A Schur Method for Balanced Model Reduction

Safonov, Michael G.; Chiang, Richard Y.

doi:10.23919/acc.1988.4789873

Cited by 105 publications

(69 citation statements)

References 4 publications

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“…In order to avoid computations with ill-conditioned truncation matrices, a balancing-free (BF) approach has been proposed in [16] in which always well-conditioned matrices L and T can be determined. These matrices are computed from two orthogonal matrices whose columns span the right and left eigenspaces of the product P Q corresponding to the first r largest eigenvalues σ 2 1 , .…”

Section: Balancing Related Model Reduction Methodsmentioning

confidence: 99%

Model Reduction Software in the SLICOT Library

Varga¹

2001

Applied and Computational Control, Signals, and Circuits

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Section: Balancing Related Model Reduction Methodsmentioning

confidence: 99%

Model Reduction Software in the SLICOT Library

Varga¹

2001

Applied and Computational Control, Signals, and Circuits

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“…Since numerical errors have been observed in the calculations of the gramians, a balanced truncation has been performed in order to reduce the number of the states of the model [25].…”

Section: B Model Order Reductionmentioning

confidence: 99%

On control structure design for a walking beam furnace

Jafari

Arranz

Gustafsson

et al. 2017

2017 25th Mediterranean Conference on Control and Automation (MED)

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Abstract-The aim of this article is to introduce a novel sparse controller design for the temperature control of an experimental walking beam furnace in steel industry. Adequate tracking of temperature references is essential for the quality of the heated slabs. However, the design of the temperature control is hindered by the multivariable (non-square) dynamic behavior of the furnace. These dynamics include significant loop interactions and time delays. Furthermore, a novel datadriven model, based on real life experimental data that relies on a subspace state representation in a closed loop approach is introduced. In the sequel, the derived model is utilized to investigate the controller's structure. By applying the relative gain array approach a decentralized feedback controller is designed. However, in spite of the optimal and sparse design of the controller, there exists interaction between loops. By analyzing the interaction between the inputs-outputs with the Σ2 Gramian-based interaction methodology, a decoupled multivariable controller is implied. The simulation result, based on the experimental modeling of the furnace, shows that the controller can successfully decrease the interaction between the loops and track the reference temperature set-points.

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“…Difficulties associated with computation of the required balanced transformation in [3] drew some attention toward devising alternative numerical methods [13]. Balancing can be badly conditioned even when some states are significantly more controllable than observable or vice versa.…”

Section: B On Stability and Numerical Implementationmentioning

confidence: 99%

“…In this case, it is suggested to reduce the system in the gramian based framework without balancing. The Schur method and square root algorithms provide projection matrices to apply balanced reduction without balanced transformation [1], [13]. This method can be easily extended to other gramian based method.…”

Section: B On Stability and Numerical Implementationmentioning

confidence: 99%