Description
Return exact exponential leak state and decrement.
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 exact exponential leak state and decrement.
When to use this tool
Use Controller Leak State Term when checking one explicit controller-state or term update.
How to use the tool and how it works
- Enter state, leakRate, timeStep. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read newState, decrement. Use the output convention below.
Return exact exponential leak state and decrement. Require nonnegative leakRate/timeStep; newState = state*exp(-rate*time), decrement = state*[-expm1(-rate*time)].1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| state | State | Required. Finite number. |
| leakRate | Leak Rate | Required. Finite number; minimum 0. |
| timeStep | Time Step | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| newState | New State | Required. Finite number. |
| decrement | Decrement | Required. Finite number. |
{
"input": {
"state": 10,
"leakRate": 0,
"timeStep": 2
},
"output": {
"newState": 10,
"decrement": 0
}
}Limitations and assumptions
- Decrement retains the state's sign; this scalar model does not infer controller stability or an actual reset operation.
- 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
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