0
Research Papers

Fixed Structure Feedforward Controller Design Exploiting Iterative Trials: Application to a Wafer Stage and a Desktop Printer

[+] Author and Article Information
Stan H. van der Meulen

Control Systems Technology Group, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlandss.h.v.d.meulen@tue.nl

Rob L. Tousain

Drives and Control Group, Department of Mechatronics, Philips Applied Technologies, High Tech Campus 7, 5656 AE Eindhoven, The Netherlandsrob.tousain@philips.com

Okko H. Bosgra

Control Systems Technology Group, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlandso.h.bosgra@tue.nl

J. Dyn. Sys., Meas., Control 130(5), 051006 (Aug 04, 2008) (16 pages) doi:10.1115/1.2957626 History: Received July 13, 2006; Revised May 07, 2008; Published August 04, 2008

In this paper, the feedforward controller design problem for high-precision electromechanical servo systems that execute finite time tasks is addressed. The presented procedure combines the selection of the fixed structure of the feedforward controller and the optimization of the controller parameters by iterative trials. A linear parametrization of the feedforward controller in a two-degree-of-freedom control architecture is chosen, which results in a feedforward controller that is applicable to a class of motion profiles as well as in a convex optimization problem, with the objective function being a quadratic function of the tracking error. Optimization by iterative trials avoids the need for detailed knowledge of the plant, achieves the controller parameter values that are optimal with respect to the actual plant, and allows for the adaptation to possible variations that occur in the plant dynamics. Experimental results on a high-precision wafer stage and a desktop printer illustrate the procedure.

Copyright © 2008 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

System with a two-degree-of-freedom control architecture

Grahic Jump Location
Figure 2

System with snap feedforward, jerk feedforward, acceleration feedforward, and velocity feedforward

Grahic Jump Location
Figure 3

Optimization of delay correction for acceleration setpoint

Grahic Jump Location
Figure 4

Closed loop system in the trial domain, including input disturbance

Grahic Jump Location
Figure 5

Bode diagram of the wafer stage dynamics in the y-direction, where the figures on the right are close-ups of the figures on the left (solid: frequency response function measurements; dashed: second-order discrete time transfer function model)

Grahic Jump Location
Figure 6

Bode diagram of the discretized feedback controller for the wafer stage dynamics in the y-direction

Grahic Jump Location
Figure 7

The position r, the velocity v, the acceleration a, the jerk j, and the snap s of the point-to-point motion

Grahic Jump Location
Figure 8

System with snap feedforward and acceleration feedforward

Grahic Jump Location
Figure 9

Experimental tracking errors obtained with the model-based approach in trials 0 (top), 1 (middle), and 5 (bottom) (solid: tracking error; dashed: scaled acceleration setpoint)

Grahic Jump Location
Figure 10

Experimental controller parameters obtained with the model-based approach

Grahic Jump Location
Figure 11

Experimental objective function obtained with the model-based approach

Grahic Jump Location
Figure 12

Meander movement in the xy-plane (solid: finite time task in the y-direction; dashed: finite time task in the x-direction; star: start position y(0); circle: end position y(N−1))

Grahic Jump Location
Figure 13

Controller parameter value kfa as a function of trial number (solid: nominal controller parameter value; dashed: optimal controller parameter value)

Grahic Jump Location
Figure 14

Bode diagram in the trial domain for transfer function el∕Δkfal, with maximum magnitude and corresponding phase plotted for each trial frequency (solid: αl=0.0; dashed: αl=0.5; dashed-dotted: αl=1.0; star: ft=1∕15 periods per trial)

Grahic Jump Location
Figure 15

Desktop printer

Grahic Jump Location
Figure 16

Bode diagram of the desktop printer dynamics (solid: frequency response function measurements; dashed: fourth-order discrete time transfer function model)

Grahic Jump Location
Figure 17

Bode diagram of the discretized feedback controller for the desktop printer dynamics

Grahic Jump Location
Figure 18

The position r, the velocity v, the acceleration a, and the Coulomb friction c of the point-to-point motion

Grahic Jump Location
Figure 19

System with Coulomb friction feedforward and acceleration feedforward

Grahic Jump Location
Figure 20

Experimental tracking errors obtained with the model-based approach in trials 0 (top), 1 (middle), and 7 (bottom) (solid: tracking error; dashed: scaled acceleration setpoint).

Grahic Jump Location
Figure 21

Experimental controller parameters obtained with the model-based approach

Grahic Jump Location
Figure 22

Experimental objective function obtained with the model-based approach

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In