lemonergy· battery engineering courses

Lemonergy · Studio block

State-space impedance

Continuous current-to-voltage linear dynamics with direct feedthrough. User supplies identified matrices.

Implementation ID
battery-state-space-impedance
Reviewed
2026-10-27

Behavior

Solves a user-supplied continuous linear state model from current inputs to voltage outputs. Dense matrices support multiple input/output channels and direct feedthrough. Matrices are displayed as rows in configuration.

Interface

State-space impedance interfaceInputs or arguments on the left, observed outputs on the right. Conserving terminals appear below the component. The tables give units and behavior.State-space impedanceStudio blockinputoutput
Original Lemonergy interface view. Lines identify ports; they are not a completed simulation circuit.
Ports and observed outputs
NameDirectionUnitMeaning
inputinputACurrent inputs; 1 channels at the default configuration.
outputoutputVVoltage outputs; 1 channels at the default configuration.

Parameters

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

Configuration fields
ParameterUnitDefaultMeaning and limits
State matrix A
A		Model-dependent[[-0.1]]Row-oriented state matrix. Dimensions must agree with B, C, D and the initial state.
Input matrix B
B		Model-dependent[[0.005]]Row-oriented input matrix. One column per input channel.
Output matrix C
C		Model-dependent[[1]]Row-oriented output matrix. One row per output channel.
Feedthrough matrix D
D		Model-dependent[[0.01]]Row-oriented direct feedthrough matrix; output rows by input columns.
Initial state vector
initial		See field order[0]Initial state vector, with one value per state.

Equations and rules

  • dx/dt = A*x + B*u
  • y = C*x + D*u

Worked example

State-space impedance worked example

Use the defaults below with Current inputs = [2] A. At 0 s, Voltage outputs is [0.02] V. Additional checks are listed below.

Open Studio example after release →
Numerical checks for the bundled synthetic example
OutputTime (s)Expected valueUnitAbsolute tolerance
Voltage outputs
output		0[0.02]V1e-08

Explore the recorded outputs

State-space impedance recorded example

State-space impedance [1]
State-space impedance [1] against timeRecorded synthetic simulation values. Time in seconds; output in V.0.0149430400.033274532.50.0516060350.069937527.50.0882690210VTime (s)
State-space impedance [1]: 0.02 V at 0 s

103 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

State-space impedance worked example

Continuous current-to-voltage linear dynamics with direct feedthrough. User supplies identified matrices.

  1. State-space impedance: Solves a user-supplied continuous linear state model from current inputs to voltage outputs. Dense matrices support multiple input/output channels and direct feedthrough. Matrices are displayed as rows in configuration.
    • Use the parameter values in the block reference.
    • Implementation tested locally; public release pending.
Open Studio example after release

Connected concepts

Limits and interpretation

  • At most 16 states and eight inputs or outputs. The model author must identify stable, physically meaningful matrices and consistent units. No automatic impedance fitting is performed.
  • The example verifies numerical behavior for synthetic parameters. Cell characterization and validation for an intended use are separate tasks.

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)