• Title/Summary/Keyword: Nonlinear Systems of Equations

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Characteristics Comparison of Axial and Radial Flux Permanent Magnet Generators for 1.5kW Class Wind Power Systems (1.5kW급 풍력발전용 축자속/반경자속 영구자석 발전기의 특성 비교)

  • Ko, Kyoung-Jin;Jang, Seok-Myeong;Koo, Min-Mo;Lee, Sung-Ho;Han, Sang-Chul;Park, Young-Tae
    • Proceedings of the KIEE Conference
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    • 2011.07a
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    • pp.1075-1076
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    • 2011
  • This paper compares performance characteristics and mechanical design specifications of outer rotor radial flux type and double-sided axial flux type permanent magnet generator for 1.5-kW class small scale wind power applications to suggest most suitable type. In order to analyze electromagnetic performances of two different type generators, this paper performs generating performance and efficiency characteristic analysis from electrical parameters obtained by using nonlinear finite element analysis using commercial software, electromagnetic losses characteristics equations and d-q characteristics equation. Considering the derived electromagnetic performance, mechanical design specifications and manufacturing cost, the best suitable model for 1.5-kW class wind power system is determined, and its experiment was performed to validate the suggested analysis method.

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NONLINEAR OUTPUT VOLTAGE CONTROLOF PWM DC-DC CONBERTERS BY FEEDBACK LINERIZATION

  • Jo, Byeong-Rim;Min, Byung-Hoon;Choi, Hang-June
    • 제어로봇시스템학회:학술대회논문집
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    • 1995.10a
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    • pp.223-226
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    • 1995
  • New output voltage control technique based on the simple feedback linearization is proposed. The system states are first divided into fast states and slow states. Then, the control stage is composed of the fast inner current control loop and the slow outer voltage control loop. From the inner loop, the average control is derived by the sliding mode concept and it is inserted into the dynamic equations of the slow states in the outer loop. Applying the feedback linearization technique to the obtained large-signal models of the PWM dc-dc converters, linearized large-signal models are obtained for the slow states. With this technique, the output voltage controller of the PWM dc-dc converters can be designed easily in the global state space and its control performance can also be much improved.

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Analytical study on cable shape and its lateral and vertical sags for earth-anchored suspension bridges with spatial cables

  • Gen-min Tian;Wen-ming Zhang;Jia-qi Chang;Zhao Liu
    • Structural Engineering and Mechanics
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    • v.87 no.3
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    • pp.255-272
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    • 2023
  • Spatial cable systems can provide more transverse stiffness and torsional stiffness without sacrificing the vertical bearing capacity compared with conventional vertical cable systems, which is quite lucrative for long-span earth-anchored suspension bridges' development. Higher economy highlights the importance of refined form-finding analysis. Meanwhile, the internal connection between the lateral and vertical sags has not yet been specified. Given this, an analytic algorithm of form-finding for the earth-anchored suspension bridge with spatial cables is proposed in this paper. Through the geometric compatibility condition and mechanical equilibrium condition, the expressions for cable segment, the recurrence relationship between catenary parameters and control equations of spatial cable are established. Additionally, the nonlinear general reduced gradient method is introduced into fast and high-precision numerical analysis. Furthermore, the analytic expression of the lateral and vertical sags is deduced and discussed. This is very significant for the space design above the bridge deck and the optimization of the sag-to-span ratio in the preliminary design stage of the bridge. Finally, the proposed method is verified with the aid of two examples, one being an operational self-anchored suspension bridge (with spatial cables and a 260 m main span), and the other being an earth-anchored suspension bridge under design (with spatial cables and a 500 m main span). The necessity of an iterative calculation for hanger tensions on earth-anchored suspension bridges is confirmed. It is further concluded that the main cable and their connected hangers are in very close inclined planes.

Longitudinal Flight Dynamic Modeling and Stability Analysis of Flapping-wing Micro Air Vehicles (날갯짓 비행 로봇의 세로방향 비행 동역학 모델링 및 안정성 해석)

  • Kim, Joong-Kwan;Han, Jong-Seob;Kim, Ho-Young;Han, Jae-Hung
    • Journal of Institute of Control, Robotics and Systems
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    • v.21 no.1
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    • pp.1-6
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    • 2015
  • This paper investigates the longitudinal flight dynamics and stability of flapping-wing micro air vehicles. Periodic external forces and moments due to the flapping motion characterize the dynamics of this system as NLTP (Non Linear Time Periodic). However, the averaging theorem can be applied to an NLTP system to obtain an NLTI (Non Linear Time Invariant) system which allows us to use a standard eigen value analysis to assess the stability of the system with linearization around a reference point. In this paper, we investigate the dynamics and stability of a hawkmoth-scale flapping-wing air vehicle by establishing an LTI (Linear Time Invariant) system model around a hovering condition. Also, a direct time integration of full nonlinear equations of motion of the flapping-wing micro air vehicle is conducted to see how the longitudinal flight dynamics appear in the time domain beyond the reference point, i.e. hovering condition. In the study, the flapping-wing air vehicle exhibited three distinct dynamic modes of motion in the longitudinal plane of motion: two stable subsidence modes and one unstable oscillatory mode. The unstable oscillatory mode is found to be a combination of a pitching velocity state and a forward/backward velocity state.

Computation of the Bow Deck Design Pressure against the Green Water Impact (Green Water 충격에 대비한 선수갑판 설계압력의 산출)

  • Kim, Yong Jig;Shin, Ki-Seok;Lee, Seung-Chul;Ha, Youngrok;Hong, Sa Young
    • Journal of the Society of Naval Architects of Korea
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    • v.56 no.4
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    • pp.343-351
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    • 2019
  • Green water impact may sometimes cause some structure damages on ship's bow deck. Prediction of proper design pressure against the green water impact is an essential task to prevent the possible damages on bow deck. This paper presents a computational method of the bow deck's design pressure against the green water impact. Large heave and pitch motions of ship are calculated by the time domain nonlinear strip method. Green water flow and pressure on bow deck are simulated by the predictor-corrector second kind upstream finite difference method. This green water simulation method is based on the shallow water wave equations expanded for moving bottom conditions. For various kind of ships such as container ship, VLCC, oil tanker and bulk carrier, the green water design pressures on bow deck are computed and discussed. Also, the obtained results of design pressure on bow deck are compared with those of the classification society rules and discussed.

Filtering Algorithms for Position Evaluation and Tracking of Tactical Objects (전술객체 위치 모의 및 추적을 위한 필터링 알고리즘 연구)

  • Kim, Seok-Kwon;Jin, Seung-Ri;Son, Jae-Won;Park, Dong-Jo
    • Journal of the Korea Society for Simulation
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    • v.19 no.4
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    • pp.199-208
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    • 2010
  • Positions of tactical objects are represented as Time, Space and Position Information(TSPI) in modeling and simulations(M&S). The format and required information record for TSPI is investigated by referring the TSPI object model of the Test and Training Enabling Architecture(TENA), which has been developed by the United States Department of Defense. The most sophisticated tactical data link, Link-16 has a Precise Participant Location and Information (PPLI) message. We study the data format for exchanging TSPI data based on the PPLI message. To evaluate and track positions of tactical objects, we consider the Kalman filter for linear systems, and the extended Kalman filter and the unscented Kalman filter for nonlinear systems. Based on motion equations of a ballistic missile, the tracking performance for the trajectory of the ballistic missile is simulated by the unscented Kalman filter.

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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Analysis of vibration characterization of a multi-stage planetary gear transmission system containing faults

  • Hao Dong;Yue Bi;Bing-Xing Ren;Zhen-Bin Liu;Yue, Li
    • Structural Engineering and Mechanics
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    • v.88 no.4
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    • pp.389-403
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    • 2023
  • In order to explore the influence of tooth root cracks on the dynamic characteristics of multi-stage planetary gear transmission systems, a concentrated parameter method was used to construct a nonlinear dynamic model of the system with 30-DOF in bending and torsion, taking into account factors such as crack depth, length, angle, error, time-varying meshing stiffness (TVMS), and damping. In the model, the energy method was used to establish a TVMS model with cracks, and the influence of cracks on the TVMS of the system was studied. By using the Runge- Kutta method to calculate the differential equations of system dynamics, a series of system vibration diagrams containing cracks were obtained, and the influence of different crack parameters on the vibration of the system was analyzed. And vibration testing experiments were conducted on the system with planetary gear cracks. The results show that when the gear contains cracks, the TVMS of the system will decrease, and as the cracks intensify, the TVMS will decrease. When cracks appear on the II-stage planetary gear, the system will experience impact effects with intervals of rotation cycles of the II-stage planetary gear. There will be obvious sidebands near the meshing frequency doubling, and the vibration trajectory of the gear will also become disordered. These situations will become more and more obvious as the degree of cracks intensifies. Through experiments, the theoretical results are in good agreement with experimental results, verifying the correctness of the theoretical model. This provides a theoretical basis for fault diagnosis and reliability research of the system.

Response of square tension leg platforms to hydrodynamic forces

  • Abou-Rayan, A.M.;Seleemah, Ayman A.;El-Gamal, Amr R.
    • Ocean Systems Engineering
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    • v.2 no.2
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    • pp.115-135
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    • 2012
  • The very low natural frequencies of tension leg platforms (TLP's) have raised the concern about the significance of the action of hydrodynamic wave forces on the response of such platforms. In this paper, a numerical study using modified Morison equation was carried out in the time domain to investigate the influence of nonlinearities due to hydrodynamic forces and the coupling effect between surge, sway, heave, roll, pitch and yaw degrees of freedom on the dynamic behavior of TLP's. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables and the nonlinear equations of motion were solved utilizing Newmark's beta integration scheme. The effect of wave characteristics such as wave period and wave height on the response of TLP's was evaluated. Only uni-directional waves in the surge direction was considered in the analysis. It was found that coupling between various degrees of freedom has insignificant effect on the displacement responses. Moreover, for short wave periods (i.e., less than 10 sec.), the surge response consisted of small amplitude oscillations about a displaced position that is significantly dependent on the wave height; whereas for longer wave periods, the surge response showed high amplitude oscillations about its original position. Also, for short wave periods, a higher mode contribution to the pitch response accompanied by period doubling appeared to take place. For long wave periods, (12.5 and 15 sec.), this higher mode contribution vanished after very few cycles.

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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