Dynamics

Delay Block

Introduces a fixed time delay to the input signal (transport lag)

Description

The Delay block introduces a fixed time delay (transport lag) to the input signal. This models communication delays, sensor latency, processing time, and other real-world system dynamics. The delay is implemented using a circular buffer that stores historical input values.

Mathematical Model

y(t) = u(t - τ)
where τ is the constant delay time

Parameters

delayTime: Duration of delay in seconds
- Default: 0.1
- Internally converted to buffer size: ceil(delayTime / sampleTime) + 1
initialOutput: Value output during startup (before delayed values are available)
- Default: 0

Examples

A pulse signal with 0.2 second delay appears shifted 0.2 seconds later.

Edge Cases

Zero delay time: Always enforces a minimum of 1 sample delay. There is no zero-delay passthrough mode — this prevents algebraic loops and discontinuities. With delayTime=0 and sampleTime=0.01, the effective delay is 0.01 seconds (1 sample).
Sub-sample delay: If delayTime < sampleTime, the delay rounds up to 1 sample.
Buffer initialization: All buffer slots start at initialOutput. During the first delay_samples steps, the output will be initialOutput.

Remarks

Buffer size automatically calculated: ceil(delayTime / sampleTime) + 1
Memory usage scales linearly with delay duration
Steady-state magnitude unchanged, only phase-shifted
Typical applications: networked control, sensor lag, transport delays
Uses write-then-read circular buffer order for consistent delay behavior