Bulanık PID kontrolörlerinin çıkış üyelik fonksiyonlarını çevrimiçi ayarlanma yöntemi
On-line adjustment of the output membership functions of fuzzy PID controllers
Yazar: MEHMET DELİBAŞ
Danışman: PROF. DR. MÜJDE GÜZELKAYA
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Kontrol ve Otomasyon Mühendisliği Ana Bilim Dalı / Kontrol ve Otomasyon Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2022
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering
Dizin: Adaptif denetim = Adaptive control ; Bulanık denetim = Fuzzy control ; PID denetleme = PID control

Özet:
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.

Abstract:
The fuzzy set theory developed by Lotfi Zadeh in 1965 adds uncertainty to classical logic. Thus, it facilitates the solution of many uncertain problems that we encounter in life. Fuzzy set logic was first applied in the control field by Mamdani and Assilian in 1975. In the following years, it has become a very important field of study by researchers. 
Most of the real systems own high order, time delays, nonlinearities, or unsatisfactory mathematical models. Conventional PID controllers are usually not effective for these real-time systems because of their linear structures. Therefore, fuzzy logic is extensively used in processes where system dynamics are very complex or exhibit a non-linear character. In this respect, fuzzy logic has been combined with PID controller designs in order to improve the control system performance. In literature, we see various PID controller types in which fuzzy logic is used. In some of them, only the gains of the conventional PID controller are tuned using fuzzy inference. The controllers that are constructed as a set of heuristic control rules, and the control signal is directly deduced from the knowledge base are referred to as fuzzy PID (FPID) controllers. The structures of these controllers are analogous to the conventional PID controllers from the input-output relationship point of view. 
The design parameters of fuzzy PID controllers can be divided into two categories: (a) tuning parameters, (b) structural parameters. The tuning parameters include input/output scaling factors and parameters of membership functions. The structural parameters of FPID controllers are input/output variables to fuzzy inference, fuzzy linguistic sets, membership functions, fuzzy rules, inference mechanism, and defuzzification mechanism. For the desired system performance, fixed scaling factor values may not be sufficient for the systems that own nonlinearities, parameter changes, and disturbances. Therefore, many tuning algorithms for the adjustment of scaling factors have been presented in the literature. For some cases scaling factor tuning algorithms may not be sufficient. Therefore, there exist some methods to tune the membership functions and fuzzy rules of the fuzzy controllers. In this respect, genetic algorithm and extended Kalman filter based methods have been used for membership function tuning of FPID controllers. The rule base structure has an important function in the performance of the fuzzy controllers. A rule base shifting method for dead-time systems is proposed. Moreover, there are methods to change the rule base structure by adjusting fuzzy rule weights. For this purpose, a method that adjusts rule weights using system error is presented. A fuzzy mechanism with normalized acceleration and system error inputs is also used to adjust the rule weights in an online manner. A fuzzy adjustment mechanism is also observed for tuning the centers of the output membership functions. 
In this thesis, firstly the error-based online rule weight adjustment method proposed in Karasakal et al. (2011) is discussed. In this study, the transient phase of the unit system response of the closed-loop system is considered. It is assumed that the transient phase of the control system step response is divided into a certain number of regions. Then, these regions are assigned in accordance with the number of membership functions defined for the error input of the fuzzy logic controller. As they create a symmetrical structure with respect to the reference signal, they are named as the approach and departure regions from the reference value. For each region, descriptive rules have been determined for obtaining the required control signal. The effect of the fuzzy rules used in obtaining the desired control signal in each region is determined and associated with the fuzzy rule weight variable. For the online adjustment of fuzzy rule weights, two simple functions of the absolute value of the system error variable are used. These functions possess a parameter. The value of this parameter is selected as "1" except one region. In the region where the error is large and the error variation is negative, it has been halved in order to prevent the system from accelerating. In this thesis, various values are given to this parameter and its effect on the system response is examined. 
Secondly, the multilevel fuzzy controller used in Xu and Shin (2005) is considered. In this paper, a multilevel fuzzy control system is proposed which can adaptively compensate the effects of external load disturbances and time-varying parameters. A fuzzy adjustment mechanism called "the output membership function adjustment mechanism" is used. The inputs of this mechanism are the error of the control system and the change of this error. The fuzzy adjustment mechanism has its own input and output membership functions and has a rule table. Its output is the "change value" that will set the center of the output membership function of the fuzzy controller. The type, number and linguistic variables of the input and output membership functions of the adjustment mechanism are the same as the type, number and linguistic variables of the input and output membership functions defined for the fuzzy controller for easy calculation purposes. When the purpose of the output membership function tuning mechanism is to reduce the overshoot and oscillation, we made the following analyzes: 
i)	Moving the center value of the membership function closer to the center slows down the system response. (So, the error converges to zero slowly). The maximum value of the control sign decreases. It reduces the oscillation and therefore the overshoot value. 
ii)	Decentralizing the center value of the membership function speeds up the system response. (So, the error converges to zero fast). The maximum value of the control sign increases. Overshoot and oscillation increase. 
The rule table of the mechanism determined in the original paper is 11x11. In our thesis, the size of the rule table of the adjustment mechanism is reduced to 5x5. Three different values are used in the table. These are "0", "1" and a free parameter "b". Different values are selected for the value "b" and the system performance over rise time, settling time and overshoot are investigated. 
Xu and Shin (2005) and Karasakal et al. (2011) are both on-line methods for adjusting the structural parameters of the fuzzy controller. One of them aims to change the center of the output membership functions, while the other aims to change the rule weights. In our thesis, we desire to make the online adjustment of two fuzzy controller design parameters simultaneously. In this respect, we propose to combine the methods in Xu and Shin (2005) and Karasakal et al. (2011)  and adjust the centers and rule weights of the output membership functions together in an online manner. The input membership functions defined for FPID are triangular membership functions and there are five in total. The output membership functions are singleton type membership functions. The design parameters of both methods are again analyzed for this combination. In order to observe the effect of the proposed method on the system responses and performance, it is compared with the traditional fuzzy PID controller, the fuzzy controller with the error-based fuzzy rule weighting method, and the fuzzy controller with the method based on the adjustment of the center of the output membership functions through simulation studies. For this purpose, linear and nonlinear systems models were used. Input and output scaling factors are kept the same for each simulation. Finally, when the system responses and performance results were compared, it is observed that the proposed method increases the system performance in certain time domain and optimal criteria respects.
The thesis was structured as follows: In Chapter 2, linguistic expressions and fuzzy system elements of fuzzy logic are explained. In Chapter 3, fuzzy PID controller structures are discussed. In Chapter 4, error-based fuzzy rule weighting method and the method based on adjusting the center of membership functions are explained, and freely selected parameters are analyzed by applying them on linear and non-linear systems. In Chapter 5, a method based on adjusting the center of output membership functions and fuzzy rule weights together is proposed, and the effect of the method on system response and performance is discussed on linear and nonlinear systems.