Pade approximation of delay block with fixed DelayTime

 Description The Pade Delay component delays the input signal by duration Delay Time. The delay is approximated by a Pade approximation, that is, by a transfer function $y\left(s\right)=\frac{{b}_{1}{s}^{m}+{b}_{2}\stackrel{m-1}{s}+\cdots +{b}_{m+1}}{{a}_{1}{s}^{n}+{a}_{2}\stackrel{n-1}{s}+\cdots +{a}_{n+1}}u\left(s\right)$ where the coefficients ${b}_{k}$ and ${a}_{k}$ are calculated such that the coefficients of the Taylor expansion of the delay ${ⅇ}^{-Ts}$ around $s=0$ are identical up to order n + m. The main advantage of this approach is that the delay is approximated by a linear differential equation system, which is continuous and continuously differentiable.

Connections

 Name Description Modelica ID $u$ Real input signal u $y$ Real output signal y

Parameters

 Name Default Units Description Modelica ID Delay Time $1$ $s$ Delay time of output with respect to input signal delayTime n $1$ Order of pade approximation n m $n$ Order of numerator m Signal Size $1$ Dimensions of input and output signals signalSize

 Modelica Standard Library The component described in this topic is from the Modelica Standard Library. To view the original documentation, which includes author and copyright information, click here.