Globally optimal robust control for large-scale sheet and film processes

Sheet and film processes such as polymer film extruders, paper machines, and coating processes are large scale and high speed. Addressing model uncertainty for these processes is critically important because model uncertainty can cause the closed loop system to perform poorly. Here an approach is developed which exploits the structure of generic sheet and film process models to design globally optimal robust controllers for these large scale systems. Theorems are given which reduce a large scale robust control problem for a generic sheet or film process to an equivalent set of independent or coupled low order robust control problems. The reduced order problems are formulated as an optimization with bilinear matrix inequality (BMI) constraints and solved to global optimality via a branch and bound algorithm. The algorithm is applied to a model of a paper machine constructed from published industrial data. The resulting robust control problem is the largest solved to date.