The numerical solution of multibody systems is not a straightforward problem. The formulation
of the equations of motion is augmented with the constraint equations that lead
to a set of differential algebraic equations (DAEs). These constraints govern the relative
motion between the system’s components at the position level (geometric constraints) and
may restrict the velocity of particular components (rolling constraints). There are several
factors that determine the effectiveness of numerical integration methods and the extent of
their applicability owing to the various motion circumstances. These factors include numerical
stability throughout the integration and computation time, as well as allowable error
percentage and the length of simulation time. In this regard, this research examines existing
approaches for constraint stabilization during numerical integration and introduces a
new methodology based on fuzzy control algorithm, whose coefficients are independent of
the dynamic characteristics of different systems. Schematics of the new methodology are
presented; two examples of spatial multibody systems with holonomic and nonholonomic
constraints are solved to evaluate the effectiveness of the proposed method. It can be concluded
that fuzzy control contributes an excellent solution for generic system configuration
and is suitable for lengthy simulations with minimal computation time. |
