Junqiang Fan

Two-dimensional frequency analysis for unconstrained model predictive control of cross-directional processes

This paper presents consistent criteria for evaluating the selection of tuning parameters for an industrial model predictive control of large-scale cross-directional (CD) processes using a two-dimensional (temporal and spatial) frequency analysis technique. The concept of rectangular circulant matrices (RCMs) and their properties are presented. It is shown that large-scale CD processes can be approximated as RCMs and then diagonalized by complex Fourier matrices, allowing analysis in terms of a family of 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.

Automated tuning of large-scale multivariable model predictive controllers for spatially-distributed processes

This paper presents an automated tuning method of a large-scale multivariable model predictive controller for multiple array paper machine cross-directional (CD) processes. Paper machine CD processes are large-scale spatially-distributed dynamical systems. Due to these systems (almost) spatially invariant nature, the closed-loop transfer functions are approximated by transfer matrices with rectangular circulant matrix blocks, whose input and output singular vectors are the Fourier components of dimension equivalent to either number of actuators or number of measurements. This approximation enables the model predictive controller for these systems to be tuned by a numerical search over optimization weights in order to shape the closed-loop transfer functions in the two-dimensional frequency domain for performance and robustness. A real industrial multiple array CD process is used for illustrating the effectiveness of this method

Approximate steady-state performance prediction of large-scale constrained model predictive control systems

When tuning the parameters of a constrained model predictive controller (MPC), one usually will use closed-loop simulations in order to predict closed-loop performance. Closed-loop simulation can be very time-consuming and inconvenient for large-scale constrained MPC, such as paper machine cross-directional (CD) predictive control. Paper machine CD processes are two-dimensional (2-D) (temporal and spatial) systems with up to 600 inputs and 6000 outputs. It is very important to predict the steady-state values for the closed-loop CD MPC systems during the tuning process, as the variances of these values are used as the control performance indexes in paper making industry. This article proposes to use a direct one-step static optimizer for approximating the closed-loop steady-state performance of constrained CD MPC. The parameters of this static optimizer can be obtained through minimizing the difference of two closed-loop transfer functions. Experiments with industrial data demonstrate that the static optimizer is computationally much more efficient (up to two orders of magnitude) than closed-loop simulation while reliably and accurately predicting the steady-state performance.

Two-dimensional frequency response analysis and insights for weight selection in cross-directional model predictive control

This paper describes the application of a technique for the two-dimensional frequency domain analysis of the closed-loop performance of a cross-directional papermaking process under industrial model predictive control (MPC). For such spatially-distributed systems, the process model and the linear portion of the controller are approximated as linear, spatially-invariant, and time-invariant. The closed-loop performance of these systems can then be analyzed in terms of a family of SISO systems by diagonalizing the large-scale transfer matrices across spatial frequencies. Familiar concepts from control engineering such as bandwidth and stability margin are extended into the two-dimensional frequency domain.

A novel model reduction method for sheet forming processes using wavelet packets

Cross-directional control of sheet forming processes, such as a paper machine, can involve up to 600 inputs and 3000 outputs. For such large-scale systems, it is necessary to find proper model reduction strategies before starting controller design. The paper introduces a model reduction method for such processes based on an efficient modified wavelet packet algorithm. The large dimensional signals in the spatial domain can be transformed into a small number of scaling and wavelet coefficients in the wavelet domain, thus the dimension of the original input-output model is reduced without losing any significant information. Two additional benefits are obtained: (1) the systems controllability can be significantly improved because the systems condition number is greatly decreased, (2) the physical limits of the actuators can be directly transformed from the original model to the reduced model.

Fundamental spatial array paper performance limitation analysis of multiple machine cross-directional processes

This paper presents a fundamental spatial performance limitation analysis method for multiple array paper machine cross-directional (CD) processes based on a two-dimensional (temporal and spatial) frequency decomposition method. Paper machine CD processes are spatially-distributed dynamical systems. Due to their (almost) spatially invariant characteristic, the models of these systems are considered as transfer matrices with rectangular circulant matrix blocks, whose input and output singular vectors are the Fourier components of dimension equivalent to number of actuators and measurements respectively. Through this method, a fundamental spatial performance limitation of multiple array CD processes can be observed. A real industrial multiple array CD process is used for illustrating the effectiveness of this method.

Two-Dimensional Frequency Analysis of Structured Uncertainty for Multiple Array Paper Machine Cross-Directional Processes

This paper provides a two-dimensional frequency analysis technique for robust controllers of large-scale multiple array paper machine cross-directional (CD) processes with structured model uncertainty. For such spatially-distributed dynamical systems, the process model and its realistic structured uncertainty are assumed to be linear, spatially-invariant, and time-invariant. These large-scale MIMO systems are rectangular circulant matrix blocks that can be conveniently transformed into a family of small dimension transfer functions in the two-dimensional frequency domain. This significantly simplifies the controller design and gives a better physical insight about the realistic structured uncertainty problem. Given a linear feedback controller, we can easily derive the robust stability condition for the closed-loop CD system in the two-dimensional frequency domain.