Stabilization Method for the Numerical Integration of Controlled Multibody Mechanical System : A Hybrid Integration Approach

Simulation of a controlled multibody mechanical system, with a nonstiff mechanical subsystem and a stiff control subsystem, usually suffers from long run time. In this paper, a hybrid integration scheme combined with the constraint stabilization method is proposed to overcome this difficulty. The dynamic equations of motion of a constrained multibody mechanical system is a mixed differential-algebraic equation (DAE). The constraint stabilization method proposed by Baumgarte is used to integrate this equation. Correct choice of the α and β coefficients used in the constraint stabilization method is found. The hybrid integration scheme consists of two parts: a nonstiff integration algorithm for the mechanical subsystem and a stiff integration algorithm for the control subsystem. Simulation results show the computational efficiency of the proposed integration scheme.