Optimization of Type-2 Fuzzy Logic Controller Design Using the GSO and FA Algorithms

This paper presents a practical implementation of an interval type-2 fuzzy logic controller for two stages photovoltaic system consisting of DC- DC boost converter and three-phase inverter. The power converter circuits are nonlinear and have uncertainties. These uncertainties cause noise and delay in the response of power systems. A photovoltaic system has also uncertainties caused by itself. The change in temperature and irradiation cause the change in parameters of photovoltaic systems. Conventional controllers and type-1 fuzzy controllers can’t overcome uncertainties. The main objective of this study is to show the superiority of interval type-2 fuzzy logic controller to overcome the uncertainties. Interval type-2 fuzzy logic controller algorithm was developed for DC- DC boost converter and three-phase space vector modulated inverter. To make comparison, the system was controlled by a type-1 and an interval type-2 fuzzy controller respectively. Simulation studies and real time application were performed. Settling time, overshoot and ripple voltage were investigated for the boost converter. Current and voltage harmonic analysis, frequency and phase angle data were analyzed for three-phase inverter. According to the simulation results and the practical results, interval type-2 fuzzy logic controller offered better solution for the whole system.

Fuzzy controllers and fuzzy sliding-mode controllers have found extensive use in a variety of applications. Generally, type-1 fuzzy sets are used for the membership functions of these controllers. However, in real-time applications, uncertainty associated with the available information always occurs. A type-2 fuzzy controller and a type-2 fuzzy sliding-mode controller are proposed that are able to solve the problem that the words used in the inference rules can mean different things to different people. Since the membership functions use type-2 fuzzy sets then, the proposed control schemes can handle the rule uncertainties when the operation is extremely uncertain and/or the membership grades cannot be exactly determined. The proposed control systems are applied to control a buck DC–DC converter. A comparison between a PI controller, a type-2 fuzzy controller and a type-2 fuzzy sliding-mode controller is made. The experimental results show that the type-2 fuzzy sliding-mode controller achieves the best control performance.

Fuzzy logic control based on the Takagi–Sugeno inference method has been applied for the yeast alcoholic fermentation running in a continuous-time biochemical reactor in this paper. A type-1 fuzzy PID controller was designed to temperature control in a biochemical reactor. The fuzzy PID controller was also designed using type-2 fuzzy sets. The advantage of the fuzzy control is that it can be used very successfully for control of strongly non-linear processes and processes that are difficult to model because of complicated reaction kinetics. Obtained simulation results confirm this fact. The disadvantage of the fuzzy control design lies in the time-consuming tuning of controllers. The subtractive clustering method was used to identify the rule base. This approach was chosen to minimize the number of rules of the designed fuzzy logic controllers and to simplify the fuzzy controller design. Simulation results confirm that fuzzy PID controllers can assure better performance than conventional PID controllers. Yeast alcoholic fermentation is an exothermic process and the cooling is necessary to maintain the optimal temperature in the reactor. Fuzzy PID control reduces coolant consumption in comparison with conventional PID control and so it assures energy-efficient control of continuous-time alcoholic fermentation. Using type-2 fuzzy sets in the fuzzy PID controller design is very promising as the type-2 fuzzy controller offers even better results than the type-1 fuzzy controller.

A new optimum interval type-2 fuzzy fractional-order controller for a class of nonlinear systems with incipient actuator and system component faults is introduced in this study. The faults of the actuator and system component (leak) are taken into account using an additive model. The Interval Type-2 Fuzzy Sets (IT2FS) is used to design an optimal fuzzy fractional order controller, and two different nature inspired metaheuristic algorithms, Follower Pollination Algorithm (FPA) and Genetic Algorithm (GA), are used to optimize the parameters of the fuzzy PID controller and Interval Type-2 Fuzzy Tilt-Integral-Derivative Controller (IT2FTID) for nonlinear system. The suggested control approach consists of two parts: an Interval Type-2 Fuzzy Logic Controller (IT2FLC) controller and a fractional order TID controller. Additionally, the two inputs of the IT2FLC are also calibrated using two fine tuning parameters and , respectively. The stability of the proposed controller is presented with some conditions. In addition to unknown dynamics, some unknown process disturbances, such as rapid changes in the control variable, are taken into account to check the efficacy of the proposed control scheme. Two nonlinear conical two-tank level systems are used in the simulation as a case study. The performance of the suggested approach is also compared to that of a widely recognized Interval Type-2 Fuzzy Proportional-Integral-Derivative (IT2FPID) Controller. Finally, the proposed control scheme's fault-tolerant behaviour is demonstrated using fault-recovery time results and statistical Z-tests for both controllers, and the proposed IT2FTID controller's effectiveness is demonstrated when compared to IT2FPID and existing passive fault tolerant controllers in recent literature.

Fuzzy logic (FL) has been regarded as a useful methodology in modelling. The modeling performance of FL heavily relies on the modeling capability of a fuzzy set (FS). However, the MF of a FS cannot be arbitrarily accurate in practice and thus the centroid as a measure of a FS cannot be accurate to any degree. In face of inaccurate MF, the sensitivity of the centroid of a FS to the deviation of its MF from the ideal MF determines the accuracy of the centroid. To evaluate the modeling capability of a type-1 (T1) FS and an interval type-2 (IT2) FS, this paper will present a comparative study of the sensitivity of the centroid of a T1 FS and an IT2 FS to the deviation of their MFs from the ideal MFs. In this paper, equations relating the amount that the centroid of a T1 FS and an IT2 FS vary with the deviation of their MFs from the ideal MFs were established. Based on the derived equations, it was found that an IT2 FS is able to provide an additional design freedom to vary the sensitivity of its centroid compared to a T1 FS. This unique characteristic may enable an IT2 FS to minimize the sensitivity of the centroid and thus to achieve higher modeling accuracy. Furthermore, guidelines for designing an IT2 FS were provided.

In the past several years, research results on type- 2 fuzzy control have started to emerge in the literature. None of them, however, are concerned with mathematical input-output relationship of a type-2 fuzzy controller. Establishing such relationship is important as it will deepen our understanding of type- 2 fuzzy controller structures, how they function, and their advantages and drawbacks as compared to type-1 fuzzy controllers and conventional controllers (e.g., the PID controller). The availability of such structure will also lay a foundation for more rigorous theoretical analysis and design of type-2 fuzzy control systems. In this paper, we derive the mathematical input-output relation of a type-2 fuzzy PD (or PI) controller that has one of the simplest possible configurations - only two interval type-2 fuzzy sets for each input variables, four fuzzy rules with Zadeh AND operator, and four interval type-2 output fuzzy sets. We relate the resulting structure to conventional control theory and show that it actually is a PD (or PI) controller with the proportional and derivative (or integral) gains changing as the input variable values vary.

Fuzzy set theory is particularly appropriate approach when data include imprecise. Type-2 fuzzy set theory captures ambiguity that associates the uncertainty of membership functions by incorporating footprints and models high level uncertainty. If the quality characteristic is a binary classification into conforming/non-conforming of product, this decision depends on human subjectivity that have ambiguity or vague. In this situation, monitoring the process with statistical control charts based on interval type-2 fuzzy sets, a special case of type-2 fuzzy sets, is more suitable due to the human imprecise judgments on quality characteristics. In this paper, interval type-2 fuzzy p-control chart is developed into the literature for the first time. Due to the interval type-2 fuzzy sets modelled more uncertainty for defining membership functions, in this paper interval type-2 fuzzy fraction nonconforming numbers used for handling more uncertainty in process. Real word application is implemented with developed fuzzy control chart.

Altitude control of a quadcopter using interval type-2 fuzzy controller with dynamic footprint of uncertainty

Compared with type-2 fuzzy sets, the secondary membership degree of interval type-3 fuzzy sets is an interval rather than crisp value, which makes interval type-3 fuzzy sets can obtain more degree of freedoms. This article studies an interval type-3 fuzzy PID controller based on interval type-3 fuzz sets. The framework of interval type-3 fuzzy PID controller is identical with type-2 fuzzy PID controller, but it contains more adjustment controller parameters and its type reduction procedure is more complex. In this paper, type reduction of interval type-3 fuzzy sets is derived from general type-2 fuzzy sets represented by α-plane and a direct NT type reduction algorithm is applied. The control effects of interval type-3 fuzzy PID controller are firstly tested by 2 nonlinear plants, the simulation results show that interval type-3 fuzzy PID controller has better control performance indexes than PID controller, type-1 fuzzy PID controller, interval type-2 fuzzy PID controller and general type-2 fuzzy PID controller. Furthermore, the interval type-3 fuzzy PID controller will be applied in rated voltage control of solid oxide fuel cells (SOFC) power plant. The output voltage control of SOFC is quite challenging because of the strong nonlinearity, limited fuel flow, and rapid variation of the load disturbance. The simulation results demonstrate the advantages and robustness of proposed interval type-3 fuzzy PID controller.

Gestures of a person symbolizing analogous pathological disorder are not always exclusive. Naturally, the gestural features of a subject suffering from the same pathological disorder vary widely over different instances. In presence of two or more gestural features, the variation of the attributes together makes the problem of pathological disorder recognition more convoluted. Wider variance in gestural features is the main source of uncertainty in the pathological disorder recognition, which has been addressed here using type-2 fuzzy sets (T2FSs). First, a type-2 fuzzy gesture space is created with the background knowledge of gestural features of different subjects for different pathological disorders. Second, the pathological disorder of an unknown gestural expression is recognized based on the consensus of the measured gestural features of the fuzzy gesture space. A fusion of interval and general type-2 Fuzzy Sets has been used to construct the fuzzy gestural space. An interval valued fuzzy set (IVFS) or interval type-2 fuzzy set (IT2FS) is constructed with primary membership functions for M gestural features obtained from N subjects, each having L instances of gestural expressions for a given pathological disorder. The corresponding general type-2 fuzzy set (GT2FS) includes the secondary memberships for individual primary upper and lower membership curves in the respective IVFS. The secondary membership of a given source, characterizing the reliability in its primary membership assignment, is determined based on the amalgamated knowledge of all the subjects’ primary membership functions. The representatives of each pathological disorder class are then evaluated by utilizing the attractive features of both IVFS and GT2FS. The pathological disorder of an unknown gestural expression is finally determined by identifying its minimal discrepancy with the existing class representatives. The adopted T2FS-based uncertainty management strategy, when applied to gender independent training and testing datasets, results in a classification accuracy of 93.41%.

This paper introduces the analytical structure of a class of interval type-2 (IT2) fuzzy PD and PI controllers that have symmetrical rule base. Two assumptions are made: (1) Zadeh AND operator is employed as the t-norm operator; (2) the centroid type-reduction method is used. The main contribution of this paper is the analytical relationship between the inputs and output of this IT2 fuzzy controller. Comparing with its T1 counterpart, the addition of two FOU parameters generated 31 extra local regions that each provides a unique relationship between the inputs and output signals. The relatively large number of local regions that results, at the cost of two extra design parameters, means that an IT2 fuzzy controller has the potential to provide better performance. Another outcome is the analysis of the centroid type-reduction algorithm yielded closed form expressions for each partition. This result may provide a platform for further theoretical study.

In this study, we will present the novel application of Type-2 (T2) fuzzy control into the popular video game called flappy bird. To the best of our knowledge, our work is the first deployment of the T2 fuzzy control into the computer games research area. We will propose a novel T2 fuzzified flappy bird control system that transforms the obstacle avoidance problem of the game logic into the reference tracking control problem. The presented T2 fuzzy control structure is composed of two important blocks which are the reference generator and Single Input Interval T2 Fuzzy Logic Controller (SIT2-FLC). The reference generator is the mechanism which uses the bird's position and the pipes' positions to generate an appropriate reference signal to be tracked. Thus, a conventional fuzzy feedback control system can be defined. The generated reference signal is tracked via the presented SIT2-FLC that can be easily tuned while also provides a certain degree of robustness to system. We will investigate the performance of the proposed T2 fuzzified flappy bird control system by providing comparative simulation results and also experimental results performed in the game environment. It will be shown that the proposed T2 fuzzified flappy bird control system results with a satisfactory performance both in the framework of fuzzy control and computer games. We believe that this first attempt of the employment of T2-FLCs in games will be an important step for a wider deployment of T2-FLCs in the research area of computer games.

A type-2 fuzzy set, which is characterized by a fuzzy membership function, involves more uncertainties than the type-1 fuzzy set. As the most widely used type-2 fuzzy set, interval type-2 fuzzy set is a very useful tool to model the uncertainty in the process of decision making. As a special case of interval type-2 fuzzy set, trapezoidal interval type-2 fuzzy set can express linguistic assessments by transforming them into numerical variables objectively. The aim of this paper is to investigate the multiple attribute group decision-making problems in which the attribute values and the weights take the form of trapezoidal interval type-2 fuzzy sets. First, we introduce the concept of trapezoidal interval type-2 fuzzy sets and some arithmetic operations between them. Then, we develop several trapezoidal interval type-2 fuzzy aggregation operators for aggregating trapezoidal interval type-2 fuzzy sets and examine several useful properties of the developed operators. Furthermore, based on the proposed operators, we develop two approaches to multiple attribute group decision making with linguistic information. Finally, a practical example is given to illustrate the feasibility and effectiveness of the developed approach.

This chapter formally introduces type-1 fuzzy sets and fuzzy logic. It is the backbone for Chap. 3 and provides the foundation upon which type-2 fuzzy sets and systems are built in later chapters. Its coverage includes: crisp sets, type-1 fuzzy sets and associated concepts [including a short biography of Prof. Zadeh (the father of fuzzy sets and fuzzy logic)], type-1 fuzzy set defined, linguistic variables, returning to linguistic variables from a numerical value of a membership function, set theoretic operations for crisp and type-1 fuzzy sets, crisp and fuzzy relations and compositionson the same or different product spaces , compositions of a type-1 fuzzy set with a type-1 fuzzy relation, hedges, the Extension Principle (which is about functions of fuzzy sets), α-cuts (which are a powerful way to represent a type-1 fuzzy set in terms of intervals), functions of type-1 fuzzy sets computed by using α-cuts, multivariable membership functions and Cartesian products, crisp logic, going from crisp logic to fuzzy logic, Mamdani (engineering) implications, some final remarks, and an appendix about properties/laws of type-1 fuzzy sets. 35 examples are used to illustrate this chapter’s important concepts.

The main purpose of this research was to introduce a classification method, which combines a rule induction procedure with the Takagi–Sugeno inference model. This proposal is a continuation of our previous research, in which a classification process based on interval type-2 fuzzy rule induction was introduced. The research goal was to verify if the Mamdani fuzzy inference used in our previous research could be replaced with the first-order Takagi–Sugeno inference system. In the both cases to induce fuzzy rules, a new concept of a fuzzy information system was defined in order to deal with interval type-2 fuzzy sets. Additionally, the introduced rule induction assumes an optimization procedure concerning the footprint of uncertainty of the considered type-2 fuzzy sets. A key point in the concept proposed is the generalization of the fuzzy information systems’ attribute information to handle uncertainty, which occurs in real data. For experimental purposes, the classification method was tested on different classification benchmark data and very promising results were achieved. For the data sets: Breast Cancer Data, Breast Cancer Wisconsin, Data Banknote Authentication, HTRU 2 and Ionosphere, the following F-scores were achieved, respectively: 97.6%, 96%, 100%, 87.8%, and 89.4%. The results proved the possibility of applying the Takagi–Sugeno model in the classification concept. The model parameters were optimized using an evolutionary strategy.