Optimal Fuzzy Controller Design Research Articles

An improved event-triggered control method for fuzzy systems under membership functions online learning

This paper is concerned with the problem of adaptive event-triggered (AET) based optimal fuzzy controller design for nonlinear networked control systems (NCSs) characterized by Takagi–Sugeno (T–S) fuzzy models. An improved AET communication scheme with a memory adaptive rule is proposed to enhance the utilization of the state response vertex data. Different from the existing ET based results, the improved AET scheme can save more communication resources and acquire better system performance. The sufficient criteria of performance analysis and controller design are presented for the closed-loop control system subject to mismatched membership functions (MFs) and AET scheme. And then, a new MFs online learning algorithm on the basis of the gradient descent approach is employed to optimize the MFs of fuzzy controller and obtain optimal fuzzy controller for further improving system performance. Finally, two simulation examples are presented to verify the advantage and effectiveness of the provided controller design technique.

A new MOPSO algorithm for solving mathematical test functions and control engineering problems

In this article, a new multiobjective particle swarm optimization (MOPSO) algorithm is introduced to improve the performance of a sliding mode based robust fuzzy proportional–integral–derivative (PID) controller. In this regard, the non-dominated solution having minimum number of neighbors is considered as the global best position, while the sigma values of the members are employed to determine the personal best position. A modified multiple-crossover operator is combined with the operators of the particle swarm optimization to significantly increase the convergence speed of the algorithm. To limit the size of the archive, a dynamical elimination scheme defined in the Euclidean space is introduced. Besides, iteration-based linear relations are implemented to adaptively compute the inertia weight and learning coefficients. To evaluate the effectiveness of the introduced MOPSO algorithm, the requirements are conducted by means of three benchmark functions with regard to generational distance, spacing, and maximum spread metrics. This analysis demonstrates that the proposed algorithm operates better through comparison with well-known elitist multiobjective evolutionary algorithms. Moreover, the MOPSO algorithm is applied for optimal design of a hybrid robust fuzzy PID controller for a pneumatic system with two bellows. Conflicting objective functions are considered as the normalized values of overshoot and settling time of the displacement between the bellows that should be simultaneously minimized. The feasibility and efficiency of the strategy are assessed in comparison with the conventional controllers.

Distributed and Asynchronous Population-Based Optimization Applied to the Optimal Design of Fuzzy Controllers

Designing a controller is typically an iterative process during which engineers must assess the performance of a design through time-consuming simulations; this becomes even more burdensome when using a population-based metaheuristic that evaluates every member of the population. Distributed algorithms can mitigate this issue, but these come with their own challenges. This is why, in this work, we propose a distributed and asynchronous bio-inspired algorithm to execute the simulations in parallel, using a multi-population multi-algorithmic approach. Following a cloud-native pattern, isolated populations interact asynchronously using a distributed message queue, which avoids idle cycles when waiting for other nodes to synchronize. The proposed algorithm can mix different metaheuristics, one for each population, first because it is possible and second because it can help keep total diversity high. To validate the speedup benefit of our proposal, we optimize the membership functions of a fuzzy controller for the trajectory tracking of a mobile autonomous robot using distributed versions of genetic algorithms, particle swarm optimization, and a mixed-metaheuristic configuration. We compare sequential versus distributed implementations and demonstrate the benefits of mixing the populations with distinct metaheuristics. We also propose a simple migration strategy that delivers satisfactory results. Moreover, we compare homogeneous and heterogenous configurations for the populations’ parameters. The results show that even when we use random heterogeneous parameter configuration in the distributed populations, we obtain an error similar to that in other work while significantly reducing the execution time.

Optimal Design of Fuzzy Controller for Photovoltaic Maximum Power Tracking Using Particles Swarm Optimization Algorithm

Solar panels have non-linear current-voltage characteristics and a specified maximum power point, which depends on environmental factors like the solar radiation and ambient temperature. The voltage-power curve of the photovoltaic system has multiple peaks under different atmospheric conditions that reduce the efficiency of the maximum power tracking techniques. This paper proposes an optimal design of a fuzzy controller using particle swarm optimization algorithm to track the maximum power point of a photovoltaic system operating under different conditions to improve its performance. The proposed system optimizes the particle swarm to produce an optimal working coefficient, which varies with photovoltaic parameters to extract maximum power. Results of simulations – performed using the MATLAB software - show the advantages of the proposed method, namely the ability to track the maximum power point in a short time and maintain the output waveform despite the relatively high variations in environmental conditions.

Metaheuristic Optimization Algorithm for Optimal Design of Type-2 Fuzzy Controller

The utilization of Le`vy flight to create new candidate solutions is one of the most powerful elements of CS. Candidate solutions are modified using this method by making a lot of minor modifications and a few big jumps. As a result, CS will be able to significantly increase the link between exploration and exploitation while also improving its search capabilities. The cuckoo search optimization (CSO) algorithm is applied to interval type-2 fuzzy logic controller (IT2FLC) in this research to determine the optimal parameters of membership functions (MFs) of interval type-2 fuzzy logic systems (IT2FLSs). The study takes into account two forms of MFs: triangular and trapezoidal. When perturbations are applied during the execution of each control issue, the CSO algorithm's performance and efficiency improve significantly. The proposed approach is tested using two benchmark control problems: water tank controller and inverted pendulum controller.

Optimal fuzzy controller design for industrial gear system by gray wolf algorithm

Optimal fuzzy controller design for industrial gear system by gray wolf algorithm

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.

Generalized Type-2 Fuzzy Parameter Adaptation in the Marine Predator Algorithm for Fuzzy Controller Parameterization in Mobile Robots

This article is oriented to the application of generalized type-2 fuzzy systems in the dynamic adjustment of the parameters of a recent metaheuristic based on nature that follows the rules of the best feeding strategies of predators and prey in ecosystems. This metaheuristic is called fuzzy marine predator algorithm (FMPA) and is presented as an improved variant of the original marine predator algorithm (MPA). The FMPA balances the degree of exploration and exploitation through its iterations according to the advancement of the predator. In the state of the art, it has been shown that type-2 fuzzy increases metaheuristic performance when adapting parameters, although there is also an increase in the execution time. The FMPA with generalized type-2 and interval type-2 parameter adaptations was applied to a group of benchmark functions introduced in the competition on evolutionary computation (CEC2017); the results show that generalized FMPA provides better solutions. A second case for FMPA is also presented, which is the optimal fuzzy control design, in the search for the optimal membership function parameters. A symmetrical distribution of these functions is assumed for reducing complexity in the search process for optimal parameters. Simulations were carried out considering different degrees of noise when analyzing the performance when simulating each of the used fuzzy methods.

Optimal Fuzzy Controller Design for Autonomous Robot Path Tracking Using Population-Based Metaheuristics

In this work, we propose, through the use of population-based metaheuristics, an optimization method that solves the problem of autonomous path tracking using a rear-wheel fuzzy logic controller. This approach enables the design of controllers using rules that are linguistically familiar to human users. Moreover, a new technique that uses three different paths to validate the performance of each candidate configuration is presented. We extend on our previous work by adding two more membership functions to the previous fuzzy model, intending to have a finer-grained adjustment. We tuned the controller using several well-known metaheuristic methods, Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), Harmony Search (HS), and the recent Aquila Optimizer (AO) and Arithmetic Optimization Algorithms. Experiments validate that, compared to published results, the proposed fuzzy controllers have better RMSE-measured performance. Nevertheless, experiments also highlight problems with the common practice of evaluating the performance of fuzzy controllers with a single problem case and performance metric, resulting in controllers that tend to be overtrained.

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.

Shadowed Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Harmony Search and Differential Evolution for Optimal Design of Fuzzy Controllers

This article mainly focuses on the utilization of shadowed type-2 fuzzy systems used to achieve the goal of dynamically adapting the parameters of two already known algorithms in the literature: the harmony search and the differential evolution algorithms. It has already been established that type-2 fuzzy logic enhances the performance of metaheuristics by enabling parameter adaptation; however, the utilization of fuzzy logic results in an increased execution time. For this reason, in this article, the shadowed type-2 fuzzy approach is put forward as a way of reducing execution time, while maintaining the good results that the complete type-2 fuzzy model produces. The harmony search and differential evolution algorithms with shadowed type-2 parameter adaptations were applied to the problem of optimally designing fuzzy controllers. The simulations were performed with the controllers working in an ideal situation, and then with a real situation under different noise levels in order to reach a conclusion regarding the performance of each of the algorithms that were applied.

Differential Evolution with Shadowed and General Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Optimal Design of Fuzzy Controllers

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. Previously, we have worked with both kinds of fuzzy systems in different types of benchmark problems and it has been found that the use of fuzzy logic in combination with the differential evolution algorithm gives good results. In some of the studies, it is clearly shown that, when compared to other algorithms, our methodology turns out to be statistically better. In this case, the mutation parameter is dynamically moved during the evolution process by using shadowed and general type-2 fuzzy systems. The main contribution of this work is the ability to determine, through experimentation in a benchmark control problem, which of the two kinds of the used fuzzy systems has better results when combined with the differential evolution algorithm. This is because there are no similar works to our proposal in which shadowed and general type 2 fuzzy systems are used and compared. Moreover, to validate the performance of both fuzzy systems, a noise level is used in the controller, which simulates the disturbances that may exist in the real world and is thus able to validate statistically if there are significant differences between shadowed and general type 2 fuzzy systems.

An Efficient Chicken Search Optimization Algorithm for the Optimal Design of Fuzzy Controllers

A proposed architecture to design the optimal parameters of Membership Functions (MFs) of Type-1 Fuzzy Logic Systems (T1FLSs) using the Chicken Search Optimization (CSO) is applied to three Fuzzy Logic Controllers (FLCs) in this paper. Two types of MFs are considered in the study: triangular and trapezoidal ones. The performance and efficiency of the CSO algorithm are particularly good when perturbations are added during the execution in each control problem. Two benchmark control problems: Water Tank Controller and Inverted Pendulum Controller are considered for testing the proposed approach. Also, the optimal design of a fuzzy controller for trajectory tracking of an Autonomous Mobile Robot (AMR) is considered to test the CSO. The main goal is to highlight the efficiency of CSO algorithm in finding optimal fuzzy controllers of non-linear plants. Two types of perturbations are considered in each control problem. Results show that the CSO algorithm presents excellent results in the field of Fuzzy Logic Controllers. Two types of Fuzzy Inference Systems: Takagi-Sugeno and Mamdani FLSs, are implemented in this paper. The most important metrics usually applied in control are used in this paper, such as: Integral Time Absolute Error (ITAE), Integral Time Squared Error (ITSE), Integral Absolute Error (IAE), Integral Square Error (ISE), Mean Square Error (MSE), and Root Mean Square Error (RMSE).

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

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.

Optimal Fuzzy PID Controller Design for Stability of FlexRay Bus in NCS

Optimal Fuzzy PID Controller Design for Stability of FlexRay Bus in NCS

Integrated Optimal Design of Speed Profile and Fuzzy PID Controller for Train With Multifactor Consideration

Speed profile design and tracking control are two important issues to ensure the performance of the automatic train operation system. Aiming to realize the maximum optimization probability of train running, this paper constructs an integrated optimal method through speed profile design and fuzzy PID controller design. In the recommended speed profile design, three typical running strategies are included in the proposed comprehensive scheme to extend solution space, and the constructed train performance simulation is combined with NSGA-II algorithm to solve such multiobjective problem. As for recommended speed profile tracking, in order to improve the tracking performance of the train, which is a nonlinear system, a fuzzy PID controller is designed to adaptively adjust PID gains. Note that multiple indicators of punctually, energy consumption, stopping accuracy and comfort are all considered in the integrated design. Taking Beijing Subway Line 8 as the numerical example, the results show that the design of speed profile and fuzzy PID controller are both effective, and energy consumption saves about 10.40% with other better indicators compared with the original data.

An Optimal Fuzzy Control Method for Nonlinear Time-Delayed Batch Processes

An optimal fuzzy controller design scheme is proposed to address the influence of time delay and disturbance on the control performance of nonlinear batch processes. First, a two-dimensional (2D) equivalent Takagi-Suguno (T-S) fuzzy error model is formulated. By introducing a quadratic performance index function and adopting 2D Lyapunov-Krasovskii theory, the existence condition of the optimal fuzzy control law is given. Furthermore, its solvable condition, which depends on time-delay bounds, is constructed in terms of linear matrix inequalities, and its gain is obtained by using an optimization algorithm. This design has the advantages of faster tracking and better tracking performance. Finally, two different algorithms (with and without optimization) are used to control the water level of a triple-capacity water tank. The results show that the presented strategy is more effective and feasible.

Optimal design of fractional order fuzzy PID controller using an intelligent hybrid algorithm for nonlinear power system

Optimal design of fractional order fuzzy PID controller using an intelligent hybrid algorithm for nonlinear power system

Optimization of fuzzy controller design using a Differential Evolution algorithm with dynamic parameter adaptation based on Type-1 and Interval Type-2 fuzzy systems

This paper proposes the use of the Differential Evolution algorithm with fuzzy logic for parameter adaptation in the optimal design of fuzzy controllers for nonlinear plants. The Differential Evolution algorithm is enhanced using Type-1 and Interval Type-2 fuzzy systems for achieving dynamic adaptation of the mutation parameter. In this paper, four control optimization problems in which the Differential Evolution algorithm optimizes the membership functions of the fuzzy controllers are presented. First, the experiments were performed with the original algorithm, second the experiments were performed with the Fuzzy Differential Evolution (in this case the mutation parameter is dynamic), and last, experiments were performed applying noise to the control plant by using Fuzzy Differential Evolution.

Dynamic parameter adaptation in the harmony search algorithm for the optimization of interval type-2 fuzzy logic controllers

At the present time there are several types of metaheuristics which have been used to solve various types of problems in the real world. These metaheuristics contain parameters that are usually fixed throughout the iterations. However, various techniques exist to adjust the parameters of an algorithm such as probabilistic, fuzzy logic, among others. This work describes the methodology and equations for building Triangular and Gaussian interval type-2 membership functions, and this methodology was applied to the optimization of a benchmark control problem with an interval type-2 fuzzy logic controller. To validate in the best way the effect of uncertainty we perform experiments using noise (Pulse generator) and without noise. Also, a statistical z-test is presented to verify the effectiveness of the proposed method. The main contribution of this article is the proposed use of the theory of interval type-2 fuzzy logic to the dynamic adjustment of parameters for the harmony search algorithm and then its application to the optimal design of interval type-2 fuzzy logic controller.