Vibration control of a servomotor-driven coupled elastic shaft-elastic beam system

2004 ◽  
Vol 218 (10) ◽  
pp. 1115-1124
Author(s):  
H Diken ◽  
A Ankarali
Keyword(s):  
Control System ◽  
Natural Frequency ◽  
Frequency Ratio ◽  
Damping Ratio ◽  
Elastic Beam ◽  
Step Response ◽  
Elastic Shaft ◽  
Disc Rotation ◽  
Frequency Ratios ◽  
System Frequency

In this study an elastodynamic control system consisting of servomotor, elastic shaft, disc and elastic beam, which is attached to the disc, is considered. Non-dimensional parametric equations of motions are obtained. The control system damping ratio, the frequency ratio of the torsional natural frequency to the beam natural frequency and also the frequency ratio of the beam natural frequency to the control system frequency are used as parameters. Simulation results are obtained for the step response of the disc rotation and for the beam tip vibration for different frequency ratios. Results show that even for highly flexible systems the effect of flexibility on the control system behaviour can be substantially reduced by proper selection of the control system frequency.

scholarly journals Dynamic Analysis and Experiment of 6-DOF Compliant Platform Based on Bridge-Type Amplifier

Micromachines ◽  
2020 ◽  
Vol 11 (11) ◽  
pp. 1024
Author(s):  
Chao Lin ◽  
Shan Zheng ◽  
Mingdong Jiang
Keyword(s):  
Dynamic Model ◽  
Natural Frequency ◽  
Theoretical Calculations ◽  
Lagrange Equation ◽  
Damping Ratio ◽  
Elastic Beam ◽  
Analytical Models ◽  
Step Response ◽  
Element Analysis ◽  
Bridge Type

In this paper, we establish a dynamic model of a six-degrees-of-freedom (6-DOF) compliant positioning platform based on bridge-type amplifiers. Based on the elastic beam theory and energy relationship, we derived the bridge-type amplifier’s dynamic model using the Lagrange equation. Then, we established a dynamic model of the compliant platform based on the equivalent mass and equivalent stiffness of the bridge-type amplifier, and the analysis formula of the natural frequency was derived. Finally, the analytical models of natural frequencies of the bridge-type amplifier and the compliant platforms were verified using the finite element analysis (FEA) method. Through modal experiments, the damping ratio and natural frequency were identified. Step response experiments in the X/Y direction and Z direction were performed. The phenomenon that the experimental results appeared to match the theoretical calculations indicates that the dynamic model was accurate.

Determination of frequency response from step response: application to fluid-filled catheters

1979 ◽  
Vol 236 (2) ◽  
pp. H376-H378 ◽  
Author(s):  
S. A. Glantz ◽  
J. V. Tyberg
Keyword(s):  
Decay Rate ◽  
Frequency Response ◽  
Natural Frequency ◽  
Damping Ratio ◽  
Step Change ◽  
Step Response ◽  
Undamped Natural Frequency

The performance of a fluid-filled catheter can be described by reporting its undamped natural frequency and damping ratio. These parameters can be measured by subjecting the catheter to sinusoidally varying pressures at a wide variety of frequencies to obtain the frequency response. They can also be computed from the response to a step change in pressure, which is often easier to produce. This paper derives the required equations and includes a graph which permits one to look up the undamped natural frequency after measuring the period and decay rate of the oscillation following a step change in pressure.

Effect of Shaft Flexibility on Control System Parameters

1999 ◽  
Vol 122 (3) ◽  
pp. 222-226 ◽  
Author(s):  
H. Diken
Keyword(s):  
Control System ◽  
Transfer Function ◽  
Natural Frequency ◽  
Robot Arm ◽  
Structural Damping ◽  
Vibratory System ◽  
Shaft Flexibility ◽  
System Equations ◽  
System Frequency ◽  
System Transfer Function

A dynamic system consisting of a servomotor, elastic shaft and inertial load, which may represent a disk or a robot arm, is chosen as an elastic control system. Equations of the torsional vibratory system are coupled with the servomotor control system equations and the transfer function of the elastic control system relating output angle to the desired input angle is obtained including not only control parameters but also the structural natural frequency and the structural damping of the torsional vibratory system. The ratio of the structural natural frequency to the substructural natural frequency and the ratio of substructural natural frequency to the control system frequency are defined as nondimensional parameters. System behavior is analyzed with respect to these parameters. The fourth order elastic control system transfer function is also reduced to the second order one and formulas for elastic control system frequency and damping are developed with respect to these parameters. [S0739-3717(00)70104-8]

Exploring the X-ray universe via timing: mass of the active galactic nucleus black hole XMMUJ134736.6+173403

2019 ◽  
Vol 15 (S356) ◽  
pp. 348-350
Author(s):  
Eva Šrámková ◽  
K. Goluchová ◽  
G. Török ◽  
Marek A. Abramowicz ◽  
Z. Stuchlík ◽  
...  
Keyword(s):  
Black Hole ◽  
Frequency Ratio ◽  
Active Galactic Nucleus ◽  
Periodic Modulation ◽  
X Ray ◽  
Upper Limit ◽  
M 10 ◽  
Frequency Ratios ◽  
Quasiperiodic Oscillations ◽  
Twin Peak

AbstractA strong quasi-periodic modulation has recently been revealed in the X-ray flux of the X-ray source XMMUJ134736.6+173403. The two observed twin-peak quasiperiodic oscillations (QPOs) exhibit a 3:1 frequency ratio and strongly support the evidence for the presence of an active galactic nucleus black hole (AGN BH). It has been suggested that detections of twin-peak QPOs with commensurable frequency ratios and scaling of their periods with BH mass could provide the basis for a method intended to determine the mass of BH sources, such as AGNs. Assuming the orbital origin of QPOs, we calculate the upper and lower limit on the AGN BH mass M, reaching M ≍ 107–109M⊙. Compared to mass estimates of other sources, XMMUJ134736.6+173403 appears to be the most massive source with commensurable QPO frequencies, and its mass represents the current observational upper limit on the AGN BH mass obtained from the QPO observations.

Analysis of a Natural Frequency Tracking System for MEMS Fatigue Testing

2001 ◽  
Author(s):  
Xiaotian Sun ◽  
Roberto Horowitz ◽  
Kyriakos Komvopoulos
Keyword(s):  
Control System ◽  
Natural Frequency ◽  
Averaging Method ◽  
Fatigue Testing ◽  
Tracking System ◽  
Frequency Tracking ◽  
At Resonance ◽  
Mems Resonator ◽  
Control Gain ◽  
Good Agreement

Abstract A nonlinear control system that can track the natural frequency of a MEMS resonator was developed in this study. Due to the evolution of fatigue damage, the natural frequency of the resonator decreases. To maintain the device at resonance, a phase-locked loop system is used to track the frequency decay and adjust the driving force accordingly. A model for the control system is introduced and the system behavior is analyzed using an averaging method. A quantitative criterion for selecting the control gain to achieve stability is derived from the analysis. Simulation results are shown to be in good agreement with the prediction of the theoretical analysis.

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