Abstract
The quality of wide film manufactured in industries is determined by the flatness of thickness along the width of the film. To control the film thickness in the inflated film process, uniform distribution of melted polymer flow velocity along the annular die gap is required and to realize this uniformity, many regulating heaters are used. The system is highly interracting since the heat generated by one heater makes changes of the film thicknesses at the adjacent heaters' positions due to the heat conduction in the die and usually more than several tens number of heaters are used. This makes it difficult to design the film control system.
In this paper, a new design method is proposed for constructing inflated film thickness control systems. Here, the controller is assumed to be a PI type decentralized one, whose gain is determined by minimizing quadratic cost. The design is performed based on the following observed fact:
By using the fact that the A-matrix of the closed-loop system comes to be a block symmetric circular matrix, it can be transformed into a block diagonal matrix by using similarity transformation which is completely determined only by the system size, not depending on the numeric characteristics of the process. This fact enables to decompose the large size matrix calculation into the small size one, and makes the stability test and the computation of cost feasible even for systems with the large number of inputs and outputs.
