No abstract

Vibration isolation tables find application in diverse production and research environments. The structure of a table is such that a designer is forced to compromise among design metrics such as transmissibility, force-disturbance rejection, and controller effort. As both structural and controller parameters impact these design metrics, we chose to perform simultaneous control-structure integrated design (CSID) to optimize the overall performance. We employed a new model that enhances physical insight and used physical programming as the optimization framework. We explored several design scenarios and effectively uncovered the appropriate compromises among the competing objectives. The results highlight the utility of the new model in this design context and the usefulness of physical programming in performing simultaneous CSID.

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.