Description
Return an exact scalar first-order lag step under held input.
Controller calculations combine state, gain, error and reset conventions. A one-step update or output-balance target describes one part of a controller and does not implement, tune or establish the stability of a complete plant-control loop.
Return an exact scalar first-order lag step under held input.
When to use this tool
Use First Order Lag Exact Step Coefficient when checking one explicit controller-state or term update.
How to use the tool and how it works
- Enter state, input, timeConstant, step. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read retention, nextState. Use the output convention below.
Return an exact scalar first-order lag step under held input. Require timeConstant > 0 and step >= 0; retention = exp(-step/tau), nextState = state+(input-state)*[-expm1(-step/tau)].1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| state | State | Required. Finite number. |
| input | Input | Required. Finite number. |
| timeConstant | Positive time constant, in the same time unit as the step or sample period. | Required. Finite number; strictly above 0. |
| step | Step duration in the same time unit used by rates and time constants. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| retention | Retention | Required. Finite number. |
| nextState | Next State | Required. Finite number. |
{
"input": {
"state": 2,
"input": 10,
"timeConstant": 1,
"step": 0.6931471805599453
},
"output": {
"retention": 0.5,
"nextState": 6
}
}Limitations and assumptions
- The model assumes constant input over the step and does not include other plant states or nonlinearities.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the full controller and plant model, numerical implementation and qualified verification for actual operation or transitions.
References
Similar or alternative tools
- Feedforward Gain Static Inverse Factor
Return static inverse feedforward input with a supplied disturbance term.
- Reference Prefilter One State Update
Update one reference-prefilter state.