On frequency weighted balanced truncation technique retaining Hankel singular values

For EMC simulation, the vector fitting model is transformed into time domain state equation model. Then the system is balanced. Then the reduced model can be obtained by removing the states corresponding to the small HSV (Hankel Singular Values). The order of the reduced model is determined by the singular curvature spectrum. Finally, balanced truncation model reduction method is used on a sample chip PDN (Power Distribution Network) and compared with the performance of the AWE (Asymptotic Waveform Evaluation) method. Simulation results show that the proposed method can operate in a wide frequency range and has smaller error and faster speed.

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On Frequency Weighted Balanced Truncation: Hankel Singular Values and Error Bounds

European Journal of Control ◽

10.3166/ejc.7.584-592 ◽

2001 ◽

Vol 7 (6) ◽

pp. 584-592 ◽

Cited By ~ 14

Author(s):

Tony Van Gestel ◽

Bart De Moor ◽

Brian D.O. Anderson ◽

Peter Van Overschee

Keyword(s):

Error Bounds ◽

Singular Values ◽

Balanced Truncation ◽

Hankel Singular Values

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Analysis of multiplicity of Hankel singular values of control systems

Automation and Remote Control ◽

10.1134/s0005117915020022 ◽

2015 ◽

Vol 76 (2) ◽

pp. 205-218 ◽

Cited By ~ 2

Author(s):

L. A. Mironovskii ◽

T. N. Solov’eva

Keyword(s):

Control Systems ◽

Singular Values ◽

Hankel Singular Values

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Estimation of the Hankel Singular Values of Fractional-Order Systems

Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C ◽

10.1115/detc2009-87289 ◽

2009 ◽

Author(s):

Jay L. Adams ◽

Robert J. Veillette ◽

Tom T. Hartley

Keyword(s):

Fractional Order ◽

Dimensional Space ◽

Ritz Method ◽

Singular Values ◽

Finite Dimensional Space ◽

Fractional Order Systems ◽

Norm Estimates ◽

Finite Dimensional ◽

Hankel Singular Values ◽

Hankel Norm

This paper applies the Rayleigh-Ritz method to approximating the Hankel singular values of fractional-order systems. The algorithm is presented, and estimates of the first ten Hankel singular values of G(s) = 1/(sq+1) for several values of q ∈ (0, 1] are given. The estimates are computed by restricting the operator domain to a finite-dimensional space. The Hankel-norm estimates are found to be within 15% of the actual values for all q ∈ (0, 1].

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