Sliding mode control for constraint stabilization in multi-body system dynamic analysis

For real-time simulation a limited computation time is available for each step and explicit numerical schemes are mandatory. In the case of constraint dynamical systems, a index reduction of the differential algebraic equation system is necessary to solve the system explicitly with respect to a specific time derivative of the original constraint. Different techniques exist to mitigate the resulting drift effect. A control-based approach, the Baumgarte stabilization, introduces a linear constraint violation error behaviour. In this paper, a non-linear control scheme for constraint stabilization is proposed. The sliding mode concepts allows a fast attenuation of the constraint error and thus, an improved numerical accuracy is possible. The continuous time control law is directly embedded into the system equations and solved by the numerical solver at discrete time instants. Typical problems such as chattering and suitable parametrizations are addressed. Both schemes are examined by the use of a theoretical example to demonstrate the performance improvement.