• Structural Engineering and Mechanics
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• v.30 no.4
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• pp.427-444
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• 2008

A mathematical model for the nonlinear dynamics of a rotating beam with flexible root attached to a rotating hub with elastic foundation is developed. The model is developed based on the large planar and flexural deformation theory and the potential energy method to account for axial shortening due to bending deformation. In addition the exact nonlinear curvature is used in the system potential energy. The Lagrangian dynamics and the assumed mode method is used to derive the nonlinear coupled equations of motion hub rotation, beam tip deflection and hub horizontal and vertical displacements. The derived nonlinear model is simulated numerically and the results are presented and discussed for the effect of root flexibility, hub stiffness, torque type, torque period and excitation frequency and amplitude on the dynamic behavior of the rotating beam-hub and on its stability.

• Journal of the Korean Society for Precision Engineering
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• v.10 no.4
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• pp.163-169
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• 1993

A flexible manipulator can move in the high speed even with the small driving torque. The dymanic equations of flexible manipulator which include 2 vibrational modes are derived using the clamped-free boundary condition. Simulation results of the 6th order model are well matched with experimental results. The hub angle of the flexible mainpulator can be controlled without vibration of the beam by the feedback of both hub angle and strain. The overshoot of the hub angle in the step response is reduced without sacrificing the rise time using the cycloidal function instead of the step function as the referenmce input.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.04b
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• pp.185-191
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• 1993

A flexible nanipulator can move in the high speed even with the small driving torque. The dynamic equations of flexible manipulator whichinclude 2 vibrationalmodes are derived using the clamped-free boundarycondition. Simulation results of the 6th order modelare well matched with experimental results. The hub angle of the flexible manipulator can be controlled without vibration of beam by the feedback of both hub angle and strain. The overshoot of the hub angle in the step resonse is reduced without sacrificing the rise time using the cycloidal function instead of the step function as the reference input.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.11
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• pp.898-906
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• 2014

This paper presents a reduction method for a straight-line path error of a flexible beam deploying from a rotating rigid hub. Previous studies discussed about only vibration phenomena of flexible beams deploying from rotating hubs; however, this study investigates a vibration reduction of a rotating beam with variable length. The equation of motion and associated boundary conditions are derived for a flexible beam deploying from a rotating rigid hub, and then they are transformed to a variational equation. By applying the Galerkin method, the discretized equations are obtained from the variational equation. Based on the discretized equations, the dynamic responses of a rotating/deploying beam are analyzed when the beam end has a straight line motion. A reduction method for the trajectory error is proposed, using the average length of a rotating/deploying beam. It is shown that the proposed method is able to reduce the residual vibration of a rotating/deploying beam.

• Smart Structures and Systems
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• v.7 no.2
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• pp.103-116
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• 2011

This paper is concerned with the trajectory tracking and vibration suppression of a single-link flexible arm by using piezoelectric materials. The dynamics of a single flexible arm with PZT patches as sensor and actuator is derived using extended Hamilton's principle. Resulting equations show that the coupled beam dynamics including beam vibration and its rigid in-plane rotation takes place in two different time scales. By using singular perturbation theory, the system dynamics is divided into two subsystems. Then, a composite control scheme is elaborated that makes the orientation of the arm track a desired trajectory while suppressing its vibration. The proposed controller has two parts: one is a tracking controller designed for the slow (rigid) subsystem, and the other one is a stabilizing controller for the fast (flexible) subsystem. The outputs considered for the system are angular position of the hub and voltage of the sensor mounted on the structure. To avoid requiring further measurements of beam vibration and also angular velocity of the hub for the fast and slow control laws, respectively, two sliding mode observers for estimating the unknown states are also designed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.7
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• pp.1307-1313
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• 1992

The end-point position control of a flexible manipulator is a non-minimum phase system. The PD feedback of the end-point position is not stable in contrast with that of the hub jangle. However, the system can be stabilized conditionally by the feedback of both the hub rate angle and the end-point position. Even in the non-minimum system, the LQG/LTR control law is more systmatic controller design method than the classical control law which uses a root-locus technique.

• Journal of Astronomy and Space Sciences
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• v.14 no.2
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• pp.367-374
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• 1997

Slewing maneuver and vibration suppression control of flexible spacecraft model by Lyapunov stability theory are considered. The specific model considered in this paper consists of a rigid hub with an elastic appendage attached to the central hub and tip mass. Attitude control to point and stabilize single axis using reaction wheel type device is tested. To control all flexible modes is so critical to designing an active control law. We therefore considered an direct output feeback control design by using Lyapunov stability theory. It is shown that the ouput feedback control law design with proposed configuration gives satisfactory result in slewing performance and vibration suppression control.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.2 s.95
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• pp.169-175
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• 2005

In this paper, a novel vibration control scheme for a single-link flexible manipulator system without using a vibration feedback sensor is proposed. In order to achieve the vibration information of the flexible link, a reaction moment estimator based on the dynamic characteristics of the flexible manipulator is proposed. While the manipulator is maneuvering the reaction moment is reciprocally acting on the flexible link and the hub inertia due to the vibration of the link. A sliding mode controller based on the equivalent rigid body dynamics corresponding to the proposed flexible manipulator is then augmented with the reaction moment estimator to realize a decentralized control system. The reaction moment estimator is implemented via the first order low pass filter. The performance of the proposed control scheme is verified by computer simulation and experiment.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.6
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• pp.1371-1381
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• 1995

A novel hybrid control scheme to actively control the endpoint position of a very flexible single-link manipulator is proposed. The control scheme consists of a motor mounted at the beam hub and a piezofilm actuator bonded to the surface of the flexible link. The control torque of the motor to produce a desired motion is firstly determined by employing the sliding mode control theory on the equation of motion of the rigid link having the same mass as that of the proposed flexible link. The torque is then applied to the flexible manipulator in order to activate the commanded motion. During the motion, undesirable oscillation is actively suppressed by applying a feedback control voltage to the piezofilm actuator. Consequently, the imposed desired position is accomplished. In order to demonstrate high control performances accrued from the proposed method, computer simulations are undertaken by treating both regulating and tracking control problems.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.233-236
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• 2004

In this paper, a new sensorless vibration control scheme is proposed for a flexible manipulator system. A robust sliding mode controller incorporating with a ‘reaction moment observer’ used for the estimation of the reaction moment reciprocally acting on flexible arm and hub inertia is introduced to achieve desired control target. The rigid body dynamics of the single-link flexible manipulator is simply considered in the design of the sliding mode controller. Then, the reaction moment is estimated by the proposed reaction moment observer to suppress the residual vibration of the flexible arm. The performance of the proposed control scheme is verified by computer simulation and experiment.