Constraint violation stabilization using input-output feedback linearization in multibody dynamic analysis

A constraint violation stabilization technique for solving differential algebraic equations (DAE) of multibody dynamic systems is presented. The technique, based on the input-output feedback linearization, is employed to transform the nonlinear DAE into a set of linear equations. On reaching the input-output linear relationship with proven stable zero dynamics, a robust control design is adopted to construct constraint forces that can be used to effectively correct the errors accumulated in the constraint equations during the process of time integration. In the present development, if the pole placement method is used in control design of the resulting linear differential equations, constraint forces based on Baumgarte's constraint violation stabilization technique are recovered. On the other hand, if variable structure control design is adopted, a new method in calculating constraint forces is obtained. Two numerical examples arc used to demonstrate the effectiveness of stabilizing the constraint violation by using the proposed technique.