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Research Papers

Optimal Web Guiding

[+] Author and Article Information
Aravind Seshadri

School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078aravind.seshadri@okstate.edu

Prabhakar R. Pagilla1

School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078pagilla@okstate.edu

If the effect of inertial forces are considered then K changes based on the transport velocity and the mass per unit length of the web. For most practical web guiding situations, the inertial forces have negligible effect and hence are neglected (1).

Detailed discussions about the derivation of lateral velocity and acceleration are presented in Ref. 1 (pp. 102–105) and Ref. 4 (pp.29–32).

The transfer function may be interpreted as the dynamics of the web with a remotely pivoted guide when the time constant τ is 1.

Under-steering is developed for a particular guide installation if a unit displacement of the guide roller results in less than a unit displacement in web lateral position. Correspondingly, over-steering is the case when the web position correction is larger than the displacement of the guide roller.

This will result in a nonminimum phase system due to the extra free span dynamics (see Sec. 2).

Note that for any KL the system would exhibit positive phase when L/x1<1 as evident from Eq. 20.

The nominal parameters correspond to the transport of an opaque plastic web. The physical web parameters and transport conditions are listed in the Appendix.

1

Corresponding author.

J. Dyn. Sys., Meas., Control 132(1), 011006 (Dec 03, 2009) (10 pages) doi:10.1115/1.4000074 History: Received December 08, 2008; Revised July 20, 2009; Published December 03, 2009; Online December 03, 2009

This paper presents an optimal web guiding strategy based on the dynamic analysis of the lateral web behavior and a new fiber optic lateral web position measurement sensor. First, a lateral dynamic model of a moving web is revisited with an emphasis on correct application of appropriate boundary conditions. Then the dynamic models of two common intermediate guides (remotely pivoted guide and offset-pivot guide) are investigated. The effect of various model parameters on lateral web behavior is analyzed and discussions on proper selection of the parameters are given. Based on the model analysis, we discuss the design of a linear quadratic optimal controller that is capable of accommodating structured parametric uncertainties in the lateral dynamic model. The optimal guide control system is evaluated by a series of experiments on a web platform with different web materials under various operating conditions. Implementation of the controller with a new fiber optic lateral sensor for different scenarios is discussed. Results show good guiding performance in the presence of disturbances and with uncertainties in the model parameters.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

An example web guide mechanism with an electromechanical actuator and a infrared edge sensor

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Figure 2

Boundary conditions for solving the partial differential Eq. 1

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Figure 3

Schematic showing the boundary conditions and angular rotation of the rollers

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Figure 4

Remotely pivoted guide schematic

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Figure 5

Offset-pivot guide schematics

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Figure 6

Frequency response of the model in Eq. 16 as a function of τ with KL=3 and L/x1≈1.5

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Figure 7

Frequency response of the model in Eq. 16 as a function of KL with τ=1 and L/x1≈1.5

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Figure 8

Relationship between KL and L/x1

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Figure 9

Frequency response of the model in Eq. 16 as a function of L/x1 with τ=1 and KL=3

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Figure 10

Fiber optic sensor working principle

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Figure 11

Fiber optic sensor installed along with an infrared sensor

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Figure 12

Web lateral position with web2

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Figure 13

Performance with web1

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Figure 14

Performance with web3

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Figure 15

Performance of PI and optimal controller with web1

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Figure 16

Performance of PI and optimal controller with web3

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