Passivity Preserving Model Order Reduction Using the Reduce Norm Method

Akram, Namra; Alam, Mehboob; Hussain, Rashida; Ali, Asghar; Muhammad, Shah; Malik, Rahila; Haq, Anwar Ul

doi:10.3390/electronics9060964

Cited by 6 publications

(4 citation statements)

References 44 publications

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“…In our proposed model, the frequency selection is performed by normally distributing the frequency of interest and selecting the interpolation points, which follow a normal distribution in the reduced norm sense. The selected frequency becomes the interpolation point for constructing the projection matrix V [33], [34]. The normal Gaussian kernel can be defined as…”

Section: A Pseudocode For Soar-gkmentioning

confidence: 99%

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Second-Order Arnoldi Reduction Using Weighted Gaussian Kernel

et al. 2022

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Modeling and design of on-chip interconnect continue to be a fundamental roadblock for high-speed electronics. The continuous scaling of devices and on-chip interconnects generates self and mutual inductances, resulting in generating second-order dynamical systems. The model order reduction is an essential part of any modern computer-aided design tool for prefabrication verification in the design of on-chip components and interconnects. The existing second-order reduction methods use expensive matrix inversion to generate orthogonal projection matrices and often do not preserve the stability and passivity of the original system. In this work, a second-order Arnoldi reduction method is proposed, which selectively picks the interpolation points weighted with a Gaussian kernel in the given range of frequencies of interest to generate the projection matrix. The proposed method ensures stability and passivity of the reduced-order model over the desired frequency range. The simulation results show that the combination of multi-shift points weighted with Gaussian kernel and frequency selective projection dynamically generates optimal results with better accuracy and numerical stability compared to existing reduction techniques.INDEX TERMS Interpolation points, Numerical methods, On-Chip Interconnects, Second-order model order reduction, Second-order Arnoldi.

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Section: A Pseudocode For Soar-gkmentioning

confidence: 99%

“…Example 3.1: Consider a second-order dynamical system of an inductor with n = 5. The state representation can be written as [33], [34],…”

Section: A Pseudocode For Soar-gkmentioning

confidence: 99%

Second-Order Arnoldi Reduction Using Weighted Gaussian Kernel

et al. 2022

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“…However, spectral zero selection using the dominant pole is computationally intensive. We may alternately select spectral zero via the frequency selective reduce norm spectral zero (RNSZ) method [43]. In the RNSZ method, the frequency intervals are uniformly placed over the frequency of interest, and the SZs are chosen on the basis of their dominance in the reduced norm sense.…”

Section: Introductionmentioning

confidence: 99%

Statistically Inspired Passivity Preserving Model Order Reduction

et al. 2023

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The continuous scaling of the on-chip devices and interconnects increases the complexity of the design space and becomes a crucial factor in the fabrication of modern integrated circuits. The ever decreasing of interconnect pitch along with process enhancement into the nanometer regime had shifted the paradigm from a device-dominated to an interconnect-dominated methodology. In the design methodology, Model Order Reduction (MOR) reduces the size of large-scale simulation of on-chip interconnect to speed up the performance of design tools and chip validation. In approximating the original system, the passivity preserving MOR technique of using spectral zeros as positive real interpolation points preserves the stability and passivity of the system. In this work, statistical distribution techniques are proposed for the selection of spectral zeros. The proposed method is based on using the gaussian, uniform, binomial, and weibull distributions to select spectral zeros to better match moments with the least absolute error between the original and reduced-order systems. The results show that the reduced-order model developed using the Gaussian distributed Spectral zeros Projection (GSP) method offers higher accuracy and numerical stability compared to other distributions.INDEX TERMS Statistical distribution, model order reduction, passivity preserving, spectral zeros, on-chip interconnects, computer aided design.

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“…The proposed interval state estimator guaranteed bounds on the observed states that are consistent with the system states. In [33] a new reduce-norm frequency selective projection method was developed by using interpolation point based on spectral zeros (SZs) of the system. This method guarantee stability and passivity, while creating the reduced models, which are fairly accurate across selected narrow range of frequencies.…”

Section: Introductionmentioning

confidence: 99%

Archives of Control Sciences

Bokam¹,

Singh

Devarapalli

et al. 2021

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In recent, modeling practical systems as interval systems is gaining more attention of control researchers due to various advantages of interval systems. This research work presents a new approach for reducing the high-order continuous interval system (HOCIS) utilizing improved Gamma approximation. The denominator polynomial of reduced-order continuous interval model (ROCIM) is obtained using modified Routh table, while the numerator polynomial is derived using Gamma parameters. The distinctive features of this approach are: (i) It always generates a stable model for stable HOCIS in contrast to other recent existing techniques; (ii) It always produces interval models for interval systems in contrast to other relevant methods, and, (iii) The proposed technique can be applied to any system in opposite to some existing techniques which are applicable to second-order and third-order systems only. The accuracy and effectiveness of the proposed method are demonstrated by considering test cases of single-inputsingle-output (SISO) and multi-input-multi-output (MIMO) continuous interval systems. The robust stability analysis for ROCIM is also presented to support the effectiveness of proposed technique.

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Passivity Preserving Model Order Reduction Using the Reduce Norm Method

Cited by 6 publications

References 44 publications

Second-Order Arnoldi Reduction Using Weighted Gaussian Kernel

Second-Order Arnoldi Reduction Using Weighted Gaussian Kernel

Statistically Inspired Passivity Preserving Model Order Reduction

Archives of Control Sciences

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