Modelling and Control of Time-Delayed Physical Systems

Individual assignment

Elements as springs and dampers are passive in continuous time. In intrinsically passive (energy based) control, this property is leveraged to create controllers that are passive and therefore stable. However, it is well known that time delays such as those present in communication lines cause energy generation in a system - causing otherwise passive components to behave actively. This jeopardizes stability. This effect is widely recognised in literature, can be understood for simple example cases and can easily be shown in simple simulations. However, it is not well understood what the effect is quantitatively.

On the other hand, traditional control approaches offer methods to design stable systems under time delay. However, this is not connected to the energy-based thinking as described above.

In this assignment, you will dig into the "physics "of energy generation due to time delay to understand the effect quantitatively and try to relate it to insights from classical control theory.

Impact of the work: As this is largely unexplored in literature, there is potential for a publication. Also, I plan to use these insights in BSc education on modeling and control.