.ModelicaTest.Blocks.PadeDelay1.PadeDelayOld

Information

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[1]*s^m + b[2]*s^[m-1] + ... + b[m+1]
   y(s) = --------------------------------------------- * u(s)
           a[1]*s^n + a[2]*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 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. 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.

Literature

Otto Foellinger: Regelungstechnik, 8. Auflage, chapter 11.9, page 412-414, Huethig Verlag Heidelberg, 1994