• Title/Summary/Keyword: mathematical errors

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Terrain-referenced Underwater Navigation using Rao-Blackwellized Particle Filter (라오-블랙웰라이즈드 입자필터를 이용한 지형참조 수중항법)

  • Kim, Taeyun;Kim, Jinwhan;Choi, Hyun-Taek
    • Journal of Institute of Control, Robotics and Systems
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    • v.19 no.8
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    • pp.682-687
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    • 2013
  • Navigation is a crucial capability for all types of manned or unmanned vehicles. However, vehicle navigation in underwater environments still remains a challenging problem since GPS signals for position fixes are not available in the water. Terrain-referenced underwater navigation is an alternative navigation technique that utilizes geometric information of the subsea terrain to correct drift errors due to dead-reckoning or inertial navigation. Terrain-referenced navigation requires the description of an undulating terrain surface as a mathematical function or table, which often leads to a highly nonlinear estimation problem. Recently, PFs (Particle Filters), which do not require any restrictive assumptions about the system dynamics and uncertainty distributions, have been widely used for nonlinear filtering applications. However, PF has considerable computational requirements which used to limit its applicability to problems of relatively low state dimensions. This study proposes the use of a Rao-Blackwellized particle filter that is computationally more efficient than the standard PF for terrain-referenced underwater navigation involving a moderate number of states, and its performance is compared with that of the extended Kalman filter algorithm. The validity and feasibility of the proposed algorithm is demonstrated through numerical simulations.

Robust motion control of a flexible micro-actuator using $H_{\infty}$ control method

  • Okugawa, Masayuki;Sasaki, Minoru;Fujisawa, Fumio
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10a
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    • pp.397-400
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    • 1996
  • In this paper, robust motion control of a flexible micro-actuator is presented. The actuator is made of a bimorph piezoelectric high-polymer material (PVDF). No mathematical model system can exactly model a physical system such a flexible micro-actuator. For this reason we must be aware of how modeling errors might adversely affect the performance of a control system for such a model. The H method addresses a wide range of the control problems, combining the frequency and time domain approaches. The design is an optimal one in the sense of minimization of the maximum of the closed-loop transfer function. It includes colored measurement and process noise. It also addresses the issues of robustness due to model uncertainties, and is applicable to the, flexible micro-actuator control problem. Therefore, we adopt the H control problem to the robust motion control of the flexible micro-actuator. Theoretical and experimental results demonstrate the satisfactory performance and the effectiveness of the designed controller. the effectiveness of the designed controller.

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An optimization of activated sludge process in wastewater treatment system utilizing fuzzy graphic simulator (퍼지 그래픽 시뮬레이터를 이용한 하수처리 시스템 활성오니공정의 최적화)

  • Nahm, Eui-Suck;Park, Jong-Jin;Woo, Kwang-Bang
    • Journal of Institute of Control, Robotics and Systems
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    • v.3 no.2
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    • pp.204-213
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    • 1997
  • In this paper, an application of fuzzy-neuron reasoning to the control of an activated sludge plant is presented. The activated sludge process is widely used in modern wastewater treatment plants. The operation control of the activated sludge process, however, is difficult due to the following reasons : 1)The complexity of the wastewater components, 2)the change of the wastewater influent, and 3)the adjustment errors in the control process. Because of these reasons, it is difficult to obtain mathematical model that really reflect the relationship between the variables and parameters in the process of wastewater treatment correctively and effectively. In this paper, the activated sludge process(A.S.P.) is modeled by a new fuzzy-neuron network representing nonlinear characteristics. These fuzzy-neurons have fuzzy rules with complementary membership function. Based on the constructed model, graphic simulator on X-window system as a graphic integrated environment is implemented. The efficacy of the proposed control scheme was evaluated and demonstrated by means of the field test.

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A Study on the Quotient and Remainder in Division of Decimal (소수 나눗셈에서 몫과 나머지에 관한 소고)

  • Jeong, Sangtae
    • Education of Primary School Mathematics
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    • v.19 no.3
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    • pp.193-210
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    • 2016
  • In the $10{\div}2.4$ problem situation, we could find that curious upper and middle level students' solution. They solved $10{\div}2.4$ and wrote the result as quotient 4, remainder 4. In this curious response, we researched how students realize quotient and remainder in division of decimal. As a result, many students make errors in division of decimal especially in remainder. From these response, we constructed fraction based teaching method about division of decimal. This method provides new aspects about quotient and remainder in division of decimal, so we can compare each aspects' strong points and weak points.

A Numerical Analysis of River-bed Variation in Alluvial Stream (충적하천(沖積河川)의 하상변동(河床變動)에 관한 수치해석(數値解析))

  • Park, Jung Eng
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.4 no.1
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    • pp.49-58
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    • 1984
  • This paper is to exhibit the numerical analysis of sediment transport in the slowly varing flow and the sediment transport relation between the steady and the unsteady flow in the alluvial stream. The gradually varied flow of alluvial stream and the sediment transport are very complicated physical phenomen. Therefore the mathematical modeling is needed to be established. Linear implicit means of modified indirect method are applied to sediment transport by numerical analysis instead of the conception of steady flow in order to decrease errors. Further more, this study has purpose on reasonable prediction of the river-bed variation by way of this numerical method.

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Specific Cutting Force Coefficients Modeling of End Milling by Using Neural Network (신경회로망을 이용한 엔드밀 가공의 비절삭력계수 모델링)

  • Lee, Sin-Young;Lee, Jang-Moo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.23 no.6 s.165
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    • pp.979-987
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    • 1999
  • In a high precision vertical machining center, the estimation of cutting forces is important for many reasons such as prediction of chatter vibration, surface roughness and so on, and cutting forces are difficult to predict because they are very complex and time variant. In order to predict the cutting forces of end-milling process for various cutting conditions, a mathematical model is important and this model is based on chip load, cutting geometry, and the relationship between cutting forces and chip loads. Specific cutting force coefficients of the model have been obtained as interpolation function types by averaging farces of cutting tests. In this paper, the coefficients are obtained by neural network and the results of the conventional method and those of the proposed method are compared. The results show that the neural network method gives more correct values than the function type and that in teaming stage as the omitted numbers of experimental data increases the average errors increase.

Duty Ratio-Displacement Model in PWM Control of Voice Coil Actuator (보이스 코일 액츄에이터의 PWM 제어에서 듀티비-변위 모델 연구)

  • Hwang, Jin-Dong;Kwak, Yong-Kil;Kim, Ju-Hyun;Kim, Sun-Ho;Ahn, Jung-Hwan
    • Journal of the Korean Society of Manufacturing Process Engineers
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    • v.6 no.2
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    • pp.59-66
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    • 2007
  • Voice coil actuator is used linear motion system that requires precision positioning control. In order to control precision positioning of voice coil actuator, relation model between duty ratio and moving displacement of voice coil actuator is needed. This paper present a duty ratio - displacement model in PWM control of voice coil actuator. Transfer function of voice coil actuator is obtained by combining voice coil motor's equation of motion with the equation of circuit and characteristic of voice coil motor. Consider to initial condition of velocity and current, transfer function is transformed mathematical model. The induced model can predict output displacement, velocity and current according to duty ratio and amplitude. The model is verified by experimental tests such as velocity and displacement response of voice coil motor. Simulated results have tracking errors of less than 10 percent of experimental results.

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Light Distribution Pattern of Optical System in Street Lights with AC COB-Type LEDs (AC COB형 LED 가로등의 광학계 배광 패턴)

  • Kim, Young-Gil;Yoo, Kyung-Sun;Lee, Chang-Soo;Hyun, Dong-Hoon
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.26 no.1
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    • pp.66-73
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    • 2017
  • This study attempted to design lights with Type II distribution suitable for LED street lights based on the regulations of street light distribution developed by the Illuminating Engineering Society of North America (IESNA). The shape of an asymmetric lens, different from that of a rotationally symmetric lens, cannot be generated using a simple mathematical formula. In the first trial, the outline of the lens was fixed and simulated to confirm the distribution type. Following ISENA regulations, some problems that occurred during simulations and repeating was be modified that process is how we detected errors. Through optical research and simulations, a lens conforming to the regulations of Type II very short, Type II short, and Type II medium distributions was developed. A prototype was developed using simulation data and it was subjected to distribution tests. The results show that it can compare with property of Type II distribution.

Modeling of Fuel Consumption Rate for Agricultural Tractors (농업용 트랙터의 연료 소비량 예측 모델)

  • Kim, Soo-Chul;Kim, Kyeong-Uk;Kim, Dae-Cheol
    • Journal of Biosystems Engineering
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    • v.35 no.1
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    • pp.1-9
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    • 2010
  • A mathematical model was developed to predict the fuel consumption rate consumed by agricultural tractors under arbitrary loaded conditions. The model utilizes the measured data on the fuel consumptions at the full load and at the rated engine speed with partial loads, which can easily be obtained from the official OECD tractor test reports. It was found from the analysis of the measured fuel consumption data that the fuel consumptions at two different speeds does not change with power. The model was developed based on this fact and validated with the measured data of the 159 tractor test reports. The fuel consumptions predicted by the model were compared with those measured under the partially loaded conditions specified in the official OECD tractor test code II. The percent errors of the predicted fuel consumptions were in a range from 0.36 to 2.86% which assured that the developed fuel consumption model can be used practically to predict the fuel consumptions at any speed and power combinations. It was also shown that the developed model predicts the fuel consumption rate better than the Grisso's model.

The Position and Speed Control of the BLDC Motor Using the Disturbance Observer (외란 관측기를 이용한 BLDCM의 위치 및 속도제어)

  • Jeon, Yong-Ho
    • The Journal of the Korea institute of electronic communication sciences
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    • v.15 no.5
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    • pp.899-906
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    • 2020
  • Motor control requires robust and precise control performance even in the presence of errors in the mathematical model of the motor and disturbances acting on the motor. For robust and precise control, a disturbance observer was designed to estimate the load fluctuation and applied to a back-stepping controller designed as a nominal system. The control performance of the designed system was verified by applying it to the 120 [W] Brushless Direct Current Motor. As a result of the position control and speed control, the disturbance is overcome from the steady state error converges to zero, and asymptotically stable results can be confirmed.