The coefficients of physically-based models are often only known within certain bounds. Such parameter uncertainty complicates the control design problem. As eliminating all uncertainty is not a realistic option, formulating the model so that its behavior over the entire uncertainty space is easily determined can facilitate design and analysis. The model form suggested in this paper is a tree-structured transfer function. Bond graph theory provides the means to synthesize a transfer function with this structure. Both tree-structured and conventional transfer functions of a vibration isolation table, with five uncertain parameters, have been synthesized, and the former simplified the robust analysis problem more than the latter. The tree-structured transfer functions allowed the response envelope to be easily determined over key frequency ranges. The advantages of tree-structured over conventional transfer functions demonstrated in this paper suggest that this alternate form may be better suited for both nominal and robust analysis.

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