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ÖgeAnalysis and design of general type-2 fuzzy logic controllers(Fen Bilimleri Enstitüsü, 2020) Sakallı, Ahmet ; Kumbasar, Tufan ; 656903 ; Kontrol ve Otomasyon Mühendisliği Bilim DalıThis 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.