  This paper studies the model order reduction of second-order index-1
descriptor systems using a tangential interpolation projection method based on
the Iterative Rational Krylov Algorithm (IRKA). Our primary focus is to reduce
the system into a second-order form so that the structure of the original
system can be preserved. For this purpose, the IRKA based tangential
interpolatory method is modified to deal with the second-order structure of the
underlying descriptor system efficiently in an implicit way. The paper also
shows that by exploiting the symmetric properties of the system the
implementing computational costs can be reduced significantly. Theoretical
results are verified for the model reduction of the piezo actuator based
adaptive spindle support which is second-order index-1 differential-algebraic
form. The efficiency and accuracy of the method are demonstrated by analyzing
the numerical results.
