Model predictive control for multiple cross-directional processes : analysis, tuning, and implementation (2009)

In this thesis, practical techniques for analyzing, tuning and implementing an industrial model predictive controller (MPC) for paper machine cross-directional (CD) processes are developed. These techniques include model reduction, performance and robust stability analysis of a linear closed-loop system, and optimal prediction of steady-state performance for constrained MPC. Paper machine cross-directional processes are large-scale two-dimensional systems. In order to make the online computational load feasible in real time, it is necessary to reduce the dimensions of the model, especially for multiple-array systems. Due to the very large dimension and ill-conditioning of the process, the plant model can be effectively reduced by wavelet matrices based on a modified wavelet packet method. The reduced model captures the controllable spatial components of CD processes. After model reduction, MPC based on the reduced model is implemented in the wavelet domain. Meanwhile, the constraints can be exactly represented in the wavelet domain. The main benefit of implementing MPC in the reduced domain is that the on-line computational time for solving the quadratic programming (QP) problem is greatly reduced compared to the implementation of MPC based on the original model while good control performance is preserved. This method is applicable for multiple-array systems. For large-scale spatially-distributed systems such as CD processes, the process model, the additive structured uncertainty, and the linear portion of the MPC controller are approximated as linear, spatially-invariant, and time-invariant. The transfer function analysis will hold as long as the disturbances are small enough magnitude that the MPC does not hit constraints. To analyze the relevant closed-loop transfer matrices, the novel concept of rectangular circulant matrices (RCMs) is proposed. RCMs can be diagonalized by complex Fourier matrices, allowing analysis in terms of a family of single-input single-output (SISO) transfer functions across the spatial frequencies. Familiar concepts from control engineering such as bandwidth and stability margin are extended into the two-dimensional frequency domain, providing intuitive measures of closed-loop performance and robustness. Consistent criteria are given for the analysis of the closed-loop effect of the industrial CD MPC tuning weights based on standard robust control theory. Properly tuning the magnitude of weights, choosing the structure of weights, and considering the structure of model uncertainty in the MPC design stage can greatly improve the performance. This method can be used to design robust CD MPC for multiple-array systems. In order to assess the steady-state performance of constrained CD MPC, the state of the art requires to run closed-loop simulations. Due to the large-scale characteristic of CD processes, especially for multiple-array systems, it is very time-consuming and inconvenient for use as a practical tuning tool. However, fast and correct prediction of the steady-state performance is necessary for tuning the CD MPC, especially for the cases with active constraints. A one-step static optimizer is proposed to predict the steady-state closed-loop performance of CD MPC. Two examples are given for demonstrating that the static optimizer is significantly more efficient (up to two orders of magnitude) than the conventional closed-loop simulation method while reliably and accurately predicting the steady-state closed-loop performance.