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.

[1]  Ronald Soeterboek,et al.  Predictive Control: A Unified Approach , 1992 .

[2]  Apostolos Rigopoulos.  Application of principal component analysis in the identification and control of sheet-forming processes , 1999 .

[3]  Junqiang Fan.  Model predictive control for multiple cross-directional processes : analysis, tuning, and implementation , 2003 .

[4]  Marko Bacic,et al.  Model predictive control , 2003 .

[5]  Stephen J. Wright,et al.  Efficient implementation of model predictive control for sheet and film forming processes , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[6]  Basil Kouvaritakis,et al.  Efficient robust predictive control , 2000, IEEE Trans. Autom. Control..

[7]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[8]  James B. Rawlings,et al.  Predictive control of sheet and film‐forming processes , 1998 .

[9]  S.-C. Chen,et al.  Optimal Control of Cross-Machine Direction Web Profile with Constraints on the Control Effort , 1986, 1986 American Control Conference.

[10]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[11]  Richard D. Braatz,et al.  SVD controllers for H2-, H∞- and μ-optimal control , 1997, Autom..

[12]  Richard D. Braatz,et al.  Fast model predictive control of sheet and film processes , 2000, IEEE Trans. Control. Syst. Technol..

[13]  Graham C. Goodwin,et al.  Study of an adaptive anti-windup strategy for cross-directional control systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[14]  William P. Heath,et al.  Self-tuning prediction and control for two-dimensional processes Part 1: Fixed parameter algorithms , 1995 .

[15]  William P. Heath,et al.  Orthogonal functions for cross-directional control of web forming processes , 1996, Autom..

[16]  Alberto Bemporad,et al.  Robust model predictive control: A survey , 1998, Robustness in Identification and Control.

[17]  Guy A. Dumont,et al.  Cross-directional control on paper machines using gram polynomials , 1996, Autom..

[18]  J. Nagy,et al.  FFT-based preconditioners for Toeplitz-block least squares problems , 1993 .

[19]  Dimitry M. Gorinevsky,et al.  Two-dimensional loop shaping , 2003, Autom..

[20]  Richard D. Braatz,et al.  Robust cross-directional control of large scale sheet and film processes , 2001 .

[21]  Dimitry M. Gorinevsky,et al.  Feedback controller design for a spatially distributed system: the paper machine problem , 2003, IEEE Trans. Control. Syst. Technol..

[22]  T. A. Badgwell,et al.  An Overview of Industrial Model Predictive Control Technology , 1997 .

[23]  R. Braatz,et al.  SVD Controllers for H 2-, H 1-, and-Optimal Control , 2022 .

[24]  Gregory E. Stewart,et al.  Constrained model predictive control for cross directional multi-array processes , 2001 .

[25]  Johan U. Backstrom,et al.  Quadratic programming algorithms for large-scale model predictive control , 2002 .

[26]  Cristian Gheorghe,et al.  Identification tool for cross-directional processes , 2003, IEEE Trans. Control. Syst. Technol..

[27]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[28]  S. R. Duncan.  The design of robust cross-directional control systems for paper making , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[29]  Junqiang Fan,et al.  A novel model reduction method for sheet forming processes using wavelet packets , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[30]  Robert M. Gray,et al.  Toeplitz and Circulant Matrices: A Review , 2005, Found. Trends Commun. Inf. Theory.

[31]  Graham C. Goodwin,et al.  Spatial frequency antiwindup strategy for cross-directional control problems , 2002 .

[32]  M. Kothare,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[33]  Yaman Arkun,et al.  Single and multiple property CD control of sheet forming processes via reduced order infinite horizon MPC algorithm , 2002 .

[34]  James G. Nagy,et al.  Block circulant preconditioners for 2D deconvolution , 1992, Optics & Photonics.

[35]  Sigurd Skogestad,et al.  Control of symmetrically interconnected plants , 1994, Autom..

[36]  Dimitry M. Gorinevsky,et al.  Performance-optimized applied identification of separable distributed-parameter processes , 2001, IEEE Trans. Autom. Control..

[37]  Stevo Mijanovic,et al.  Paper machine cross-directional control near spatial domain boundaries , 2004 .

[38]  A. W. M. van den Enden,et al.  Discrete Time Signal Processing , 1989 .

[39]  Francis J. Doyle,et al.  Customization strategies for the solution of linear programming problems arising from large scale model predictive control of a paper machine , 1999 .

[40]  Richard D. Braatz,et al.  Identification and Control of Sheet and Film Processes , 2000 .

[41]  Richard D. Braatz,et al.  Robust performance of cross-directional basis-weight control in paper machines , 1993, Autom..

[42]  Stephen Duncan,et al.  The spatial bandwidth of cross-directional control systems for web processes , 1997, Autom..

[43]  M. ALAMIRf,et al.  Stability of a Truncated Infinite Constrained Receding Horizon Scheme : the General Discrete Nonlinear Case * , 2003 .

[44]  Manfred Morari,et al.  Model predictive control: Theory and practice - A survey , 1989, Autom..