Search results for: fuzzy linear parameters

Authors: Bader Alkandari, Jamal Y. Madouh, Ahmad M. Alkandari, Anwar A. Alnaqi

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A new formulation of fuzzy linear estimation problem is presented. It is formulated as a linear programming problem. The objective is to minimize the spread of the data points, taking into consideration the type of the membership function of the fuzzy parameters to satisfy the constraints on each measurement point and to insure that the original membership is included in the estimated membership. Different models are developed for a fuzzy triangular membership. The proposed models are applied to different examples from the area of fuzzy linear regression and finally to different examples for estimating the electrical load on a busbar. It had been found that the proposed technique is more suited for electrical load estimation, since the nature of the load is characterized by the uncertainty and vagueness.

Keywords: fuzzy regression, load estimation, fuzzy linear parameters, electrical load estimation

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Authors: S. H. Nasseri, A. Ebrahimnejad

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Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. In this paper, we consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy primal simplex algorithms for solving these problems. Finally, we give illustrative examples.

Keywords: fuzzy linear programming, fuzzy numbers, duality, sensitivity analysis

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Authors: B. Güney, Ç. Teke

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In recent years, rapid and correct decision making is crucial for both people and enterprises. However, uncertainty makes decision-making difficult. Fuzzy logic is used for coping with this situation. Thus, fuzzy linear programming models are developed in order to handle uncertainty in objective function and the constraints. In this study, a problem of a factory in food industry is investigated, required data is obtained and the problem is figured out as a fuzzy linear programming model. The model is solved using Zimmerman approach which is one of the approaches for fuzzy linear programming. As a result, the solution gives the amount of production for each product type in order to gain maximum profit.

Keywords: food industry, fuzzy linear programming, fuzzy logic, linear programming

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Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi

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In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.

Keywords: fuzzy multi-objective linear programming problems, triangular fuzzy numbers, fuzzy ranking, supplier selection problem

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Authors: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: Lavinia B. Dulla

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The exploration study of the fuzzy regression approach attempts to present that fuzzy regression can be used as a possible alternative to classical regression. It likewise seeks to assess the differences and characteristics of simple linear regression and fuzzy regression using the width of prediction interval, mean absolute deviation, and variance of residuals. Based on the simple linear regression model, the fuzzy regression approach is worth considering as an alternative to simple linear regression when the sample size is between 10 and 20. As the sample size increases, the fuzzy regression approach is not applicable to use since the assumption regarding large sample size is already operating within the framework of simple linear regression. Nonetheless, it can be suggested for a practical alternative when decisions often have to be made on the basis of small data.

Keywords: fuzzy regression approach, minimum fuzziness criterion, interval regression, prediction interval

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Authors: Aquil Ahmed, Srikant Gupta, Irfan Ali

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In this paper, we study a multi-objective capacitated transportation problem (MOCTP) with mixed constraints. This paper is comprised of the modelling and optimisation of an MOCTP in a fuzzy environment in which some goals are fractional and some are linear. In real life application of the fuzzy goal programming (FGP) problem with multiple objectives, it is difficult for the decision maker(s) to determine the goal value of each objective precisely as the goal values are imprecise or uncertain. Also, we developed the concept of linearization of fractional goal for solving the MOCTP. In this paper, imprecision of the parameter is handled by the concept of fuzzy set theory by considering these parameters as a trapezoidal fuzzy number. α-cut approach is used to get the crisp value of the parameters. Numerical examples are used to illustrate the method for solving MOCTP.

Keywords: capacitated transportation problem, multi objective linear programming, multi-objective fractional programming, fuzzy goal programming, fuzzy sets, trapezoidal fuzzy number

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Authors: E. Koyuncu

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The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.

Keywords: fuzzy mathematical programming, fuzzy ranking, order acceptance, single machine scheduling

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Authors: Shih-Pin Chen, Shih-Syuan You

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Fuzzy regression models are useful for investigating the relationship between explanatory variables and responses in fuzzy environments. To overcome the deficiencies of previous models and increase the explanatory power of fuzzy data, the graded mean integration (GMI) representation is applied to determine representative crisp regression coefficients. A fuzzy regression model is constructed based on the modified dissemblance index (MDI), which can precisely measure the actual total error. Compared with previous studies based on the proposed MDI and distance criterion, the results from commonly used test examples show that the proposed fuzzy linear regression model has higher explanatory power and forecasting accuracy.

Keywords: dissemblance index, fuzzy linear regression, graded mean integration, mathematical programming

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Authors: Karunambigai Mevani Govindasamy, Sathishkumar Ayyappan

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In this paper, we formulate the algorithm to find out the dominating function parameters of Intuitionistic Fuzzy Graphs(IFG). The methodology we adopted here is converting any physical problem into an IFG, and that has been transformed into Intuitionistic Fuzzy Matrix. Using Linear Program Solver software (LiPS), we found the defined parameters for the given IFG. We obtained these parameters for a path and cycle IFG. This study can be extended to other varieties of IFG. In particular, we obtain the definition of edge dominating function, minimal edge dominating function, fractional edge domination number (γ_if^') and upper fractional edge domination number (Γ_if^') of an intuitionistic fuzzy graph. Also, we formulated an algorithm which is appropriate to work on LiPS to find fractional edge domination number and upper fractional edge domination number of an IFG.

Keywords: fractional edge domination number, intuitionistic fuzzy cycle, intuitionistic fuzzy graph, intuitionistic fuzzy path

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Authors: Aouiche Abdelaziz, Soudani Mouhamed Salah, Aouiche El Moundhe

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The present paper addresses the utilization of Artificial Neural Networks (ANNs) and Fuzzy Inference Systems (FISs) for the identification and control of dynamical systems with some degree of uncertainty. Because ANNs and FISs have an inherent ability to approximate functions and to adapt to changes in input and parameters, they can be used to control systems too complex for linear controllers. In this work, we show how ANNs and FISs can be put in order to form nets that can learn from external data. In sequence, it is presented structures of inputs that can be used along with ANNs and FISs to model non-linear systems. Four systems were used to test the identification and control of the structures proposed. The results show the ANNs and FISs (Back Propagation Algorithm) used were efficient in modeling and controlling the non-linear plants.

Keywords: non-linear systems, fuzzy set Models, neural network, control law

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Authors: Peng Li, Chuanri Li, Tao Li

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Reliability allocation is quite important during early design and development stages for a system to apportion its specified reliability goal to subsystems. This paper improves the reliability fuzzy allocation method and gives concrete processes on determining the factor set, the factor weight set, judgment set, and multi-grade fuzzy comprehensive evaluation. To determine the weight of factor set, the modified trapezoidal numbers are proposed to reduce errors caused by subjective factors. To decrease the fuzziness in the fuzzy division, an approximation method based on linear programming is employed. To compute the explicit values of fuzzy numbers, centroid method of defuzzification is considered. An example is provided to illustrate the application of the proposed reliability allocation method based on fuzzy arithmetic.

Keywords: reliability allocation, fuzzy arithmetic, allocation weight, linear programming

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Authors: Liang-Hsuan Chen, Sheng-Shing Nien

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This study aims to develop approaches to formulate intuitionistic fuzzy regression (IFR) models for many decision-making applications in the fuzzy environments using intuitionistic fuzzy observations. Intuitionistic fuzzy numbers (IFNs) are used to characterize the fuzzy input and output variables in the IFR formulation processes. A mathematical programming problem (MPP) is built up to optimally determine the IFR parameters. Each parameter in the MPP is defined as a couple of alternative numerical variables with opposite signs, and an intuitionistic fuzzy error term is added to the MPP to characterize the uncertainty of the model. The IFR model is formulated based on the distance measure to minimize the total distance errors between estimated and observed intuitionistic fuzzy responses in the MPP resolution processes. The proposed approaches are simple/efficient in the formulation/resolution processes, in which the sign of parameters can be determined so that the problem to predetermine the sign of parameters is avoided. Furthermore, the proposed approach has the advantage that the spread of the predicted IFN response will not be over-increased, since the parameters in the established IFR model are crisp. The performance of the obtained models is evaluated and compared with the existing approaches.

Keywords: fuzzy sets, intuitionistic fuzzy number, intuitionistic fuzzy regression, mathematical programming method

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Authors: A. Mansouri, F. Krim

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This paper discusses the implementation and design of both linear PI and fuzzy controllers for DC-DC boost converters. Design of PI controllers is based on temporal response of closed-loop converters, while fuzzy controllers design is based on heuristic knowledge of boost converters. Linear controller implementation is quite straightforward relying on mathematical models, while fuzzy controller implementation employs one or more artificial intelligences techniques. Comparison between these boost controllers is made in design aspect. Experimental results show that the proposed fuzzy controller system is robust against input voltage and load resistance changing and in respect of start-up transient. Results indicate that fuzzy controller can achieve best control performance concerning faster transient response, steady-state response good stability and accuracy under different operating conditions. Fuzzy controller is more suitable to control boost converters.

Keywords: boost DC-DC converter, fuzzy, PI controllers, power electronics and control system

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Authors: O. Poleshchuk, E. Komarov

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This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: interval type-2 fuzzy sets, fuzzy regression, weighted interval

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Authors: Ali Koam, Ismail Ibedou, S. E. Abbas

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In this paper, it is introduced the notion of r-fuzzy ideal separation axioms Tᵢi = 0; 1; 2 based on a fuzzy ideal I on a fuzzy topological space (X; τ). An r-fuzzy ideal connectedness related to the fuzzy ideal I is introduced which has relations with a previous r-fuzzy fuzzy connectedness. An r-fuzzy ideal compactness related to Ι is introduced which has also relations with many other types of fuzzy compactness.

Keywords: fuzzy ideal, fuzzy separation axioms, fuzzy compactness, fuzzy connectedness

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Authors: Mandar Ghodekar, Sharad Jadhav, Sangram Jadhav

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Speed control of rotor during startup and under varying load conditions is one of the most difficult tasks of gas turbine operation. In this paper, power plant gas turbine (GE9001E) is considered for this purpose and fuzzy and fuzzy-PI rotor speed controllers are designed. The goal of the presented controllers is to keep the turbine rotor speed within predefined limits during startup condition as well as during operating condition. The fuzzy controller and fuzzy-PI controller are designed using Takagi-Sugeno method and Mamdani method, respectively. In applying the fuzzy-PI control to a gas-turbine plant, the tuning parameters (Kp and Ki) are modified online by fuzzy logic approach. Error and rate of change of error are inputs and change in fuel flow is output for both the controllers. Hence, rotor speed of gas turbine is controlled by modifying the fuel ƒflow. The identified linear ARX model of gas turbine is considered while designing the controllers. For simulations, demand power is taken as disturbance input. It is assumed that inlet guide vane (IGV) position is fixed. In addition, the constraint on the fuel flow is taken into account. The performance of the presented controllers is compared with each other as well as with H∞ robust and MPC controllers for the same operating conditions in simulations.

Keywords: gas turbine, fuzzy controller, fuzzy PI controller, power plant

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Authors: Raziyeh Shamsi

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In this paper, we present a multiple objective linear programming (MOLP) problem in full fuzzy case and find Data Envelopment Analysis(DEA) targets. In the presented model, we are seeking the least inputs and the most outputs in the production possibility set (PPS) with the variable return to scale (VRS) assumption, so that the efficiency projection is obtained for all decision making units (DMUs). Then, we provide an algorithm for finding DEA targets interactively in the full fuzzy case, which solves the full fuzzy problem without defuzzification. Owing to the use of interactive methods, the targets obtained by our algorithm are more applicable, more realistic, and they are according to the wish of the decision maker. Finally, an application of the algorithm in 21 educational institutions is provided.

Keywords: DEA, MOLP, full fuzzy, target

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Authors: Walied Hanora

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This paper presents the problem of robust state feedback H∞ for discrete time nonlinear system represented by Takagi-Sugeno fuzzy systems. Based on fuzzy lyapunov function, the condition ,which is represented in the form of Liner Matrix Inequalities (LMI), guarantees the H∞ performance of the T-S fuzzy system with uncertainties. By comparison with recent literature, this approach will be more relaxed condition. Finally, an example is given to illustrate the proposed result.

Keywords: fuzzy lyapunov function, H∞ control , linear matrix inequalities, state feedback, T-S fuzzy systems

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Authors: S. Gherbi, F. Bouchareb

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This paper deals with the novel intelligent bio-inspired control strategies, it presents a novel approach based on an optimal fuzzy immune PID parameters tuning, it is a combination of a PID controller, inspired by the human immune mechanism with fuzzy logic. Such controller offers more possibilities to deal with the delayed systems control difficulties due to the delay term. Indeed, we use an optimization approach to tune the four parameters of the controller in addition to the fuzzy function; the obtained controller is implemented in a modified Smith predictor structure, which is well known that it is the most efficient to the control of delayed systems. The application of the presented approach to control a three tank delay system shows good performances and proves the efficiency of the method.

Keywords: delayed systems, fuzzy immune PID, optimization, Smith predictor

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Authors: M. Bouferhane, A. Boukhebza, L. Hatab

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In this paper, the position control of linear induction motor using fuzzy sliding mode controller design is proposed. First, the indirect field oriented control LIM is derived. Then, a designed sliding mode control system with an integral-operation switching surface is investigated, in which a simple adaptive algorithm is utilized for generalised soft-switching parameter. Finally, a fuzzy sliding mode controller is derived to compensate the uncertainties which occur in the control, in which the fuzzy logic system is used to dynamically control parameter settings of the SMC control law. The effectiveness of the proposed control scheme is verified by numerical simulation. The experimental results of the proposed scheme have presented good performances compared to the conventional sliding mode controller.

Keywords: linear induction motor, vector control, backstepping, fuzzy-sliding mode control

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Authors: Liang-Hsuan Chen, Chia-Jung Chang

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Fuzzy random variables have been introduced as an imprecise concept of numeric values for characterizing the imprecise knowledge. The descriptive parameters can be used to describe the primary features of a set of fuzzy random observations. In fuzzy environments, the expected values are usually represented as fuzzy-valued, interval-valued or numeric-valued descriptive parameters using various metrics. Instead of the concept of area metric that is usually adopted in the relevant studies, the numeric expected value is proposed by the concept of distance metric in this study based on two characters (fuzziness and randomness) of FRVs. Comparing with the existing measures, although the results show that the proposed numeric expected value is same with those using the different metric, if only triangular membership functions are used. However, the proposed approach has the advantages of intuitiveness and computational efficiency, when the membership functions are not triangular types. An example with three datasets is provided for verifying the proposed approach.

Keywords: fuzzy random variables, distance measure, expected value, descriptive parameters

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Authors: Sergey Sorokin, Irina Sorokina, Alexander Yazenin

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We present a solution to the Maxmin u/E parameters estimation problem of possibility distributions in m-dimensional case. Our method is based on geometrical approach, where minimal area enclosing ellipsoid is constructed around the sample. Also we demonstrate that one can improve results of well-known algorithms in fuzzy model identification task using Maxmin u/E parameters estimation.

Keywords: possibility distribution, parameters estimation, Maxmin u\E estimator, fuzzy model identification

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Authors: Yas Barzegar, Atrin Barzegar

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Drinking water quality assessment is a major issue today; technology and practices are continuously improving; Artificial Intelligence (AI) methods prove their efficiency in this domain. The current research seeks a hierarchical fuzzy model for predicting drinking water quality in Rome (Italy). The Mamdani fuzzy inference system (FIS) is applied with different defuzzification methods. The Proposed Model includes three fuzzy intermediate models and one fuzzy final model. Each fuzzy model consists of three input parameters and 27 fuzzy rules. The model is developed for water quality assessment with a dataset considering nine parameters (Alkalinity, Hardness, pH, Ca, Mg, Fluoride, Sulphate, Nitrates, and Iron). Fuzzy-logic-based methods have been demonstrated to be appropriate to address uncertainty and subjectivity in drinking water quality assessment; it is an effective method for managing complicated, uncertain water systems and predicting drinking water quality. The FIS method can provide an effective solution to complex systems; this method can be modified easily to improve performance.

Keywords: water quality, fuzzy logic, smart cities, water attribute, fuzzy inference system, membership function

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Authors: N. Kaewpraek, W. Assawinchaichote

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This paper considers an H_∞ TS fuzzy state-derivative feedback controller for a class of nonlinear dynamical systems. A Takagi-Sugeno (TS) fuzzy model is used to approximate a class of nonlinear dynamical systems. Then, based on a linear matrix inequality (LMI) approach, we design an H_∞ TS fuzzy state-derivative feedback control law which guarantees L₂-gain of the mapping from the exogenous input noise to the regulated output to be less or equal to a prescribed value. We derive a sufficient condition such that the system with the fuzzy controller is asymptotically stable and H_∞ performance is satisfied. Finally, we provide and simulate a numerical example is provided to illustrate the stability and the effectiveness of the proposed controller.

Keywords: h-infinity fuzzy control, an LMI approach, Takagi-Sugano (TS) fuzzy system, the photovoltaic systems

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Authors: G. S. Thakur

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In this paper, four new operators (O1, O2, O3, O4) are proposed, defined and considered to study the new properties and identities on hesitant fuzzy sets. These operators are useful for different operation on hesitant fuzzy sets. The various theorems are proved using the new operators. The study of the proposed new operators has opened a new area of research and applications.

Keywords: vague sets, hesitant fuzzy sets, intuitionistic fuzzy set, fuzzy sets, fuzzy multisets

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Authors: Mounir Bekaik, Messaoud Ramdani

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We present in this work a new technique of stabilization for fault nonlinear systems. The approach we adopt focus on a fuzzy Luenverger observer. The T-S approximation of the nonlinear observer is based on fuzzy C-Means clustering algorithm to find local linear subsystems. The MOESP identification approach was applied to design an empirical model describing the subsystems state variables. The gain of the observer is given by the minimization of the estimation error through Lyapunov-krasovskii functional and LMI approach. We consider a three tank hydraulic system for an illustrative example.

Keywords: nonlinear system, fuzzy, faults, TS, Lyapunov-Krasovskii, observer

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Authors: Muhammad M. A. S. Mahmoud

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Natural gas sweetening process is a controlled process that must be done at maximum efficiency and with the highest quality. In this work, due to complexity and non-linearity of the process, the H₂S gas separation and the intelligent fuzzy controller, which is used to enhance the process, are simulated in MATLAB – Simulink. The new design of fuzzy control for Gas Separator is discussed in this paper. The design is based on the utilization of linear state-estimation to generate the internal knowledge-base that stores input-output pairs. The obtained input/output pairs are then used to design a feedback fuzzy controller. The proposed closed-loop fuzzy control system maintains the system asymptotically-stability while it enhances the system time response to achieve better control of the concentration of the output gas from the tower. Simulation studies are carried out to illustrate the Gas Separator system performance.

Keywords: gas separator, gas sweetening, intelligent controller, fuzzy control

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Authors: R. S. Sheu, H. Usman, M. S. Lawal

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Takagi-Sugeno (T-S) fuzzy model based control of a load frequency deviation in a single machine with limit nonlinearity on power coefficient is presented in the paper. Two T-S fuzzy rules with only rotor angle variable as input in the premise part, and linear state space models in the consequent part involving characteristic matrices determined from limits set on the power coefficient constant are formulated, state feedback control gains for closed loop control was determined from the formulated Linear Matrix Inequality (LMI) with eigenvalue optimization scheme for asymptotic and exponential stability (speed of esponse). Numerical evaluation of the closed loop object was carried out in Matlab. Simulation results generated of both the open and closed loop system showed the effectiveness of the control scheme in maintaining load frequency stability.

Keywords: T-S fuzzy model, state feedback control, linear matrix inequality (LMI), frequency deviation control

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Authors: S. Yaman, S. Rostami

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In this study, a black box modeling of the coupled-tank system is obtained by using fuzzy sets. The derived model is tested via adaptive neuro fuzzy inference system (ANFIS). In order to achieve a better control performance, the parameters of three different controller types, classical proportional integral controller (PID), fuzzy PID and function tuner method, are tuned by one of the evolutionary computation method, genetic algorithm. All tuned controllers are applied to the fuzzy model of the coupled-tank experimental setup and analyzed under the different reference input values. According to the results, it is seen that function tuner method demonstrates better robust control performance and guarantees the closed loop stability.

Keywords: function tuner method (FTM), fuzzy modeling, fuzzy PID controller, genetic algorithm (GA)

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