• Title/Summary/Keyword: Nonlinear state equations

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Speed, Depth and Steering Control of Underwater Vehicles with Four Stem Thrusters - Simulation and Experimental Results (네 대의 주 추진기를 이용한 무인잠수정의 속도, 심도 및 방위각 제어 - 시뮬레이션 및 실험)

  • JUN BONG-HUAN;LEE PAN-MOOK;LI JI-HONG;HONG SEOK-WON;LEE JIHONG
    • Journal of Ocean Engineering and Technology
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    • v.19 no.2 s.63
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    • pp.67-73
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    • 2005
  • This paper describes depth, heading and speed control of an underwater vehicle that has four stern thrusters of which forces are coupled in the diving and, steering motion, as well as the speed of the vehicle. The optimal linear quadratic controller is designed based on a linearized- state space model, developed by combining the dynamic equations of speed, steering and diving motion. The designed controller gives provides an optimal thrust distribution, minimizing the given performance index to control speed, depth and heading simultaneously. To validate the performance of the controller, a simulation and tank-test are carried out with DUSAUV (Dual Use Semi-Autonomous Underwater Vehicle), developed by KORDI as a test-bed for testing new underwater technologies. Optimal gains of the controller are tuned, using a computer simulation environment with a nonlinear 6-DOF numerical DUSAUV model, developed by PMM (Planner Motion Mechanism) test. To verify the performance of the presented controller in experiment, a tank-test with DUSAUV is carried out in the ocean engineering basin in KORDI. The experimental results are also compared with the simulation results to investigate the accordance of the numerical and the real mode.

A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations

  • Attia, Amina;Bousahla, Abdelmoumen Anis;Tounsi, Abdelouahed;Mahmoud, S.R.;Alwabli, Afaf S.
    • Structural Engineering and Mechanics
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    • v.65 no.4
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    • pp.453-464
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    • 2018
  • In this paper, an efficient higher-order shear deformation theory is presented to analyze thermomechanical bending of temperature-dependent functionally graded (FG) plates resting on an elastic foundation. Further simplifying supposition are made to the conventional HSDT so that the number of unknowns is reduced, significantly facilitating engineering analysis. These theory account for hyperbolic distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Nonlinear thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from the principle of virtual displacements. Analytical solutions for the thermomechanical bending analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent FG plates and validated with those of other shear deformation theories. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature field on the thermomechanical bending characteristics. It can be concluded that the present theory is not only accurate but also simple in predicting the thermomechanical bending responses of temperature-dependent FG plates.

Buckling Analysis of Axisymmetric Shells by Incremental Finite Element Mothod (증분형(增分形) 유한요소법(有限要素法)에 의한 축대칭(軸對稱) Shell구조(構造)의 좌굴해석(挫屈解析))

  • J.B.,Kim;C.Y.,Kim
    • Bulletin of the Society of Naval Architects of Korea
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    • v.22 no.1
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    • pp.21-30
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    • 1985
  • This paper deals whth the buckling as well as postbuckling analysis of axisymmertric shells taking the initial deflection effects into account. Incremental equilibrium equations, based on the principle of virtual work, were derived by the finite element method, the successive step-by-step Newton-Raphson iterative technique was adopted. To define the transition pattern of postbuckling behavior from the prebuckling state more accurately, a simple solution method was developed, i.e. the critical load was calculated by the load extrapolation method with the determinant of tangent stiffness matrix and the equilibrium configuration in the immediate postbuckling stage was obtained by perturbation scheme and eigenvalue analysis. Degenerated isoparametric shell elements were used to analyse the axisymmetric shell of revolution. And by the method developed in this paper, the computer program applicable to the nonlinear analysis of both thin and moderately thick shells was constructed. To verify the capabilities and accuracies of the present solution method, the computed results were compared with the results of analytical solutions. These results coincided fairly well in both the small deflection and large deflection ranges. Various numerical analyses were done to show the effect of initial deflection and shape of shells on buckling load and postbuckling behavior. Futhermore, corrected directions of applied loads at every increment steps were used to determine the actual effects of large deflection in non-conservative load systems such as hydrostatic pressure load. The following conclusions can be obtained. (1) The method described in this paper was found to be both economic and effective in calculating buckling load and postbuckling behavior of shell structure. (2) Buckling and postbuckling behavior of spherical caps is critically dependent upon their geometric configuration, i.e. the shape of spherical cap and quantities of the initial deflection. (3) In the analysis of large deflection problems of shells by the incremental method, corrections of the applied load directions are needed at every incremental step to compensate the follower force effects.

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Underwater Docking of an AUV Using a Visual Servo Controller (비쥬얼 서보 제어기를 이용한 자율무인잠수정의 도킹)

  • Lee, Pan-Mook;Jeon, Bong-Hwan;Lee, Chong-Moo
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2002.10a
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    • pp.142-148
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    • 2002
  • Autonomous underwater vehicles (AUVs) are unmanned underwater vessels to investigate sea environments, oceanography and deep-sea resources autonomously. Docking systems are required to increase the capability of the AUVs to recharge the batteries and to transmit data in real time for specific underwater works, such as repeated jobs at sea bed. This paper presents a visual servo control system for an AUV to dock into an underwater station with a camera mounted at the nose center of the AUV. To make the visual servo control system, this paper derives an optical flow model of a camera, where the projected motions of the image plane are described with the rotational and translational velocities of the AUV. This paper combines the optical flow equation of the camera with the AUVs equation of motion, and derives a state equation for the visual servoing AUV. This paper proposes a discrete-time MIMO controller minimizing a cost function. The control inputs of the AUV are automatically generated with the projected target position on the CCD plane of the camera and with the AUVs motion. To demonstrate the effectiveness of the modeling and the control law of the visual servoing AUV, simulations on docking the AUV to a target station are performed with the 6-dof nonlinear equations of REMUS AUV and a CCD camera.

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Improvement of WRF forecast meteorological data by Model Output Statistics using linear, polynomial and scaling regression methods

  • Jabbari, Aida;Bae, Deg-Hyo
    • Proceedings of the Korea Water Resources Association Conference
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    • 2019.05a
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    • pp.147-147
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    • 2019
  • The Numerical Weather Prediction (NWP) models determine the future state of the weather by forcing current weather conditions into the atmospheric models. The NWP models approximate mathematically the physical dynamics by nonlinear differential equations; however these approximations include uncertainties. The errors of the NWP estimations can be related to the initial and boundary conditions and model parameterization. Development in the meteorological forecast models did not solve the issues related to the inevitable biases. In spite of the efforts to incorporate all sources of uncertainty into the forecast, and regardless of the methodologies applied to generate the forecast ensembles, they are still subject to errors and systematic biases. The statistical post-processing increases the accuracy of the forecast data by decreasing the errors. Error prediction of the NWP models which is updating the NWP model outputs or model output statistics is one of the ways to improve the model forecast. The regression methods (including linear, polynomial and scaling regression) are applied to the present study to improve the real time forecast skill. Such post-processing consists of two main steps. Firstly, regression is built between forecast and measurement, available during a certain training period, and secondly, the regression is applied to new forecasts. In this study, the WRF real-time forecast data, in comparison with the observed data, had systematic biases; the errors related to the NWP model forecasts were reflected in the underestimation of the meteorological data forecast by the WRF model. The promising results will indicate that the post-processing techniques applied in this study improved the meteorological forecast data provided by WRF model. A comparison between various bias correction methods will show the strength and weakness of the each methods.

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Design of Key Sequence Generators Based on Symmetric 1-D 5-Neighborhood CA (대칭 1차원 5-이웃 CA 기반의 키 수열 생성기 설계)

  • Choi, Un-Sook;Kim, Han-Doo;Kang, Sung-Won;Cho, Sung-Jin
    • The Journal of the Korea institute of electronic communication sciences
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    • v.16 no.3
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    • pp.533-540
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    • 2021
  • To evaluate the performance of a system, one-dimensional 3-neighborhood cellular automata(CA) based pseudo-random generators are widely used in many fields. Although two-dimensional CA and one-dimensional 5-neighborhood CA have been applied for more effective key sequence generation, designing symmetric one-dimensional 5-neighborhood CA corresponding to a given primitive polynomial is a very challenging problem. To solve this problem, studies on one-dimensional 5-neighborhood CA synthesis, such as synthesis method using recurrence relation of characteristic polynomials and synthesis method using Krylov matrix, were conducted. However, there was still a problem with solving nonlinear equations. To solve this problem, a symmetric one-dimensional 5-neighborhood CA synthesis method using a transition matrix of 90/150 CA and a block matrix has recently been proposed. In this paper, we detail the theoretical process of the proposed algorithm and use it to obtain symmetric one-dimensional 5-neighborhood CA corresponding to high-order primitive polynomials.

Influence of Heat Treatment Conditions on Temperature Control Parameter ((t1) for Shape Memory Alloy (SMA) Actuator in Nucleoplasty (수핵성형술용 형상기억합금(SMA) 액추에이터 와이어의 열처리 조건 변화가 온도제어 파라미터(t1)에 미치는 영향)

  • Oh, Dong-Joon;Kim, Cheol-Woong;Yang, Young-Gyu;Kim, Tae-Young;Kim, Jay-Jung
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.34 no.5
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    • pp.619-628
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    • 2010
  • Shape Memory Alloy (SMA) has recently received attention in developing implantable surgical equipments and it is expected to lead the future medical device market by adequately imitating surgeons' flexible and delicate hand movement. However, SMA actuators have not been used widely because of their nonlinear behavior called hysteresis, which makes their control difficult. Hence, we propose a parameter, $t_1$, which is necessary for temperature control, by analyzing the open-loop step response between current and temperature and by comparing it with the values of linear differential equations. $t_1$ is a pole of the transfer function in the invariant linear model in which the input and output are current and temperature, respectively; hence, $t_1$ is found to be related to the state variable used for temperature control. When considering the parameter under heat treatment conditions, $T_{max}$ was found to assume the lowest value, and $t_1$ was irrelevant to the heat treatment.

Convergence Analysis of the Least Mean Fourth Adaptive Algorithm (최소평균사승 적응알고리즘의 수렴특성 분석)

  • Cho, Sung-Ho;Kim, Hyung-Jung;Lee, Jong-Won
    • The Journal of the Acoustical Society of Korea
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    • v.14 no.1E
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    • pp.56-64
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    • 1995
  • The least mean fourth (LMF) adaptive algorithm is a stochastic gradient method that minimizes the error in the mean fourth sense. Despite its potential advantages, the algorithm is much less popular than the conventional least mean square (LMS) algorithm in practice. This seems partly because the analysis of the LMF algorithm is much more difficult than that of the LMS algorithm, and thus not much still has been known about the algorithm. In this paper, we explore the statistical convergence behavior of the LMF algorithm when the input to the adaptive filter is zero-mean, wide-sense stationary, and Gaussian. Under a system idenrification mode, a set of nonlinear evolution equations that characterizes the mean and mean-squared behavior of the algorithm is derived. A condition for the conbergence is then found, and it turns out that the conbergence of the LMF algorithm strongly depends on the choice of initial conditions. Performances of the LMF algorithm are compared with those of the LMS algorithm. It is observed that the mean convergence of the LMF algorithm is much faster than that of the LMS algorithm when the two algorithms are designed to achieve the same steady-state mean-squared estimation error.

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