Abstract
With a focus on the multivariable coupling characteristics in a cross-directional (CD) basis weight control system, we study the coupling characteristics of a CD control system and decoupling control, and we propose a novel multivariable interpolation decoupling control strategy and a real-time decomposition algorithm in this paper. Based on a model of the CD basis weight profile, a system non-square interaction matrix of high-dimensional data is analyzed by experimental studies and numerical simulation. Along the diagonal of the interaction matrix, the matrix block method is adopted to reduce the system dimension and convert it into a square system. A multivariable control system with high dimensionality is divided into several subsystems. For the high-dimensional Toeplitz symmetric subsystem with small-scale coupling characteristics, an interpolation decoupling algorithm is proposed. Then, a decoupling compensator with the structure of a symmetric Toeplitz matrix was obtained. Compared with the conventional diagonal decoupling matrix, the branch number of the new decoupling network is reduced from 2408 to 186, which realizes the fast decoupling of multivariable systems. The results were even better when we used a double size interaction matrix obtained by interpolation between actual values. By designing the diagonalized controller for the new decoupled system, a decouped CD control system for corrugated paper with a basis weight of 133 g/m2 was implemented in an actual project in a paper mill.
Highlights
Paper-making is by far the most complex and complicated of all the pulp and paper processes.An important quality characteristic in the production of paper sheets is the range of functions in the basis weight, which should be kept as small as possible
The quality of the manufactured paper is assessed in two dimensions: one is the maintenance of the average sheet property profile along the paper sheet as it moves while it is being manufactured, which is referred to as machine directional (MD)
In the process of modern high-speed paper machines, it is necessary to monitor and control the performance of paper continuously to ensure that the quality of paper meets the requirements of MD and CD [1]
Summary
Paper-making is by far the most complex and complicated of all the pulp and paper processes.An important quality characteristic in the production of paper sheets is the range of functions in the basis weight, which should be kept as small as possible. The quality of the manufactured paper is assessed in two dimensions: one is the maintenance of the average sheet property profile along the paper sheet as it moves while it is being manufactured, which is referred to as machine directional (MD). Control, and the other is the maintenance of the sheet profile across the width of the paper machine, which is referred to as cross-directional (CD) control. Control of the CD basis weight on paper machines has long been known as an especially difficult problem. This is due to several difficulties including the high dimensionality of the cross-directional system, the high lateral space interaction between actuators, the uncertainty of the model, and the limited control authority of the actuator [2]
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