Delay1 Block

First-order exponential delay. The output exponentially approaches the input over the specified delay time.

Description

The Delay1 block implements a first-order exponential delay. It is used to represent processes where there is a lag between a change in a cause and the full realization of its effect, such as the time it takes for a person to adjust their expectations or the time it takes for a chemical to mix.

Mathematical Model

d(Out)/dt = (In - Out) / τ

The output $Out$ changes at a rate proportional to the difference between the input $In$ and the current output, divided by the delayTime $\tau$:

$$\frac{d(Out)}{dt} = \frac{In - Out}{\tau}$$

This results in an exponential approach to the input value.

Parameters

delayTime

The average time constant $\tau$. A larger value results in a slower, more sluggish response.

• Default: 1
• Tooltip: Average time entities stay in the delay

initialValue

The starting value of the output at t=0.

• Default: 0
• Tooltip: Starting value of the output

Ports

in (Input)

The signal to be delayed.

out (Output)

The delayed output signal.

See Also

• Smooth: Closely related to Delay1, often used for information filtering.
• Stock: Delay1 can be thought of as a Stock with a linear outflow.
• Delay: A pure transportation lag (fixed time delay).