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Model Öngörülü Kontrol (Model, Predictive Control, MPC), günümüzde endüstriyel sistemlerden gıdaya, ilaçtan petrole, tarımdan lojistiğe, finanstan sağlığa kadar hemen hemen her alanda kullanılabilmektedir. Bu tez çalışmasındaki temel amaç, yaygın bir kullanım alanına sahip olan MPC performanslarının arttırılmasına yönelik olarak, içerisine yapılacak yeni eklentiler yolu ile yeni algoritmalar önerilmesidir. Bu doğrultuda hazırlanan tez çalışmasında, MPC yöntemi, literatürde yaygın olan metasezgisel algoritmalar ve bunun yanı sıra yapay sinir ağları tanıtılmış ve çalışma mantıkları açıklanmıştır. Ardından metasezgisel algoritmalarda kullanılacak olan kaos bilimi üzerine yoğunlaşılmıştır. Spesifik olarak, kesirli dereceden bir kaotik sistem ele alınmış ve ilgili sistemin analizi ve kontrolü gerçekleştirilmiştir. Tez çalışmasının devamında, metasezgisel algoritmalar içerisinde kaotik haritaların kullanılması veya farklı metasezgisel algoritmaların birbirleri ile hibritleştirilme çalışmaları gerçekleştirilmiştir. Önerilen yeni algoritmalar, literatürde yaygın olan benchmark problemler üzerinde test edilmiş ve performansları istatistiksel olarak karşılaştırılmıştır. Sonuçlardaki istatistiksel güvenilirlik için, Wilxocon ve Friedman Analizleri kullanılarak, elde edilen analiz sonuçları karşılaştırılmış ve yorumlanmıştır.
Tez çalışmasının son kısmında Otomatik Voltaj Regülatör (Automatic Voltaj Regulator, AVR) Sistemi ele alınarak, MPC yöntemi üzerine yoğunlaşılmıştır. Denetlenen AVR sisteminin sonuçları, tablolarda verilmiş ve yorumlanmıştır. Yapılan çalışmalarda, MPC'de kullanılan algoritmalardaki hesaplama sürelerinin, örnekleme zamanını aştığı görülmüştür. Bu sorunun üstesinden gelebilmek için AVR sisteminin, LSTM ile kontrol edilmesi gerçekleştirilmiştir. Bunun yanı sıra, MPC için kontrol işaretini destekleyici ileri komut denetleyici ve PI denetleyici gibi yapılar önerilmiştir. Bu yapılar AVR üzerinde test edilmiş ve sonuçları karşılaştırılarak yorumlanmıştır.
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Model Predictive Control (MPC) can be used in almost every field, from industrial systems to food, from pharmaceuticals to petroleum, from agriculture to communications, from logistics to finance and health. In MPC, using the system model, it is a controller that determines the control rule that should be applied to the system along a certain precdiction horizon. The control rule is optimized according to an objective function that includes the future states of the system and is calculated at each sampling time. The aim of this thesis is to use metaheuristic optimization techniques that have become popular recently to increase the performance of MPC and to make different additions to the structure of the MPC method to increase its performance.
The use of classical optimization techniques used in MPC causes the suboptimal solution to be produced. The reason for this is that when classical optimization techniques are used in constrained problems with more than one local minimum, the solution is still a minimum but still a local solution. However, metaheuristic algorithms are successful algorithms with higher performance that have the ability to produce solutions globally for problems with more than one local minimum. In this direction, in the literature of the thesis, firstly MPC, metaheuristic algorithms and then the researches on chaos theory, which is the subject of the thesis, were examined.
Classes and formulations of optimization problems that are still used since Chinese history are given. Then, the mathematical backgrounds and flowcharts of various metaheuristic algorithms, which have become a popular topic in recent years, are tried to be given. Following this, the basis, theory, advantages and disadvantages of MPC used in the industry are given. After these two different bases are given, it is explained that metaheuristic algorithms can be used in MPC. Since another subject used in the thesis study is Artificial Neural Networks, information about the definition, theory, properties, types, and usage areas of Artificial Neural Networks is given. Then, the main background of the use of Artificial Neural Networks with MPC is mentioned.
As a result of the studies on the use of chaos science in metaheuristic algorithms, fractional order chaotic systems have also been examined. Therefore, different fractional derivative and integral structures are introduced in the thesis. Then, the analysis of a fractional chaotic system was carried out. The analysis of the chaotic state of the fractional chaotic system is carried out in detail on the Bifurcation diagrams, Phase portraits, Lyapunov exponents. Then, the sliding mode controller design, which is a controller that allows the system to be controlled by changing the fractional order of the chaotic system from fractional order, was carried out. It has been seen that the system can be successfully controlled at different fraction levels with the sliding mode controller.
In the continuation of the thesis, hybridization studies were carried out by using chaotic systems on metaheuristic algorithms and utilizing the strengths of different metaheuristic algorithms. In particular, the main purpose of proposing new algorithms is to better find the global minimum value of new algorithms between global and local solutions. The proposed new algorithms have been tested on difficult to solve, complex and multivariate, continuous and/or discontinuous, linear and/or nonlinear benchmark problems that are widely used in the literature. After these analyzes were performed, statistical values such as minimum, expected value and standard deviation of the obtained results were calculated. The results obtained were given in tables and graphs, and the results were evaluated and interpreted. In addition, Wilxocon and Friedman Analyzes, one of the statistical reliability tests, were used to determine whether there were statistically significant differences in the results used in the thesis. The obtained analysis results were compared and interpreted.
In the last part of the thesis, Automatic Voltage Regulator System (AVR), which is an electrical system, is considered and concentrated on the MPC method. Constrained optimization is performed in MPC. Therefore, in the optimization process performed in MPC, metaheuristic algorithms are used because they have the ability to find global solutions better . While the AVR system was controlled by MPC, different prediction and control horizon values of MPC and different swarm numbers and maximum iteration numbers of metaheuristic algorithms were used. While evaluating the results of the algorithms, during the simulation period of the controlled AVR system, the minimum objective criteria values, the minimum objective criteria value generation numbers, ISE values and the minimum computation times for generating the control signal during the optimization and the number of situations for generating the control signal in the least time between them are given in the tables. The results were examined depending on each parameter, and a summary table was given where all the results were evaluated together. In this table, it was seen that the metaheuristic algorithms proposed within the scope of the thesis produced more successful results.
It has been observed that the time required to generate the optimal control signal exceeds the sampling time, since the metaheuristic algorithms used in MPC have high calculation burdens. A dataset was created to overcome this problem. By training this dataset with the LSTM structure, the AVR system was controlled with LSTM. It has been observed that the obtained results are similar in terms of ISE values, but the processing time is accelerated with LSTM and the system becomes real-time applicable. In addition, there may be situations in which a sudden change of the reference sign in MPC causes the control sign to not change rapidly for various reasons. Therefore, an advanced command controller has been proposed to support the control signal of the system when the reference sign of the system changes abruptly. This proposed structure is implemented over AVR. The results were compared and it was seen that the system approached the reference signal faster. Finally, by adding a PI controller to the MPC controller structure, the system is controlled by MPC, which is optimized by using metaheuristic algorithms. While the control signal to be applied to the system is generated from the PI controller, the parameters of the PI controller, which controls the dynamics of the system, are controlled by the MPC throughout the prediction horizon. The proposed structure is named PI MPC. However, the proposed structure did not depict the desired performance and a control signal was added to support PI controller. This proposed structure is named PI+U MPC. It has been observed that the proposed PI+U MPC structure performs better for the AVR system than plain MPC and PI MPC. |
