In textile exhaust dyeing, the control of dyebath pH is a critical factor in order to achieve optimum colour yield and levelness. Conventional controllers have not proved entirely successful in controlling dyebath pH since it is difficult to develop an exact mathematical model for the dyeing process. One method is to apply fuzzy control to the dyeing process. For the fuzzy controller to operate successfully, it is important to understand how the dyeing system responds to given reference pH/time profiles. A dynamic model for the dyeing process has been developed and this allows the fuzzy controller to be fine-tuned by computer simulation. Results of the control system simulation showed very satisfactory tracking performances of the pH profiles. This provides a starting point for further fine-tuning of the system under practical dyeing conditions.
The tensile behaviour of a flexible sheet, for example a woven fabric, draped on a complex surface is modelled based on the knowledge of the geometry of the deformed object. A draping simulation is used to determine the coordinates of the material as it is deformed to conform to a complex surface. The simulation in turn is based on the local geometry of the surface. To conform to a doubly curved surface a flat flexible material will bend and shear. The degree of bending and shearing at different locations on the surface will depend on the local Gaussian curvature. The geometry of the deformed material is used to calculate local tow or yarn displacements. The strain energy in each segment of the material is then calculated based on a shear model that assumes no slippage at crossover points. Finally the forces required in each yarn are calculated from the total strain energy in the yarn as well as the total displacement the forces have to undergo to drape the fabric.
A fitting algorithm is presented that can be applied to any surface described numerically or analytically. The algorithm that is based on differential geometry is more robust and faster than the traditional kinetic‐model based algorithms and it also allows for more flexible initial conditions.
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