{
  "abstract": "The Module of Integral Absolute Complex Error (MIACE) was created by me 23 years ago. It gave very nice behaviour to the transient response of the controlled systems I tested. It combines absolute tracking-error and equilibrium-centered command areas. For a stable unit-gain plant with known pure delay, an exact identity separates squared MIACE excess into a negative-area penalty and a weighted area imbalance. The resulting lower bound depends on the plant's first low-frequency moment and the delay. Every attaining response of a positive cascade is monotone, independently of controller structure. For a first-order plant, output variation and peak overshoot also admit quantitative bounds. Exact conditions identify the unique positive PI controller attaining the delayed bound; filtered PID extends attainment beyond this PI range. For cascades of arbitrary order, Hermite interpolation and a finite-support delay remainder construct proper rational controllers of the same order, with internal exponential stability proved by positive convolution representations. An exponential-moment characterization then closes the attainment question when internal delay blocks are allowed: an ordinary command attains the bound if and only if $α>μ+δ-1$. An explicit internal-model controller realizes every feasible weight and delay. A sharp amplitude-cap condition determines the least command peak among all attaining responses and the complete capped sign-preserving area front. A small-gain estimate supplies an explicit MIACE deviation bound under delay error. A storage balance also extends the exact MIACE identity and monotone attainment to a nonlinear first-order class without delay. Independent physical integrations retain delays exactly; quadratic comparisons provide complementary benchmarks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32401",
  "author_total": 1,
  "authors": [
    {
      "name": "Latchezar Tomov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvw325bzs8r70.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32401",
  "fulltext_url": null,
  "id": "fvw325bzs8r70",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32401",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Advanced Control Systems Design"
    ]
  ],
  "openalex": "W7223659780",
  "pdf_url": "https://arxiv.org/pdf/2610.32401",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fvw325bzs8r70.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32401",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32401"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "MIACE and Monotone Tracking: Exact Tuning for First-Order Plants and Positive Cascades with Pure Delay",
  "title_text": "MIACE and Monotone Tracking: Exact Tuning for First-Order Plants and Positive Cascades with Pure Delay",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/fvw325bzs8r70",
  "venue": "arXiv",
  "versions": []
}