Sheet and film processes, which include coating, papermaking, and polymer film extrusion processes, are of worldwide industrial importance. Existing identification and estimation techniques require much more input-output data than are usually available for poorly conditioned large-scale sheet and film processes. The objective of this project is to exploit the inherent structure of these processes to improve numerical conditioning and the robustness of model and state estimates. This is leading to the development of an automatic identification procedure, where the model and an estimate of its accuracy are iteratively improved as opportunities for increased input-output testing become available.

Numerous researchers over the last few decades have proposed techniques to rigorously address model inaccuracies in multivariable systems. The purpose of this project is to draw theoretical connections between various branches of robust control theory. This is leading to relationships between modern and classical control methods, theoretical justifications of ad hoc methods for the synthesis of robust controllers, and to the removal of computational limitations posed by these methods for the analysis of robust controllers.

Robustness analysis requires that the uncertain system be written as a linear fractional transformation of the uncertain parameters. This problem is algebraically equivalent to the problem of deriving the state space realization for a multidimensional transfer function matrix. We are developing multidimensional realization algorithms which are applicable to large-scale uncertain systems, which have large numbers of uncertain parameters, states, and manipulated, measured, and controlled variables.

We are developing computational approaches for designing globally optimal controllers for large-scale sheet and film processes. The resulting controllers are robust to inaccuracies in physical properties of the sheet or film and to faults and/or failures in measured and manipulated variables. One of the key ideas in these approaches is to exploit nonlocalized structural characteristics of the sheet or film.

The objective of this research is to develop approaches for the black and grey box modeling of large-scale nonlinear dynamic processes. These techniques, which involve time-scale, chemometric, and decomposition data reduction methods, incorporate a priori known causality information and are applicable also to the detection and isolation of process faults.

Numerous researchers over the last few decades have worked to develop efficient methods for computing robustness margins. We are studying how uncertainty representation affects the computational difficulty associated with robustness margin computations for large-scale systems. Computational complexity theory is used to show which robustness margins may be efficiently computed and for which uncertainty representations there does not exist any algorithm that can calculate the robustness margin in polynomial time as a function of the size of the system. This theory is key to motivating the development of polynomial time upper and lower bounding and globally convergent branch-and-bound algorithms.