Rack feeders for the automated operation of high bay rackings are of high practical importance. They are characterized by a horizontally movable carriage supporting a tall and flexible vertical beam structure, on which a cage containing the payload can be positioned in vertical direction. To shorten the transport times by using trajectories with increased maximum acceleration and jerk values, accompanying control measures can be introduced counteracting or avoiding undesired vibrations of the flexible structure. In this contribution, both the control-oriented modeling for an experimental setup of such a flexible rack feeder and the model-based design of a gain-scheduled feedforward and feedback control structure are presented. Whereas, a kinematical model is sufficient for the vertical axis, the horizontal motion of the rack feeder is modeled as a planar elastic multibody system with the cage position as scheduling parameter. For the mathematical description of the bending deflections, a one-dimensional Ritz ansatz is introduced. The tracking control design is performed separately for both the horizontal and the vertical axes using decentralized state-space representations. Remaining model uncertainties are estimated by a disturbance observer. The resulting tracking accuracy of the proposed control concept is shown by measurement results from the experimental setup. Furthermore, these results are compared to those obtained with an alternative control concept from previous work.

References

References
1.
Aschemann
,
H.
, and
Ritzke
,
J.
,
2009
, “
Adaptive aktive Schwingungsdämpfung und Trajektorienfolgeregelung für hochdynamische Regalbediengeräte (in German)
,”
Schwingungen in Antrieben
,
Vorträge der 6, VDI-Fachtagung
,
Leonberg, Germany
.
2.
Bachmayer
,
M.
,
Rudolph
,
J.
, and
Ulbrich
,
H.
,
2008
, “
Flatness Based Feed Forward Control for a Horizontally Moving Beam With a Point Mass
,”
European Conference on Structural Control
,
St. Petersburg, Russia
, pp.
74
81
.
3.
Bachmayer
,
M.
,
Rudolph
,
J.
, and
Ulbrich
,
H.
,
2008
, “
Acceleration of Linearly Actuated Elastic Robots Avoiding Residual Vibrations
,”
Proceedings of the 9th International Conference on Motion and Vibration Control
,
Munich, Germany
.
4.
Kostin
,
G. V.
, and
Saurin
,
V. V.
,
2006
, “
The Optimization of the Motion of an Elastic Rod by the Method of Integro-Differential Relations
,”
J. Comput. Syst. Sci. Int.
,
45
, pp.
217
225
.10.1134/S1064230706020067
5.
Aschemann
,
H.
, and
Ritzke
,
J.
,
2010
, “
Gain-Scheduled Tracking Control for High-Speed Rack Feeders
,”
Proc. of the First Joint International Conference on Multibody System Dynamics (IMSD), 2010
,
Lappeenranta, Finland
.
6.
Aschemann
,
H.
, and
Schindele
,
D.
,
2010
, “
Model Predictive Trajectory Control for High-Speed Rack Feeders
,”
T.
Zheng
, ed.,
Model Predictive Control
,
Sciyo
, online edition www.sciyo.com
7.
Staudecker
,
M.
,
Schlacher
,
K.
, and
Hansl
,
R.
,
2008
, “
Passivity Based Control and Time Optimal Trajectory Planning of a Single Mast Stacker Crane
,”
Proc. of the 17th IFAC World Congress
,
Seoul, Korea
, pp.
875
880
.
8.
Shabana
,
A. A.
,
2005
,
Dynamics of Multibody Systems
,
Cambridge University
,
Cambridge, UK
.
9.
Löfberg
,
J.
,
2004
, “
YALMIP: A Toolbox for Modeling and Optimization in MATLAB
,”
Proc. of IEEE Intl. Symposium on Computer Aided Control Systems Design
, pp.
284
289
.
10.
Sturm
,
J. F.
,
1999
, “
Using SeDuMi 1.02, A MATLAB Toolbox for Optimization Over Symmetric Cone
,”
Optim. Methods Software
,
11–12
(
1–4
), pp.
625
653
.10.1080/10556789908805766
11.
Friedland
,
B.
,
1996
,
Advanced Control System Design
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
You do not currently have access to this content.