• Title/Summary/Keyword: Quadratic stability

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Stabilization Position Control of a Ball-Beam System Using Neural Networks Controller (신경회로망 제어기을 이용한 볼-빔 시스템의 안정화 위치제어)

  • 탁한호;추연규
    • Journal of the Korean Institute of Navigation
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    • v.23 no.3
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    • pp.35-44
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    • 1999
  • This research aims to seek active control of ball-beam position stability by resorting to neural networks whose layers are given bias weights. The controller consists of an LQR (linear quadratic regulator) controller and a neural networks controller in parallel. The latter is used to improve the responses of the established LQR control system, especially when controlling the system with nonlinear factors or modelling errors. For the learning of this control system, the feedback-error learning algorithm is utilized here. While the neural networks controller learns repetitive trajectories on line, feedback errors are back-propagated through neural networks. Convergence is made when the neural networks controller reversely learns and controls the plant. The goals of teaming are to expand the working range of the adaptive control system and to bridge errors owing to nonlinearity by adjusting parameters against the external disturbances and change of the nonlinear plant. The motion equation of the ball-beam system is derived from Newton's law. As the system is strongly nonlinear, lots of researchers have depended on classical systems to control it. Its applications of position control are seen in planes, ships, automobiles and so on. However, the research based on artificial control is quite recent. The current paper compares and analyzes simulation results by way of the LQR controller and the neural network controller in order to prove the efficiency of the neural networks control algorithm against any nonlinear system.

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A Study on Control Characteristic and Application of Optimal Modulation Controller for HVDC Transmission System (초고압 직류 송전 시스템에 대한 최적 변조 제어기의 적용 및 제어 특성에 관한 연구)

  • Lee, J.M.;Hur, D.R.;Chung, D.I.;Chung, H.H.
    • Proceedings of the KIEE Conference
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    • 1999.07c
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    • pp.1318-1320
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    • 1999
  • Recently, according to the growth of national economy and the improvement of lining conditions, electric power demand is increasing gradually. So it is being examined to construct large thermal power plants or nuclear plants. For the effective use of lands and for the economy of generations sites, the distance between generation and demand locations becomes farther and farther. At the same time, people desire higher quality or electric power. So in this paper, the optimal modulation controller for HVDC transmission system are designed by a recursive algorithm that determines the state weighting matrix Q of a linear quadratic performance. It means that the application of optimal modulation controller in HVDC transmission system can contribute the propriety to the improvement of the stability in HVDC transmission system.

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A Design of Suspension Controller for Magnetic Levitation System Using Gain Scheduling Control (이득계획제어에 의한 자기부상시스템의 부상제어기 설계)

  • Byun, Yeun-Sub;Cho, Tae-Shin;Kim, Young-Chol
    • Journal of the Korean Institute of Telematics and Electronics S
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    • v.36S no.6
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    • pp.57-66
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    • 1999
  • In this paper, we propose design methods of suspension controller for magnetically levitated system(MAGLEV). In this interior, the study of Electromagnetic Suspension(EMS) which has several advantages is chiefly achieved but, because the EMS has highly nonlinear and unstable property it is difficult to design the suspension controller maintaining stability and high performance. Here a Gain Scheduling Control(GSC) based on pole-placement scheme and on linear quadratic gaussian(LQG) design is separately presented. The several control performance is shown by simulation.

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A Study of Optimal Design of the Proportional Load-Frequency Controller for a Self-service Power Station (주파수제어를 위한 비열제어기구의 최적설계에 관한 연구)

  • 장세훈;임화영
    • 전기의세계
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    • v.26 no.2
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    • pp.99-103
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    • 1977
  • The object of this work is to study an optimal design problem of the proportional load-frequency controller for the single-control area power system. The selfservice power station is still a popular means as a power supplying source on ships or in a certain manufacturing area. The power system of this kind can be formulated as a single control-area system and it attracts a certain academic interest in controlling the system frequency under disturbances. In this paper, the single control-area system is mathematically formulated as a linear, time-invariant system in state-space under certain assumptions. The optimal proportional control law and the realization of the controller in closed loop-version is studied so that the final system designed can attain the system frequency to the nominal stationing value after the small load-disturbance. As in general cases of optimal design problems, the performance index is assumed to be quadratic in states and the control effort, and the infinite time control process is assumed in this work. The final control system realized depicts certain improvements in case study; in stability, transient responses and in steady-state frequency deviation, even though the steady state error did not attain the zero value.

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A Planar Curve Intersection Algorithm : The Mix-and-Match of Curve Characterization, Subdivision , Approximation, Implicitization, and Newton iteration (평면 곡선의 교점 계산에 있어 곡선 특성화, 분할, 근사, 음함수화 및 뉴턴 방법을 이용한 Mix-and-Mntch알고리즘)

  • 김덕수;이순웅;유중형;조영송
    • Korean Journal of Computational Design and Engineering
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    • v.3 no.3
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    • pp.183-191
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    • 1998
  • There are many available algorithms based on the different approaches to solve the intersection problems between two curves. Among them, the implicitization method is frequently used since it computes precise solutions fast and is robust in lower degrees. However, once the degrees of curves to be intersected are higher than cubics, its computation time increases rapidly and the numerical stability gets worse. From this observation, it is natural to transform the original problem into a set of easier ones. Therefore, curves are subdivided appropriately depending on their geometric behavior and approximated by a set of rational quadratic Bezier cures. Then, the implicitization method is applied to compute the intersections between approximated ones. Since the solutions of the implicitization method are intersections between approximated curves, a numerical process such as Newton-Raphson iteration should be employed to find true intersection points. As the seeds of numerical process are close to a true solution through the mix-and-match process, the experimental results illustrates that the proposed algorithm is superior to other algorithms.

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Optimal Control Design-based Gain Selection of an LCL-filtered Grid-connected Inverter in State-Space under Distorted Grid Environment

  • Tran, Vi-Thuy;Yoon, Seung-Jin;Kim, Kyeong-Hwa
    • Proceedings of the KIPE Conference
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    • 2018.07a
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    • pp.344-345
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    • 2018
  • In order to alleviate the negative impacts of harmonically distorted grid condition on grid-connect inverters, an optimal control design-based gain selection scheme of an LCL-filtered grid-connected inverter and its ability to compensate selective harmonics are presented in this paper. By incorporating resonant terms into the control structure in the state-space to provide infinity gain at selected frequencies, the proposed control offers an excellent steady-state response even under distorted grid voltage. The proposed control scheme is achieved by using a state feedback controller for stabilization purpose and by augmenting the resonant terms as well as intergral term into a control structure for reference tracking and harmonic compensation. Furthermore, the optimal linear quadratic control approach is adopted for choosing an optimal feedback gain to ensure an asymptotic stability of the whole system. A discrete-time full state observer is also introduced into the proposed control scheme for the purpose of reducing a total number of sensors used in the inverter system. The simulation results are given to prove the effectiveness and validity of the proposed control scheme.

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Stability of a slender beam-column with locally varying Young's modulus

  • Kutis, Vladimir;Murin, Justin
    • Structural Engineering and Mechanics
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    • v.23 no.1
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    • pp.15-27
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    • 2006
  • A locally varying temperature field or a mixture of two or more different materials can cause local variation of elasticity properties of a beam. In this paper, a new Euler-Bernoulli beam element with varying Young's modulus along its longitudinal axis is presented. The influence of axial forces according to the linearized 2nd order beam theory is considered, as well. The stiffness matrix of this element contains the transfer constants which depend on Young's modulus variation and on axial forces. Occurrence of the polynomial variation of Young's modulus has been assumed. Such approach can be also used for smooth local variation of Young's modulus. The critical loads of the straight slender columns were studied using the new beam element. The influence of position of the local Young's modulus variation and its type (such as linear, quadratic, etc.) on the critical load value and rate of convergence was investigated. The obtained results based on the new beam element were compared with ANSYS solutions, where the number of elements gradually increased. Our results show significant influence of the locally varying Young's modulus on the critical load value and the convergence rate.

Responses of a roll-pitch coupled nonlinear system to the primary resonance of the roll mode (횡동요 모드와 주공진 된 횡-종동요연성 비선형계의 응답)

  • 오일근
    • Journal of Ocean Engineering and Technology
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    • v.11 no.3
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    • pp.107-115
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    • 1997
  • 비성형 동력학계로 모델링된 부유수송체의 동적응답을 조사하고 그 운동의 안정성을 해석하였다. 종동요 모우드의 고유주파수가 횡동요 모우드의 고유주파수의 두배가 되는, 즉, 2:1 내부공진 혹은 자기계수공진인 조건하에서, 이부유수송체는 한 운동 모우드의 직접가진에 의해 간접가진된 다른 모우드가 대진폭 응답을 보일 수 있음을 밝혔다. 또항, 종동요 모우드의 감쇠력은 비교적 넓은 범위의 운동에 대해 선형적임에 반해, 횡동요 모우드의 감쇠력은 점성의 영향이 대단히 커서 비선형성이 대단히 강한 것으로 알려져 왔다. 이 문제를 수학적으로 모델링하기 위하여, 종동요 모우드의 운동방정식에는 선형및 제곱형의 합의 형태인 감쇠력 모형을 사용하였다. 다중척도법을 사용하여 이 두가지 운동 모우드의 주기적 응답및 그의 안정성에 미치는 제곱형 비선형 횡동요 감쇠력의 영향을 밝혔다. 조우주기가 횡동요 모우드의 고유주기와 근사한 경우에 대하여 이 비선형계의 응답을 구하고 주파수-응답 곡선으로 나타내었다.

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Robust Optimal Nonlinear Control with Observer for Position Tracking of Permanent Magnet Synchronous Motors

  • Ha, Dong-Hyun;Lim, Chang-Soon;Hyun, Dong-Seok
    • Journal of Power Electronics
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    • v.13 no.6
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    • pp.975-984
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    • 2013
  • This paper proposes a robust optimal nonlinear control with an observer to reject the offset errors of position tracking for surface mounted permanent magnet synchronous motors. We provide the control method to reject offset errors and load torque for designing field oriented control (FOC) based the alternating current (AC) frame. The proposed method consists of a torque generator, a commutation scheme, an electrical controller, and a load torque observer. The mechanical controller is designed to compensate for load torque and the offset error and generate the desired torque. The commutation scheme is proposed to create the desired currents for the desired torque. The electrical controller is developed to guarantee the desired currents. The observer is designed to estimate both the velocity and the load torque. In order to obtain the robustness to parameter uncertainties and a gain tuning guide, the linear quadratic regulator method is applied to the proposed method. The closed-loop stability is proven. A detailed process for the FOC design and an analysis of the control methods based on the AC frame are presented. The performance of the proposed method was validated via experiments. The proposed method obtains the FOC based on the AC frame. Furthermore, the position tracking performance of the proposed method is superior to that of the conventional method.

A Proposal of 3 Point Search Algorithm for Optimal Design (최적 설계를 위한 3점 탐색 알고리즘의 제안)

  • 김주홍;공휘식
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.16 no.7
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    • pp.640-650
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    • 1991
  • In the paper, the threepoint search algorithm used direct search method for optimal design is proposed. Proposed algorithm is composed of two iteration procedure to determine the minimum value of performance index. The minumum value of three-point existing in the inner N-order searching is firstly determined and next searching space is then reduced by the result of first procedure. To compute performance index. 3N iteration for a searching is necessary. 3N searching method is also described and confirmed with exception of parameter included multiphicator and divisor. Proposed algorithm have good stability and reliability when performance index is linear or quadratic function.

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