lemonergy· battery engineering courses

Lemonergy · Studio block

Second-order integrator

Integrates acceleration into velocity and position.

Implementation ID
native-second-order-integrator
Reviewed
2026-10-27

Behavior

d position/dt = velocity; d velocity/dt = acceleration. The worked example connects this operation to signals in Lemonergy Studio.

Interface

Second-order integrator interfaceInputs or arguments on the left, observed outputs on the right. Conserving terminals appear below the component. The tables give units and behavior.Second-order integratorStudio blockin0out0out1
Original Lemonergy interface view. Lines identify ports; they are not a completed simulation circuit.
Ports and observed outputs
NameDirectionUnitMeaning
in0input1Acceleration; real scalar.
out0output1Position; real scalar.
out1output1Velocity; real scalar.

Parameters

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

Configuration fields
ParameterUnitDefaultMeaning and limits
Initial position
tables[0]		1[0]Configured coefficients or initial values in column-major order.
Initial velocity
tables[1]		1[0]Configured coefficients or initial values in column-major order.

Equations and rules

  • d position/dt = velocity; d velocity/dt = acceleration

Worked example

Second-order integrator — worked example

Acceleration = 2. Position at 1 s = 1; Velocity at 1 s = 2.

Open Studio example after release →
Numerical checks for the bundled synthetic example
OutputTime (s)Expected valueUnitAbsolute tolerance
Position
out0		1112e-06
Velocity
out1		1212e-06

Explore the recorded outputs

Second-order integrator recorded example

Second-order integrator / Position
Second-order integrator / Position against timeRecorded synthetic simulation values. Time in seconds; output in —.-0.0800.210.250.50.50.790.751.081—Time (s)
Second-order integrator / Position: 0 — at 0 s

13 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

Second-order integrator — worked example

Integrates acceleration into velocity and position.

  1. Second-order integrator: d position/dt = velocity; d velocity/dt = acceleration. 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

  • Position and velocity states, configurable initial values; no external reset or state-limit event handling.
  • 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)