Model order reduction with preservation of passivity, non-expansivity and Markov moments

IEEE Trans. Circuits Syst. I

2014

Abstract-The demands for miniature sized circuits with higher operating speeds have increased the complexity of the circuit, while at high frequencies it is known that effects such as crosstalk, attenuation and delay can have adverse effects on signal integrity. To capture these high speed effects a very large number of system equations is normally required and hence model order reduction techniques are required to make the simulation of the circuits computationally feasible. This paper proposes a higher order Krylov subspace algorithm for model order reduction of time-delay systems based on a Laguerre expansion technique. The proposed technique consists of three sections i.e., first the delays are approximated using the recursive relation of Laguerre polynomials, then in the second part, the reduced order is estimated for the time-delay system using a delay truncation in the Laguerre domain and in the third part, a higher order Krylov technique using Laguerre expansion is computed for obtaining the reduced order time-delay system. The proposed technique is validated by means of real world numerical examples.

“…Note that it is usually required that sE − A is a regular matrix pencil [24]. The i th Laguerre polynomial is defined as…”

Section: Overview Of Laguerre-based Model Order Reductionmentioning

confidence: 99%

Section: Higher-order Laguerre Approximation Technique (Hlat)mentioning

confidence: 99%

See 1 more Smart Citation

Model Order Reduction of Time-Delay Systems Using a Laguerre Expansion Technique

IEEE Trans. Circuits Syst. I

2014

“…If D + D T is only semi-positive definite, i.e., det(D + D T ) = 0, the situation is much more complicated and the approaches in [26,27] may provide solutions. However, the Riccati approach may also be rescued by means of the following theorem: …”

Section: Riccati Equationsmentioning

confidence: 99%

Passive Parametric Macromodeling by Using Sylvester State-Space Realizations

Informatics in Control, Automation and Robotics

2014

Abstract. A judicious choice of the state-space realization is required in order to account for the assumed smoothness of the state-space matrices with respect to the design parameters. The direct parameterization of poles and residues may be not appropriate, due to their possible nonsmooth behavior with respect to design parameters. This is avoided in the proposed technique, by converting the a pole-residue description to a Sylvester description which is computed for each root macromodel.This technique is used in combination with suitable parameterizing schemes for interpolating a set of state-space matrices, and hence the poles and residues indirectly, in order to build accurate parametric macromodels. The key features of the present approach are first the choice of a proper pivot matrix and second, finding a well-conditioned solution of a Sylvester equation. Stability and passivity are guaranteed by construction over the design space of interest. Pertinent numerical examples validate the proposed Sylvester technique for parametric macromodeling.

“…Model order reduction (MOR) techniques are now standard for reducing the complexity of large scale models and the computational cost of the simulations, while retaining the important physical features of the original system (Feldmann and R. Freund, 1995;Gallivan et al, 1996;Odabasioglu et al, 1998;Knockaert and De Zutter, 2000;Freund, 2000;Phillips et al, 2003;Phillips, 2004;Knockaert et al, 2011). Existing approaches based on Krylov subspaces are very efficient.…”

Section: Introductionmentioning

confidence: 99%

Passivity Preserving Multipoint Model Order Reduction using Reflective Exploration

Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics

2014

Abstract:Reduced state-space models obtained by model order reduction methods must be accurate over the whole frequency range of interest and must also preserve passivity. In this paper, we propose multipoint reduction technique using reflective exploration for adaptively choosing the expansion points. The projection matrices obtained from the expansion points are merged to form the overall projection matrix. In order to obtain a more compact model the projection matrix is truncated based on its singular values. Finally, the reduced order model is obtained, while ensuring that the passivity of the reduced system is preserved during the reduction process.