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

Fan, Junqiang; Gregory, Stewart; Dumont, Guy A.

doi:10.1016/j.automatica.2004.07.002

Cited by 24 publications

(27 citation statements)

References 28 publications

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“…Spatial multiplexing under free-space conditions may seem like a contradiction, but this very concept has been investigated in various forms for almost a decade [9] [10] [11] [12]. When restricting ourselves to using circular antenna arrays, the SVD-based analysis in combination with properties of circulant matrices [13] [14] can deliver the same beam-forming and the same OAM properties as in [1] [2]. The beam forming process for all eigenmodes/OAM states can be performed by a discrete Fourier transform (DFT) c 2011 IEEE.…”

Section: Introductionmentioning

confidence: 99%

Is Orbital Angular Momentum (OAM) Based Radio Communication an Unexploited Area?

Edfors

Johansson

2012

IEEE Trans. Antennas Propagat.

468

275

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Section: Introductionmentioning

confidence: 99%

Is Orbital Angular Momentum (OAM) Based Radio Communication an Unexploited Area?

Edfors

Johansson

2012

IEEE Trans. Antennas Propagat.

468

275

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“…Instead of tune g , e and g , e in full and frequency ranges, two dimensional loop shaping approach decouples the spatial tuning and dynamic tuning by firstly tuning the controller at zero spatial frequency, i.e., setting = , and then tuning the controller at zero dynamic frequency, i.e., setting = . The theoretical proof of this strategy can be founded in (Fan 2004). From spatial tuning, the value of the weighting matrices and can be determined, and from the dynamic tuning, the value of are determined.…”

Section: Fig 19 the Implementation Of The Cd-mpc Controllermentioning

confidence: 99%

“…It has been proven that defines the relative importance of quality measurements, defines the dynamic characteristics of the closed-loop CD-MPC system, and and define the spatial frequency characteristics of the closed-loop CD-MPC system. is for the high spatial frequency behaviours and is for the low spatial frequencies (Fan 2004). Strictly speaking, the CD-MPC tuning problem requires analyzing the robust stability of a closed-loop control system with nonlinear optimization.…”

Section: Fig 19 the Implementation Of The Cd-mpc Controllermentioning

confidence: 99%

“…F and F are m-points and n-points Fourier matrices, respectively. The detailed definitions of Fourier matrices can be found in (Fan 2004). The two-dimensional frequent representation g , e and g , e are block diagonal matrices.…”

Section: Fig 19 the Implementation Of The Cd-mpc Controllermentioning

confidence: 99%

“…However, in practice it is very challenging; almost impossible to derive the explicit solution to (32) due to the large size of CD-MPC problems. A novel two-dimensional loop shaping approach is proposed in (Fan 2004) to overcome limitations for large scaled MPC systems. The algorithm consists of four steps:…”

Section: Fig 19 the Implementation Of The Cd-mpc Controllermentioning

confidence: 99%

See 2 more Smart Citations

Model Predictive Control and Optimization for Papermaking Processes

Chu¹,

Forbes²,

Backström³

et al. 2011

Advanced Model Predictive Control

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Automatic tuning of robust constrained cross‐direction controllers

Ammar

Dumont

2015

Adaptive Control & Signal

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SummaryThe paper machine cross‐directional (CD) process is a large‐scale spatially distributed system. It is known to be severely ill‐conditioned as the gain rolls down to zero for some of the process directions. Model uncertainties in the process are inevitable resulting in a challenging robust control design problem. CD actuators are subject to min–max constraints while slice lip actuators are subject to additional bending moment limits. Because of the large number of input constraints, the industrial practice is to tune the CD controller assuming inactive constraints. The robustness of CD feedback loops to model uncertainties under constrained internal model control satisfies an integral quadratic inequality. This work develops an automatic tuning algorithm that guarantees robust stability and performance of the constrained CD feedback loop. Spatial response models are identified in a prediction error frame delivering bounds on the CD process pseudo‐singular values. The CD controller is synthesized online through a linear matrix inequalities feasibility problem taking into consideration the modal space uncertainty rising from the uncertainties in the estimated parameters and the expected variations in the dynamic response. The developed tuning technique is suitable for paper machines producing different grades of paper as the CD process spatial and dynamic responses change for each grade. The performance of the tuned constrained internal model control controller is validated through comparing it to an industrial CD controller that has been implemented in paper mills as part of a commercial product. Copyright © 2015 John Wiley & Sons, Ltd.

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

Cited by 24 publications

References 28 publications

Is Orbital Angular Momentum (OAM) Based Radio Communication an Unexploited Area?

Is Orbital Angular Momentum (OAM) Based Radio Communication an Unexploited Area?

Model Predictive Control and Optimization for Papermaking Processes

Automatic tuning of robust constrained cross‐direction controllers

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