This paper presents a model for predicting fabric drape profiles using polar coordinates. The drape coefficient (DC%), node locations, node numbers, and node shape in the fabric drape profile can be predicted accurately with this model. Polar coordinate fitting is used to determine the constants in the drape profile model, and good agreement is obtained between the theoretical and experimental drape profiles of thirty-five woven fabrics. In addition, constants in the drape profile model may also be obtained by bending and shear hysteresis using regression analysis. Good agreements are found between the calculated DC% and the experimental DC% for the fabrics examined in this study. This means a drape profile may be directly predicted from bending and shear hysteresis. Moreover, better prediction of the fabric drape profile may be obtained from the mean value taken in the warp, weft, and ±45° directions than that in the warp and weft directions.

SUMMARYThe control direction is the multiplier of the control term. In this study, the control direction is considered as an unknown function of state and allowed to cross zero and change its sign smoothly. Based on the analysis of system dynamics at the points where the control direction is zero, a robust controller is proposed by integrating with a bounding function and a Nussbaum-type gain. Under the proposed controller, the system approaches zero if zero is accessible, or to the accessible point closest to zero if zero is not accessible by any control. The control performance is illustrated by simulated examples.

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