Noncausal modeling and closed-loop optimal input design for cross-directional processes of paper machines

We propose to use noncausal transfer functions to model the spatial behavior of cross-directional (CD) processes so as to circumvent the high-dimensionality of a causal transfer function. This noncausal representation is shown to have a causal-equivalent form. We prove that the covariance of maximum likelihood estimate of the causal-equivalent model asymptotically converges to that of the noncausal model. This result is then used to design optimal inputs in closed-loop for the original noncausal model of the CD process. An illustrative example is provided to highlight the advantage of using optimally designed excitation signal for CD closed-loop identification over white noise excitation or the current industrial practice of spatial bump excitation.