Design and Experimental Study of a VCM-Based Stewart Parallel Mechanism Used for Active Vibration Isolation
Abstract
:1. Introduction
2. Kinematics and Dynamics Analysis of the Stewart Platform
2.1. Coordinate Transformation
2.2. Kinematics and Dynamics of a Leg
2.3. Dynamical Equations of the Payload
3. Control Strategy of the Vibration Isolation System
3.1. The State Space Model and the H∞ Control Law
3.2. Selection of Weighting Functions
3.3. Simulation Results
Parameters | Values |
---|---|
Top Platform Radius | 0.165 m |
Height | 0.079 m |
Length of legs | 0.162 m |
Mass of top platform | 3.29 kg |
Moment of Inertia of top platform | |
Moment of Inertia of upper leg | |
Moment of Inertia of lower leg | |
Mass of each upper leg | 0.0793 kg |
Mass of each lower leg | 1.16 kg |
Stiffness of diaphragm spring | |
Natural Frequency | 14.5 Hz |
Mass of payload | 4.85 kg |
Leg extension range | ±5 mm |
4. System Implementation and Experimental Results
4.1. Experimental Setup
4.2. Experimental Results
4.2.1. Sinusoidal Sweeping-Frequency Vibration Tests
Damping | Resonance Frequency (Hz) | Vibration Amplitude (m/s2) | Magnification (dB) |
---|---|---|---|
Without damping | 14.524 | 2.000 | 12.041 |
Passive damping | 14.117 | 0.916 | 5.259 |
H∞ control | 15.375 | 0.253 | −5.917 |
Damping | Resonance Frequency (Hz) | Vibration Amplitude (m/s2) | Magnification (dB) |
---|---|---|---|
Without damping | 14.524 | 2.539 | 14.114 |
Passive damping | 14.905 | 0.815 | 4.244 |
H∞ control | 11.650 | 0.442 | −1.071 |
Damping | Resonance Frequency (Hz) | Vibration Amplitude (m/s2) | Magnification (dB) |
---|---|---|---|
Without damping | 14.562 | 10.878 | 26.752 |
Passive damping | 14.905 | 3.854 | 17.739 |
H∞ control | 15.576 | 2.502 | 13.986 |
4.2.2. Fixed-Frequency Vibration Tests
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
position of platform | |
position of upper end of ith leg | |
position of lower end of ith leg | |
position of center of mass of payload | |
vector of the ith leg | |
transformation matrix | |
rotation matrix | |
moment of inertia | |
rotation angle | |
acceleration | |
angular velocity | |
force vector between the upper and the lower legs | |
active control force | |
external force on the top platform | |
external torque on the top platform | |
the mass of the top platform | |
stiffness matrix of the legs | |
damping matrix of the legs |
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Chi, W.; Cao, D.; Wang, D.; Tang, J.; Nie, Y.; Huang, W. Design and Experimental Study of a VCM-Based Stewart Parallel Mechanism Used for Active Vibration Isolation. Energies 2015, 8, 8001-8019. https://doi.org/10.3390/en8088001
Chi W, Cao D, Wang D, Tang J, Nie Y, Huang W. Design and Experimental Study of a VCM-Based Stewart Parallel Mechanism Used for Active Vibration Isolation. Energies. 2015; 8(8):8001-8019. https://doi.org/10.3390/en8088001
Chicago/Turabian StyleChi, Weichao, Dengqing Cao, Dongwei Wang, Jie Tang, Yifan Nie, and Wenhu Huang. 2015. "Design and Experimental Study of a VCM-Based Stewart Parallel Mechanism Used for Active Vibration Isolation" Energies 8, no. 8: 8001-8019. https://doi.org/10.3390/en8088001