A web refers to any material in continuous flexible strip form which is either endless or very long compared to its width, and very wide compared to its thickness. This paper discusses the dynamic analysis and control of the lateral and longitudinal motions of a moving web which correspond to fluctuations perpendicular and parallel, respectively, to the primary direction of web transport. Historical perspectives are provided, from the early work of Osborne Reynolds in the late 1800s to current research. An overview of the control of both lateral and longitudinal web motion, which includes the control of tension, is presented. Present limitations in understanding and controlling lateral and longitudinal web behavior are discussed. The Journal of Dynamic Systems, Measurement, and Control has played a pivotal role in the advancement of research in this area.
When the friction between the web and a roller between two web spans is small enough that the tension distribution across the web in the downstream span affects the tension distribution in the upstream span interaction will occur. A model is developed which extends the work of one of the authors to this case and utilizes beam theory which is valid when the web is not in a wrinkled or slack edge state. The boundary conditions and static solutions for the three different types of interaction are established. In the circumferential slippage mode a negative steering effect has been identified. A steering effect description function is established which will allow prediction of this phenomenon which can be avoided by proper choice of system parameters.
The methods of Gaussian linearization along with a new Gaussian Criterion used in the prediction of the stationary output variances of stable nonlinear oscillators subjected to both stochastic parametric and external excitations are presented. The techniques of Gaussian linearization are first derived and the accuracy in the prediction of the stationary output variances is illustrated. The justification of using Gaussian linearization a priori is further investigated by establishing a Gaussian Criterion. The non-Gaussian effects due to system nonlinearities and/or large noise intensities in a Duffing oscillator are also illustrated. The validity of employing the Gaussian Criterion test for assuring accuracy of Gaussian linearization is supported by performing the Chi-square Gaussian goodness-of-fit test.
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