{
  "id": "srm-map-dynamics",
  "lesson_ids": [
    "II08.1",
    "II08.2",
    "II08.3"
  ],
  "title": "SRM: нелинейная карта, коммутация и возврат энергии",
  "intro": [
    "У вентильно-индукторной машины нет постоянных магнитов и обмотки возбуждения на роторе. Ток статора создаёт поле, которое стремится перевести ротор к меньшему магнитному сопротивлению. Знак момента зависит от положения ротора и от того, на каком участке изменения индуктивности включена фаза.",
    "Нативный комплект содержит 703 статических состояния: 37 углов и 19 значений тока. По ним строится нелинейная карта Ψ(I,θ), а динамика электрической цепи и идеального преобразователя рассчитывается встроенным Python. Это редуцированная модель на полевых картах; FEMM не объявляется универсальным нестационарным магнитным решателем."
  ],
  "theory": [
    {
      "heading": "Момент и дифференциальная индуктивность",
      "paragraphs": [
        "Без постоянных магнитов коэнергия при фиксированном θ определяется интегралом Ψ по току. Производная коэнергии по углу при неизменном токе даёт момент. В линейной модели Ψ=LI это сводится к ½I² dL/dθ; при насыщении используют полный интеграл.",
        "Полная производная потокосцепления по времени включает изменение тока и положения. Поэтому уравнение напряжения содержит Lдиф dI/dt и скоростную ЭДС ω∂Ψ/∂θ. При сильном насыщении отношение Ψ/I нельзя подставлять вместо ∂Ψ/∂I.",
        "Практически устойчивее интегрировать потокосцепление dΨ/dt=u−RI, а ток восстанавливать обращением монотонной карты в текущем положении. Выход за измеренный токовый диапазон запрещён, отрицательный ток исключён соглашением об идеальном однофазном преобразователе."
      ],
      "formulas": [
        {
          "latex": "W^{\\prime}(I,\\theta)=\\int_0^I\\Psi(i,\\theta)\\,\\mathrm di,\\qquad T=\\left.\\frac{\\partial W^{\\prime}}{\\partial\\theta}\\right|_I",
          "explanation": "Угол в производной выражается в радианах; положительное направление совпадает с поворотом геометрии."
        },
        {
          "latex": "u=RI+\\frac{\\mathrm d\\Psi}{\\mathrm dt}=RI+L_{\\mathrm{диф}}\\frac{\\mathrm dI}{\\mathrm dt}+\\omega\\frac{\\partial\\Psi}{\\partial\\theta},\\qquad L_{\\mathrm{диф}}=\\left.\\frac{\\partial\\Psi}{\\partial I}\\right|_{\\theta}",
          "explanation": "Равенство получается по правилу полной производной функции двух переменных."
        }
      ]
    },
    {
      "heading": "Коммутация и энергетический контроль",
      "paragraphs": [
        "Идеальный асимметричный мост задаёт +24 В при нарастании тока, режим удержания и −24 В при возврате магнитной энергии источнику. Углы выключения 5° и 10° меняют длительность тока после участка положительного момента.",
        "Баланс источника, нагрева меди, изменения магнитной энергии и механической работы проверяется интегрированием во времени. Возврат энергии означает отрицательный вклад uI в мощность источника; его нельзя прибавлять к полезной работе как независимый источник энергии.",
        "Сравниваются шаги 100 и 50 мкс, грубая и тонкая карты. Дополнительно три состояния динамики пересчитаны свежими полевыми задачами: они проверяют интерполяцию карты, а не весь экспериментальный привод."
      ],
      "formulas": [
        {
          "latex": "\\int_0^t uI\\,\\mathrm dt=\\int_0^t RI^2\\,\\mathrm dt+\\Delta W_{\\mathrm{маг}}+\\int_{\\theta_0}^{\\theta}T\\,\\mathrm d\\theta,\\qquad W_{\\mathrm{маг}}=I\\Psi-W^{\\prime}",
          "explanation": "Баланс верен при оговорённых обратимых материалах и исключённых дополнительных видах потерь."
        }
      ]
    }
  ],
  "parameters": [
    {
      "name": "Углы карты",
      "value": 37,
      "unit": ""
    },
    {
      "name": "Токи карты",
      "value": 19,
      "unit": ""
    },
    {
      "name": "Число статических полей",
      "value": 703,
      "unit": ""
    },
    {
      "name": "Период ротора",
      "value": 90,
      "unit": "°"
    },
    {
      "name": "Питание",
      "value": 24,
      "unit": "В"
    },
    {
      "name": "Сопротивление",
      "value": 2,
      "unit": "Ом"
    },
    {
      "name": "Начальная скорость",
      "value": 100,
      "unit": "рад/с"
    },
    {
      "name": "Включение",
      "value": -20,
      "unit": "°"
    },
    {
      "name": "Выключение",
      "value": "5;10",
      "unit": "°"
    },
    {
      "name": "Длительность",
      "value": 32,
      "unit": "мс"
    }
  ],
  "steps": [
    "Запустите reproduce.py для нового поля одного из фактических динамических состояний.",
    "Изучите source-map.json и определения статической и динамической индуктивности. На фиксированном угле сравните Ψ/I и центральную производную по I.",
    "Полные программы, названные далее, запускайте через run-series.py из корня распакованного комплекта: выберите SERIES_NUMBER по списку README.html. Диспетчер сам устанавливает подпапку и контекст исходной программы; прежний рабочий каталог FEMM не важен.",
    "Для повторения карты выполните reference/rebuild-complete-map.py. Для полной динамической обработки с тремя свежими полями используйте reference/reproduce.py.",
    "Сопоставьте токи при выключении 5° и 10°, энергию возврата и относительный остаток баланса. Сравнение выполните при одинаковых временных шагах.",
    "Отдельно проверьте влияние шага и густоты карты; объясните, какие дополнительные уравнения потребовались бы для тепловой и переключательной модели реального привода."
  ],
  "table": {
    "columns": [
      {
        "key": "off",
        "label": "Выключение",
        "unit": "°"
      },
      {
        "key": "dt",
        "label": "Шаг",
        "unit": "мкс"
      },
      {
        "key": "map",
        "label": "Карта",
        "unit": ""
      },
      {
        "key": "peak",
        "label": "Максимальный ток",
        "unit": "А"
      },
      {
        "key": "returned",
        "label": "Возврат источнику",
        "unit": "Дж"
      },
      {
        "key": "res",
        "label": "Энергетический остаток",
        "unit": "%"
      }
    ],
    "rows": [
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        "off": 5.0,
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        "peak": 3.0925981525797397,
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        "res": 0.5585955782952219
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      {
        "off": 5.0,
        "dt": 50.0,
        "map": "Тонкая",
        "peak": 3.084553707158193,
        "returned": 0.11425102034427047,
        "res": 0.32255514177674594
      },
      {
        "off": 5.0,
        "dt": 50.0,
        "map": "Грубая",
        "peak": 3.0456257925834507,
        "returned": 0.11578976188333687,
        "res": 0.3686459302203447
      },
      {
        "off": 10.0,
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        "peak": 3.0925981525797397,
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        "res": 0.5029665635487257
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      {
        "off": 10.0,
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        "peak": 3.084553707158193,
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      {
        "off": 10.0,
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        "peak": 3.0456257925834507,
        "returned": 0.16840609926714734,
        "res": 0.24321055000137737
      }
    ]
  },
  "series": [
    {
      "title": "Ток: выключение 5°",
      "x_label": "Время, мс",
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