Robust Cross Directional Controller Design for Paper Machine Spatial Distributed System

The paper manufacturing process is a large-scale process in which the control performance is required to be optimal in the machine direction (MD) and cross direction (CD). This work focuses on CD control, which is more complicated than MD control. Uncertainties in the process arise from different sources, so there is a requirement for better modeling techniques. The control of paper profile properties, namely basis weight, moisture, and caliper, is done with the help of actuators that are distributed spatially. Basis weight is taken as the profile parameter in this work. The work aims to improve robust performance and simplify the control design problem. Here, $\mu $ synthesis methods are used for controller design, as this method provides guaranteed robust performance. To simplify the design problem two-dimensional modeling is explained explicitly. The conventional methods of $\mu $ analysis are extended to spatial coordinates. The performance of the $\mu $ synthesis designed method is compared with the open loop shaping method. Control performance is judged in terms of sensitivity, stability margin, $\sigma $ performance, and robust performance. The effectiveness of the developed $\mu $ synthesis designed method is demonstrated using the industrial example from the pulp and paper industry.