• Title/Summary/Keyword: State space equation

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Attitude Stability of Satellite using Lyapunov equation (Lyapunov 방정식을 이용한 위성체 자세 안정화)

  • 천현경;문종우;이우승;박종국
    • Proceedings of the IEEK Conference
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    • 1999.11a
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    • pp.720-723
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    • 1999
  • For that the attitude control performance test of the satellite, dynamic analysis of satellite structure performed in reference with KOREASAT, and the equation of motion of rigid bodies was derivated. For attitude stability, Lyapunov's stability theorem and state space expression were applied to dynamic equation of satellite. To prove efficiency of our method, simulations are performed and result are shown.

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Design of H Repetitive Control Systems using State Feedback (상태 궤환을 이용한 H 반복 제어 시스템 설계)

  • Doh, Tae-Yong
    • Journal of Institute of Control, Robotics and Systems
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    • v.20 no.1
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    • pp.6-11
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    • 2014
  • Repetitive control is a specialized control scheme to track and/or attenuate a periodic reference trajectory and/or disturbance. Most researches about repetitive control have been performed in the frequency domain. Recently, several approaches to deal with repetitive control systems in the state space are developed by representing a q filter as a state-space equation. This paper presents a design method of a repetitive control system in the state space to satisfy $H_{\infty}$ performance. The overall system is composed of a plant, a repetitive controller, and a state-feedback controller, which can be converted to a standard form used in $H_{\infty}$ control. A LMI (Linear Matrix Inequality)-based stability condition is derived for fixed state-feedback gains. Under a given q filter, another LMI condition is derived to improve $H_{\infty}$ performance and is employed to find state-feedback gains by solving an optimization problem. Finally, to verify the feasibility of the proposed method, a numerical example is demonstrated.

가변 풍량 유닛에 의한 실내 공간의 온도제어를 위한 공간의 분할 모델과 상태궤환 제어기의 개발에 관한 연구

  • 박세화;신승철
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.13 no.10
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    • pp.947-959
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    • 2001
  • We propose a control scheme to control the indoor zone temperature via variable air volume (VAV) unit. To control the room temperature, state space model of the conditioned zone which is partitioned into nine artificial sectional regions is derived. The nonlinearity of the damper motion and actuator are considered for the practical use in the state space system description. The temperature control of the room temperature is performed by manipulating the degree of openness of the damper in relation to the local room temperature and the supplied air flow rate. In general, since a local temperature in the conditioned zone is measured, it is required to estimate the temperature values in each regions for the precise temperature control. We thus design a state observer to estimate the regional temperature, and use these values in the controller. The overall control system consists of the state observer based state feedback with the integral control. We compared the control results of the proposed scheme with those of cascade proportional and integral (PI) control, and showed that the scheme achieved precise control of the conditioned system.

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Kalman Filter Design For Aided INS Considering Gyroscope Mixed Random Errors (자이로의 불규칙 혼합잡음을 고려한 보조항법시스템 칼만 필터 설계)

  • Seong, Sang-Man
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.34 no.4
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    • pp.47-52
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    • 2006
  • Using the equivalent ARMA model representation of the mixed random errors, we propose Klaman filter design methods for aided INS(Inertial Navigation System) which contains the gyroscope mixed random errors. At first step, considering the characteristic of indirect feedback Kalman filter used in the aided INS, we perform the time difference of equivalent ARMA model. Next, according to the order of the time differenced ARMA model, we achieve the state space conversion of that by two methods. If the order of AR part is greater than MA part, we use controllable or observable canonical form. Otherwise, we establish the state apace equation via the method that several step ahead predicts are included in the state variable, where we can derive high and low order models depending on the variable which is compensated from gyroscope output. At final step, we include the state space equation of gyroscope mixed random errors into aided INS Kalman filter model. Through the simulation, we show that both the high and low order filter models proposed give less navigation errors compared to the conventional filter which assume the mixed random errors as white noise.

Online Dynamic Modeling of Ubiquitous Sensor based Embedded Robot Systems using Kalman Filter Algorithm (칼만 필터 알고리즘을 이용한 유비쿼터스 센서 기반 임베디드 로봇시스템의 온라인 동적 모델링)

  • Cho, Hyun-Cheol;Lee, Jin-Woo;Lee, Young-Jin;Lee, Kwon-Soon
    • Journal of Institute of Control, Robotics and Systems
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    • v.14 no.8
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    • pp.779-784
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    • 2008
  • This paper presents Kalman filter based system modeling algorithm for autonomous robot systems. State of the robot system is measured using embedded sensor systems and then carried to a host computer via ubiquitous sensor network (USN). We settle a linear state-space motion equation for unknown robot system dynamics and modify a popular Kalman filter algorithm in deriving suitable parameter estimation mechanism. To represent time-delay nature due to network media in system modeling, we construct an augmented state-space model which is mainly composed of original state and estimated parameter vectors. We conduct real-time experiment to test our proposed estimation algorithm where speed state of the constructed robot is used as system observation.

An INS Filter Design Considering Mixed Random Errors of Gyroscopes

  • Seong, Sang-Man;Kang, Ki-Ho
    • 제어로봇시스템학회:학술대회논문집
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    • 2005.06a
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    • pp.262-264
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    • 2005
  • We propose a filter design method to suppress the effect of gyroscope mixed random errors at INS system level. It is based on the result that mixed random errors can be represented by a single equivalent ARMA model. At first step, the time difference of equivalent ARMA process is performed, which consider the characteristic of indirect feedback Kalman filter used in INS filter. Next, a state space conversion of time differenced ARMA model is achieved. If the order of AR is greater than that of MA, the controllable or observable canonical form is used. Otherwise, we introduce the state equation of which the state variable is composed of the ARMA model output and several step ahead predicts of that. At final step, a complete form state equation is presented. The simulation results shows that the proposed method gives less transient error and better convergence compared to the conventional filter which assume the mixed random errors as white noise.

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The Research on the Modeling and Parameter Optimization of the EV Battery (전기자동차 배터리 모델링 및 파라미터 최적화 기법 연구)

  • Kim, Il-Song
    • The Transactions of the Korean Institute of Power Electronics
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    • v.25 no.3
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    • pp.227-234
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    • 2020
  • This paper presents the methods for the modeling and parameter optimization of the electric vehicle battery. The state variables of the battery are defined, and the test methods for battery parameters are presented. The state-space equation, which consists of four state variables, and the output equation, which is a combination of to-be-determined parameters, are shown. The parameter optimization method is the key point of this study. The least square of the modeling error can be used as an initial value of the multivariable function. It is equivalent to find the minimum value of the error function to obtain optimal parameters from multivariable function. The SIMULINK model is presented, and the 10-hour full operational range test results are shown to verify the performance of the model. The modeling error for 25 degrees is approximately 1% for full operational ranges. The comments to enhance modeling accuracy are shown in the conclusion.

Derivation Algorithm of State-Space Equation for Production Systems Based on Max-Plus Algebra

  • Goto, Hiroyuki;Masuda, Shiro
    • Industrial Engineering and Management Systems
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    • v.3 no.1
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    • pp.1-11
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    • 2004
  • This paper proposes a new algorithm for determining an optimal control input for production systems. In many production systems, completion time should be planned within the due dates by taking into account precedence constraints and processing times. To solve this problem, the max-plus algebra is an effective approach. The max-plus algebra is an algebraic system in which the max operation is addition and the plus operation is multiplication, and similar operation rules to conventional algebra are followed. Utilizing the max-plus algebra, constraints of the system are expressed in an analogous way to the state-space description in modern control theory. Nevertheless, the formulation of a system is currently performed manually, which is very inefficient when applied to practical systems. Hence, in this paper, we propose a new algorithm for deriving a state-space description and determining an optimal control input with several constraint matrices and parameter vectors. Furthermore, the effectiveness of this proposed algorithm is verified through execution examples.

An Accurate Model of Multi-Type Overcurrent Protective Devices Using Eigensystem Realization Algorithm and Practice Applications

  • Cheng, Chao-Yuan;Wu, Feng-Jih
    • Journal of Electrical Engineering and Technology
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    • v.11 no.1
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    • pp.9-19
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    • 2016
  • Accurate models of the characteristics of typical inverse-time overcurrent (OC) protective devices play an important role in the protective coordination schemes. This paper presents a novel approach to determine the OC protective device parameters. The approach is based on the Eigensystem Realization Algorithm which generates a state space model to fit the characteristics of OC protective devices. Instead of the conventional characteristic curves, the dynamic state space model gives a more exact fit of the OC protective device characteristics. This paper demonstrates the feasibility of decomposing the characteristic curve into smooth components and oscillation components. 19 characteristic curves from 13 typical and 6 non-typical OC protective devices are chosen for curve-fitting. The numbers of fitting components required are determined by the maximum absolute values of errors for the fitted equation. All fitted equations are replaced by a versatile equation for the characteristics of OC protective devices which represents the characteristic model of a novel flexible OC relay, which in turn may be applied to improve the OC coordination problems in the sub-transmission and distribution systems.

Dynamic Characteristics of Moving Coil Type Linear Oscillatory Actuator (가동코일형 리니어 왕복 액추에이터의 동특성)

  • Jang, S.M.;Jeong, S.S.;Kweon, C.;Park, H.C.;Moon, S.J.;Park, C.I.;Chung, T.Y.
    • The Transactions of the Korean Institute of Electrical Engineers B
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    • v.49 no.3
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    • pp.180-187
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    • 2000
  • A moving-coil-type linear oscillatory actuator(LOA) consists of the NdFeB permanent magnets with high specific energy as the stator, a coil-wrapped nonmagnetic hollow rectangular structure. The LOA system was represented by the voltage equation of coil and the mechanical equation of motion. This set of equations was manipulated in state-space form. The EMF constant kE of equation parameters in state-space form can be obtained by using the induced voltage in armature coils at open circuit test. kE and other parameters provide the system matrices and transfer function for frequency response and dynamic simulation. Voltage source inverter-fed LOA is examined aiming to compare with results of simulation.

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