Delays the input signal by a fixed delay time, computed by Pade approximation

Description

The Pade Delay component delays the input signal, $u$, by a given time instant, $\mathrm{delayTime}$. Before the first time delay is reached in the simulation, the output value of FixedDelay, $y$, is equal to the value of input, $u$, at the starting time. The difference between the Fixed Delay component and the Pade Delay component is that the Pade Delay component uses Pade approximation to compute the delay. The equation of this component is

 $y\left(s\right)=\frac{{b}_{1}\cdot {s}^{m}+{b}_{2}\cdot {s}^{m-1}+...+{b}_{m+1}}{{a}_{1}\cdot {s}^{n}+{a}_{2}\cdot {s}^{n-1}+...+{a}_{n+1}}\cdot u\left(s\right)$

where the coefficients b[:] and a[:] are calculated such that the coefficients of the Taylor expansion of the delay ${ⅇ}^{-Ts},$at s = 0, are identical up to the 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.

The Signal Size parameter allows the block to operate on a vector of signals rather than a single signal.

Connections

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

Parameters

 Symbol Default Units Description Modelica ID Delay Time $1$ $s$ Delay time of the output with respect to the input signal delayTime $n$ $1$ - Order of the Pade approximation n $m$ $n$ - Order of the numerator m Signal Size $1$ - Dimension of input and output signals signalSize