ABSTRACT
In this chapter, we discuss the model reduction of second-order index 1 descriptor systems. First we show second-order-to-first-order reduction via balanced truncation and interpolatory projections then the second-order-to-second-order reduction method is discussed via balanced truncation and PDEG (projection onto the dominant eigenspace of the Gramian). In case of second-to-first-order reduction, the second-order system is converted into its equivalent first-order form which is exactly like the first-order index 1 system; then we exploit the techniques discussed in Chapter 7. On the other hand, for second-order-to-second-order reduction the second-order descriptor system is converted into the second-order standard system. Then we apply the model reduction onto the standard system; we, however, do this without ever forming the standard system explicitly. We also discuss how to solve the Lyapunov equations arising from the second-order index 1 system efficiently by LR-ADI iteration. The methods are applied to a structural FEM model of a micro-mechanical piezo-actuator based adaptive spindle support (ASS). In the end, numerical results are presented to illustrate the efficiency of the techniques.
