Interval Type-2 Fuzzy Controller Research Articles

Interval type-2 fuzzy control for nonlinear discrete-time systems with time-varying delays

This paper is concerned with the problem of fault-tolerant control for discrete-time interval type-2 (IT2) fuzzy time delay system with actuator faults under imperfect premise matching. The time-varying delay and actuator fault are first taken into account for the IT2 fuzzy discrete-time systems. The novel IT2 state-feedback controller and the IT2 fuzzy model share different lower and upper membership functions. The fault-tolerant controller is designed to compensate for the effect of faults by stabilizing the closed-loop system under the actuator failures. Furthermore, the standard IT2 state-feedback controller is designed such that the closed-loop system is asymptotically stable and has an H∞ performance. The obtained conditions of the fault-tolerant controller and the standard IT2 controller can be expressed by the convex optimization problems. A numerical example is presented to show the effectiveness of the proposed results.

Finishing mill strip gage setup and control by interval type-1 non-singleton type-2 fuzzy logic systems

The setup and control of the finishing mill roll gap positions required to achieve the desired strip head thickness as measured by the finish mill exit X-ray gauge sensor is made by an intelligent controller based on an interval type-2 fuzzy logic system. The controller calculates the finishing mill stand screw positions required to achieve the strip finishing mill exit target thickness. The interval type-2 fuzzy head gage controller uses as inputs the transfer bar thickness, the width and the temperature at finishing mill entry, the strip target thickness, the width and the temperature at finishing mill exit, the stand work roll diameter, the stand work roll speed, the stand entry thickness, the stand exit thickness, the stand rolling force, and the %C of the strip. Taking into account that the measurements and inputs to the proposed system are modeled as type-1 non-singleton fuzzy numbers, we present the so called interval type-1 non-singleton type-2 fuzzy logic roll gap controller. As reported in the literature, interval type-2 fuzzy logic systems have greater non-linear approximation capacity than that of its type-1 counterpart and it has the advantage to develop more robust and reliable solutions than the latter. The experiments of these applications were carried out for three different types of coils, from a real hot strip mill. The results proved the feasibility of the developed system for roll gap control. Comparison against the mathematical based model shows that the proposed interval type-2 fuzzy logic system equalizes the performance in finishing mill stand screw positions setup and enhances the achieved strip thickness under the tested conditions characterized by high uncertainty levels.

Derivation and stability analysis of the analytical structures of the interval type-2 fuzzy PID controller

In this paper, we derive the analytical structure of the interval type-2 fuzzy proportional – integral – derivative (IT2F-PID) controller, which consists of a parallel combination of the IT2F-PD controller and the IT2F-PI controller. The IT2F-PID controller uses the following identical elements: two interval T2 triangular input fuzzy sets for each of the two input variables, three interval triangular output fuzzy sets, the Mamdani interval type-2 fuzzy rule based, a Zadeh AND T-norm, a Lukasiewicz OR T-conorm, and a new method for type-reduction that we propose, which called simplified type-reduction method. This new method of type-reduction reduces the computational cost of the output processing for the interval type-2 fuzzy logic controller (IT2-FLC). We relate the resulting structure to conventional PID control theory and prove that the proposed IT2F-PID controller is a nonlinear PID with variable gains changing as the input variables values vary. Moreover, the sufficient conditions for the bounded-input bounded-output (BIBO) stability of the IT2F-PID control system have established using the well-known small gain theorem. The simulation results show that the IT2F-PID controller based on the proposed type-reduction method is able to improve the system performance compared with other type-reduction methods.

Interval type-2 fuzzy adaptive tracking control design for PMDC motor with the sector dead-zones

This paper deals with the permanent magnet DC motor system with sector dead-zones and external disturbances via interval type-2 fuzzy adaptive tracking control scheme to achieve H∞ tracking performance. The type-2 fuzzy dynamic model is used to approximate the motor dynamics without constructing sector dead-zone inverse, where the parameters of the fuzzy model are obtained both from the fuzzy inference and online update laws. Based on the Lyapunov criterion and Riccati-inequality, the control scheme is derived to stabilize the closed-loop system such that all states of the system are guaranteed to be bounded and H∞ tracking performance is achieved due to uncertainties, dead-zone nonlinearities, and external disturbances. The advantage of the proposed control scheme is that it can better handle the vagueness or uncertainties inherent in linguistic words using fuzzy set membership functions with adaptation capability by linear analytical results instead of estimating non-linear system functions as the system parameters are unknown. Finally, the simulations of the PMDC motor system with sector dead-zone nonlinearities are used to illustrate the effectiveness of the proposed control scheme and the performance comparisons with the three-dimensional autonomous Ro¨ssler system (Wang and Chua, 2008) are used to validate the H∞ tracking performance of the PMDC motor system.

A simplified adaptive interval Type-2 fuzzy control in practical industrial application

Adaptive Type-2 fuzzy control possesses control performance better than the traditional adaptive fuzzy control. However, heavy computation burden obviously blocks the utilization of adaptive Type-2 fuzzy control in industrial application. By adopting novel piecewise fuzzy sets and center-average type-reduction, a simplified adaptive interval Type-2 fuzzy controller involving less computation is developed for practical industrial application. In the proposed controller, the inputs are divided into several subintervals and then two piecewise fuzzy sets are used for each subinterval. With the manner of piecewise fuzzy sets and a novel fuzzy rules inference engine, only part of fuzzy rules are simultaneously activated in one control loop, which exponentially decreases the computation and makes the controller appropriate in industrial application. The simulation and experimental study, involving the popular magnetic levitation platform, shows the predicted system with theoretical stability and good tracking performance. The analysis indicates that there is far less computation of the proposed controller than the traditional adaptive interval Type-2 fuzzy controller, especially when the number of fuzzy rules and fuzzy sets is large, and the controller still maintains good control performance as the traditional one.

Big Bang–Big Crunch optimization based interval type-2 fuzzy PID cascade controller design strategy

Fuzzy logic control is a recognized approach for handling the faced uncertainties within control applications. However, type-1 fuzzy controllers using crisp type-1 fuzzy sets might not be able to fully handle the high levels of uncertainties and nonlinear dynamics associated with real world control applications. On the other hand, interval type-2 fuzzy controllers using Interval Type-2 Fuzzy Sets (IT2-FSs) might be able to handle such uncertainties to produce a better control performance. However, the systematic design of interval type-2 fuzzy controllers is still a challenging problem due to the difficulty in determining the parameters of the IT2-FSs. In this paper, we will present the novel application of Big Bang–Big Crunch optimization (BB–BC) approach to optimize the antecedent membership parameters of Interval Type-2 Fuzzy PID (IT2-FPID) controllers in a cascade control structure. Since the IT2-FPID control structure involves more design parameters compared to its type-1 counterpart, it is beneficial to employ the BB–BC method which has a low computational cost and a high convergence speed. The presented BB–BC based optimized IT2-FPID cascade structure will be compared with its Type-1 Fuzzy PID (T1-FPID) and conventional PID controller counterparts which were also optimized with the BB–BC optimization. In addition, the proposed IT2-FPID structure will be compared with a self-tuning T1-FPID control structure. We will then present the novel application of the cascade control architecture to solve the path tracking control problem of mobile robots which inherits large amounts of uncertainties caused by the internal dynamics and/or feedback sensors of the controlled system. Several experiments were performed in simulation and in real world using the PIONEER 3-DX mobile robot which will act as a platform to evaluate the proposed control systems in this paper. The results illustrated that the IT2-FPID structure enhanced significantly the control performance even in the presence of uncertainties and disturbances when compared to the PID, T1-FPID and self-tuning T1-FPID structures. Moreover, it has been shown that the reason for the superior control performance of the IT2-FPID under high levels of uncertainty and noise is not merely for its use of extra parameters, but rather its different way of dealing with the uncertainties and noise present in real world environments by comparing with a self-tuning T1-FPID structure.

Interval type-2 fuzzy neural network controller for a multivariable anesthesia system based on a hardware-in-the-loop simulation

This manuscript describes the use of a hardware-in-the-loop simulation to simulate the control of a multivariable anesthesia system based on an interval type-2 fuzzy neural network (IT2FNN) controller. The IT2FNN controller consists of an interval type-2 fuzzy linguistic process as the antecedent part and an interval neural network as the consequent part. It has been proposed that the IT2FNN controller can be used for the control of a multivariable anesthesia system to minimize the effects of surgical stimulation and to overcome the uncertainty problem introduced by the large inter-individual variability of the patient parameters. The parameters of the IT2FNN controller were trained online using a back-propagation algorithm. Three experimental cases are presented. All of the experimental results show good performance for the proposed controller over a wide range of patient parameters. Additionally, the results show better performance than the type-1 fuzzy neural network (T1FNN) controller under the effect of surgical stimulation. The response of the proposed controller has a smaller settling time and a smaller overshoot compared with the T1FNN controller and the adaptive interval type-2 fuzzy logic controller (AIT2FLC). The values of the performance indices for the proposed controller are lower than those obtained for the T1FNN controller and the AIT2FLC. The IT2FNN controller is superior to the T1FNN controller for the handling of uncertain information due to the structure of type-2 fuzzy logic systems (FLSs), which are able to model and minimize the numerical and linguistic uncertainties associated with the inputs and outputs of the FLSs.

Static Output Feedback Control for Interval Type‐2 T‐S Fuzzy Systems Based on Fuzzy Lyapunov Functions

AbstractThis study aims to design an interval type‐2 (IT2) fuzzy static output feedback controller to stabilize the IT2 Takagi‐Sugeno (T‐S) fuzzy system. Conservative results may be obtained when a common quadratic Lyapunov function is utilized to investigate the stability of T‐S fuzzy systems. A fuzzy Lyapunov function is employed in this study to analyze the stability of the IT2 fuzzy closed‐loop system formed by the IT2 T‐S fuzzy model and the IT2 fuzzy static output feedback controller. Stability conditions in the form of linear matrix inequalities are derived. Several slack matrices are introduced to further reduce the conservativeness of stability analysis. The membership‐function shape‐dependent analysis approach is also employed to relax the stability results. The numerical examples illustrate the effectiveness of the proposed conditions.

Control Design for Interval Type-2 Fuzzy Systems Under Imperfect Premise Matching

This paper focuses on designing interval type-2 (IT2) control for nonlinear systems subject to parameter uncertainties. To facilitate the stability analysis and control synthesis, an IT2 Takagi-Sugeno (T-S) fuzzy model is employed to represent the dynamics of nonlinear systems of which the parameter uncertainties are captured by IT2 membership functions characterized by the lower and upper membership functions. A novel IT2 fuzzy controller is proposed to perform the control process, where the membership functions and number of rules can be freely chosen and different from those of the IT2 T-S fuzzy model. Consequently, the IT2 fuzzy-model-based (FMB) control system is with imperfectly matched membership functions, which hinders the stability analysis. To relax the stability analysis for this class of IT2 FMB control systems, the information of footprint of uncertainties and the lower and upper membership functions are taken into account for the stability analysis. Based on the Lyapunov stability theory, some stability conditions in terms of linear matrix inequalities are obtained to determine the system stability and achieve the control design. Finally, simulation and experimental examples are provided to demonstrate the effectiveness and the merit of the proposed approach.

State feedback control of interval type-2 Takagi–Sugeno fuzzy systems via interval type-2 regional switching fuzzy controllers

The interval type-2 Takagi–Sugeno fuzzy systems have been proposed to handle nonlinear systems subject to parameter uncertainties. In this paper, a new type of state feedback controller, namely, interval type-2 regional switching fuzzy controller, is proposed to conceive less-conservative stabilisation conditions, which is switched by basing on the values of system states. To further reduce the conservativeness in the stability analysis, the information of lower and upper membership functions is also considered. Stability conditions for the interval type-2 fuzzy closed-loop systems are presented in the form of linear matrix inequalities (LMIs). Simulation examples are provided to illustrate the effectiveness of the proposed method.

Performance comparison of shunt active power filter for interval type-2 fuzzy and adaptive backstepping controllers

The control technique used with the three-phase shunt active power filter (SAPF), has an important role in its performance. In this paper, a comparison between the SAPF performance controlled with interval type-2 fuzzy controller (IT2FC), adaptive backstepping non-linear control (ABNC), and proportional integral (PI) controllers is accomplished. The simulation results show the key features of each technique. It is also found that the parameters’ variations and uncertainties of the system can be compensated by ABNC or IT2FC controllers without any prior knowledge of real parameters. However, ABNC has better performance than the IT2FC.

A New Controlling Approach of Type 1 Diabetics Based on Interval Type-2 Fuzzy Controller

Augmented Minimal Model which is developed in consideration of the patient is taken into attention and uncertainties in this model which can occur by factors such as blood glucose, daily meals or sudden stress in considered. In addition to eliminate the effects of uncertainty, different control methods may be utilized. In this article, fuzzy control as a logical tool is used to transform words into control actions. To enhance the system performance, an interval type-2 Fuzzy controller has been implemented. To date, because of computational complexity of using a general type-2 fuzzy set (T2 FS) in a T2 fuzzy logic system (FLS), most people only use an interval T2 FS, the result being an interval T2 FLS (IT2 FLS). A daily meal disturbance is injected to model to consider the real environment for simulation. Finally, the control method tuned by standard tuning procedure and simulation results show the efficiency of method in regulating the blood glucose level in presentment of daily meal disturbance.

Design of Type-1 and Interval Type-2 Fuzzy PID Control for Anesthesia Using Genetic Algorithms

This paper presents the automatic drug administration for the regulation of bispectral (BIS) index in the anesthesia process during the clinical surgery by controlling the concentration target of two drugs, namely, propofol and remifentanil. To realize the automatic drug administration, real clinical data are collected for 42 patients for the construction of patients’ models consisting of pharmacokinetic and pharmacodynamic models describing the dynamics reacting to the input drugs. A nominal anesthesia model is obtained by taking the average of 42 patients’ models for the design of control scheme. Three PID controllers are employed, namely linear PID controller, type-1 (T1) fuzzy PID controller and interval type-2 (IT2) fuzzy PID controller, to regulate the BIS index using the nominal patient’s model. The PID gains and membership functions are obtained using genetic algorithm (GA) by minimizing a cost function measuring the control performance. The best trained PID controllers are tested under different scenarios and compared in terms of control performance. Simulation results show that the IT2 fuzzy PID controller offers the best control strategy regulating the BIS index while the T1 fuzzy PID controller comes the second.

A practical application of the interval type-2 fuzzy controller for a photovoltaic sourced DC – DC boost converter

This paper presents an implementation of type-2 fuzzy controller for DC - DC boost converter fed by photovoltaic panels. High power boost converter is the imperative part of the renewable energy power system that transfers energy to the utility or standalone study. Power circuit applications require fast dynamic response, lower overshoot and lower steady state error. Intelligent control algorithms are used to obtain these features. Type-1 fuzzy logic control is one of the intelligent control algorithms. Power circuits are non-linear structure and contain uncertainties. Conventional controllers and type-1 fuzzy controllers cannot be enough to overcome uncertainties. In this study, type-2 fuzzy controller which has high performance for modeling uncertainties has been developed as control algorithm for DC - DC boost converter. The converter has been also controlled with proportional-integral (PI) and type-1 fuzzy controller separately to show the superiority of the developed type-2 fuzzy controller. The converter has been controlled with TMS320F28335 DSP for real time application. Each control algorithm has been used to control of the converter individually. Settling time, overshoot and load variation responses have been investigated for the converter. Results showed that type-2 fuzzy controller has pointed out the best performance.

Intelligent control for nonlinear inverted pendulum based on interval type-2 fuzzy PD controller

The interval type-2 fuzzy logic controller (IT2-FLC) is able to model and minimize the numerical and linguistic uncertainties associated with the inputs and outputs of a fuzzy logic system (FLS). This paper proposes an interval type-2 fuzzy PD (IT2F-PD) controller for nonlinear inverted pendulum. The proposed controller uses the Mamdani interval type-2 fuzzy rule based, interval type-2 fuzzy sets (IT2-FSs) with triangular membership function, and the Wu–Mendel uncertainty bound method to approximate the type-reduced set. The proposed controller is able to minimize the effect of the structure uncertainties and the external disturbances for the inverted pendulum. The results of the proposed controller are compared with the type-1 fuzzy PD (T1F-PD) controller in order to investigate the effectiveness and the robustness of the proposed controller. The simulation results show that the performance of the proposed controller is significantly improved compared with the T1F-PD controller. Also, the results show good performance over a wide range of the structure uncertainties and the effect of the external disturbances.

A simple design method for interval type-2 fuzzy pid controllers

In this study, a design method for single Input interval type-2 fuzzy PID controller has been developed. The most important feature of the proposed type-2 fuzzy controller is its simple structure consisting of a single input variable. The presented simple structure gives an opportunity to the designer to form the type-2 fuzzy controller output in closed form formulation for the first time in literature. This formulation cannot be achieved with present type-2 fuzzy PID controller structures which have employed the Karnik-Mendel type reduction. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Elaborations are done on the derived closed form output and a simple strategy is presented for a single input type-2 fuzzy PID controller design. The presented interval type-2 fuzzy controller structure still keeps the most preferred features of the PID controller such as simplicity and easy design. We will illustrate how the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets can be used to enhance the control performance on linear and nonlinear benchmark systems by simulations. Moreover, the type-2 fuzzy controller structure has been implemented on experimental pH neutralization. The simulation and experimental results will illustrate that the proposed type-2 fuzzy controller produces superior control performance and can handle nonlinear dynamics, parameter uncertainties, noise and disturbances better in comparison with the standard PID controllers. Hence, the results and analyses of this study will give the control engineers an opportunity to draw a bridge and connect the type-2 fuzzy logic and control theory.

Evolutionary Robot Wall-Following Control Using Type-2 Fuzzy Controller With Species-DE-Activated Continuous ACO

This paper proposes evolutionary wall-following control of a mobile robot using an interval type-2 fuzzy controller (IT2FC) with species-differential-evolution-activated continuous ant colony optimization (SDE-CACO). Both the position and speed of a mobile robot are controlled by using two IT2FCs to improve noise resistance ability. A new cost function is defined to accurately evaluate the wall-following performance of an evolutionary IT2FC. A two-stage training approach is proposed that learns a position IT2FC followed by a speed IT2FC to optimize both the wall-following accuracy and the moving speed. The proposed learning approach avoids the time consuming task of the exhaustive collection of supervised input-output training pairs. All fuzzy rules are generated online using a clustering-based approach during the evolutionary learning process. All of the free parameters in an online-generated IT2FC are optimized using SDE-CACO, in which an SDE mutation operation is incorporated within a continuous ACO to improve its explorative ability. The proposed SDE-CACO is compared with various population-based optimization algorithms to demonstrate its efficiency and effectiveness in the wall-following control problem. This study also includes experiments that demonstrate wall-following control utilizing a real mobile robot.

Stability analysis and controller design of interval type-2 fuzzy systems with time delay

The type-2 fuzzy models can handle the system uncertainties directly based on the type-2 fuzzy sets. In this paper, the Takagi–Sugeno fuzzy model approach is extended to the stability analysis and controller design for interval type-2 (IT2) fuzzy systems with time-varying delay. Delay-dependent robust stability criteria are developed in terms of linear matrix inequalities by using the improvement technique of free-weighting matrices. Less conservative results are obtained by considering the information contained in the footprint of uncertainty. Finally, two simulation examples are presented to illustrate the effectiveness of the theoretical results. One is provided to show the merits of the proposed method, the other based on the continuous stirred tank reactor model is given to illustrate the design processes of IT2 fuzzy controller for a nonlinear system with parameter uncertainties.

Study of Interval Type-2 Fuzzy Controller for the Twin-tank Water Level System

For dealing with large static error due to poor immunity of the traditional fuzzy control, a novel interval type-2 fuzzy control system is proposed. By extending the typical membership functions to interval type-2 membership functions, the proposed control system can efficiently reduce the uncertain disturbance from real environment without increasing the design complexity. The simulation results on the water tank level control system showed that the proposed method succeeded in better static and dynamic control with stronger robust performance than the traditional fuzzy control method.

A nonlinear voltage controller based on interval type 2 fuzzy logic control system for multimachine power systems

In this paper, we propose an interval type-2 fuzzy controller that has the ability to enhance the transient stability and achieve voltage regulation simultaneously for multimachine power systems. The design of this controller involves the direct feedback linearization (DFL) technique. The DFL compensated system model is transformed into an equivalent type 1 T–S fuzzy model using linearly independent functions. This paper highlights the mathematical foundations for analyzing the stability and facilitating the design of stabilizing controllers of the interval type 2 Takagi–Sugeno fuzzy control systems (IT2 T–S FLCSs). Sufficient conditions for designing the interval type-2 fuzzy controller with meeting quadratic D stability constraints are obtained by using Linear Matrix Inequalities (LMIs). Based on only local measurements, the designed controller guarantees transient stability, voltage regulation and satisfies desired transient responses. The proposed controller is applied to two-generator infinite bus power system. Simulation results illustrate the performance of the developed approach regardless of the system operating conditions.