• Title/Summary/Keyword: state-space equation

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An Approach of Solving the Constrained Dynamic Programming - an Application to the Long-Term Car Rental Financing Problem

  • Park, Tae Joon;Kim, Hak-Jin;Kim, Jinhee
    • Journal of the Korea Society of Computer and Information
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    • v.26 no.12
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    • pp.29-43
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    • 2021
  • In this paper, a new approach to solve the constrained dynamic programming is proposed by using the constraint programming. While the conventional dynamic programming scheme has the state space augmented with states on constraints, this approach, without state augmentation, represents states of constraints as domains in a contraining programming solver. It has a hybrid computational mechanism in its computation by combining solving the Bellman equation in the dynamic programming framework and exploiting the propagation and inference methods of the constraint programming. In order to portray the differences of the two approaches, this paper solves a simple version of the long-term car rental financing problem. In the conventional scheme, data structures for state on constraints are designed, and a simple inference borrowed from the constraint programming is used to the reduction of violation of constraints because no inference risks failure of a solution. In the hybrid approach, the architecture of interface of the dynamic programming solution method and the constraint programming solution method is shown. It finally discusses the advantages of the proposed method with the conventional method.

Integrated Algorithm for Identification of Long Range Artillery Type and Impact Point Prediction With IMM Filter (IMM 필터를 이용한 장사정포의 탄종 분리 및 탄착점 예측 통합 알고리즘)

  • Jung, Cheol-Goo;Lee, Chang-Hun;Tahk, Min-Jea;Yoo, Dong-Gil;Sohn, Sung-Hwan
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.50 no.8
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    • pp.531-540
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    • 2022
  • In this paper, we present an algorithm that identifies artillery type and rapidly predicts the impact point based on the IMM filter. The ballistic trajectory equation is used as a system model, and three models with different ballistic coefficient values are used. Acceleration was divided into three components of gravity, air resistance, and lift. And lift acceleration was added as a new state variable. The kinematic condition that the velocity vector and lift acceleration are perpendicular was used as a pseudo-measurement value. The impact point was predicted based on the state variable estimated through the IMM filter and the ballistic coefficient of the model with the highest mode probability. Instead of the commonly used Runge-Kutta numerical integration for impact point prediction, a semi-analytic method was used to predict impact point with a small amount of calculation. Finally, a state variable initialization method using the least-square method was proposed. An integrated algorithm including artillery type identification, impact point prediction and initialization was presented, and the validity of the proposed method was verified through simulation.

Finite Element Analysis of Unbalance Response of a High Speed Flexible Polygon Mirror Scanner Motor Considering the Flexibility of Supporting Structure (지지구조의 유연성을 고려한 고속 유연 폴리곤 미러 스캐너 모터의 유한 요소 불평형 응답 해석)

  • Jung, Kyung-Moon;Seo, Chan-Hee;Kim, Myung-Gyu;Jang, Gun-Hee
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2007.05a
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    • pp.859-865
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    • 2007
  • This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered bearing and flexible supporting structures by using the finite element method and the mode superposition method. The appropriate finite element equations for polygon mirror are described by rotating annular sector element using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. The rotating components except for the polygon mirror are modeled by Timoshenko beam element including the gyroscopic effect. The flexible supporting structures are modeled by using a 4-node tetrahedron element and 4-node shell element with rotational degrees of freedom. Finite element equations of each component of the polygon mirror scanner motor and the flexible supporting structures are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between sleeve and sintered bearing to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. Unbalance responses in time and frequency domain are performed by superposing the eigenvalues and eigenvectors from the free vibration analysis. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results. This research also shows that the flexibility of supporting structures plays an important role in determining the unbalance response of the polygon mirror scanner motor.

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(Design of Neural Network Controller for Contiunous-Time Chaotic Nonlinear Systems) (연속 시간 혼돈 비선형 시스템을 위한 신경 회로망 제어기의 설계)

  • O, Gi-Hun;Choe, Yun-Ho;Park, Jin-Bae;Im, Gye-Yeong
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.39 no.1
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    • pp.51-65
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    • 2002
  • This paper presents a design method of the neural network-based controller using an indirect adaptive control method to deal with an intelligent control for chaotic nonlinear systems. The proposed control method includes the identification and control Process for chaotic nonlinear systems. The identification process for chaotic nonlinear systems is an off-line process which utilizes the serial-parallel structure of multilayer neural networks and simple state space neural networks. The control process is an on-line process which uses the trained neural networks as the system model. An error back-propagation method was used for training of identification and control for chaotic nonlinear systems. The performance of the proposed neural network controller was evaluated by application to the Duffing equation and the Lorenz equation, and the proposed controller was compared with other neural network-based controllers by computer simulations.

Aerodynamic Drag Reduction on High-performance EMU Train by Streamlined Shape Modification (유선형 형상 개선을 통한 고성능 EMU 열차의 공기저항 저감 연구)

  • Kwon, Hyeok-Bin;Hong, Jai-Sung
    • Journal of the Korean Society for Railway
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    • v.16 no.3
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    • pp.169-174
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    • 2013
  • The effect of modifying the shape of a high-performance EMU train on the aerodynamic drag is studied here using Computational Fluid Dynamics(CFD) based on three dimensional Steady-state Navier-Stokes equation and two equation turbulence modeling. FLUENT 12 and Gambit 2.4.6 are employed for a numerical simulation of the aerodynamic drag of a streamlined-shape train as well as a proto type train. The characteristics of the aerodynamic drag of trains in tunnels are analyzed in a comparison with these characteristics in an open space. The contribution of the aerodynamic drag of each case is also investigated to establish principal pertaining to drag reduction for urban trains in tunnels. The aerodynamic drag of a streamlined train was reduced to 9.8% relative to a proto-type train with a blunt nose and a protruding roof facility and underbody shape: the running resistance is expected to be reduced by as much as 4% at a running speed of 80km/h.

A Robust Controller Design for the Position Control of a Spring-Mass System (탄성-질량시스템의 위치제어를 위한 강건 제어기 설계)

  • 박종우;이상철
    • Journal of the Korean Institute of Telematics and Electronics T
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    • v.36T no.3
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    • pp.41-49
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    • 1999
  • In this paper, we design a controller using the $\mu$-synthesis method and apply it for the spring-mass system with noncollocated sensors and actuators. We assume that the values of the spring stiffness and load mass of the plant are uncertain. The plant is modeled with parametric uncertainty by using the state space equation, especially the descriptor form. The $H_\infty$ controller designed by the $\mu$-synthesis method is compared with the standard $H_\infty$ controller To compare performances of two $H_\infty$ controllers, it is assumed that both controllers were designed with same weighting functions except that the $\mu$-synthesis controller has structured uncertainties. By compared with the standard $H_\infty$ controller, we show that the designed controller has satisfactory robust performance as well as robust stability by simulations and experiments.

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Optimal Design of Outrigger Damper using Multi-objective Genetic Algorithm (다목적 유전자 알고리즘을 이용한 아웃리거 댐퍼의 최적설계)

  • Kim, Hyun-Su;Yoon, Sung-Wook;Kang, Joo-Won
    • Journal of Korean Association for Spatial Structures
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    • v.14 no.4
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    • pp.97-104
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    • 2014
  • Recently, a concept of damped outrigger system has been proposed for tall buildings. Structural characteristics and design method of this system were not sufficiently investigated to date. In this study, control performance of damped outrigger system for building structures subjected to seismic excitations has been investigated. And optimal design method of damped outrigger system has been proposed using multi-objective genetic algorithm. To this end, a simplified numerical model of damped outrigger system has been developed. State-space equation formulation proposed in previous research was used to make a numerical model. Multi-objective genetic algorithms has been employed for optimal design of the stiffness and damping parameters of the outrigger damper. Based on numerical analyses, it has been shown that the damped outrigger system control dynamic responses of the tall buildings subjected to earthquake excitations in comparison with a traditional outrigger system.

Tire Lateral Force Estimation System Using Nonlinear Kalman Filter (비선형 Kalman Filter를 사용한 타이어 횡력 추정 시스템)

  • Lee, Dong-Hun;Kim, In-Keun;Huh, Kun-Soo
    • Transactions of the Korean Society of Automotive Engineers
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    • v.20 no.6
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    • pp.126-131
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    • 2012
  • Tire force is one of important parameters which determine vehicle dynamics. However, it is hard to measure tire force directly through sensors. Not only the sensor is expensive but also installation of sensors on harsh environments is difficult. Therefore, estimation algorithms based on vehicle dynamic models are introduced to estimate the tire forces indirectly. In this paper, an estimation system for estimating lateral force and states is suggested. The state-space equation is constructed based on the 3-DOF bicycle model. Extended Kalman Filter, Unscented Kalman Filter and Ensemble Kalman Filter are used for estimating states on the nonlinear system. Performance of each algorithm is evaluated in terms of RMSE (Root Mean Square Error) and maximum error.

Modeling and Control of a Two-Stage DC-DC-AC Converter for Battery Energy Storage System (배터리 에너지 저장 장치를 위한 2단 DC-DC-AC 컨버터의 모델링 방법)

  • Hyun, Dong-Yub;Jung, Seok-Eon;Hyun, Dong-Seok
    • The Transactions of the Korean Institute of Power Electronics
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    • v.19 no.5
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    • pp.422-430
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    • 2014
  • This study proposes a small-signal model and control design for a two-stage DC-DC-AC converter to investigate its dynamic characteristics in relation to battery energy storage system. When the circuit analysis of the two-stage DC-DC-AC converter is attempted simultaneously, the mathematical procedure of deriving the dynamic equation is complex and difficult. The main idea of modeling the two-stage DC-DC-AC converter states that this topology is separated into a bidirectional DC-DC converter and a single-phase inverter with an equivalent current source corresponding to that of the inverter or converter. The dynamic equations for the separated converter and inverter are then derived using the state-space averaging technique. The procedures of building the small-signal model of the two-stage DC-DC-AC converter are described in detail. Based on the derived small-signal model, the individual controllers are designed through a frequency-domain analysis. The simulation and experimental results verify the validity of the proposed modeling approach and controller design.

A Study on the Robust Compensator of An Inverted Pendulum Using $H_{\infty}$ Optimal Control Theory ($H_{\infty}$ 최적제어 이론을 이용한 도립진자의 견실한 보상기 설계에 관한 연구)

  • 김대현;정규홍;이석재;이교일
    • 제어로봇시스템학회:학술대회논문집
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    • 1991.10a
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    • pp.213-218
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    • 1991
  • A new model which contains the dynamics of the motor system and the kinematics of the timing belt system is derived for an inverted pendulum system in FAPA Lab. Generalized standard compensator configuration(SCC) which contains the variable design parameters Kl, K2, .., K5 is proposed so that any desired design specification can be achieved. The robust controller which has robust property against the influence of sensor noise, system parameter variation and model uncertainty is designed minimizing the H$_{\infty}$-norm of transfer function from exogenous input to controlled output. The method of solving the two Riccati equations in state space and determining the controller uses on iteration method where the unique stabilizing solution to two algebraic Riccati equation must be positive definite and the spectral radius of their product less than .gamma.$^{2}$. Some cases are derived by varying the design parameter for simulation on a digital computer and experimenting the H$_{\infty}$- controller on an analog computer. The design parameters of controller which satisfies the desired control specification is selected on the basis of the simulation result and experimenting. The reasonableness and validity of the simulation and the robustness of the controller is established.d.

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