Development of a constraint stabilization method of multibody systems based on fuzzy logic control

Abstract 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.