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This paper studies the model order reduction of second-order index-1descriptor systems using a tangential interpolation projection method based onthe Iterative Rational Krylov Algorithm (IRKA). Our primary focus is to reducethe system into a second-order form so that the structure of the originalsystem can be preserved. For this purpose, the IRKA based tangentialinterpolatory method is modified to deal with the second-order structure of theunderlying descriptor system efficiently in an implicit way. The paper alsoshows that by exploiting the symmetric properties of the system theimplementing computational costs can be reduced significantly. Theoreticalresults are verified for the model reduction of the piezo actuator basedadaptive spindle support which is second-order index-1 differential-algebraicform. The efficiency and accuracy of the method are demonstrated by analyzingthe numerical results.

Tangential interpolatory projections for a class of second-order index-1 descriptor systems and application to Mechatronics