Eigenstructure assignment is a widely used technique to impose the desired natural frequencies and mode shapes of vibrating systems through structural modification or active control (such as state feedback). This approach has been effectively used in time delayed systems where delays perturb the system poles deteriorating the overall system stability and performances. The undesired shift of the system poles is referred to as spillover. In this work, eigenstructure assignment is used for the correction of the co-simulation which is an emerging technique to determine the dynamic behaviour of complex engineering applications. In this simulation paradigm, the overall system dynamics is split into several subsystems that evolve in time separately. This enables to use ad-hoc solution methods which are tailored for the specific nature of the subsystem to be simulated. The overall system dynamics is obtained through the exchange of information between subsystems to provide the inputs for the simulation of the others. This process is handled through a discrete-time interface that manages the co-simulation performing the numerical extrapolation of the data. In this light, the limited exchange of data can cause accuracy and stability issues in the simulation leading to inaccurate results. This work provides an analysis of this critical problem, revealing that coupling subsystems through a co-simulation interface introduces a time-delay in the exchange of data. This makes the poles of the co-simulated system to spillover altering their locations with respect to those of the original system to be simulated. Then, a correction algorithm based on the paradigm of eigenstructure assignment is proposed to compensate the problem. The effectiveness of the proposed method is shown through its application to the explicit co-simulation of a meaningful linear vibrating system. The results show that the proposed method can effectively correct the co-simulation.
USING EIGENSTRUCTURE ASSIGNMENT FOR SPILLOVER COMPENSATION IN EXPLICIT CO-SIMULATION OF LINEAR VIBRATING SYSTEMS
Iacopo Tamellin
;
2024-01-01
Abstract
Eigenstructure assignment is a widely used technique to impose the desired natural frequencies and mode shapes of vibrating systems through structural modification or active control (such as state feedback). This approach has been effectively used in time delayed systems where delays perturb the system poles deteriorating the overall system stability and performances. The undesired shift of the system poles is referred to as spillover. In this work, eigenstructure assignment is used for the correction of the co-simulation which is an emerging technique to determine the dynamic behaviour of complex engineering applications. In this simulation paradigm, the overall system dynamics is split into several subsystems that evolve in time separately. This enables to use ad-hoc solution methods which are tailored for the specific nature of the subsystem to be simulated. The overall system dynamics is obtained through the exchange of information between subsystems to provide the inputs for the simulation of the others. This process is handled through a discrete-time interface that manages the co-simulation performing the numerical extrapolation of the data. In this light, the limited exchange of data can cause accuracy and stability issues in the simulation leading to inaccurate results. This work provides an analysis of this critical problem, revealing that coupling subsystems through a co-simulation interface introduces a time-delay in the exchange of data. This makes the poles of the co-simulated system to spillover altering their locations with respect to those of the original system to be simulated. Then, a correction algorithm based on the paradigm of eigenstructure assignment is proposed to compensate the problem. The effectiveness of the proposed method is shown through its application to the explicit co-simulation of a meaningful linear vibrating system. The results show that the proposed method can effectively correct the co-simulation.
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