The generalized-alpha scheme as a linear multistep integrator: Toward a general mechatronic simulator

This paper presents a consistent formulation of the generalized-alpha time integration scheme for mechanical and mechatronic systems. The algorithm can deal with a nonconstant mass matrix, controller dynamics; and kinematic constraints. The theoretical background relies on the analogy with linear multistep formulas, which leads to elegant results related to consistency, order conditions for constant and variable step-size methods, as well as global convergence. Those results are illustrated for a controlled spring-mass system, and the method is also applied for the simulation of a vehicle semi-active suspension.