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Lemonergy · Studio block

Discrete integrator

Accumulates a signal over elapsed sample intervals with optional output bounds.

Implementation ID
native-discrete-integrator
Reviewed
2026-10-27

Behavior

x[k] = clamp(x[k−1] + gain × elapsed_time × u[k], lower, upper). The worked example connects this operation to signals in Lemonergy Studio.

Interface

Discrete integrator interfaceInputs or arguments on the left, observed outputs on the right. Conserving terminals appear below the component. The tables give units and behavior.Discrete integratorStudio blockin0out0
Original Lemonergy interface view. Lines identify ports; they are not a completed simulation circuit.
Ports and observed outputs
NameDirectionUnitMeaning
in0input1Value; real scalar.
out0output1Integral; real scalar.

Parameters

Defaults are initial model values. Select values for your own model and operating conditions.

Configuration fields
ParameterUnitDefaultMeaning and limits
Sample period
sampleTimeS		s0.1Exact sample grid period. Elapsed-time integration begins after initialization.
Minimum 1e-06
Gain
params[0]		11Configured finite numerical parameter.
Lower limit
params[1]		1-1000000000Configured finite numerical parameter.
Upper limit
params[2]		11000000000Configured finite numerical parameter.
Initial values
tables[0]		1[0]Configured coefficients or initial values in column-major order.

Equations and rules

  • x[k] = clamp(x[k−1] + gain × elapsed_time × u[k], lower, upper)

Worked example

Discrete integrator — worked example

Value = 2. Integral at 1 s = 2.

Open Studio example after release →
Numerical checks for the bundled synthetic example
OutputTime (s)Expected valueUnitAbsolute tolerance
Integral
out0		1211e-08

Explore the recorded outputs

Discrete integrator recorded example

Discrete integrator
Discrete integrator against timeRecorded synthetic simulation values. Time in seconds; output in —.-0.1600.420.2510.51.580.752.161—Time (s)
Discrete integrator: 0 — at 0 s

11 actual recorded samples. Lines are visual guides between samples. Synthetic example, not measured cell data.

Download the recorded samples (JSON) · Open this Studio example after release

Use in a workflow

Discrete integrator — worked example

Accumulates a signal over elapsed sample intervals with optional output bounds.

  1. Discrete integrator: x[k] = clamp(x[k−1] + gain × elapsed_time × u[k], lower, upper). The worked example connects this operation to signals in Lemonergy Studio.
    • Use the block reference for settings and connections.
    • Implementation tested locally; public release pending.
Open Studio example after release

Connected concepts

Limits and interpretation

  • Elapsed-time rectangular integration with configured gain, initial value and bounds; zero elapsed duration at initialization.
  • Shapes and element types are explicit. Values must be finite; automatic reshaping and unit conversion are not performed.

Scientific and mathematical references

These sources explain the scientific and mathematical background. The behavior, interface and limits above define the Lemonergy implementation; a citation does not imply every model option in the source is implemented.

  1. Feedback Systems: An Introduction for Scientists and Engineers, second edition

    Karl J. Åström, Richard M. Murray · Princeton University Press; author-maintained FBSwiki · 2021

    Technical reference · State-space modeling, feedback and PID control. These mathematical foundations do not establish a particular software implementation.

Implementation sources

This reference follows the public interface and locally verified numerical checks for an upcoming release.

Contract: Lemonergy Studio public contract · Verification record: verification-2026-10-27

  • docs/glossary/native-block-verification.json

This implementation and its workflow uses (JSON) · Knowledge graph (JSON-LD)