Optimal Fuzzy Controller Design Research Articles

An Optimal Fuzzy PID Controller Design Based on Conventional PID Control and Nonlinear Factors

This paper proposes an optimal fuzzy proportional–integral–derivative (PID) controller design based on conventional PID control and nonlinear factors. With the equivalence between fuzzy logic controllers (FLCs) and conventional PID controllers, a conventional PID controller design can be rapidly transformed into an equivalent FLC by defining the operating ranges of the input/output of the controller. The proposed nonlinear factors can further tune the nonlinearity of the membership functions (MFs) distributed in the operating ranges. In this manner, a fuzzy PID controller can be developed with less parameters and optimized by using the genetic algorithm (GA). In addition, the aforementioned equivalent FLC can act as one individual in the initial population of GA, and significantly enhances the GA efficiency. Simulation results demonstrate the feasibility of this technique. This resulted in an optimal fuzzy PID controller design with only eight parameters with a concise controller structure, and most importantly, the optimal fuzzy PID controller design is now more systematic.

Optimal fuzzy controller based on non-monotonic Lyapunov function with a case study on laboratory helicopter

ABSTRACTThis paper presents a new approach to design an observer-based optimal fuzzy state feedback controller for discrete-time Takagi–Sugeno fuzzy systems via LQR based on the non-monotonic Lyapunov function. Non-monotonic Lyapunov stability theorem proposed less conservative conditions rather than common quadratic method. To compare with optimal fuzzy feedback controller design based on common quadratic Lyapunov function, this paper proceeds reformulation of the observer-based optimal fuzzy state feedback controller based on common quadratic Lyapunov function. Also in both methodologies, the dependence of optimisation problem on initial conditions is omitted. As a practical case study, the controllers are implemented on a laboratory twin-rotor helicopter to compare the controllers' performance.

Optimal Design of a Stable Fuzzy Controller for Beyond Pull-In Stabilization of Electrostatically Actuated Circular Microplates

The current paper aims to provide an optimal stable fuzzy controller to extend the travel range of a pair of flexible electrostatically actuated circular microplates beyond their pull-in limit. The single mode assumption is utilized to derive the equation of motion of the system based on a Lagrangian approach. The static behavior of the system is studied using the proposed model, and the utilized assumption and the relevant results are closely verified by nonlinear finite element simulations. The open-loop dynamic analysis is also performed to derive the linguistic rules governing the voltage-deflection behavior of the system. The mentioned rules are then employed for designing a fuzzy controller, which controls the deflection of the microplates. The controller is then optimized to provide better response specifications. The performance of the optimal fuzzy controller is compared with that of the optimal proportional–integral–derivative (PID) controller and obvious superiorities in terms of noise suppression and stability enhancement are observed. To guarantee the stability of the closed-loop system, another higher level controller is designed to oversee the behavior of the fuzzy controller. Simulation results reveal that the superintended fuzzy controller can prevent instability, while fairly extending the travel range of system and providing it with a better transient response. The suggested design approach proposed in this paper may be used to improve the performance of many nano/micro devices and nano/micro positioning systems.

Optimal design of fuzzy PID controller for deregulated LFC of multi-area power system via mine blast algorithm

This paper presents a novel optimal fuzzy proportional–integral–derivative (fuzzy PID) controller for load frequency control (LFC) designed by a proposed approach of mine blast algorithm (MBA) for multi-interconnected areas. The system includes reheat thermal connected power systems with the effect of the governor dead zone and turbine generation rate constraint nonlinearity. The proposed approach is used to determine the optimal parameters of the fuzzy PID controller to minimize the integral time absolute error. The proposed controller is inserted in multi-interconnected power systems which are built in Simulink/MATLAB library; triangular membership function is used for fuzzy PID controller. Additionally, the optimum adjustment of the fuzzy PID controller parameters under contracted scenario for large step demands and disturbances is investigated by MBA. The obtained results are compared to those obtained via antlion optimizer, artificial bee colony, hybrid differential evolution particle swarm optimization and hybrid PSO pattern search algorithm. The obtained results confirmed the superiority of the proposed MBA in designing the fuzzy PID-LFC as it provides less error with best statistical parameters compared to the others.

A generalized type-2 fuzzy logic approach for dynamic parameter adaptation in bee colony optimization applied to fuzzy controller design

In this work a Generalized type-2 Fuzzy Logic System (GT2FLS) approach for dynamic parameter adaptation in metaheuristics and for optimal fuzzy controller design is presented. In these two cases, the efficiency of the GT2FLS approach is verified with simulation results. In the first case, the GT2FLS provides an approach to dynamically find the optimal values of the heuristic parameters that are a critical part of the Bee Colony Optimization (BCO) algorithm performance. In the second case, the GT2FLS approach provides the basis for building a Generalized type-2 Fuzzy Logic Controller (GT2FLC), which can be optimized with the traditional BCO, specifically to find the optimal design of the Membership Functions (MFs) in the Fuzzy Controller. In both cases, the GT2FLS approach shows advantages in the optimization of the solutions to the problems. For both cases, we can considered them as hybrid systems combining GT2FLS and BCO although the combination is made in a different way, and it can be noted that a GT2FLS presents better stability in the minimization of the errors when applied to benchmark control problems. Simulation results illustrate that the implementation of the Generalized type-2 Fuzzy Logic Controller (GT2FLC) approach improves its performance when using the BCO algorithm and the stability of the fuzzy controller is better when compared with respect to a type-1 Fuzzy Logic Controller (T1FLC) and an Interval type-2 Fuzzy Logic Controller (IT2FLC).

Multi-objective optimal design of fuzzy controller for structural vibration control using Hedge-algebras approach

In this paper, the problem of multi-objective optimal design of hedge-algebras-based fuzzy controller (HAC) for structural vibration control with actuator saturation is presented. The main advantages of HAC are: (i) inherent order relationships among linguistic values of each linguistic variable are always ensured; (ii) instead of using any fuzzy sets, linguistic values of linguistic variables are determined by an isomorphism mapping called semantically quantifying mapping (SQM) based on a few fuzziness parameters of each linguistic variable and hence, the process of fuzzy inference is very simple due to SQM values occurring in the fuzzy rule base and (iii) when optimizing HAC, only a few design variables which are above fuzziness parameters are needed. As a case study, a HAC and optimal HACs (opHACs) based on multi-objective optimization view point have been designed to active control of a benchmark structure with active bracing system subjected to earthquake excitation. Control performance of controllers is also discussed in order to shown advantages of the proposed method.

Erratum to: Optimal Fuzzy Controller Design Using an Evolutionary Strategy-Based Particle Swarm Optimization for Redundant Wheeled Robots

Erratum to: Optimal Fuzzy Controller Design Using an Evolutionary Strategy-Based Particle Swarm Optimization for Redundant Wheeled Robots

Optimization of fuzzy controller design using a new bee colony algorithm with fuzzy dynamic parameter adaptation

In this paper we are presenting a modification of a bio-inspired algorithm based on the bee behavior (BCO, bee colony optimization) for optimizing fuzzy controllers. BCO is a metaheuristic technique inspired by the behavior presented by bees in nature, which can be used for solving optimization problems. First, the traditional BCO is tested with the optimization of fuzzy controllers. Second, a modification of the original method is presented by including fuzzy logic to dynamically change the main parameter values of the algorithm during execution. Third, the proposed modification of the BCO algorithm with the fuzzy approach is used to optimize benchmark control problems. The comparison of results show that the proposed fuzzy BCO method outperforms the traditional BCO in the optimal design of fuzzy controllers.

Editorial Message: Special Section on Fuzzy Theory and Its Applications

As the guest editors of the special section on fuzzy theory and its applications, we are very pleased to express short remarks on this very section, which is aimed to publish the latest, innovative, and outstanding research results in the International Journal of Fuzzy Systems (IJFS) in a very short review period. This section was called for participation in the 2014 international conference on fuzzy theory and its applications (iFUZZY 2014) held in Kaohsiung, Taiwan, over November 26–28, 2014, and 13 papers were submitted to the special IJFS session. They were initially reviewed and accepted as the oral presentations by the two guest editors. By following the rigorous paper review procedure of IJFS, we invited four IJFS associate editors, Prof. Shun-Feng Su (the current Editor-in-Chief of IJFS), Prof. Chin-Wang Tao, Prof. Chia-Feng Juang, and Prof. Ching-Chih Tsai, as the referees to raise questions and make comments for all the oral presentations in iFUZZY 2014. No-show papers are automatically rejected for possible publication in this special section. Based on the three review criteria on technical contributions, novelty, and completeness, six papers were provisionally accepted and asked for quality improvements according to the reviewers’ comments and suggestions. These six papers have finally been accepted for publication in the IJFS special section on fuzzy theory and its applications after substantial and detailed revisions. By looking into presented contents of these six papers in the special section, we are very delightful to make brief introductions to their contributions and novelty on fuzzy theory and its applications. These articles provide new, interesting, and timely useful results covering L-E-fuzzy lattices, fuzzy inference-enhanced VC-DRSA model for technical analysis in investment decision aid, optimal fuzzy controller design using an evolutionary strategy based on particle swarm optimization for redundant wheeled robots, improving mobile commerce adoption using a new hybrid fuzzy MADM model, performance of soft computing controllers in hemodialysis machines, and a fuzzy-neural adaptive terminal iterative learning control for fed-batch fermentation processes. All the six papers are collected together in the current issue in order to illustrate the main technical achievements of the 2014 IJFS special session in iFUZZY 2014. Last but not least, this editorial message not only delineates the paper submission, rigorous review, and quality assurance of the 2014 IJFS special session papers in detail, but also significantly encourages your kind paper submissions to the 2015 IJFS special session in iFUZZY 2015. We look forward to receiving your paper submissions this year. Guest Editors, 2014 IJFS special section on fuzzy theory and its applications

Optimal Fuzzy Controller Design Using an Evolutionary Strategy-Based Particle Swarm Optimization for Redundant Wheeled Robots

This paper presents an optimal fuzzy controller design method using an evolutionary strategy-based particle swarm optimization (ESPSO) to four-wheeled redundant mobile robots, called FC-ESPSO. In comparison with conventional fuzzy controllers, this approach takes the advantages of evolutionary strategy, fuzzy control, and PSO, thereby obtaining better population diversity, avoiding premature convergence, and achieving self-adaptive redundant control. This hybrid computing is then applied to develop an optimal fuzzy controller of redundant wheeled robots. The optimal parameters of the dynamic controller are self-adaptive via the proposed FC-ESPSO to resolve trajectory-tracking problem. Simulation results are given to exhibit the merits of the proposed FC-ESPSO than other related control methods for redundant wheeled robots.

Optimal control for a linear quadratic neuro Takagi--Sugeno fuzzy singular system using genetic programming

Optimal control for a linear neuro Takag--Sugeno fuzzy singular system with quadratic performance is obtained using genetic programming (gp). To obtain the optimal control, the solution of a matrix Riccati differential equation is computed by solving a differential algebraic equation using the gp approach. The obtained solution is equivalent or very close to the exact solution of the problem. The accuracy of the solution computed by the gp approach is qualitatively better than the traditional Runge--Kutta method. An illustrative numerical example is presented for the proposed method. References P. Balasubramaniam, J. Abdul Samath, N. Kumaresan and A. Vincent Antony Kumar, Solution of matrix Riccati differential equation for the linear quadratic singular system using neural networks, Appl. Math. Comput. 182(2):1832–1839, 2006. doi:10.1016/j.amc.2006.06.020 G. Da Prato and A. Ichikawa, Quadratic control for linear periodic systems, Appl. Math. Opt. 18:39–66, 1988. doi:10.1007%2FBF01443614 D. E. Goldberg, Genetic algorithms in search, optimization and machine learning , Addision Wesley, 1989. http://dl.acm.org/citation.cfm?id=534133 J. Jang, ANFIS: adaptive-network-based fuzzy inference systems, IEEE T. Syst. Man. Cyb. 23(3):665–685, 1993. doi:10.1109/21.256541 J. R. Koza, Genetic programming: on the programming of computers by means of natural selection . MIT Press, 1992. http://mitpress.mit.edu/books/genetic-programming M. O'Neill and C. Ryan, Evolutionary automatic programming in an arbitrary language, Genetic Programming, Vol. 4 , Kluwer Academic Publishers, 2003. http://www.springer.com/computer/ai/book/978-1-4020-7444-8 N. Kumaresan, Optimal control for stochastic linear quadratic singular periodic neuro Takagi–Sugeno fuzzy system with singular cost using ant colony programming, Appl. Math. Model. , 35:3797–3808, 2011. doi:10.1016/j.apm.2011.02.017 T. Takagi and M. Sugeno, Derivation of fuzzy control rules from human operator's actions, IFAC-IFIP-IFORS Symp., Fuzzy information, knowledge representation and decision analysis , 55–60, 1983. http://dl.acm.org/citation.cfm?id=577582 I. G.Tsoulos and I. E. Lagaris, Solving differential equations with genetic programming, Genet. Program. Evolv. M. , 7:33–54, 2006. doi:10.1007/s10710-006-7009-y S.-J. Wu, H.-H. Chiang, H.-T. Lin and T.-T. Lee, Neural-nerwork-based optimal fuzzy controller design for nonlinear systems, Fuzzy Set. Syst. , 154:182–207, 2005. doi:10.1016/j.fss.2005.03.011

Optimal fuzzy PID controller design for an active magnetic bearing system based on adaptive genetic algorithms

We propose an adaptive genetic algorithm (AGA) for the multi-objective optimisation design of a fuzzy PID controller and apply it to the control of an active magnetic bearing (AMB) system. Unlike PID controllers with fixed gains, a fuzzy PID controller is expressed in terms of fuzzy rules whose consequences employ analytical PID expressions. The PID gains are adaptive and the fuzzy PID controller has more flexibility and capability than conventional ones. Moreover, it can be easily used to develop a precise and fast control algorithm in an optimal design. An adaptive genetic algorithm is proposed to design the fuzzy PID controller. The centres of the triangular membership functions and the PID gains for all fuzzy control rules are selected as parameters to be determined. We also present a dynamic model of an AMB system for axial motion. The simulation results of this AMB system show that a fuzzy PID controller designed using the proposed AGA has good performance.

Linguistic Controller Design of LDS upon Cell-to-Cell Mapping

The theory of linguistic dynamic system (LDS) focuses on modeling, analysis, control and evaluation of complex systems at a linguistic level through computing with words. The concepts, frameworks and methods in conventional dynamic systems (CDS) are adopted in research of LDS. This paper is concerned about linguistic controller design of LDS upon cell mapping concept. In view of the studies of controller design for type-I and type-II LDS and optimal fuzzy controller design and tuning methods based on cell-to-cell mapping, two approaches to construct optimal linguistic controller for LDS using cell-to-cell mapping techniques are outlined in this paper.

Design of optimized fuzzy model-based controller for nonlinear systems using hybrid intelligent strategies

This paper introduces three hybrid methods for the generation and optimization of rules and membership functions of a fuzzy logic controller for nonlinear systems. The proposed methods overcome the deficiency of a systematic approach for optimal design of fuzzy controllers. An optimally designed fuzzy logic controller should have the least number of fuzzy variables and fuzzy rules and the best possible configuration of fuzzy rules in the rule table. The first strategy of this paper is a two-phase optimization problem: in the first phase, the number of fuzzy variables and their arrangement in the rule table are optimized by a genetic algorithm; in the second phase, the parameters of the membership functions are optimized via extended Kalman filtering. The second strategy tries to achieve the goals of the first method all in one phase by modifying the chromosome structure of the genetic algorithm. Then in the next step, a local search algorithm is utilized to improve the obtained results. The third strategy is similar to the second strategy in structure. However, along with optimizing the number of fuzzy variables and membership parameters, the number of fuzzy rules is also optimized. The first and second strategies are obliged to use every possible combination of fuzzy variables in the rule table; however, the third strategy is capable of distinguishing between useful and useless fuzzy rules in the rule table. The introduced strategies are applied to an automotive cruise control system. The results of the simulations show the effectiveness of the proposed methods and the superiority of the latter approaches over the former ones.

Bio-inspired Optimization of Fuzzy Logic Controllers for Robotic Autonomous Systems with PSO and ACO

In this paper we describe the use of bio-inspired optimization techniques, such as ant colony optimization and particle swarm optimization, for the design of optimal fuzzy logic controllers of autonomous wheeled mobile robots. The results obtained by the simulations with ant colony optimization and particle swarm optimization are statistically compared with previous optimization results obtained with genetic algorithms in order to find out the best optimization technique for a particular robotics problem.

Design of cluster-wise optimal fuzzy logic controllers to model input-output relationships of some manufacturing processes

In the present study, fuzzy logic (FL)-based approaches have been developed to determine the input-output relationships of some manufacturing processes, which may be non-linear in nature. Moreover, the degree of non-linearity may not be the same over the entire range of the variables. The input-output space has been clustered based on the similarity of the data points and cluster-wise linear regressions have been carried out. Takagi and Sugeno's approach of fuzzy logic controller (FLC) has been implemented cluster-wise using the pre-determined regression equations. A genetic algorithm (GA) has been utilised to optimise both cluster-properties as well as knowledge base of the FLCs developed based on two types of clustering algorithm, namely entropy-based approach and fuzzy C-means algorithm. The performances of above two FLCs have been compared in the present work.

Multi-objective optimal design of fuzzy logic controller using a self configurable swarm intelligence algorithm

This paper presents a multi-objective fuzzy logic controller (PSO–FLC) for active vibration control of seismically exited buildings by combining a new self configurable multi-objective PSO (particle swarm optimisation) algorithm with fuzzy logic controller. The rule base of the proposed PSO–FLC is tuned for optimal control performance by simultaneously optimizing displacement, drift ratio, acceleration and average control force. In addition, the proposed PSO–FLC algorithm also optimises the number as well as the optimal locations of the actuators. Six and 10 storey framed structures subjected to seismic excitations are considered as numerical examples to demonstrate the superior performance of the PSO–FLC algorithm over other control algorithms.

Reply to "Further Comment on 'Optimal Fuzzy Controller Design: Local Concept Approach'"

We proposed two approaches to solve a quadratic optimal problem of Takagi-Sugeno (T-S) fuzzy-model-based nonlinear systems. These two approaches are totally different in both concept and derivation even they deal with the same issue and the adopted notations look similar. Readers are suggested to clear local-concept approach away from their brains and reexamine the global-concept approach. Then, you will find out that in global-concept approach, via the proposed synthetical matrices, a quadratic optimal fuzzy problem is transformed into a general nonlinear quadratic optimal problem; a numerical approach (dynamic decomposition algorithm) is further introduced to speed up numerical solution and to keep the global optimality at the same time. The stability analysis, the derivation of controller, and the minimum energy are derived fully on the basis of nonlinear systems. Their formulation or representation are all in form of entire fuzzy system instead of fuzzy subsystems. Therefore, the mentioned issue is not the case for global approach. Those are only related to local-concept approach. In this article, we clarify the pointed issue and focus on reinforcing our theorem.

Further Comment on “Optimal Fuzzy Controller Design: Local Concept Approach”

Stability analysis and optimality are important in any systems. In the paper, fuzzy controller design: local concept approach, optimal fuzzy controller is design for Takagi-Sugeno fuzzy model. Unfortunately, it seems that some errors are happen and no simple correction can be done. In this paper, we show that some errors exit in the aforementioned paper with simple and clear examples.

Neural–Fuzzy Gap Control for a Current/Voltage-Controlled 1/4-Vehicle MagLev System

A magnetically levitated (MagLev) vehicle prototype has independent levitation (attraction) and propulsion dynamics. We focus on the levitation behavior to obtain precise gap control of a 1/4 vehicle. An electromagnetic levitation system is highly nonlinear and naturally unstable, and its equilibrium region is severely restricted. It is therefore a tough task to achieve high-performance vehicle-levitated control. In this paper, a MagLev system is modeled by two self-organizing neural-fuzzy techniques to achieve linear and affine Takagi-Sugeno (T-S) fuzzy systems. The corresponding linear-type optimal fuzzy controllers are then used to regulate both physical systems (voltage- and current-controlled systems). On the other hand, an affine-type fuzzy control design scheme is proposed for the affine-type systems. Control performance and robustness to an external disturbance are shown in simulation results. Affine T-S fuzzy representation provides one more adjustable parameter in the neural-fuzzy learning process. Therefore, an affine T-S-based controller possesses better performance for a current-controlled system since it is nonlinear not only to system states but also to system inputs. This phenomenon is shown in simulation results. Technical contributions include a nonlinear affine-type optimal fuzzy control design scheme, self-organizing neural-learning-based linear and affine T-S fuzzy modeling for both MagLev systems, and the achievement of an integrated neural-fuzzy technique to stabilize current- and voltage-controlled MagLev systems under minimal energy-consumption conditions.