• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.185-200
• /
• 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
• /
• v.32 no.6
• /
• pp.753-767
• /
• 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.

• Journal of Wind Energy
• /
• v.2 no.1
• /
• pp.74-81
• /
• 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.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.26 no.1
• /
• pp.16-22
• /
• 2016

The research on two-wheeled inverted pendulum (TWIP) mobile robots has been ongoing in a number of robotic laboratories around the world. In this paper, we consider a robust controller design for the TWIP mobile robot driving on uniform slopes. We use a 2 degree-of-freedom (DOF) model which is obtained by restricting the spinning motion in a 3 DOF motion dynamic equation. In order to design the robust controller guaranteeing stability of the TWIP mobile robot driving on inclined surface, we propose a sliding mode control based on the theory of variable structure systems and design a sliding surface using the theory of the linear quadratic regulation (LQR). For simulation, the dynamic model of the TWIP mobile robot is constructed using Mathworks' Simulink and the sliding mode control is also implemented using Simulink. From simulation results, we show that the proposed controller effectively controls the TWIP mobile robot driving on slopes.

• Proceedings of the KIEE Conference
• /
• 2004.11b
• /
• pp.183-186
• /
• 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.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.14 no.12
• /
• pp.1330-1337
• /
• 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.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.59 no.7
• /
• pp.1309-1313
• /
• 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.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 1998.10a
• /
• pp.93-99
• /
• 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.

• IEMEK Journal of Embedded Systems and Applications
• /
• v.13 no.6
• /
• pp.297-303
• /
• 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
• /
• v.14 no.1
• /
• pp.142-149
• /
• 1997

This paper applied one of the well-known optimal control theory, namely, linear quadratic regulator(LQR), to the station-keeping maneuvers(SKM) for a geostationary satellite. The boundary conditions to transfer the system with a good accuracy at a terminal time were based upon the predicted orbital data which are created due to the Earth's non-uniform mass distribution's effect during 14 days and due to luni-solar effect during 28 days. Through the linearization of the nonlinear system equation with respect to reference orbit and the numerical integration of Riccati equation, the optimal trajectories and the corresponding control law have been obtained by using LQR. From the comparison of ${\Delta}V$ obtained by LQR with the ${\Delta}V$ obtained anatically by geometric method, Station Keeping Maneuvers(SKM) via LQR may provide comparable results to a real system. Furthermore it will demonstrate the possibility in fuel optimization and life extension of geostationary satellite.