lemonergy· battery engineering courses

Lemonergy · Studio block

Continuous pole-zero model

Simulates a real-coefficient continuous model defined by poles, zeros and gain.

Implementation ID
native-zero-pole
Reviewed
2026-10-27

Behavior

H(s) = gain × ∏(s − zeroᵢ)/∏(s − poleⱼ). The worked example connects this operation to signals in Lemonergy Studio.

Interface

Continuous pole-zero model interfaceInputs or arguments on the left, observed outputs on the right. Conserving terminals appear below the component. The tables give units and behavior.Continuous pole-zero modelStudio blockin0out0
Original Lemonergy interface view. Lines identify ports; they are not a completed simulation circuit.
Ports and observed outputs
NameDirectionUnitMeaning
in0input1Input; real scalar.
out0output1Output; real scalar.

Parameters

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

Configuration fields
ParameterUnitDefaultMeaning and limits
Gain
params[0]		12Configured finite numerical parameter.
Zeros
tables[0]		1[]Complex roots as real, imaginary pairs; conjugate pairs required.
Poles
tables[1]		1[-2, 0]Real, imaginary pairs.
Initial companion state
tables[2]		1[0]Configured coefficients or initial values in column-major order.

Equations and rules

  • H(s) = gain × ∏(s − zeroᵢ)/∏(s − poleⱼ)

Worked example

Continuous pole-zero model — worked example

Input = 1. Output at 1 s = 0.8646647167633873.

Open Studio example after release →
Numerical checks for the bundled synthetic example
OutputTime (s)Expected valueUnitAbsolute tolerance
Output
out0		10.864664716763387312e-06

Explore the recorded outputs

Continuous pole-zero model recorded example

Continuous pole-zero model
Continuous pole-zero model against timeRecorded synthetic simulation values. Time in seconds; output in —.-0.0691731800.18157960.250.43233230.50.68308510.750.93383791—Time (s)
Continuous pole-zero model: 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

Continuous pole-zero model — worked example

Simulates a real-coefficient continuous model defined by poles, zeros and gain.

  1. Continuous pole-zero model: H(s) = gain × ∏(s − zeroᵢ)/∏(s − poleⱼ). 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

  • Real-coefficient proper models; complex roots must form conjugate-compatible real polynomials, degree≤64.
  • 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)