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Research Papers

Adaptive LQR-Control Design and Friction Compensation for Flexible High-Speed Rack Feeders

[+] Author and Article Information
Harald Aschemann

Chair of Mechatronics
e-mail: Harald.Aschemann@uni-rostock.de
University of Rostock,
Rostock D-18059, Germany

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 29, 2012; final manuscript received August 30, 2013; published online October 14, 2013. Assoc. Editor: Johannes Gerstmayr.

J. Comput. Nonlinear Dynam 9(1), 011011 (Oct 14, 2013) (9 pages) Paper No: CND-12-1188; doi: 10.1115/1.4025351 History: Received October 29, 2012; Revised August 30, 2013

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.

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Figures

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Fig. 1

Experimental setup of the high-speed rack feeder

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Fig. 2

Elastic multibody model of the rack feeder

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Fig. 3

Feedback control gains—normalized with their corresponding SI-units—as function of the dimensionless vertical position κ as scheduling parameter

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Fig. 4

Closed-loop eigenvalues in dependency on the dimensionless scheduling parameter κ

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Fig. 5

Comparison of the measured friction force and the experimentally identified friction force

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Fig. 6

Implementation of the cascaded control structure

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Fig. 7

Desired trajectories for the cage motion: desired position in horizontal direction (a), desired position in vertical direction (c), desired velocity in horizontal direction (b) and desired velocity in vertical direction (d)

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Fig. 8

Tracking error ey for the cage motion in horizontal direction (a) and tracking error ex for the cage motion in vertical direction (b)

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Fig. 9

Comparison of the desired values v1d and the actual values v1 for the bending deflection

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Fig. 10

Transient response after a manual excitation of the bending deflection: at first without feedback control, after approx. 2.5 s with active control

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Fig. 11

Comparison of the tracking error ey with and without considering the disturbance compensation by the feedforward friction compensation part FSR,FF and the estimated lumped disturbance force F∧U

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Fig. 12

Comparison of the estimated disturbance force F∧U with and without employing the feedforward friction compensation FSR,FF

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Fig. 13

Comparison of the tracking error ey (a) and the bending deflection v1 (b) for employing either the drive force or the carriage velocity as input variable

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