Add PID tuning evidence and arbitrary-input plant identification

[jamestjsp]

Summary

Process Lab's PID workspace needs controller families and formulas, direct frequency-response tuning, and plant estimation from arbitrary input/output records. Add these numerical APIs while preserving the existing Pidtune behavior.

• Independent integration and derivative formulas, ideal versus filtered derivative families, bounded tuning with tracking/rejection focus, and fixed or optimized two-degree-of-freedom weights.
• Direct FRD designs with explicit measured-band limitations and achieved crossover/margin evidence.
• Physical process-model fitting with exact held-input fractional delays, plus state-space order proposals with separate training and held-out validation.
• Bounded work, cancellation, typed diagnostics, and independent analytic regressions.

Validation and limits

go test ./... and go vet ./... pass. Tests cover formula realizations, independent target/margin equations, direct FRD agreement, noise-free and noisy identification, initialization, bounds and cancellation.

These are native numerical methods with explicit evidence, not bit-identical proprietary MATLAB algorithms. Finite-band FRD and exact-delay margins do not certify global stability. Process Lab consumes immutable revision d7d37f683e40 through a module pseudo-version.

[chatgpt-codex-connector]

Codex Review Summary

This comment shows the latest Codex review activity on this pull request.

Review	Status	Commit	Review trigger
📝 Code Review	✅ Completed 2026-09-16T00:03:57.549847Z	d7d37f6	PR opened

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[chatgpt-codex-connector]

💡 Codex Review

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Reviewed commit: d7d37f683e

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[chatgpt-codex-connector]

Preserve hidden modes in ideal-derivative stability checks

When tuning an ideal PD/PID (Kd != 0 and Tf == 0), this path checks a transfer-function characteristic instead of the full state-space interconnection. TransferFunction eliminates uncontrollable or unobservable modes, so a nonminimal plant containing a hidden unstable mode can be accepted and reported with Stability == "closed-loop-poles", even though the corresponding feedback interconnection retains that unstable state. Check the original plant's internal modes or preserve the full closed-loop dynamics before certifying stability.

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[chatgpt-codex-connector]

Normalize the lag-one residual metric correctly

When residual energy changes over the validation interval, dividing the lag product only by the current-sample power does not produce a valid lag-one correlation or regression coefficient. For example, residuals beginning [10, 1, 0.1] yield a value near 10, despite a correlation being bounded by 1. Normalize by both lagged powers (and consistently center the sequences) so ResidualLagOne remains an interpretable diagnostic.

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