization of adhesion coefficient seems to be the only way of increasing braking and tractive efforts. Moreover, efficient utilization of adhesion can also reduce operating costs with avoiding early wheel and rail damages and minimizing trip time. On the other hand, adhesion between the rail and the wheel is a highly dynamic function of many parameters such as environmental conditions, speed and slip ratio. The aim of this thesis is construction of a slip - slide control scheme which maximizes adhesion utilization in addition to avoid excessive situations resulting in component failures. Two different control approaches are proposed in the scope of this thesis. The first method relies on an Event Based Slip - Slide Control Scheme. In this approach, the excessive slip - slide situations are detected with wheel acceleration information which is derived from the measured wheel speed. If the wheel acceleration is higher than the predefined threshold that is chosen considering the maximum possible/permissible acceleration/deceleration of the vehicle, the controller takes action and decreases the magnitude of the reference motor torque in order to return the adhesion status back to the micro - slip area. During such a recovery mode, the phase shift between the input and the output of the traction system is observed using the orthogonal correlation method to accelerate the proposed control strategy by determining the adhesion status in advance. Then, the controller tries to maximize adhesion utilization by holding the phase shift value between the predefined upper and lower limits. Finally, the control action is terminated as soon as the braking/tractive effort fulfills the driver request due to recuperation on road conditions. The developed Event Based Slip - Slide Control Method forms the desired phase shift area with constant borders (upper and lower limits) for all possible vehicle velocities. Although the optimal lower limit of the desired phase shift area does not show any noticeable change with the varying vehicle velocity, using a constant value for the upper limit restricts the performance of the slip - slide control system since the adhesion formation process is largely affected by the vehicle velocity. The second slip - slide control system proposed in the scope of this thesis is an alternative form of the Event Based Slip - Slide Control System which uses adaptive upper limit for the desired phase shift area with respect to the vehicle velocity in order to improve adhesion utilization. Two different benchmark approaches which are Disturbance Observer Based Control and Direct PD Control of Phase Shift are tested with the proposed methods under different driving scenarios and adhesion conditions. The adhesion utilization of an Optimal Controller which has an access to both accurate vehicle velocity and friction coefficient is used as a reference performance criterion. The test results show that both the proposed Adaptive and Event Based Slip - Slide Control Systems provide rapid response to quickly changing adhesion conditions and driver requests while maximizing the braking/tractive effort even in poor adhesion conditions. In addition to their better performances in adhesion utilization, the proposed control schemes do not need the calculated wheel acceleration during the control phase and the possible stability problem of the Disturbance Observer Based Controller is prevented. What is more, the proposed controllers react extremely fast to the recuperated road conditions unlike the Disturbance Observer Based Controller, since the adhesion status is continuously estimated during the control phase using the observed phase shift information. Last but not least, the proposed approaches do not necessitate the persistent stimulation of the traction system as it is needed in the Direct Phase Shift Control method which might cause early damages in the traction system components. However, it is also shown that the adaptive form of the proposed method increases the adhesion utilization compared to the conventional one by using the phase shift information more efficiently.