• Journal for History of Mathematics
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• v.20 no.3
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• pp.147-166
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• 2007

This study is about the law of cosines. It dealt with its historical origin and the developmental process of the age of Greece, Islam and Modern age. Especially, we tried to find out how the extension of the law of cosines for spherical triangles and tetrahedron from the law of cosines for plane was done. On the basis of this analysis, we investigated how the law of cosines was generated and proved it through the logical demonstration and mathematical induction. This made us find out the mathematical meaning of mathematical concepts.

• Proceedings of the KIEE Conference
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• 1989.07a
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• pp.48-53
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• 1989

We attempt to achieve both high dynamic performance and maximal power efficiency by means of linear decoupling of rotor speed (or motor torque) and rotor flux. The induction motor with our controller possesses the input-output dynamic characteristics of a linear system such that the rotor speed (or motor torque) and the rotor flux are decoupled. The rotor speed (or motor torque) responses are not affected by abrupt changes in the rotor flux and vice versa. The rotor flux need not be measured but is estimated by the well-known flux simulator. The effect of large variation in the rotor resistance on the control performances is minimized by employing a parameter adaptation method. To illuminate the significance of our work. we present simulation and experimental results as well as mathematical performance analyses.

• Proceedings of the KIEE Conference
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• 1999.07f
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• pp.2610-2612
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• 1999

In controlling vector of induction motor, PID controller is required much time as the expert should control manually a gain of controller according to plant or a change of circumstances. Accordingly, this paper has gotten a gain of PID controller used neural network by self-funning method in order to settle above problem. The neural network can describe an input/output features in spite of non-linear system which is hard to get mathematical model by controlling the strength of connection by learning. It has a strong character against a distortion and noise of input information, and is suitable modeling of diver-variable system which is composed of several input/output. This paper has represented the self-tunning method for gain of PID controller used neural network when using PID controller to control speed of induction motor, and has checked strong characters against distortion and noise of input information through simulation.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.10
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• pp.1066-1074
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• 1990

In this paper, we attempt to control induction motors with high power efficiency as well as high dynamic performance by utilizing the recently developed theories : singular perturbation technique and noninteracting feedback control. Our controller consists of three subcontrollers` a saturation current controller, a decoupling controller, and a well-known flux simulator. The decoupling controller decouples rotor speed (or motor torque) and rotor flux linearly. Our controller does not need the rotor resistance that varies widely with the machine temperature. To illuminate the practical significance of our results, we present simulation and experimental results as well as mathematical performance analysis.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.5B no.4
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• pp.350-357
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• 2005

This paper presents a mechanical sensorless vector-controlled system with parameter identification by the aid of image processor. Based on the flux observer and the model reference adaptive system method, the proposed sensorless system includes rotor speed estimation and stator resistance identification using flux errors. Since the mathematical model of this system is constructed in a synchronously rotating reference frame, a linear model is easily derived for analyzing the system stability, including motor operating state and parameter variations. Because it is difficult to identify rotor resistance simultaneously while estimating rotor speed, a low-accuracy image processor is used to measure the mechanical axis position for calculating the rotor speed at a steady-state operation. The rotor resistance is identified by the error between the estimated speed using the estimated flux and the calculated speed using the image processor. Finally, the validity of this proposed system has been proven through experimentation.

• Proceedings of the KIEE Conference
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• 2000.07b
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• pp.1260-1263
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• 2000

Vector control of a single phase induction machine(SPIM) is usually employed by mechanical methods than electrical ones. The disadvantage of a SPIM has large noise at the starting. Using auxiliary winding which is only utilized for starting, the SPIM can be controlled with the vector control method. Regarding a auxiliary winding one phase, the SPIM is analyzed by the unsymmetrical two phase motor and phase transformation is unnecessary such as three phase IM. Including a auxiliary winding, SPIM is modeled by mathematical getting by component of turns ratio with main to auxiliary winding. It will be take with complicated resultant formula, by comparison to symmetrical three phase TM. For using the vector control theory, it must be decoupled of rotor flux and torque component. stator current is controlled and decoupled. This paper presents a variable-speed control system of SPIM, which to decoupled with flux and torque component and to use machine equivalent circuit referred to rotor, conventionally three phase IM by similar method.

• The Proceedings of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.7 no.4
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• pp.42-50
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• 1993

This paper was proposed drive strategy Induction Motor using the fuzzy algorithm of auto-tuning PID control. In fuzzy control, the 1M driving system is controlled in trial and error without the mathematical modeling and using fuzzy lookup table the real time control is possible. Also, ,dividing the fuzzy rules in several zone, the stability and response of the 1M driving system is improved. The parameters of 1M are varying according to the environmental conditions, the variance of the parameters is affected with the driving characteristics of 1M. Using the fuzzy algorithm of the driving system which has the auto tuning control function for high performance, high accuracy of the driving system, a designed and proposed through the comparision with the PID control method and the driving characteristics is reviewed and analyzed.

• The Transactions of the Korean Institute of Power Electronics
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• v.27 no.3
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• pp.256-264
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• 2022

The frequency power control method (FCM) which has a wide operating frequency range is adopted for induction heating (IH) cooktops. When FCM is applied to the full-bridge series resonant converter (FB-SRC) based IH system, high-frequency switching of the inverter is required compared to the half-bridge SRC (HB-SRC)-based IH system. Therefore, the switching loss of the inverter increases, and applying FCM under the condition that the inverter operating frequency range is limited is difficult. Therefore, this paper proposes a control strategy with the phase shift power control method considering that limited frequency conditions are presented. Loss analysis following the control method is performed through simulation and mathematical analysis. In addition, the validity of the proposed control strategy is verified by analyzing the heating performance following the control method through the test results of the 3,200[W] prototype.

• The Transactions of the Korean Institute of Power Electronics
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• v.27 no.5
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• pp.425-430
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• 2022

A pumped storage power station is an important means to solve the problem of peak load regulation and ensures the safety of power grid operation. The doubly fed variable-speed pumped storage (DFVSPS) system adopts a doubly fed induction machine (DFIM) to replace the synchronous machine used in traditional pumped storage. The stator of DFIM is connected to the power grid, and the three-phase excitation windings are symmetrically distributed on the rotor. Excitation current is supplied by the converter. The active and reactive power of the unit can be quickly adjusted by adjusting the amplitude, frequency, and phase of the rotor-side voltage or current through the converter. Compared with a conventional pumped storage hydropower station (C-PSH), DFVSPS power stations have various operating modes and frequent start-up and shutdown. This study introduces the structure and principle of the DFVSPS unit. Mathematical models of the unit, including a model of DFIM, a model of the pump-turbine, and a model of the converter and its control, are established. Fast power control strategies are proposed for the unit model. A 300 MW model of the DFVSPS unit is established in MATLAB/Simulink, and the response characteristics in generating mode are examined.

• Journal of Elementary Mathematics Education in Korea
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• v.1 no.1
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• pp.87-98
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• 1997

A practice is classified into the practice as a content and the practice as a method. The former means that the practical nature of mathematical knowledge itself should be a content of mathematics and the latter means that one should teach the mathematical knowledge in such a way as the practical nature is not damaged. The practical nature of mathematics means mathematician's activity as it is actually done. Activities of the mathematician are not only discovering strict proofs or building axiomatic system but informal thinking activities such as generalization, analogy, abstraction, induction etc. In this study, it is found that the most instructive ones for the future users of mathematics are such practice as content. For the practice as a method, students might learn, by becoming apprentice mathematicians, to do what master mathematicians do in their everyday practice. Classrooms are cultural milieux and microsoms of mathematical culture in which there are sets of beliefs and values that are perpetuated by the day-to-day practices and rituals of the cultures. Therefore, the students' sense of ‘what mathematics is really about’ is shaped by the culture of school mathematics. In turn, the sense of what mathematics is really all about determines how the students use the mathematics they have learned. In this sense, the practice on which classroom instruction might be modelled is that of mathematicians at work. To learn mathematics is to enter into an ongoing conversation conducted between practitioners who share common language. So students should experience mathematics in a way similar to the way mathematicians live it. It implies a view of mathematics classrooms as a places in which classroom activity is directed not simply toward the acquisition of the content of mathematics in the form of concepts and procedures but rather toward the individual and collaborative practice of mathematical thinking.