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Deadzone Output Residual Tool

Compare an explicit symmetric continuous deadzone with a measured output.

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Description

Compare measured output with a symmetric deadzone model.

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.

Compare measured output with a symmetric deadzone model.

When to use this tool

Use Deadzone Output Residual when checking a supplied saturation, hysteresis or local stability condition.

How to use the tool and how it works

  1. Enter input, halfWidth, measuredOutput. Use the units and conventions below.
  2. Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
  3. Read expectedOutput, residual. Use the output convention below.

Compare measured output with a symmetric deadzone model. Require halfWidth >= 0; expectedOutput is zero inside and on the edges, otherwise input-sign(input)*halfWidth; residual = measured-expected.1

Input fieldMeaning and unitsAccepted input
inputInputRequired. Finite number.
halfWidthHalf WidthRequired. Finite number; minimum 0.
measuredOutputMeasured OutputRequired. Finite number.
Output fieldInterpretationReturned shape
expectedOutputExpected OutputRequired. Finite number.
residualSigned difference in the direction defined above, using the same units as its compared quantities.Required. Finite number.
json
{
  "input": {
    "input": 5,
    "halfWidth": 2,
    "measuredOutput": 4
  },
  "output": {
    "expectedOutput": 3,
    "residual": 1
  }
}

Limitations and assumptions

  • This is a continuous deadzone convention, not a physical actuator identification or hysteresis model.
  • 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

  1. Calculation and input contract: cybernetics/deadzone-output-residual — tool.io

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