• International Journal of Computer Science & Network Security
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• v.21 no.12
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• pp.223-227
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• 2021

A treatment based on the algebraic operations on fuzzy numbers is used to replace the fuzzy problem into an equivalent crisp one. The finite difference technique is used to replace the continuous boundary value problem (BVP) of arbitrary order 1<α≤2, with fuzzy boundary parameters into an equivalent crisp (algebraic or differential) system. Three numerical examples with different behaviors are considered to illustrate the treatment of the singular perturbed case with different fractional orders of the BVP (α=1.8, α=1.9) as well as the classical second order (α=2). The calculated fuzzy solutions are compared with the crisp solutions of the singular perturbed BVP using triangular membership function (r-cut representation in parametric form) for different values of the singular perturbed parameter (ε=0.8, ε=0.9, ε=1.0). Results are illustrated graphically for the different values of the included parameters.

• Proceedings of the KIEE Conference
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• 2007.04a
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• pp.201-203
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• 2007

The paper concerns the successive optimization for structure and parameters of fuzzy inference systems that is based on parallel Genetic Algorithms (PGA) and information data granulation (IG). PGA is multi, population based genetic algorithms, and it is used tu optimize structure and parameters of fuzzy model simultaneously, The granulation is realized with the aid of the C-means clustering. The concept of information granulation was applied to the fuzzy model in order to enhance the abilities of structural optimization. By doing that, we divide the input space to form the premise part of the fuzzy rules and the consequence part of each fuzzy rule is newly' organized based on center points of data group extracted by the C-Means clustering, It concerns the fuzzy model related parameters such as the number of input variables to be used in fuzzy model. a collection of specific subset of input variables, the number of membership functions according to used variables, and the polynomial type of the consequence part of fuzzy rules, The simultaneous optimization mechanism is explored. It can find optimal values related to structure and parameter of fuzzy model via PGA, the C-means clustering and standard least square method at once. A comparative analysis demonstrates that the Dnmosed algorithm is superior to the conventional methods.

• Journal of Drive and Control
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• v.15 no.1
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• pp.28-37
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• 2018

When the wind speed rises above the rated wind speed, the produced power of the wind turbines exceeds the rated power. Even more, the excessive power results in the undesirable mechanical load and fatigue. A solution to this problem is pitch control of the wind turbines. This paper presents a systematic design method of a collective pitch controller for the wind turbines using a discrete fuzzy Proportional-Integral (PI) controller. Unlike conventional PI controllers, the fuzzy PI controller has variable gains according to its input variables. Generally, tuning the parameters of fuzzy PI controller is complex due to the presence of too many parameters strongly coupled. In this paper, a systematic method for the fuzzy PI controller is presented. First, we show the fact that the fuzzy PI controller is a superset of the PI controller in the discrete-time domain and the initial parameters of the fuzzy PI controller is selected by using this relationship. Second, for simplicity of the design, we use only four rules to construct nonlinear fuzzy control surface. The tuning parameters of the proposed fuzzy PI controller are also obtained by the aforementioned relationship between the PI controller and the fuzzy PI controller. As a result, unlike the PI controller, the proposed fuzzy PI controller has variable gains which allow the pitch control system to operate in broader operating regions. The effectiveness of the proposed controller is verified with computer simulations using FAST, a NREL's primary computer-aided engineering tool for horizontal axis wind turbines.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.7
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• pp.807-815
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• 2004

This paper describes the design principle of a fuzzy PID controller with fixed parameters, proposes the simulified form of a fuzzy PID controller to increase the computational efficiency and analyzes stability of a proposed fuzzy PID controller. After a detailed stability analysis using ‘small gain theorem’, a simple and practical sufficient condition for the BIBO stability of the overall feedback control system is derived. The derived stability condition offers a calculation method to obtain parameters of a fuzzy PID controller from parameters of a stable PID controller. Finally several computer simulations are executed to confirm the effectiveness of the fuzzy PID controller with fixed parameters.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.16 no.4
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• pp.225-237
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• 2016

In conventional transportation problem (TP), all the parameters are always certain. But, many of the real life situations in industry or organization, the parameters (supply, demand and cost) of the TP are not precise which are imprecise in nature in different factors like the market condition, variations in rates of diesel, traffic jams, weather in hilly areas, capacity of men and machine, long power cut, labourer's over time work, unexpected failures in machine, seasonal changes and many more. To counter these problems, depending on the nature of the parameters, the TP is classified into two categories namely type-2 and type-4 fuzzy transportation problems (FTPs) under uncertain environment and formulates the problem and utilizes the trapezoidal fuzzy number (TrFN) to solve the TP. The existing ranking procedure of Liou and Wang (1992) is used to transform the type-2 and type-4 FTPs into a crisp one so that the conventional method may be applied to solve the TP. Moreover, the solution procedure differs from TP to type-2 and type-4 FTPs in allocation step only. Therefore a simple and efficient method denoted by PSK (P. Senthil Kumar) method is proposed to obtain an optimal solution in terms of TrFNs. From this fuzzy solution, the decision maker (DM) can decide the level of acceptance for the transportation cost or profit. Thus, the major applications of fuzzy set theory are widely used in areas such as inventory control, communication network, aggregate planning, employment scheduling, and personnel assignment and so on.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.4
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• pp.767-778
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• 2003

This paper presents a method for generating optimal fuzzy rules using a genetic algorithm. Fuzzy rules are generated from the training data in the first stage. In this stage, fuzzy c-Means clustering method and cluster validity are used to determine the structure and initial parameters of the fuzzy inference system. A cluster validity is used to determine the number of clusters, which can be the number of fuzzy rules. Once the structure is figured out in the first stage, parameters relating the fuzzy rules are optimized in the second stage. Weights and variance parameters are tuned using genetic algorithms. Variance parameters are also managed with left and right for asymmetrical Gaussian membership function. The method ensures convergence toward a global minimum by using genetic algorithms in weight and variance spaces.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.12
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• pp.985-992
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• 2001

This paper proposes a self-organizing fuzzy modeling(SOFUM)which an create a new hyperplane shaped cluster and adjust parameters of the fuzzy model in repetition. The suggested algorithm SOFUM is composed of four steps: coarse tuning. fine tuning cluster creation and optimization of learning rates. In the coarse tuning fuzzy C-regression model(FCRM) clustering and weighted recursive least squared (WRLS) algorithm are used and in the fine tuning gradient descent algorithm is used to adjust parameters of the fuzzy model precisely. In the cluster creation, a new hyperplane shaped cluster is created by applying multiple regression to input/output data with relatively large fuzzy entropy based on parameter tunings of fuzzy model. And learning rates are optimized by utilizing meiosis-genetic algorithm in the optimization of learning rates To check the effectiveness of the suggested algorithm two examples are examined and the performance of the identified fuzzy model is demonstrated via computer simulation.

• International Journal of Control, Automation, and Systems
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• v.2 no.1
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• pp.68-75
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• 2004

In this paper, an estimator with an appropriate adaptive law for updating parameters is designed and analyzed based on the Lyapunov theory. The adaptive law is designed so that the estimation model follows the parameterized plant model. Using the proposed estimator, the parameters of the T-S fuzzy model can be estimated by observing the behavior of the system and it can be a basis for indirect adaptive fuzzy control.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.228-231
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• 2000

A hybrid fuzzy controller by means of the genetic algorithms is presented. The control input for the system in the HFC is a convex combination of the FLC's output in transient state and PlD's output in steady state by a fuzzy variable. The HFC combined a PID controller with a fuzzy controller concurrently produces the better output performance than any other controller. A auto-tuning algorithms is presented to automatically improve the performance of hybrid fuzzy controller using genetic algorithms. The algorithms estimates automatical Iy the optimal values of scaling factors, PID parameters and membership function parameters of fuzzy control rules. Especially, in order to auto-tune scaling factors and PID parameters of HFC using GA three kinds of estimation modes are effectively utilized. The HFCs are applied to the second process with time-delay. Computer simulations are conducted at step input and the performances of systems are evaluated and also discussed in ITAE(Integral of the Time multiplied by the Absolute value of Error ) and other ways.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2545-2547
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• 2000

In this paper, a hybrid fuzzy controller using genetic algorithm based on parameter estimation mode to obtain optimal control parameter is presented. First, The control input for the system in the HFC is a convex combination of the FLC's output in transient state and PID's output in steady state by a fuzzy variable, namely, membership function of weighting coefficient. Second, genetic algorithms is presented to automatically improve the performance of hybrid fuzzy controller utilizing the conventional methods for finding PID parameters and estimation mode of scaling factor. The algorithms estimates automatically the optimal values of scaling factors, PID parameters and membership function parameters of fuzzy control rules according to the rate of change and limitation condition of control input. Computer simulations are conducted to evaluate the performance of proposed hybrid fuzzy controller. ITAE, overshoot and rising time are used as a performance index of controller.