• International Journal of Control, Automation, and Systems
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• 제5권2호
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• pp.170-183
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• 2007

This paper presents a delay-dependent approach to robust filtering for linear parameter-varying (LPV) systems with discrete and distributed time-invariant delays in the states and outputs. It is assumed that the state-space matrices affinely depend on parameters that are measurable in real-time. Some new parameter-dependent delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs) such that the filtering process remains asymptotically stable and satisfies a prescribed $H_{\infty}$ performance level. Using polynomially parameter-dependent quadratic (PPDQ) functions and some Lagrange multiplier matrices, we establish the parameter-independent delay-dependent conditions with high precision under which the desired robust $H_{\infty}$ filters exist and derive the explicit expression of these filters. A numerical example is provided to demonstrate the validity of the proposed design approach.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.251-266
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• 2004

We consider a controlled nonlinear mechanical system described by the Lagrange equations. We determine the control forces $Q_1$ and the restrictions for the perturbations $Q_2$ acting on the mechanical system which allow to guarantee the asymptotic stability of the program motion of the system. We solve the problem of stabilization by the direct Lyapunov's method and the method of limiting functions and systems. In this case we can use the Lyapunov's functions having nonpositive derivatives. The following examples are considered: stabilization of program motions of mathematical pendulum with moving point of suspension and stabilization of program motions of rigid body with fixed point.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2006년도 춘계학술대회논문집
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• pp.254-257
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• 2006

In this paper a dynamic behavior(natural frequency) of a cracked cantilever and simply supported pipe conveying fluid is presented. In addition, an analysis of the flutter and buckling instability of a cracked pipe conveying fluid subjected to a follower compressive load is presented. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

• Structural Engineering and Mechanics
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• 제76권5호
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• pp.619-629
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• 2020

In current study, surface/interface effects for pull-in voltage and viscous fluid velocity effects on dimensionless natural frequency (DNF) of fluid-conveying piezoelectric nanosensor (FCPENS) subjected to direct electrostatic voltage DC with nonlinear excitation, harmonic force and also viscoelastic foundation (visco-pasternak medium and structural damping) are investigated using Gurtin-Murdoch surface/interface (GMSIT) theory. For this analysis, Hamilton's principles, the assumed mode method combined with Lagrange-Euler's are used for the governing equations and boundary conditions. The effects of surface/interface parameters of FCPENS such as Lame's constants (λI,S, μI,S), residual stress (τ0I,S), piezoelectric constants (e31psk,e32psk) and mass density (ρI,S) are considered for analysis of dimensionless natural frequency respect to viscous fluid velocity u̅f and pull-in voltage V̅DC.

• 한국운동역학회지
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• 제24권4호
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• pp.375-383
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• 2014

The purpose of this study was to assess the inter-segmental trunk motion during which multi-segmental movements of the spinal column was designed to interpret the effect of segmentation on the total measured spine motion. Also it analyzed the relative motion at three types of the spine models in drop landing. A secondary goal was to determine the intrinsic algorithmic errors of spine motion and the usefulness of such an approach as a tool to assess spinal motions. College students in the soccer team were selected the ten males with no history of spine symptoms or injuries. Each subject was given a fifteen minute adaptation period of drop landing on the 30cm height box. Inter-segmental spine motion were collected Vicon Motion Capture System (250 Hz) and synchronized with GRF data (1000 Hz). The result shows that Model III has a more increased range of motion (ROM) than Model I and Model II. And the Lagrange energy has significant difference of at E3 and E4 (p<.05). This study can be concluded that there are differences in the three models of algorithm during the phase of load absorption. Especially, Model III shows proper spine motion for the inter-segmental joint motion with the interaction effects using the seven segments. Model III shows more proper observed values about dynamic equilibrium than Model I & Model II. The findings have shown that the dynamic stability strategy of Model III toward multi-directional spinal motion supports for better function of the inter-segmental motor-control than the Model I and Model II.

• 한국구조물진단유지관리공학회 논문집
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• 제25권3호
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• pp.21-30
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• 2021

건축문화재들은 다양한 환경적 요인들로 인해 많은 손상이 발생된다. 손상된 문화재를 보존하기 위해서 예방보존 및 장기적인 보존관리가 더욱 중요해지고 있다. 그래서 정기적인 점검 시에 적용 가능한 과학적인 비파괴 검사 방법에 대한 연구가 요구되고 있다. 관련된 연구를 위해서, 여러 문화재들 중에서 높은 깃대 형상의 당간을 연구 대상으로 선정하였다. 보존되고 있는 당간들 중에서 보물 제49호 나주 석당간을 선정하여, 구조 안정성을 평가하기 위한 분석 기법에 대한 기초적인 연구를 진행하였다. 이상화된 모델을 제시하고, 다자유도 운동방정식을 유도하였다. 그리고 연결부 위치별 임계 강성 값을 추정할 수 있는 식을 제시하였다.

• 제어로봇시스템학회논문지
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• 제19권1호
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• pp.1-9
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• 2013

This paper presents a new control algorithm for dynamic control of a unicycle robot. The unicycle robot motion consists of a pitch that is controlled by an in-wheel motor and a roll that is controlled by a reaction wheel pendulum. The unicycle robot doesn't have any actuator for a yaw axis control, which makes the derivation of the dynamics relatively simple. The Euler-Lagrange equation is applied to derive the dynamic equations of the unicycle robot to implement the dynamic speed control of the unicycle robot. To achieve the real time speed control of the unicycle robot, the sliding mode control and LQ regulator are utilized to guarantee the stability while maintaining the desired speed tracking performance. In the roll controller, the sigmoid-function based sliding mode controller has been adopted to minimize the chattering by the switching function. The LQR controller has been implemented for the pitch control to drive the unicycle robot to follow the desired velocity trajectory in real time using the state variables of pitch angle, angular velocity, angle and angular velocity of the wheel. The control performance of the two control systems form a single dynamic model has been demonstrated by the real experiments.

• 한국생산제조학회지
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• 제26권1호
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• pp.144-149
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• 2017

There have been lots of interest on service and entertainment robots. To ensure that robots work in harmony with humans, their stability and compactness are some of the key issues. Obviously, robots with fewer wheels occupy a smaller floor area compared to those with more wheels. In addition, robots with fewer wheels, whose posture stabilities are maintained by feedback control, are stable even under larger accelerations and/or higher locations of the center of mass. To facilitate controller design, it is assumed that both pitch and roll dynamics are decoupled. The dynamic equations of motion for the proposed robot are derived from the Euler-Lagrange equation. To obtain the optimal balancing control law, linear quadratic regulator control methods are applied to the linearized dynamic equations. Simulation and experimental results verify the effectiveness and performance of the proposed balancing control algorithm for a single-wheeled mobile robot.

• Structural Engineering and Mechanics
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• 제67권6호
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• pp.565-578
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• 2018

This research article reported the nonlinear finite solutions of the nonlinear flexural strength and stress behaviour of nano sandwich graded structural shell panel under the combined thermomechanical loading. The nanotube sandwich structural model is derived mathematically using the higher-order displacement polynomial including the full geometrical nonlinear strain-displacement equations via Green-Lagrange relations. The face sheets of the sandwich panel are assumed to be carbon nanotube-reinforced polymer composite with temperature dependent material properties. Additionally, the numerical model included different types of nanotube distribution patterns for the sandwich face sheets for the sake of variable strength. The required equilibrium equation of the graded carbon nanotube sandwich structural panel is derived by minimizing the total potential energy expression. The energy expression is further solved to obtain the deflection values (linear and nonlinear) via the direct iterative method in conjunction with finite element steps. A computer code is prepared (MATLAB environment) based on the current higher-order nonlinear model for the numerical analysis purpose. The stability of the numerical solution and the validity are verified by comparing the published deflection and stress values. Finally, the nonlinear model is utilized to explore the deflection and the stresses of the nanotube-reinforced (volume fraction and distribution patterns of carbon nanotube) sandwich structure (different core to face thickness ratios) for the variable type of structural parameter (thickness ratio, aspect ratio, geometrical configurations, constraints at the edges and curvature ratio) and unlike temperature loading.

• 제어로봇시스템학회논문지
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• 제22권7호
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• pp.502-507
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• 2016

In this paper, we propose a tracking control method for a quadrotor equipped with a 2-DOF manipulator, which is based on the multiple sliding surface control (MSSC) method. To derive the model of a quadrotor equipped with a 2-DOF manipulator, we obtain the models of a quadrotor and a 2-DOF manipulator based on the Lagrange-Euler formulation separately - and include the inertia and the reactive torque generated by a manipulator when these obtained models are combined. To make a quadrotor equipped with a manipulator track the desired path, we design a double-loop controller. The desired position is converted into the desired angular position in the outer controller and the system's angle tracks the desired angular position through the inner controller based on the MSSC method. We prove that the position-tracking error asymptotically converges to zero based on the Lyapunov stability theory. Finally, we demonstrate the effectiveness of the proposed control system through a computer simulation.