Interval Type-2 Fuzzy Controller Research Articles

Optimal fractional order interval type-2 fuzzy controller for upside-down asymmetric multilevel inverter based dynamic voltage restorer to accurately compensate faulty network voltage

Optimal fractional order interval type-2 fuzzy controller for upside-down asymmetric multilevel inverter based dynamic voltage restorer to accurately compensate faulty network voltage

Observer-Based Event-Triggered Control for Interval Type-2 Fuzzy Networked System With Network Attacks

This paper is focused on the adaptive event-based interval type-2 (IT-2) fuzzy security control problem for networked control systems with multiple network attacks. In order to save the network resources, this paper proposes an improved adaptive event-triggered model, which can adjust the threshold dynamically according to the change of current signal and previous triggering signal. In addition, due to the change of external environment, the impact of randomly occurring output bias is considered in the systems. Taking the effects of multiple network attacks and adaptive event-triggered scheme into consideration, a class of augmented error fuzzy system model is established. Next, some sufficient conditions are obtained for the stochastic stability with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance index via the Lyapunov stability analysis method. The corresponding paraments of the IT-2 fuzzy controllers and observers are also derived by some linear matrix inequalities (LMIs). Finally, two simulation examples are given to support the advantages of the proposed method.

Behavioral Analysis of an Interval Type-2 Fuzzy Controller Designed with Harmony Search Enhanced with Shadowed Type-2 Fuzzy Parameter Adaptation

The challenges we face in today’s world are increasingly complex, and effectively managing uncertainty when modeling control problems can yield significant benefits. However, the complexity of these models often leads to higher computational costs. Therefore, the main contribution of this article is the use of the theory of shadowed type-2 fuzzy sets to address these challenges and to control the search space exploration in the harmony search algorithm by employing two alpha planes, and with this, it was possible to reduce the computational cost and obtain effective results. Furthermore, the application of this approach aims to find optimal parameters for the membership functions of a type-2 fuzzy controller and analyze its behavior. By adopting the proposed methodology, it becomes possible to minimize computational costs while still achieving feasible solutions for interval type-2 control problems. A key aspect is that symmetry is considered in the design of the controller to also obtain good results. To validate the effectiveness of the approach, extensive simulations were conducted with varying levels of noise introduced to the type-2 controller. This comprehensive analysis allowed for a thorough examination of the results obtained. The findings of the simulations are presented, showcasing the advantages of the proposed methodology. By incorporating noise into the system, it was observed that the objective function, in this case, the root mean square error (RMSE), was reduced. Moreover, the signal obtained with the presence of noise demonstrated a superior performance compared to the noise-free reference. In conclusion, the proposed approach of utilizing shadowed type-2 fuzzy systems, combined with the harmony search algorithm, offers a promising solution for managing complex control problems. By carefully analyzing the behavior of the system through simulations, it is evident that the inclusion of noise helps improve the system’s performance.

Speed control of doubly fed induction motor using backstepping control with interval type-2 fuzzy controller

Speed control of doubly fed induction motor using backstepping control with interval type-2 fuzzy controller

Real-Time Interval Type-2 Fuzzy Control of an Unmanned Aerial Vehicle with Flexible Cable-Connected Payload

This study presents the design and real-time applications of an Interval Type-2 Fuzzy PID (IT2-FPID) control system on an unmanned aerial vehicle (UAV) with a flexible cable-connected payload in comparison to the PID and Type-1 Fuzzy PID (T1-FPID) counterparts. The IT2-FPID control has significant stability, disturbance rejection, and response time advantages. To prove and show these advantages, the DJI Tello, a commercial UAV, is used with a flexible cable-connected payload to test the robustness of PID, T1-FPID, and IT2-FPID controllers. First, the optimal coefficients of the compared controllers are found using the Big Bang–Big Crunch algorithm via the nonlinear UAV model without the payload. Second, once optimised, the controllers are tested using several scenarios, including disturbing the payload and the coverage path planning area to examine their robustness. Third, the controller performance results are evaluated according to reference achievement and point-based tracking under disturbances. Finally, the superiority of the IT2-FPID controller is shown via simulations and real-time experiments with a better overshoot, a faster settling time, and good properties of disturbance rejection compared with the PID and the T1-FPID controllers.

Structure Analysis of General Type-2 Fuzzy Controller and Its Application

In this paper, a general type-2 fuzzy controller is proposed. The proposed general type-2 fuzzy controller is based on α-plane representation, which converts the centroid of general type-2 fuzzy sets to centroids of several interval type-2 fuzzy sets. Also, the mathematical expression of general type-2 fuzzy controller is derived by fuzzy product operate and NT type reduction. By the mathematical expression, the relation between general type-2 fuzzy controller output with parameter of triangular secondary membership function is discussed. Finally, the control performances of proposed general type-2 fuzzy controller are compared with conventional PID controller, tradition type-1 fuzzy controller, and interval type-2 fuzzy controller. Furthermore, to show the effective and practical of the proposed controller, a nonlinear inverted pendulum system is tested. The simulation results show that general type-2 fuzzy controller achieves better control efforts than other compared controllers.

New results on [formula omitted] control for interval type-2 fuzzy singularly perturbed systems with fading channel: The weighted try-once-discard protocol case

This article deals with the interval type-2 (IT2) fuzzy model-based H∞ control problem for networked singularly perturbed systems (SPSs) under fading channel. To prevent data collision, a weighted try-once-discard (WTOD) communication scheme is adopted to adjust the communication sequence of sensor nodes. Based on this transmission strategy, only one sensor with more considerable difference is allowed to be transmitted at each time instant. On the other hand, a time-varying stochastic process model is introduced to describe the behavior of the fading channels in unreliable networks. Based on fading state signal and known bounds, the imperfectly matched membership functions (MFs) are reconstructed in the controller. Accordingly, under the effect of fading channels and WTOD protocol, a new IT2 fuzzy controller is constructed for the networked IT2 fuzzy SPSs. Meanwhile, by constructing a singular perturbation parameter (SPP) dependent Lyapunov function, sufficient conditions are established to guarantee the mean square stability of networked IT2 fuzzy SPSs, and the numerical stiffness issue is avoided. Finally, the practicability of the proposed methods is proved through a tunnel diode circuit simulation.

Interval type-2 Fuzzy control and stochastic modeling of COVID-19 spread based on vaccination and social distancing rates

Background and objectiveBesides efforts on vaccine discovery, robust and intuitive government policies could also significantly influence the pandemic state. However, such policies require realistic virus spread models, and the major works on COVID-19 to date have been only case-specific and use deterministic models. Additionally, when a disease affects large portions of the population, countries develop extensive infrastructures to contain the condition that should adapt continuously and extend the healthcare system's capabilities. An accurate mathematical model that reasonably addresses these complex treatment/population dynamics and their corresponding environmental uncertainties is necessary for making appropriate and robust strategic decisions. MethodsHere, we propose an interval type-2 fuzzy stochastic modeling and control strategy to deal with the realistic uncertainties of pandemics and manage the size of the infected population. For this purpose, we first modify a previously established COVID-19 model with definite parameters to a Stochastic SEIAR (S2EIAR) approach with uncertain parameters and variables. Next, we propose to use normalized inputs, rather than the usual parameter settings in the previous case-specific studies, hence offering a more generalized control structure. Furthermore, we examine the proposed genetic algorithm-optimized fuzzy system in two scenarios. The first scenario aims to keep infected cases below a certain threshold, while the second addresses the changing healthcare capacities. Finally, we examine the proposed controller on stochasticity and disturbance in parameters, population sizes, social distance, and vaccination rate. ResultsThe results show the robustness and efficiency of the proposed method in the presence of up to 1% noise and 50% disturbance in tracking the desired size of the infected population. The proposed method is compared to Proportional Derivative (PD), Proportional Integral Derivative (PID), and type-1 fuzzy controllers. In the first scenario, both fuzzy controllers perform more smoothly despite PD and PID controllers reaching a lower mean squared error (MSE). Meanwhile, the proposed controller outperforms PD, PID, and the type-1 fuzzy controller for the MSE and decision policies for the second scenario. ConclusionsThe proposed approach explains how we should decide on social distancing and vaccination rate policies during pandemics against the prevalent uncertainties in disease detection and reporting.

Interval type-2 fuzzy neural network-based adaptive compensation control for omni-directional mobile robot

Interval type-2 fuzzy neural network-based adaptive compensation control for omni-directional mobile robot

Robot Path Planning Based on Interval Type-2 Fuzzy Controller Optimized by an Improved Aquila Optimization Algorithm

Robot Path Planning Based on Interval Type-2 Fuzzy Controller Optimized by an Improved Aquila Optimization Algorithm

Membership function dependent stabilization of discrete time interval type-2 fuzzy systems with mixed actuator faults

This paper investigates the problem of mixed actuator failures for discrete-time interval type-2 (IT-2) fuzzy systems with time-varying delays and external disturbances. Applying the non-parallel compensation strategy, the IT-2 fuzzy controller is designed. Considering the nonlinear fault factors of actuator, the linear fault model is expanded, which is more general than the conventional mixed actuator failure model. The information of membership function is introduced by staircase function approximation. Based on Lyapunov stability theory and a series of matrix inequality scaling techniques, a membership function dependent stability criterion with H∞ performance is obtained. Then, the effectiveness of the proposed conclusion is verified by two simulation examples.

A class of general type-2 fuzzy controller based on adaptive alpha-plane for nonlinear systems

This study introduces a general type-2 Takagi–Sugeno–Kang fuzzy controller (GT2-TSKFC) for controlling uncertain systems. The proposed GT2-TSKFC uses equidistant type-2 triangular membership functions (MFs) for the antecedents, Larsen’s implication method, type-1 fuzzy sets for the consequent parameters, and a direct defuzzification method. The analytical structure of the proposed controller indicates that the alpha-plane and apex of the secondary MFs have a noticeable effect on calculating the control signal. Adaptation of the alpha-plane and apex of the secondary MFs is performed using the Lyapunov function to achieve the stability of the controlled system. The proposed controller is applied to an uncertain nonlinear inverted pendulum system. The results of the proposed control algorithm are compared with those of a general type-2 fuzzy controller with a specific number of alpha-planes, a quasi type-2 fuzzy controller, an interval type-2 fuzzy controller, and a type-1 fuzzy controller to demonstrate the robustness and effectiveness of the proposed scheme.

Influence of interval type-2 fuzzy control approach for a grid-interconnected doubly-fed induction generator driven by wind energy turbines in variable-speed system

This paper suggests a developed control technique using an interval type-2 fuzzy logic control (FLC) tuned PI for optimum torque adjustment for wind turbines operated by doubly fed induction generator (DFIG). The suggested control regulates the error of the mechanical rotor speed to enhance the performance of the torque and the output power results in the study system's overall performance improving. The suggested control combines the advantages of the two techniques: fast response of conventional PI control and adaptively properties of interval type-2 FLC. The studied system is a wind farm of 9 MW composed of 6 wind turbines of 1.5 MW each. Wind speed functions of several types are studied such as step change, extreme change, and constant high speed. The results indicate how the power and optimal torque have fast response with interval type-2 FLC tuned PI compared to the type-1 fuzzy tuned PI and conventional PI control. The simulated results deduce that the suggested interval type-2 FLC can enhance the wind energy system's stability and reliability in a better manner compared to the type-1 FLC and conventional PI.

Analytical Structure and Performance of Interval Type-2 Fuzzy Two-Term Controllers with Varying Footprint of Uncertainty

While type-2 fuzzy control has gained a lot of attention in the recent years, several challenges still remain with respect to controller design. The footprint of uncertainty (FoU) plays a very important role in designing type-2 fuzzy controllers, since the performance of type-2 fuzzy controllers largely depends on the choice of FoU. In this paper, we propose a simplified model of interval type-2 (IT2) fuzzy two-term controllers of Takagi–Sugeno (TS) type with only two rules in the rule base. The controller model is derived with varying FoUs based on only two type-2 input fuzzy sets (the simplest case). An extension to multiple input fuzzy sets is also presented. We investigate the variation in control surface and computational aspects of the IT2 fuzzy two-term controller as the FoU is varied. The performance of the proposed IT2 fuzzy controller with respect to varying FoUs is evaluated in the simulation study.

Finite-Time Dynamic Event-Triggered Fuzzy Output Fault-Tolerant Control for Interval Type-2 Fuzzy Systems

The finite-time dynamic event-triggered fuzzy output feedback fault-tolerant control problem is studied in this article for the interval type-2 (IT2) Takagi–Sugeno fuzzy system with parameter uncertainties and actuator faults. A fuzzy state observer is first developed to solve the immeasurable state problem. Second, by using the sampled estimating states and measured output signals, a dynamic event-triggered mechanism is formulated via integrating sensor-to-observer with observer-to-controller. Third, an observer-based finite-time event-triggered fuzzy fault-tolerant controller is synthesized via the nonparallel distribution compensation design principle. Consequently, the finite-time stable conditions of the addressed IT2 fuzzy system are established by constructing an appropriate Lyapunov function. Furthermore, an output feedback control design algorithm of solving control and observer gains is given in terms of the established sufficient finite-time stable conditions. Finally, a practical example of a nonlinear tunnel diode circuit system is provided to verify the effectiveness of the proposed IT2 fuzzy control scheme.

Shadowed Type-2 Fuzzy Sets in Dynamic Parameter Adaption in Cuckoo Search and Flower Pollination Algorithms for Optimal Design of Fuzzy Fault-Tolerant Controllers

In recent, various metaheuristic algorithms have shown significant results in control engineering problems; moreover, fuzzy sets (FSs) and theories were frequently used for dynamic parameter adaption in metaheuristic algorithms. The primary reason for this is that fuzzy inference system (FISs) can be designed using human knowledge, allowing for intelligent dynamic adaptations of metaheuristic parameters. To accomplish these tasks, we proposed shadowed type-2 fuzzy inference systems (ST2FISs) for two metaheuristic algorithms, namely cuckoo search (CS) and flower pollination (FP). Furthermore, with the advent of shadowed type-2 fuzzy logic, the abilities of uncertainty handling offer an appealing improved performance for dynamic parameter adaptation in metaheuristic methods; moreover, the use of ST2FISs has been shown in recent works to provide better results than type-1 fuzzy inference systems (T1FISs). As a result, ST2FISs are proposed for adjusting the Lèvy flight (P) and switching probability (P′) parameters in the original cuckoo search (CS) and flower pollination (FP) algorithms, respectively. Our approach investigated trapezoidal types of membership functions (MFs), such as ST2FSs. The proposed method was used to optimize the precursors and implications of a two-tank non-interacting conical frustum tank level (TTNCFTL) process using an interval type-2 fuzzy controller (IT2FLC). To ensure that the implementation is efficient compared with the original CS and FP algorithms, simulation results were obtained without and then with uncertainty in the main actuator (CV1) and system component (leak) at the bottom of frustum tank two of the TTNCFLT process. In addition, the statistical z-test and non-parametric Friedman test are performed to analyze and deliver the findings for the best metaheuristic algorithm. The reported findings highlight the benefits of employing this approach over traditional general type-2 fuzzy inference systems since we get superior performance in the majority of cases while using minimal computational resources.

Interval Type2 Fuzzy Logic Based STATCOM Controller for Stabilizing a Mixed Electrical Network System

Adding renewable energy plants to the electrical grid reduces the performance of energy systems. This results in problems including power fluctuations and poor voltage quality. This paper presents an interval type2 fuzzy logic-based controller, consisting of current and voltage regulators, that is applied to a STATCOM to regulate the DC voltage under various operating conditions. a membership functions not used before in this filed have been used to generate IT2FL sets output. The STATCOM has been connect with the high voltage bus bar in order to use one STATCOM for all the loads According to comparative studies, the proposed method outperforms traditional PI and type1 fuzzy logic-based controllers.The simulation has been implemented using MATLAB/SIMULINK software and the results confirm the feasibility of the proposed system.

Robust Tracking Control of Interval Type-2 Positive Takagi–Sugeno Fuzzy Systems With External Disturbance

Nonlinear positive systems are ubiquitous in practical applications. The constraint of positive conditions makes the design of this system still quite challenging even for the existing advanced control theory. In addition, when uncertainty and external disturbance also act on the positive nonlinear system at the same time, it will aggravate the complexity of the problem. In response to this problem, for the first time, this article presents a feasible robust tracking control strategy for the positive nonlinear systems with external disturbance and subject to uncertainty. In the proposed control strategy, the positive Takagi–Sugeno (T–S) fuzzy model is used to effectively represent the nonlinearity of the positive system, and the interval type-2 (IT2) fuzzy sets are used to deal with the uncertainty. The focus of tracking control is to design a reasonable IT2 fuzzy controller, which can make the states of the plant follow those of the given stable positive reference system as accurately as possible under the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance. Different from the tracking control research of general systems in the existing literature, in the tracking control analysis of positive systems, the generation of nonconvex conditions is inevitable. This article smoothly removes the obstacle of this problem. In addition, this article successfully attempts to relax the conservativeness of the basic analysis conditions by improving IT2 membership-function-dependent method, thereby improving the tracking effect under <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance. Finally, a detailed simulation example is given to verify the effectiveness of the proposed strategy.

Analysis of the difference between footprints of uncertainty for interval type-2 fuzzy PI controllers

Analysis of the difference between footprints of uncertainty for interval type-2 fuzzy PI controllers

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

Footprint of uncertainty (FOU) characteristics of interval type-2 membership functions (IT2-MFs) play an important role in the performance and robustness of interval type-2 fuzzy controllers (IT2-FCs). In literature, fixed FOU structures are used in almost all IT2-FC designs. In this study, an IT2-FC with dynamic FOU is proposed to provide high performance and robustness in the altitude control of a quadcopter. A proportional–derivative (PD) type FC with Takagi–Sugeno rule structure is used in the design procedure of the proposed controller. Additionally, input variables (error and derivative of error) are defined by using triangular IT2-MFs. To provide a dynamic FOU structure, the height of the lower MF (LMF) of each interval type-2 fuzzy set is defined as a function of the system error. In this way, FOU levels of IT2-MFs are adjusted dynamically since the height value of the LMF directly determines the FOU level of the IT2-MF. To evaluate the effectiveness of the proposed controller, comparison studies are performed under different conditions, including unmodeled measurement noises, an external disturbance, and a system parameter uncertainty. A classical PD, a type-1 fuzzy PD, and an interval type-2 fuzzy PD with fixed FOU controllers are used in the comparisons. The comparison results demonstrate that the proposed interval type-2 fuzzy PD controller with dynamic FOU exhibits better performance and more robustness than the other controllers.