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In this paper, we present a technique for automatically extracting nonlinear macromodels of biomedical microelectromechanical systems devices from physical simulation. The technique is a modification of the recently developed trajectory piecewise-linear approach, but uses ideas from balanced truncation to produce much lower order and more accurate models. The key result is a perturbation analysis of an instability problem with the reduction algorithm, and a simple modification that makes the algorithm more robust. Results are presented from examples to demonstrate dramatic improvements in reduced model accuracy and show the limitations of the method.