Description
Update a leaking integral state with an error increment.
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.
Update a leaking integral state with an error increment.
When to use this tool
Use Error Integral Leakage One Step when checking one explicit controller-state or term update.
How to use the tool and how it works
- Enter integral, error, retention, gain, step. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read next. Use the output convention below.
Update a leaking integral state with an error increment. Require retention in [0,1] and step >= 0; next = retention*integral+gain*error*step.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| integral | Integral | Required. Finite number. |
| error | Error | Required. Finite number. |
| retention | Retention | Required. Finite number; minimum 0; maximum 1. |
| gain | Gain | Required. Finite number. |
| step | Step duration in the same time unit used by rates and time constants. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| next | Next | Required. Finite number. |
{
"input": {
"integral": 10,
"error": 2,
"retention": 0.9,
"gain": 1,
"step": 1
},
"output": {
"next": 11
}
}Limitations and assumptions
- Retention is supplied per step; saturation, antiwindup and actual controller stability are not evaluated.
- 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
- Discrete Pid One Integral Increment
Return one rectangular-rule integral increment and updated state.
- Antiwindup Back Calculation One Step
Return a back-calculation tracking correction and integral step.