Evaluate a complete transfer-model response
Complete SISO continuous-model response with certified roots and explicit phase branches.
Source and model
Declare a complete transfer model and frequency grid, then inspect every complex response and the selected phase branch.
One strict UTF-8 JSON source: paste or native File, 4 MiB and 512 UTF-8 filename bytes. Clear pasted text before selecting a File; mixed sources, duplicate JSON keys, prototype keys and accessor inputs are rejected.
Use complete real descending numerator/denominator coefficients (256 each) or conjugate-symmetric zeros/poles/gain, mutually exclusive. All 510 root occurrences are retained; uncertain multiplicity refuses the whole model.
- Choose either numerator/denominator or all zeros/poles/gain.
- Provide all positive omega values or logRange start/end/count.
Grid and phase policy
Positive strictly increasing omega in rad/s, at most 200,000 frequencies, or explicit logRange start/end/count. Every frequency is delivered; principal, structural and reference are options of this task.
Structural phase sums every declared/certified factor; origin contributes +90 degrees per zero and -90 per pole, negative gain starts +180, and upper RHP complex roots continue across the negative-real-axis branch. Principal is [-180,180). Reference adds the nearest whole turn to structural phase at the first defined frequency; ties choose the higher turn. This is a declared branch, not unique physical absolute phase.
| Policy | Reference | Meaning |
|---|---|---|
| structural | all pole/zero factors | explicit continuous branch |
| principal | [-180,180) | wrapped complex argument |
| reference | initial angle / first defined frequency | nearest whole-turn shift |
Complete delivery and refusal
Finite binary64 only. Full root residual/product/multiplicity and phase modulo certificates are required. Ambiguous near repeated TF roots, coefficient/Horner/response overflow, underflow to false zero or certificate failure reject the whole job. Undefined pole/zero/cancelled-factor points remain complete rows and split SVG paths.
All joint budgets apply: 50 million charged work units, files+full text+preview 64 MiB, full typed JSON 8 MiB, aggregate 72 MiB, binary+full metadata 96 MiB, conservative owned peak 1024 MiB and one absolute 120 seconds. Output and work intersections may refuse an individually valid axis.
Actual EVD loop bodies and QR increments are charged before original operations. Fixed matrix overhead and encoding/verification reservations are conservative units; degree-cubed is never reported as actual iteration work. Maximum joint capacity, maximum heap and browser performance remain unmeasured.
- response.csv: every complex/magnitude/principal/structural/chosen/status value
- frequency-report.json: all source roots, multiplicities and certificates
- bode.svg: every defined point and real singular gaps
- source-original.json + settings.json: exact original bytes and captured settings
What the original issue establishes
The original request used 1/s³ and also tried 1/s⁴ and 1/s²/(s+10). The last public comment says s still appeared as -270 rather than +90 after the issue was closed. We preserve these complete golden outputs; closure does not establish that the final counterexample was solved. No stock python-control execution or original image reconstruction is claimed.
Correct the whole model or grid and rerun with the same original File; cancellation never publishes a late result.
References
- Original request, all five comments and the final s counterexample
The issue closed before the final public counterexample; closure does not establish its resolution.
Tools in this category
Expand a tool to see its steps, options and supported formats, then open its workspace.
Control model frequency responseComplete SISO continuous-model response with certified roots and explicit phase branches.
Declare a complete transfer model and frequency grid, then inspect every complex response and the selected phase branch.
Steps
- Choose either numerator/denominator or all zeros/poles/gain.
- Provide all positive omega values or logRange start/end/count.
- Select a phase policy and inspect singular statuses.
- Download five complete files; copying retains the complete response CSV.
Available options
- Phase branch
- Structural continuous branch · Principal [-180,180) · Initial reference branch
- Initial reference (degrees; zero outside reference mode)
- 0
- Artifact language
- English · 中文
Capabilities and limits
- One strict UTF-8 JSON source: paste or native File, 4 MiB and 512 UTF-8 filename bytes. Clear pasted text before selecting a File; mixed sources, duplicate JSON keys, prototype keys and accessor inputs are rejected.
- Use complete real descending numerator/denominator coefficients (256 each) or conjugate-symmetric zeros/poles/gain, mutually exclusive. All 510 root occurrences are retained; uncertain multiplicity refuses the whole model.
- Positive strictly increasing omega in rad/s, at most 200,000 frequencies, or explicit logRange start/end/count. Every frequency is delivered; principal, structural and reference are options of this task.
- All joint budgets apply: 50 million charged work units, files+full text+preview 64 MiB, full typed JSON 8 MiB, aggregate 72 MiB, binary+full metadata 96 MiB, conservative owned peak 1024 MiB and one absolute 120 seconds. Output and work intersections may refuse an individually valid axis.
- Actual EVD loop bodies and QR increments are charged before original operations. Fixed matrix overhead and encoding/verification reservations are conservative units; degree-cubed is never reported as actual iteration work. Maximum joint capacity, maximum heap and browser performance remain unmeasured.