Type-2 fuzzy controller design using a sliding-mode approach for application to DC–DC converters

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.

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.

Cascade fuzzy control of a tubular chemical reactor

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.

Type-1 fuzzy PID controllers are widely used in industrial control systems due to their well-established theoretical foundation, simplicity of structure, and ease of operation. However, as control systems become increasingly complex and demands for higher control performance intensify, the limitations of Type-1 fuzzy controllers become more apparent. Additionally, the difficulty in tuning PID parameters and the inability to adjust these parameters online as the controlled system changes further constrain the effectiveness of traditional PID controllers. To address these challenges, this paper introduces a generalized Type-2 fuzzy logic control approach. The generalized Type-2 fuzzy controller extends the capabilities of interval Type-2 fuzzy controllers, offering enhanced ability to handle higher-order uncertainties. Moreover, the integration of memristor devices enables online adaptive tuning of controller parameters. By combining the generalized Type-2 fuzzy logic with memristor-based PID control, a novel memristor-based controller was designed, which allows for real-time adaptive adjustment of the controller parameters. Theoretical analysis is followed by simulations and experimental validation. The results demonstrate that the proposed memristor-based controller with generalized Type-2 fuzzy logic exhibits superior robustness. Specifically, when evaluated using the Integral of Time-weighted Absolute Error (ITAE) performance index, the controller achieves improvements of 65.9% and 40.2% compared to traditional PID and Type-1 fuzzy PID controllers, respectively. These findings confirm the excellent tracking performance and robustness of the proposed control system.

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.

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.

This paper presents a comparative study between the firefly algorithm (FA) and the galactic swarm optimization (GSO) method, where the performance of both methods is observed and tested in the optimization of a fuzzy controller for path tracking of an autonomous mobile robot. The main contribution of this work is finding the best method that generates an optimal vector of values for the membership function optimization of the fuzzy controller. This with the goal of improving the performance of the controller and thus the trajectory generated by the autonomous robot is closer to the desired trajectory. It should be noted that the fuzzy controller that is optimized is an interval type-2 fuzzy controller, which has a greater capability for managing uncertainty than a type-1 fuzzy controller. In this case, the limiting membership functions in the interval type-2 fuzzy sets are themselves type-1 fuzzy sets that define the footprint of uncertainty. Type-2 fuzzy controllers have been shown in previous works to handle better the control of robotic systems under noisy and dynamic conditions and this is why their optimal design is very important. Simulation results show that GSO outperforms FA in the optimal design of interval type-2 fuzzy controllers.

In this paper mathematical models of Mamdani type fuzzy PI or PD controllers via Center of Gravity (CoG) defuzzification are obtained. These controllers are called the simplest fuzzy PI or PD controllers as minimal number of fuzzy sets (two fuzzy sets on each of the two-input variables and three fuzzy sets on the output variable) are employed. The basic components of these models are L-type and Y-type membership functions on each input variable, trapezoidal or triangular membership functions on output variable, minimum / algebraic product t-norm, maximum OR operator, three linear fuzzy control rules, minimum / algebraic product inference and CoG defuzzification. Mathematical models of fuzzy controller via CoG defuzzification were not reported in the literature and are therefore presented for the first time in this paper.

In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively. The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed. The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances.

Photovoltaic (PV) is one of the renewable sources of energy which is used widely in industry and distribution companies consumers. Nonlinear behavior of photovoltaic panels and their output power dependency on the atmospheric conditions motivate researchers to focus on extracting maximum available power from PV panels in order to reduce the cost and maximize the efficiency. In other words, output power of PV panel is dependent on I-P and V-P characteristics and every irradiation and surface temperature of PV. Therefore, maximum power point tracking requires to be addressed to reduce transient time, power fluctuations and increase the efficiency. This is realized by controlling switching elements in DC-DC boost convertor transferring energy from PV panel to the load. This paper presents a new method in maximum power point tracking (MPPT) of PV system based on fuzzy type-2 controller, and also compares its performance with MPPT of fuzzy logic controller type one (FLC1). The PV system composed of a PV panel, DC-DC boost convertor, FLC unit and a DC load, is simulated in Matlab /Simulink. Also, experimental tests have been done for validation. Finally, the simulation results reveal that the FLC2 has better performance in providing MPPT.

The paper describes the development of two different type-2 adaptive fuzzy logic controllers and their use for the control of a non linear system that is characterized by the presence of bifurcations and parameter uncertainty. Although a type-2 fuzzy logic controller is able to handle the non linearities and the uncertainties present in a system, its robustness and effectiveness can be increased by the use of an opportune adaptive algorithm. A simulation study was conducted to compare the behavior of adaptive controllers with that of simple type-1 and type-2 fuzzy logic controllers. The system to be controlled, used for the simulation, is a continuous bioreactor for the treatment of mixed wastes in which a culture of Pseudomonas Putida is carried out while phenol and glucose are carbon and energy sources. From simulations results it can be seen that both adaptive controllers, but in particular the self tuning controller, have a better performance being able to eliminate oscillations that are present with basic fuzzy controllers.

Hybrid fuzzy control for the goethite process in zinc production plant combining type-1 and type-2 fuzzy logics

The interval type-2 fuzzy Proportional-Integral (PI) controller (IT2-FPI) might be able to handle high levels of uncertainties to produce a satisfactory control performance, which could be potentially due to the robust performance as a result of the smoother control surface around the steady state. However, the transient state and disturbance rejection performance of the IT2-FPI may degrade in comparison with the type-1 fuzzy PI (T1-FPI) counterpart. This drawback can be resolved via general type-2 fuzzy PI controllers which can provide a tradeoff between the robust control performance of the IT2-FPI and the acceptable transient and disturbance rejection performance of the type-1 PI controllers. In this paper, we will present a zSlices-based general type-2 fuzzy PI controller (zT2-FPI), where the secondary membership functions (SMFs) of the antecedent general type-2 fuzzy sets are adjusted in an online manner. We will examine the effect of the SMF on the closed-system control performance to investigate their induced performance improvements. This paper will focus on the case followed in conventional or self-tuning fuzzy controller design strategies, where the aim is to decrease the integral action sufficiently around the steady state to have robust system performance against noises and parameter variations. The zSlices approach will give the opportunity to construct the zT2-FPI controller as a collection of IT2-FPI and T1-FPI controllers. We will present a new way to design a zT2-FPI controller based on a single tuning parameter where the features of T1-FPI (speed) and IT2-FPI (robustness) are combined without increasing the computational complexity much when compared with the IT2-FPI structure. This will allow the proposed zT2-FPI controller to achieve the desired transient state response and provide an efficient disturbance rejection and robust control performance. We will present several simulation studies on benchmark systems, in addition to real-world experiments that were performed using the PIONEER 3-DX mobile robot that will act as a platform to evaluate the proposed systems. The results will show that the control performance of the self-tuning zT2-FPI control structure enhances both the transient state and disturbance rejection performances when compared with the type-1 and IT2-FPI counterparts. In addition, the self-tuning zT2-FPI is more robust to disturbances, noise, and uncertainties when compared with the type-1 and interval type-2 fuzzy counterparts.

in this paper, we use an interval type-2 fuzzy logic system integrated with sliding mode control for synchronization of two different chaotic systems in presence of system unmodeling and external disturbances. To reduce the chattering and improve the robustness of reaching phase of the sliding mode control (SMC) an interval type-2 fuzzy logic controller is used. In addition, an adaptive interval type-2 fuzzy approximator is proposed (as equivalent control part of SMC) to approximate the unknown parts of the uncertain chaotic systems. Using type-2 fuzzy systems makes more effective synchronization results in presence of system uncertainty and disturbances in comparison with type-1 fuzzy systems. The stability analysis for the proposed control scheme is provided and simulation results compare the performance of proposed interval type-2 fuzzy controller with type-1 fuzzy controllers to verify the effectiveness of the proposed method.