Conference article

Using Baumgarte’s Method for Index Reduction in Modelica

Scott A. Bortoff
Mitsubishi Electric Research Laboratories, Cambridge, MA, USA

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Published in: Proceedings of the 13th International Modelica Conference, Regensburg, Germany, March 4–6, 2019

Linköping Electronic Conference Proceedings 157:34, p. 10

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Published: 2019-02-01

ISBN: 978-91-7685-122-7

ISSN: 1650-3686 (print), 1650-3740 (online)


We show by example how Baumgarte’s method can be used in a Modelica model to reduce the differential algebraic equation index prior to compilation. This has advantages for some constrained mechanical systems especially those with closed-chain kinematics, including improved initialization and enabling model-based control system design. We derive models for a simple pendulum, a delta robot and for elevator cable sway as case studies. The models are used for simulation and also for dynamic analysis and to design and realize feedback controllers.


DAE, index reduction, robotics, control


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