Pade approximation of delay block with fixed DelayTime
The Input signal is delayed by a given time instant, or more precisely:
y = u(time - delayTime) for time > time.start + delayTime = u(time.start) for time ≤ time.start + delayTime
The delay is approximated by a Pade approximation, i.e., by a transfer function
b*s^m + b*s^[m-1] + ... + b[m+1] y(s) = --------------------------------------------- * u(s) a*s^n + a*s^[n-1] + ... + a[n+1]
where the coefficients b[:] and a[:] are calculated such that the coefficients of the Taylor expansion of the delay exp(-T*s) around s=0 are identical upto 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. For example, it is uncritical to linearize a system containing a Pade-approximated delay.
The standard text book version uses order "m=n", which is also the default setting of this block. The setting "m=n-1" may yield a better approximation in certain cases.
Otto Foellinger: Regelungstechnik, 8. Auflage, chapter 11.9, page 412-414, Huethig Verlag Heidelberg, 1994
|u||RealInput||Connector of Real input signal|
|y||RealOutput||Connector of Real output signal|
|delayTime||Time||Delay time of output with respect to input signal|
|n||Integer||1||Order of pade approximation|
|m||Integer||n||Order of numerator|