Pith Number

pith:JNVWINJD

pith:2026:JNVWINJDIZZFGK6NHCOKQB2AZW

not attested not anchored not stored refs pending

Analytical PI Tuning for Second-Order Plants with Monotonic Response and Minimum Settling Time

Senol Gulgonul

Two closed-form PI tunings cover all second-order plants with real poles and deliver the minimum settling time for monotonic response.

arxiv:2604.21294 v4 · 2026-04-23 · eess.SY · cs.SY

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Claims

C1strongest claim

This study presents two analytical closed-form PI controller tuning solutions for second-order plants with real poles, each achieving monotonic step response and minimum settling time. The two solutions coincide at the boundary pole ratio of two and together form a continuous piecewise-analytical tuning covering the full range of plant pole ratios.

C2weakest assumption

The plant is exactly a second-order linear system with known real poles and no unmodeled dynamics, delays, or nonlinearities; the desired closed-loop poles can be placed freely without actuator limits.

C3one line summary

Two analytical PI tunings for second-order real-pole plants achieve minimum settling time with monotonic responses, plus a universal Ms independent of pole location for repeated-pole closed loops.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T02:05:43.467357Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b6b6435234672532bcd389ca80740cd939a477875f44ed13a27d362a6dc75bd

Aliases

arxiv: 2604.21294 · arxiv_version: 2604.21294v4 · doi: 10.48550/arxiv.2604.21294 · pith_short_12: JNVWINJDIZZF · pith_short_16: JNVWINJDIZZFGK6N · pith_short_8: JNVWINJD

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JNVWINJDIZZFGK6NHCOKQB2AZW \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 4b6b6435234672532bcd389ca80740cd939a477875f44ed13a27d362a6dc75bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b79d5a0deb35c3b83ec77e02405c0552a8bf09b10f61e207dbd634d540eca106",
    "cross_cats_sorted": [
      "cs.SY"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2026-04-23T05:15:10Z",
    "title_canon_sha256": "459eea5fc8d158de36effb4468508810b5ce8df393869a62e700cfbacf49e8de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.21294",
    "kind": "arxiv",
    "version": 4
  }
}