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Perturbation Analysis of TBR Model Reduction in Application to Trajectory-Piecewise Linear Algorithm for MEMS Structures

D. Vasilyev, M. Rewienski and J.K. White
Massachusetts Institute of Technology, US

Keywords: model order reduction, nonlinear systems, truncated balanced realization

MEMS devices generate challenging test cases for nonlinear model order reduction methods, due to their strongly nonlinear behavior. One of the model order reduction methods which can handle this nonlinear behavior is a Trajectory-Piecewise linear model order reduction (TPWL MOR) algorithm [1]. In our previous paper [2] we addressed one of the most important questions for TPWL MOR, namely the choice of linear reduction procedures. In the above mentioned paper we have showed that a truncated-balanced realization (TBR) linear reduction produces much more accurate reduced TPWL models than ones in which the Krylov-subspace linear reduction methods were used. However, for the case of a micromachined switch example we observed unexpected behavior. Some of the reduced models were very accurate, but some were unstable. This observation raised a totally new question - how can we choose a correct order for linear reduction in such way as to account for perturbations in linear model caused by nonlinearity In this paper we use perturbation theory approach to analyze using truncated balanced realization (TBR) linear reduction in a Trajectory-Piecewise linear (TPWL) nonlinear model reduction method. We show that the most important factor affecting perturbation properties of the reduction basis of TBR is a spacing of Hankel singular values. The result is applied to choosing an order of reduction basis. References: [1] M. Rewienski, J.White A Trajectory Piecewise-Linear Approach to Model Order Reduction and Fast Simulation of Nonlinear Circuits and Micromachined Devices, IEEE Transactions on Computer-Aided Design, vol. 22, no. 2, pp. 155-170, 2003. [2] D. Vasilyev, M. Rewienski, J.White A TBR-based Trajectory Piecewise-Linear Algorithm for Generating Accurate Low-order Models for Nonlinear Analog Circuits and MEMS, in proceedings of the 40th Design Automation Conference, 2003.

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