Description
Compare one supplied derivative magnitude with an explicit tolerance.
Control terms depend on error sign, units, sample timing, saturation direction and state conventions. Hysteresis retains state between thresholds, while deadband mapping and output clamping describe different operations. A negative loop-sign product or small scalar derivative does not establish closed-loop stability or safe operation.
Compare one supplied derivative magnitude with an explicit tolerance.
When to use this tool
Use Equilibrium State Residual when you already have stateDerivative, suppliedTolerance and need to compare one supplied derivative magnitude with an explicit tolerance.
How to use the tool and how it works
- Enter stateDerivative, suppliedTolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read absoluteResidual, withinTolerance. Inspect withinTolerance before interpreting the associated values.
Require suppliedTolerance>=0; return abs(stateDerivative) and abs(derivative)<=tolerance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| stateDerivative | State Derivative | Required. Finite number. |
| suppliedTolerance | Supplied Tolerance | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| absoluteResidual | Absolute Residual | Required. Finite number. |
| withinTolerance | abs(stateDerivative)<=suppliedTolerance; one scalar check, not complete equilibrium or stability. | Required. Boolean. |
{
"input": {
"stateDerivative": 0.02,
"suppliedTolerance": 0.05
},
"output": {
"absoluteResidual": 0.02,
"withinTolerance": true
}
}Limitations and assumptions
- Equality passes. This checks one scalar only, not complete equilibrium, model accuracy, stability, convergence or safe 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 a complete plant, controller, actuator and timing model with verified operating constraints for control decisions. Check interactions among saturation, integrator state, gains and delays; individual algebraic terms do not tune a controller or validate system stability or safety.
References
Similar or alternative tools
- Control Error Deadband Edge Distance
Calculate signed error beyond a symmetric supplied deadband.
- Actuator Command Measurement Residual
Measure a supplied actuator observation's signed difference from command.