A Piecewise-Linear Moment-Matching Approach to Parameterized Model Order Reduction for Highly Nonlinear Systems

The automatic extraction of parameterized macromodels for modern mixed signal System-on-Chips is an extremely challenging task due to the presence of several nonlinear analog circuits and Micro-Electro- Mechanical (MEM) components. The ability to generate Parameterized Reduced Order Models (PROM) of nonlinear dynamical systems could serve as a first step toward the automatic and accurate characterization of geometrically complex components and subcircuits, eventually enabling their synthesis and optimization.

The approach to this problem combines elements of a non-parameterized trajectory piecewise linear method for nonlinear systems with a moment matching parameterized technique for linear systems. By building on these two existing methods, we have created an algorithm for generating PROMs for nonlinear systems. The algorithms were tested on three different systems: a MEM switch, and two nonlinear analog circuits. All of the examples contain distributed strong nonlinearities and possess some dependence on several geometric parameters.

In addition, we have proposed a model-construction procedure in which we approximate the system sensitivity to parameters of interest for the purpose of efficiently sampling important regions of the parameter space. The output of one PROM created for the example and compared to the field solver output of the full nonlinear system at several parameter values is shown. Typical PROMs constructed in this manner can be accurately reduced in size by a factor of 10 yielding a speedup of a factor of 10 in general.