Type-2 Fuzzy Controller Research Articles

An improved moth swarm algorithm based fractional order type-2 fuzzy PID controller for frequency regulation of microgrid system

ABSTRACT This research work introduces an improvised moth swarm algorithm (i-MSA) to resolve the load frequency control issue of microgrid (MG) systems. A microgrid system is a cluster of distributed generation (DG) power sources like photovoltaic (PV), wind power systems along with electric storage devices such as electrochemical batteries, flywheel systems, and electric vehicles. The unpredictable responses of DG sources influence a large frequency deviation, which creates frequency regulation problems taken as the problem objective for this research work. In the preliminary stage, the effectiveness of the i-MSA has been established by performing a comparative analysis considering single/multidimensional benchmark test functions. To validate the superiority of the i-MSA method, the technical viability has been measured by comparing the outcomes of the proposed approach with those of some newly recommended optimization methods. Furthermore, an advanced hybrid fractional order type-2 fuzzy PID (FO-T2F-PID) controller is projected for frequency control of the MG system. The uncertainties due to DG source penetration in the MG system and the impact of storage devices including the EV system to regulate the frequency have been studied using the proposed approach. The effect of operational parameter variations has been studied through a sensitivity test. From the data analysis, it is observed that the i-MSA-scaled FO-T2F-PID approach presents advancement in the fitness function of 29.11%, 33.53%, 47.16%, and 55.37% as compared to h-DE-PS: 2DOF/PID, I-JAYA: fuzzy PD/PI-PD, hybrid DFPS: TID, and Kriging: FOPID approaches, respectively. Similarly, the improvement in the settling interval for the proposed approach is observed to be 33.83%, 35.82%, 38.12%, and 42.18% as related to h-DE-PS: 2DOF/PID, I-JAYA: fuzzy PD/PI-PD, hybrid DFPS: TID, and Kriging: FOPID approaches, respectively. To indorse the practicability of the i-MSA-based FO-T2F-PID method, real-time simulation testing has been carried out in the MATLAB-interfaced OPAL-RT experimental setup. Finally, the optimum results obtained from the proposed approaches are confirmed by relating the same to some recently published frequency regulation outcomes in a benchmark power system model. It is observed that the i-MSA-based FO-T2F-PID method delivers advancement in microgrid frequency control compared to recent research outcomes.

A Type-2 Fuzzy Controller for Floating Tension-Leg Platforms in Wind Turbines

This paper proposes a type-2 fuzzy controller for floating tension-leg platforms in wind turbines. Its main objective is to stabilize and control offshore floating wind turbines exposed to oscillating motions. The proposed approach assumes that the dynamics of all units are completely unknown. The latter are approximated using the proposed Sugeno-based type-2 fuzzy approach. A nonlinear Kalman-based algorithm is developed for parameter optimization, and linear matrix inequalities are derived to analyze the system’s stability. For the fuzzy system, both rules and membership functions are optimized. Additionally, in the designed approach, the estimation error of the type-2 fuzzy approach is also considered in the stability analysis. The effectiveness and performance of the proposed approach is assessed using a simulation study of a tension leg platform subject to various disturbance modes.

Virtual-clock-dependent [formula omitted] controller design for discrete-time switched interval type-2 fuzzy systems with intermittent control inputs

This paper is devoted to the study of intermittent H∞ control problem for discrete-time switched interval type-2 fuzzy systems (DSIT2FSs) under minimum dwell time switching. A novel virtual-clock-dependent H∞ intermittent interval type-2 (IT2) fuzzy controller design scheme is proposed. Firstly, we transform the N-mode DSIT2FS with intermittent control inputs into a new one with N controller-busy modes and N controller-free modes. Then, by constructing a class of non-increasing virtual-clock-dependent multiple quadratic Lyapunov functions (VMQLFs), sufficient conditions on the existence of the H∞ intermittent IT2 fuzzy controllers are obtained for DSIT2FSs with dwell time constraints. The controller gains can be gotten by solving a set of strict linear matrix inequalities (LMIs). The obtained results are also applicable to non-switched IT2 fuzzy systems. It is shown that the designed IT2 fuzzy controllers work intermittently but still can guarantee stability and H∞ performance of the close-loop systems. Finally, a tunnel diode circuit system model and a single link robot arm model are provided to illustrate the effectiveness and advantages of the results.

Design of type-2 fuzzy fractional-order proportional-integral-derivative controller and multi-objective parameter optimization under load reduction condition of the pumped storage unit

Pumped storage unit (PSU) is an effective regulation tool of the smart power grid system. The inherent “S” characteristics caused by the reversible design of the pump-turbine will make the PSU run into a state of instability, resulting in severe hydraulic fluctuation, unit speed, and frequency oscillation. PSU load reduction is an operation condition often encountered in the process of peak load regulation and frequency regulation. The operation stability of this condition is very important to the safety of the power station and power grid. Firstly, a mathematical model suitable for the numerical calculation of all working conditions transition process in the power generation direction of pumped storage unit regulating system (PSURS) is established. Further, the load reduction condition under typical water heads is selected. Through numerical calculation and analysis, it is found that when the PSU operates in the low water head-small load area and encounters load reduction to no-load, the PSURS is easy to fall into an unstable state. Therefore, an interval type-2 fuzzy fractional-order proportional-integral-derivative (PID) controller is proposed for the load reduction condition of the PSU under low water head and small load operation. And a multi-objective joint optimization strategy is proposed for tuning controller parameters. The experimental results show that the interval type-2 fuzzy fractional-order PID controller after parameters optimization has better control performance than traditional controllers. Compared with the PID control method, the double objective optimal result index is reduced by 0.025 and 47.98 respectively, the rotational speed regulation time of the PSU is reduced by 20.27 s, the maximum water hammer pressure is reduced by 9.2 m. The novel method effectively solves the instability problem of PSU under low water head load reduction conditions.

Opposition-based spiral dynamic algorithm with an application to optimize type-2 fuzzy control for an inverted pendulum system

This paper presents two variants of the Opposition-based Spiral Dynamic Algorithm (ObSDA) for an application to optimize a type-2 fuzzy logic controller for an inverted pendulum system. Spiral Dynamic Algorithm (SDA) is a group-based optimization algorithm formulated based on the concept of a natural spiral phenomenon on earth. It has the theory of diversification and intensification in its strategy, which allows the algorithm to present itself as a good deterministic type of optimization tool to solve various engineering problems. Despite the good concept and strategy, the algorithm still suffers from getting trapped in a local optima solution. This is due to the limitation of the deterministic strategy that prevents the search agents from sufficiently exploring the whole feasible search space. The search operation only occurs within the area covered by the search agents, and thus there is a low opportunity to thoroughly diverse outside the covered area. Quasi-reflected and Quasi opposition-based strategies were incorporated into the SDA to overcome the exploration problem of the search agents. It helped the search agents to explore the opposite location of the current location of the agents. The opposition strategy also offered varying step sizes to the agents during the movement. The proposed QR-ObSDA and Q-ObSDA were tested on various benchmark functions comprising multimodal and unimodal fitness landscapes. They are also applied to optimize a type-2 fuzzy logic controller for an inverted pendulum system in comparison to SDA, Spotted Hyena Optimizer, Tunicate Swarm Algorithm, and Sooty Tern Optimization Algorithm. A statistical analysis on the accuracy achievement was conducted using Friedman and Wilcoxon Sign Rank methods. The result had shown that the proposed ObSDA variants had outperformed the original SDA in locating the theoretical optima solution of the benchmark functions. Application of the control problem had shown the accuracy performance of ObSDA variants had significantly improved compared to the existing SDA variants and outperformed the other three optimization algorithms.

Fuzzy-based metaheuristic algorithm for optimization of fuzzy controller: fault-tolerant control application

PurposeFuzzy-based metaheuristic algorithm is used to optimize the fuzzy controllers for the nonlinear level control system subject to uncertainty specially in the main actuator that has lost effectiveness (LOE). To optimize the fuzzy controller, type-1 harmonic search (HS) and interval type-2 (HS) will be used.Design/methodology/approachThe type-1 and type-2 fuzzy-based HS algorithms are designed for optimization of fuzzy controllers for Fault-Tolerant Control (FTC) applications, and this research proposes a fuzzy-based HS metaheuristic method. The performance of a fuzzy logic-based HS algorithm applied to a nonlinear two-tank level control process with a main actuator that has lost effectiveness (LOE) and also the same controller will be tested on DC motor angular position control with and without noise.FindingsThe key contribution of this work is the discovery of the best approach for generating an optimal vector of values for the fuzzy controller's membership function optimization. This is done in order to improve the controller's performance, bringing the process value of the two-tank level control process closer to the target process value (set point). It is worth noting that the type-1 fuzzy controller that has been optimized is an interval type-2 fuzzy system, which can handle more uncertainty than a type-1 fuzzy system.Originality/valueThe type-1 and type-2 fuzzy-based HS algorithms are designed for optimization of fuzzy controllers for FTC applications, and this research proposes a fuzzy-based HS metaheuristic method. The performance of a fuzzy logic-based HS algorithm applied to a nonlinear two-tank level control process with a main actuator that has LOE will be tested on DC motor angular position control with noise. Two nonlinear uncertain processes are used to demonstrate the effectiveness of the proposed control scheme.

Fuzzy Logic Based Metaheuristic Algorithm for Optimization of Type-1 Fuzzy Controller: Fault-Tolerant Control for Nonlinear System with Actuator Fault

This research offers a fuzzy-based harmonic search (HS) metaheuristic technique for optimizing type-1 fuzzy controller for Fault-Tolerant Control (FTC) for nonlinear level control application subject to two uncertainties (i.e. actuator fault and external process disturbances), using type-1 and interval type-2 fuzzy-based HS algorithms. The effectiveness of a fuzzy logic-based adaptive HS algorithm in a nonlinear two-tank level control process with the primary actuator has dwindled (LOE). The work key contribution is the discovery of the best technique for constructing an optimal vector of values for the fuzzy controller’s membership functions (MFs) optimization. This is made to improve dynamic response by bringing the process value of the two-tank level control process close to the target process value (set-point). It’s worth noting that the type-1 fuzzy controller’s optimized MFs use an interval type-2 fuzzy system for parameter adaptation of the HS algorithm, which can handle greater uncertainty than a type-1 fuzzy system. In this case, the limiting MFs of interval type-2 fuzzy sets are type-1 fuzzy sets, which defne the footprint of uncertainty (FOU). Simulation results show that FHSO using an interval type-2 fuzzy system outperforms FHSO using a type-1 fuzzy system in the optimal design of a type-1 fuzzy controller.

GWO-Based Optimal Tuning of Controllers for Shape Memory Alloy Wire Actuators

The purpose of this paper is to design the optimal controllers for nonlinear processes with Shape Memory Alloy (SMA) wire actuators viewed as controlled processes. Optimal process models are first derived. A comparative analysis is done between the evolved Takagi-Sugeno-Kang (TSK) fuzzy models of SMA wire actuators, two linear dynamic system models with parameters optimally tuned using the recent metaheuristic Grey Wolf Optimiser (GWO) algorithm and one linear dynamic system model obtained in a previous paper using the System Identification Toolbox. Measured input-output data is involved in this comparison. The parameters of two Proportional-Integral-Derivative controllers, a type-1 fuzzy controller and an interval type-2 fuzzy controller are next optimally tuned using GWO, and a comparative analysis of these linear and nonlinear controllers is done. The simulation results illustrate that the type-2 fuzzy controller ensure good performance for these processes.

Stable optimal self-tuning interval type-2 fuzzy controller for servo position control system

An optimal self-tuning interval type-2 fuzzy controller for servo position control systems is reported here. To achieve precise positioning of the actuator, input scaling factors of an interval type-2 fuzzy proportional-integral controller are updated online depending on the latest operating conditions in terms of closed loop tracking error and change of error. To ensure desired performance, input scaling factors are obtained by adaptive cuckoo search-based optimisation algorithm. Efficacy of the proposed scheme is substantiated through performance comparison with recently reported peak observer based and online self-tuning based interval type-2 fuzzy PID, interval type-2 fuzzy PI, and also type-1 fuzzy PI controllers through simulation study along with real-time validation on a DC servo position control system. Lyapunov function-based stability analysis for the proposed controller is also provided.

Optimized Type-2 Fuzzy Frequency Control for Multi-Area Power Systems

The objective of this study is minimizing the frequency deviation due to the load variations and fluctuations of renewable energy resources. In this paper, a new type-2 fuzzy control (T2FLC) approach is presented for load frequency control (LFC) in power systems with multi-areas, demand response (DR), battery energy storage system (BESS), and wind farms. BESS is used to reduce the frequency deviations caused by wind energy, and DR is utilized to increase network stability due to fast load changes. The suggested T2FLC is online tuned based on the extended Kalman filter to improve the LFC accuracy in coordination of DR, BESS, and wind farms. The system dynamics are unknown, and the system Jacobian is extracted by online modeling with a simple multilayer perceptron neural network (MLP-NN). The designed LFC is evaluated through simulating on 10-machine New England 39-bus test system (NETS-39b) in four scenarios. Simulation results verifies the desired performance, indicating its superiority compared to a classical PI controllers, and type-1 fuzzy logic controllers (FLCs). The mean of improvement percentage is about 20%.

Modelling and analysis of an interval type-2 Mamdani fuzzy PID controller

From the last decade, modelling of Interval Type-2 (IT2) fuzzy controllers has become an exciting area of research in the field of control systems engineering. The input-output relationship of the fuzzy controller gives insights into the exact structure of the controller. From the literature, it is observed that IT2 fuzzy controllers handle plant uncertainty in a better way than their Type 1 (T1) counterparts due to the presence of additional Degree of Freedom (DoF) provided by the Footprint of Uncertainty (FoU) present in the membership functions of Interval Type-2 Fuzzy Sets (IT2FSs). Further, it is also noticed that controllers obtained with non-uniformly distributed fuzzy sets control the uncertain and nonlinear plants in a better way than their uniformly distributed counterparts. To take advantage of these two, in this study, the authors have made an attempt to unveil the exact input-output relationship of an Interval Type-2 Fuzzy PID (IT2FPID) controller, where the modelling is done using a particular type of FoU and non-uniformly distributed fuzzy sets. Apart from modelling, the properties of the newly derived controller are analysed. Moreover, to justify the theoretical development made in this manuscript, the applicability of the controller is shown through simulation, where an unstable chemical reactor plant with a large time delay is controlled. Finally, the effectiveness of the proposed controller is delineated by comparing its performance with that of some recently developed controllers.

The Synchronization of Hyperchaotic Systems Using a Novel Interval Type-2 Fuzzy Neural Network Controller

This paper proposed a novel interval type-2 fuzzy neural network controller (NT2FC) to synchronize 5-D hyperchaotic systems with noise disturbance and system uncertainties. In the proposed controller, the type 2 fuzzy set is designed with the 3-dimensional Gaussian membership functions (3DGMFs) to increase the system’s ability to respond to uncertainty. The parameters of the NT2FC controller are updated online via adaptation laws, which are built based on the gradient descent approach. The system stability is ensured through the Lyapunov stability analysis. In addition, the modified Jaya algorithm (MJA) is applied to optimize the learning rates in adaptation laws. Finally, the efficiency of the proposed NT2FC is examined by the numerical simulation of the hyperchaotic system’s synchronization.

Derivation and structural analysis of a three-input interval type-2 TS fuzzy PID controller

Derivation and structural analysis of a three-input interval type-2 TS fuzzy PID controller

Investigation of chaotic behavior and adaptive type-2 fuzzy controller approach for Permanent Magnet Synchronous Generator (PMSG) wind turbine system

<abstract> <p>This article begins with a dynamical analysis of the Permanent Magnet Synchronous Generator (PMSG) in a wind turbine system with quadratic nonlinearities. The dynamical behaviors of the PMSG are analyzed and examined using Poincare map, bifurcation model, and Lyapunov spectrum. Finally, an adaptive type-2 fuzzy controller is designed for different flow configurations of the PMSG. An analysis of the performance for the proposed approach is evaluated for effectiveness by simulating the PMSG. In addition, the proposed controller uses advantages of adaptive type-2 fuzzy controller in handling dynamic uncertainties to approximate unknown non-linear actions.</p> </abstract>

Adaptive Interval Type-2 Fuzzy Controller for Variable-speed Wind Turbine

In this paper, an adaptive interval type-2 fuzzy controller is proposed for variable-speed and variable-pitch wind turbines. Because of attractive features of the well-known wind turbine baseline controller, the proposed controller acts as an augmented controller and works in parallel to the baseline controller. As typical variable-speed wind turbines have different controllers for different operation regions, for each operation region, a dedicated interval type-2 fuzzy controller is designed. Because of the uncertainty in wind speed measurement, modern control techniques try to estimate this value. However, in contrast to these modern control techniques, the proposed controller is independent of the wind speed estimation. Thus, there is a better saving in cost and computational burden. To evaluate the effectiveness of the proposed controller, simulations are conducted with wind profiles which span all operation regions. Results show that, compared with the baseline controller, the proposed controller enhances power generations and reduces mechanical loads concurrently.

A Class of General Type-2 Fuzzy Controller Based on Adaptive Alpha-Plane for Nonlinear Systems

A Class of General Type-2 Fuzzy Controller Based on Adaptive Alpha-Plane for Nonlinear Systems

Construction of Novel Self-Adaptive Dynamic Window Approach Combined With Fuzzy Neural Network in Complex Dynamic Environments

The traditional Dynamic Window Approach (DWA) with constant weight values of the evaluation function leads to the inability of obstacle avoidance for the Automated Guided Vehicles (AGV) to perform obstacle avoidance and path planning in the complex environment. Effective avoidance of complex obstacles requires adaptive weight adjustment to address the evaluation function’s challenges. This paper proposes an adaptive DWA (ADWA), which introduces neural network training on the basis of the Mamdani DWA (MDWA). Firstly, the Mamdani type fuzzy controller is designed, and then the adaptive neuro-fuzzy controller is obtained by neural network training. Then, experiments are carried out through the MATLAB simulation environment. The simulation experiment results show that the improved DWA compared to traditional DWA can make the AGV pass the obstacle environment with a better trajectory and reduce the time. The improved DWA improves the autonomous obstacle avoidance capability of AGVs, which not only perfectly fits our task requirements, but also has apparent scientific and practical significance in developing AGV autonomous obstacle avoidance technology.

Design and experimental research of observer-based adaptive type-2 fuzzy steering control for automated vehicles with prescribed performance

Steer-by-Wire (SbW) system is a significant electromechanical subsystem of automated vehicles. This paper proposes an observer-based type-2 fuzzy control method for the SbW system with uncertain nonlinearity, unknown modeling parameters, and unavailable state. First, an interval type-2 fuzzy logic system (IT2 FLS) and an IT2 FLS-based state observer are constructed to estimate the uncertain nonlinearity and unavailable state of SbW systems. Then, a prescribed performance control (PPC) method is proposed to achieve the prescribed tracking performance of SbW systems. Much importantly, a modified performance function is incorporated in this control method, such that the prescribed tracking performance can be guaranteed within a finite time regardless of the initial state. Finally, simulation and vehicle experiments are given to verify the effectiveness and superiority of the proposed methods.

Decentralized robust interval type-2 fuzzy model predictive control for Takagi–Sugeno large-scale systems

Here, decentralized robust interval type-2 (IT2) fuzzy model predictive control (MPC) for Takagi–Sugeno (T-S) large-scale systems is studied. The large-scale system consists of many IT2 fuzzy T–S subsystems. Important necessities that limit the practical application of MPC are the online computational cost and burden of the frameworks. For MPC of T–S fuzzy large-scale systems, the online computational burden is even worse, and in some cases, they cannot be solved timely. Especially for severe, large-scale systems with disturbances, the MPC of T–S fuzzy large-scale systems usually give a conservative solution. So, researchers have many challenges and in finding a reasonable solution in a short time. Although more comfortable results can be achieved by the proposed fuzzy MPC approach, which adopts T–S large-scale systems with nonlinear subsystems, many restrictions are not considered. In this paper, challenges are solved, and the MPC is designed for a nonlinear IT2 fuzzy large-scale system with uncertainties and disturbances. Besides, the online optimization problem is solved, and results are proposed. Consequently, the online computational cost of the optimization problem is reduced considerably. Finally, the effectiveness of the proposed algorithm is illustrated with two practical examples.

Trajectory tracking control of underactuated tendon‐driven truss‐like manipulator based on type‐1 and interval type‐2 fuzzy logic approach

This paper deals with the trajectory tracking control problem of a planar underactuated tendon-driven truss-like manipulator (UTTM) by using fuzzy logic control methods, including type-1 fuzzy and interval type-2 fuzzy approaches. The UTTM is a novel designed underactuated robot that excels in manipulating in harsh environments due to its tendon-driven parallelogram structure. This unique structure, however, poses challenges for UTTM's trajectory tracking controller design, including underactuation, excessive nonlinearity, parameter uncertainty, and so on. To solve these problems, a fuzzy logic-based approach is proposed. First, the dynamic model of UTTM is transformed into a partially linearized form. Then a type-1 fuzzy controller is designed according to a linear quadratic regulator controller for the linearized system. Then by blurring the membership functions of type-1 fuzzy controllers, an interval type-2 fuzzy logic controller is designed, aiming at dealing with uncertainties. The proposed type-1 and interval type-2 fuzzy logic controllers are validated through simulations, and made comparisons with each other, especially when the system is involved with uncertainties. Simulation results show that the interval type-2 fuzzy-based trajectory tracking controller provides better performance than the type-1 counterpart in terms of tracking accuracy and capacity against uncertainties.