A Comparison of Runge Kutta and Novel L-Stable Methods for Real-Time Integration Methods for Dynamic Substructuring

In this paper we compare the performance of Runge-Kutta and novel L-stable real-time (LSRT) integration algorithms for real-time dynamic substructuring testing. Substructuring is a hybrid numerical-experimental testing method which can be used to test critical components in a system experimentally while the remainder of the system is numerically modelled. The physical substructure and the numerical model must interact in real time in order to replicate the behavior of the whole (or emulated) system. The systems chosen for our study are mass-spring-dampers, which have well known dynamics and therefore we can benchmark the performance of the hybrid testing techniques and in particular the numerical integration part of the algorithm. The coupling between the numerical part and experimental part is provided by an electrically driven actuator and a load cell. The real-time control algorithm provides bi-directional coupling and delay compensation which couples together the two parts of the overall system. In this paper we consider the behavior of novel L-stable real-time (LSRT) integration algorithms, which are based on Rosenbrock's method. The new algorithms have considerable advantages over 4th order Runge-Kutta in that they are unconditionally stable, real-time compatible and less computationally intensive. They also offer the possibility of damping out unwanted high frequencies and integrating stiff problems. The paper presents comparisons between 4th order Runge-Kutta and the LSRT integration algorithms using three experimental configurations which demonstrate these properties.