Transport Delay Approximation: simulation and comparison of options (PDE, Padé, finite element)

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 17:38

*Enlace a Spanish version

Summary:

This video discusses what transport delay is, with transfer function $exp(-ds)$, and proposes three approximations of it to a finite order $N$:

• Pade approximation of order $N$

• Approximation of $N$ finite elements of first order (each of them approximated with Pade of order 1)

• $N$ finite element approximation with only poles.

The initial part reviews the transport partial differential equation (PDE) and its solution by Laplace (just a fast sketch, not the main objective; development is similar to the video [termedpsolEN]). You can skip it and fast forward to minute 3 if you are not interested in the transport EDP, don’t worry.

The video compares the temporal (three cases: step, ramp and 1st order filtered inputs) and frequency responses with different values of $N$ and draws conclusions about the validity conditions of the approximations.

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.