# 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`.