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Research Papers

# Active Vibration Control for a Machine Tool With Parallel Kinematics and Adaptronic Actuator

[+] Author and Article Information
Alexandra Ast

Institute of Engineering and Computational Mechanics,  University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany

Peter Eberhard

Institute of Engineering and Computational Mechanics,  University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germanyeberhard@itm.uni-stuttgart.de

J. Comput. Nonlinear Dynam 4(3), 031004 (May 19, 2009) (8 pages) doi:10.1115/1.3124089 History: Received February 28, 2008; Revised July 24, 2008; Published May 19, 2009

## Abstract

The use of adaptronic components opens up interesting new possibilities for modern machine tools such as parallel kinematics. In this paper, two active vibration control concepts are designed for an adaptronic component of a parallel kinematic machine tool. The machine tool is modeled as a flexible multibody system model including a nonlinear flatness-based position control. Both the combination of a frequency shaped linear quadratic regulator with an active damping concept in a high authority control/low authority control approach and the $H2$ optimal control with gain scheduling show a high potential in the simulation to significantly increase the disturbance rejection or the tracking performance of the machine tool.

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## Figures

Figure 1

Picture of the machine tool with lambda kinematics (source www.ifw.uni-stuttgart.de)

Figure 2

Cross-sectional view of the actuator (source www.ifw.uni-stuttgart.de)

Figure 3

Schematic view of the multibody system model of the machine tool

Figure 4

SIMPACK model of the machine tool with adaptronic rod

Figure 5

Schematic view of the HAC/LAC approach

Figure 6

Schematic view of the frequency shaped LQR with observer

Figure 7

Frequency dependent weighting functions h and r

Figure 8

Sinusoidal trajectory in TCP coordinates

Figure 9

Elongation of piezo-actuator Δx and elongation of the complete adaptronic rod Δxend for the machine tool model with the sinusoidal trajectory without active vibration control (dotted), with IFF as LAC alone (dashed) and with HAC/LAC (solid)

Figure 10

Trajectory error of the TCP Δe for the machine tool model with the sinusoidal trajectory without active vibration control (dotted), with IFF as LAC alone (dashed) and with HAC/LAC (solid)

Figure 11

Schematic view of a system with H2 optimal control

Figure 12

H2 norm of the linearized system with (dashed) and without (solid) optimal control for the original model with varying relative support positions Δs

Figure 13

Frequency response of Δxend to disturbances FTCP,x (left) and FTCP,y (right) for the machine tool linearized with respect to Δs=0.8 m

Figure 14

Frequency response of Δxend to disturbances FTCP,x (left) and FTCP,y (right) for the machine tool linearized with respect to Δs=1.7 m

Figure 15

Simulation results of the machine tool model for a chirp excitation with (bottom) and without (top) H2 optimal control, Δs=0.8 m,

Figure 16

Simulation results of the machine tool model for a chirp excitation with (bottom) and without (top) H2 optimal control, Δs=1.7 m

Figure 17

Simulation results of the trajectory error Δe for the sinusoidal trajectory with a process force acting between ≈2 s and 11 s with (right) and without (left) H2 optimal control

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