• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.185-200
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• 2004

A stochastic optimal LQR control problem under some integral quadratic (IQ) constraints is studied, with cross terms in both the cost and the constraint functionals, allowing all the control weighting matrices being indefinite. Sufficient conditions for the well-posedness of this problem are given. When these conditions are satisfied, the optimal control is explicitly derived via dual theory.

• Steel and Composite Structures
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• 제32권6호
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• pp.753-767
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• 2019

Vibration control in mechanical equipments is an important problem where unwanted vibrations are vanish or at least diminished. In this paper, free vibration active control of the porous sandwich piezoelectric polymeric nanocomposite microbeam with microsensor and microactuater layers are investigated. The aim of this research is to reduce amplitude of vibration in micro beam based on linear quadratic regulator (LQR). Modified couple stress theory (MCST) according to sinusoidal shear deformation theory is presented. The porous sandwich microbeam is rested on elastic foundation. The core and face sheet are made of porous and three-phase carbon nanotubes/resin/fiber nanocomposite materials. The equations of motion are extracted by Hamilton's principle and then Navier's type solution are employed for solving them. The governing equations of motion are written in space state form and linear quadratic regulator (LQR) is used for active control approach. The various parameters are conducted to investigate on the frequency response function (FRF) of the sandwich microbeam for vibration active control. The results indicate that the higher length scale to the thickness, the face sheet thickness to total thickness and the considering microsensor and microactutor significantly affect LQR and uncontrolled FRF. Also, the porosity coefficient increasing, Skempton coefficient and Winkler spring constant shift the frequency response to higher frequencies. The obtained results can be useful for micro-electro-mechanical (MEMS) and nano-electro-mechanical (NEMS) systems.

• 풍력에너지저널
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• 제2권1호
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• pp.74-81
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• 2011

This paper deals with the application of LQ control to the power curve tracking control of wind turbine. However, two more additional tasks are required to apply the LQR theory to wind turbine control. One is the tracking problem instead of regulation, because the wind turbine is controlled as variable speed and variable pitch. The other is LQ integral control., because the rotor speed should be tightly controlled without any steady state error. Starting from the analysis of wind characteristics, design requirement of a wind turbine control system is defined. A design procedure of LQ tracking with integral control is introduced. The performance of LQ tracking system is analyzed and evaluated by numeric simulation.

• 한국지능시스템학회논문지
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• 제26권1호
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• pp.16-22
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• 2016

세계적으로 수많은 로봇연구실에서 이륜 도립진자 이동로봇에 대한 연구가 진행되고 있다. 본 논문에서는 이런 이륜 도립진자 이동로봇이 평탄한 경사면에서 안정적으로 주행할 수 있도록 하는 강인 제어기를 개발하는 것으로 고려한다. 경사면에서 이륜 도립진자 이동로봇의 균형을 위해 3 자유도의 운동방정식에서 선회운동을 제한한 2 자유도 동력학식을 사용하며, 가변구조시스템 이론을 근간으로 하는 슬라이딩 모드 제어기를 제안하고 LQR 이론을 이용하여 슬라이딩 운동이 일어나는 슬라이딩 평면을 설계한다. 시뮬레이션을 위해 Mathworks사의 Simulink를 활용하여 이륜 도립진자 이동로봇의 2 자유도 모델을 실현하고, 슬라이딩 모드 제어기 또한 Simulink를 이용하여 구현한다. 시뮬레이션 결과를 통해 제안된 제어기가 경사면을 주행하는 이륜 도립진자 이동로봇을 효과적인 제어한다는 것을 보인다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 추계학술대회 논문집 전력기술부문
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• pp.183-186
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• 2004

본 논문에서는 Lie Group 및 Lie Transformation의 수학적인 근원을 분석하고 이를 비선형 제어기에 제공하였다. 제어기의 구성형태는 Lead-Lag와 LQR 관측기를 결합한 혼합형 비선형 전력계통안정화장치(NPSS)이다. 이 분석에 사용된 제어기는 첫째로 기존의 PSS type인 Lead-Lag 형태의 선형화 제어기이다. 둘째로 제안된 제어기는 Lie group theory를 적용하여 이를 상태변수에 반영한 Lead-Lag와 LQR 관측기를 결합한 것이다. 제안된 혼합형 비선형 전력계통안정화장치(NPSS)의 효과분석은 MATLAB을 이용하였다. 분석모델은 1기 4차 비선형 전력계통의 모델에 적용하였다.

• 한국소음진동공학회논문집
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• 제14권12호
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• pp.1330-1337
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• 2004

In this study, the equations of motion of a rigid rotor supported by magnetic bearings are derived via Hamilton's principle, and transformed to a state-space form for control purpose. The optimal motion control of rotor magnetic bearing system based on the LQR(linear quadratic regulator) theory is addressed. New schemes related to the selection of the state weighting matrix Q and the control weighting matrix R involved in the quadratic functional to be minimized are proposed. And the robust control of the system with an LMI(linear matrix inequality) based H$_{\infty}$ theory is dealt with in this paper. Loop shapings of TFM (transfer function matrix) are used to increase the performance of control capability of the system. The control abilities of LQR and H$_{\infty}$ controller are compared by simulation and experimental tests and show that the capability of H$_{\infty}$ controller is superior to that of LQR.

• 전기학회논문지
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• 제59권7호
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• pp.1309-1313
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• 2010

In this paper, we propose a novel guidance law for controlling an UAV(Unmanned Air-Vehicle) to follow a reference line in vertical plane. A kinematics model representing the relative motion of the UAV to the reference line is derived. And then LQR(Linear Quadratic Regulator) theory is applied to the model to derive the VLFG(Vertical Line Following Guidance) law. The resultant guidance law forms a gain-scheduling controller scheduled by a simple parameter $\sigma$ which is a function of the UAV's velocity, axial acceleration, gravity, and the slope of the reference line. Also derived is a stability condition for the $\sigma$ variation based on Lyapunov theory. Simulation results show that the proposed guidance law can be applied effectively to UAV guidance algorithm design.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 1998년도 추계 학술발표회 논문집 Proceedings of EESK Conference-Spring 1998
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• pp.93-99
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• 1998

Mathematical model can be obtained by physical law or engineering theory. However it is always incomplete expression of the real system. In active controls to suppress vibration due to earthquake or wind load, modeling errors can often cause the problems of instability and performance degradation. In this paper, robust optimal controller design method using H$\infty$ control theory is developed for the systems which have uncertain natural frequency and design constraints. Numerical results show that the proposed H$\infty$ controller can avoid the performance degradation due to several errors and has better performance than conventional LQR method.

• 대한임베디드공학회논문지
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• 제13권6호
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• pp.297-303
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• 2018

Recently, the tasks assigned to surface ship are becoming diverse and important. In this trend, shipboard directional pedestals are widely used for surveillance and electronic warfare because ships are always under angular motion such as rolling, pitching and yawing. To estimate the performance of pedestal, the motion responses of vessel as well as mechanical characteristics of pedestal should be considered. In this study, both the motion responses of vessel which the pedestal will be mounted and the behavior of 3-axis pedestal are considered. Numerical analysis based on potential theory is used to obtained motion characteristics of vessel and then 6-DOF motions of vessel are simulated under operational condition. 1st-order time delay model and LQR control algorithm are used for modeling of pedestal drive model and control model, respectively. By using coordinate transform, the angular motions which the pedestal should compensate are calculated from the vessel's angular motion. Through these M&S methodologies, time history of pedestal behavior and maximum angular error of each pedestal axis are obtained. Overall M&S results show that 3-axis pedestal compensate the angular motion induced by vessel, efficiently.

• Journal of Astronomy and Space Sciences
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• 제14권1호
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• pp.142-149
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• 1997

잘 알려진 최적제어 이론의 선형제차조절법을 정지궤도 위성의 위치보존 궤도조정 문제에 적용하였다. 정지궤도 위성의 운동에 가장 큰 영향을 미치는 섭동향을 선택하여 동서방향과 남북방향 궤도조정의 경우 각각 14일간 지구비대칭 중력장의 영향, 28일간 태양과 달의 영향을 예측한 결과로 궤도조정할 경계조건을 적절하게 설정하였다. 비선형방정식을 선형화하여 리카티 방정식(Riccati Equation)을 두 번 적분함으로써 최적궤도와 이에 상응하는 추진 가속도를 알아내었다. 선형제차조절법으로 구한 속도변화량과 기하학적으로 계산한 ${\Delta}V$(속도변화량)을 비교해 봄으로써 제어이론을 통한 궤도조정 방법이 실제상황에 거의 근사한 해를 제공할 수 있는가와 제어이론을 위치보존 궤도조정 문제에 적용한 방법이 경제적인 측면에서의 연료최적화와 이에 따른 정지궤도 위성의 수명연장에 기여할 수 있는가에 대한 해석을 시도하였다.