{"paper":{"title":"Analytical PI Tuning for Second-Order Plants with Monotonic Response and Minimum Settling Time","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Two closed-form PI tunings cover all second-order plants with real poles and deliver the minimum settling time for monotonic response.","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Senol Gulgonul","submitted_at":"2026-04-23T05:15:10Z","abstract_excerpt":"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 first solution employs pole-zero cancellation, placing the controller zero at the slower plant pole and reducing the closed-loop dynamics to a critically damped second-order system. The second solution, applicable when the plant pole ratio is less than two, places all three closed-loop poles at a common location without cancelling any plant pole, yielding a closed-loop transfer function with a triple real po"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Two closed-form PI tunings cover all second-order plants with real poles and deliver the minimum settling time for monotonic response.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"30230d367469e4757e1d11679ad2e312a120a2230312df5a000d2e28d1357cf4"},"source":{"id":"2604.21294","kind":"arxiv","version":4},"verdict":{"id":"64cb8c17-be68-44b1-a577-0305d0f9acb5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T07:25:07.954176Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"Two closed-form PI tunings cover all second-order plants with real poles and deliver the minimum settling time for monotonic response."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.21294/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-20T01:09:10.767976Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"cb72063dd7492ba196fdc4e4b947f8ae30e7a04476f75ded7489c566b36ed9a9"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"ffe09822bbabd64fbb5d11feaccea461ac6ed50f5416b87dd1c70aa5c73fca71"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}