Reliable simulation of mechatronic systems using Newmark algorithms

In the framework of flexible multibody systems simulation, the stability and the accuracy of the time integration process can be guaranteed by a family of implicit integrators derived from the Newmark scheme (Hilber-Hughes-Taylor and Generalized- methods). This paper deals with the extension of those reliable integrators for the simulation of mechatronic systems.
In order to account for the strong coupling between the mechanism and the control system, the coupled set of equations contains mechanical and control variables. The generation of those equations, their numerical treatment and their time integration may become unmanageable for realistic control systems. In many cases, it is however sufficient to consider a weak coupling, which means that the action of the control system is treated as an external force disturbing the dynamic equilibrium. The weak coupling assumption is fully justified when a digital controller is present in the control loop.
Then, the control actions exhibit discontinuous transitions at each sampling instant. The standard form of the Newmark scheme assumes continuity of the acceleration variables, and is thus not appropriate for this situation. Therefore, we propose an adapted Newmark scheme which achieves an explicit treatment of the acceleration jumps throughout the integration process, so that the proper simulation of the mechatronic system is guaranteed.
The paper describes the detailed modifications of the integration algorithm. Illustrative examples are used to point out the critical situations where they prevent from substantial integration errors.