Description
Return complex closed-loop sensitivity at one frequency.
Control boundaries and stability terms depend on state history, sign conventions and the full system dynamics. A finite scalar factor, one pole or one frequency sample is not sufficient to establish safe closed-loop behavior.
Return complex closed-loop sensitivity at one frequency.
When to use this tool
Use Closed Loop Sensitivity One Frequency Term when checking a supplied saturation, hysteresis or local stability condition.
How to use the tool and how it works
- Enter loopReal, loopImaginary. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read sensitivityReal, sensitivityImaginary, magnitude. Use the output convention below.
Return complex closed-loop sensitivity at one frequency. Reject loop (-1,0); compute 1/(1+loop) using component scaling to reduce intermediate overflow, returning real, imaginary and magnitude.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| loopReal | Loop Real | Required. Finite number. |
| loopImaginary | Loop Imaginary | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| sensitivityReal | Real component of 1/(1+L), using a scaled complex division. | Required. Finite number. |
| sensitivityImaginary | Imaginary component of 1/(1+L); singular L=-1 is rejected. | Required. Finite number. |
| magnitude | Magnitude | Required. Finite number. |
{
"input": {
"loopReal": 3,
"loopImaginary": 0
},
"output": {
"sensitivityReal": 0.25,
"sensitivityImaginary": 0,
"magnitude": 0.25
}
}Limitations and assumptions
- A single-frequency value does not establish robustness or overall stability; finite precision remains bounded.
- 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
Analyze the complete dynamic system and practical constraints before interpreting a local result as robust or safe operation.
References
Similar or alternative tools
- Feedback Sign Convention Loop Factor
Return scalar closed-loop factor under a feedback-sign choice.
- Loop Transfer Phase Margin Reference
Compare supplied phase with a phase-margin target.