Time delay
Constant delay of input signal

Simple shift
Copies all time points t from the input stream In to the output stream Out at the timepoint t + \Delta t, delaying the signal by a constant value \Delta t.
Norm-based
\frac{dm}{dt} = \dot{m}_{in}(t-\Delta t) - m
To correctly take into account the dynamics of the process, norms of each overall parameter (mass flow, temperature, pressure) are maintained as:
\frac{d||X||}{dt} = (X(t) - X(t-1))^2 - ||X||
For phase fractions:
\frac{d||P||}{dt} = \sqrt{\sum_{i}^{N_{P}}{(w_{i}(t) - w_{i}(t-1))^2}} - ||P||
For compound fractions in each phase:
\frac{d||C_{i}||}{dt} = \sqrt{\sum_{j}^{N_{C_{i}}}{(w_{i,j}(t) - w_{i, j}(t-1))^2}} - ||C||
For each distributed parameter:
\frac{d||D_{i}||}{dt} = \sqrt{\sum_{j}^{N_{D_{i}}}{(w_{i,j}(t) - w_{i,j}(t-1))^2}} - ||D||
Note
Notations:
{m} – current mass
\dot{m}_{in} – input mass flow
\Delta t – time delay
X(t) – value of an overall parameter at time point t
w(t) – mass fraction at time point t
N_{P} – number of defined phases
N_{C_{i}} – number of defined compounds in phase i
N_{D_{i}} – number of classes in distribution i
Note
Model parameters:
Name |
Symbol |
Description |
Units |
Boundaries |
---|---|---|---|---|
Time delay |
Model to use |
Norm based, Simple shift |
||
Time delay |
\Delta t |
Time delay |
[s] |
>=0 |
Relative tolerance |
Relative tolerance for DAE solver |
[-] |
>0 (0 for flowsheet-wide value) |
|
Absolute tolerance |
Absolute tolerance for DAE solver |
[-] |
>0 (0 for flowsheet-wide value) |
See also
a demostration file at Example Flowsheets/Units/Time Delay.dlfw
.