Multi-dimensional passive sampled Port-Hamiltonian systems

Passivity of virtual environments running in discrete time is a sufficient condition for stability of the system. The framework for passive sampled Port-Hamiltonian systems allows multi-dimensional virtual environments exhibiting internal dynamic behavior to be computed on a discrete medium in a passive manner. It is shown that a causality analysis is required in the framework to detect if any of the model elements have, a time dependent change of energy function in the energy balance of the system. The Standard Linear Solid model, which is often used to simulate the visco-elastic interaction with soft biological tissue is used as an example. Simulated and experimental results are provided to demonstrate the benefit of the described framework. It is shown that using this approach a multi-dimensional model which is passive in the continuous domain remains passive in the discrete domain, whereas a standard discretization approach can become non-passive.