Моделирование антиблокировочной системы
В данном примере будет продемонстрировано моделирование антиблокировочной тормозной системы (ABS). Модель имитирует динамическое поведение транспортного средства в условиях резкого торможения и представляет собой одно колесо, которое может быть воспроизведено несколько раз для создания модели многоколесного транспортного средства.
Колесо вращается с начальной угловой скоростью, которая соответствует скорости транспортного средства до нажатия на педаль тормоза. Для расчета проскальзывания, которое определяется в блоке уравнений, мы используем две скорости. Скорость транспортного средства выражается в виде угловой скорости.
(равна угловой скорости колеса, если нет пробуксовки)
Блок уравнений
где:
- - скорость транспортного средства, деленная на радиус колеса,
- - линейная скорость транспортного средства,
- - радиус колеса,
- - угловая скорость колеса.
Из этих выражений мы видим, что проскальзывание равно нулю, когда скорость колеса и скорость транспортного средства равны, и проскальзывание равно единице, когда колесо заблокировано. Целевое значение проскальзывания равно 0,2, что означает, что число оборотов колеса в 0,8 раза должно превышать число оборотов в режиме без торможения при той же скорости автомобиля. Это максимизирует сцепление шины с дорогой и минимизирует тормозной путь при имеющемся трении.
Коэффициент трения между шиной и дорожным покрытием, mu, является эмпирической функцией скольжения, известной как кривая mu-скольжения. Мы создали кривые mu-скольжения, передав переменные MATLAB в блок-схему, используя таблицу поиска Simulink. Модель умножает коэффициент трения, mu, на вес колеса, чтобы получить силу трения, действующую на окружность шины. Сила трения делится на массу транспортного средства для получения замедления, которое модель интегрирует для получения скорости.
В этой модели мы использовали идеальный антиблокировочный контроллер торможения, который использует управление, основанное на разнице между фактическим и желаемым проскальзыванием. Мы устанавливаем желаемое проскальзывание на величину проскальзывания, при которой кривая mu-slip достигает максимального значения, что является оптимальным значением для минимального тормозного пути (см. примечание ниже).
Примечание: В реальном транспортном средстве пробуксовку невозможно измерить напрямую, поэтому данный алгоритм управления непрактичен. В этом примере он используется для иллюстрации концептуального построения такой имитационной модели. Реальная инженерная ценность подобного моделирования заключается в том, чтобы показать потенциал концепции управления до решения конкретных вопросов реализации.
Запуск модели с включённой АБС
Подключение бэкенда - метода этображения графики:
Начальные условия, определяющие включение или выключение АБС:
Загрузка и запуск модели:
Building...
Progress 0%
Progress 49%
Progress 100%
Progress 100%
Out[0]:
SimulationResult(
"stopping distance.main_out" => WorkspaceArray{Float64}("absbrake/stopping distance.main_out")
,
"slp" => WorkspaceArray{Float64}("absbrake/slp")
)
Выделение из переменной simout данных, описывающих тормозной путь и скольжение:
Out[0]:
2-element Vector{WorkspaceArray}:
WorkspaceArray{Float64}("absbrake/stopping distance.main_out")
WorkspaceArray{Float64}("absbrake/slp")
Определение данных из модели в соответствующие переменные:
Out[0]:
1501×2 DataFrame
1476 rows omitted
1 | 0.0 | 0.0 |
2 | 0.01 | 0.88 |
3 | 0.02 | 1.76 |
4 | 0.03 | 2.64 |
5 | 0.04 | 3.52 |
6 | 0.05 | 4.4 |
7 | 0.06 | 5.28 |
8 | 0.07 | 6.15999 |
9 | 0.08 | 7.03998 |
10 | 0.09 | 7.91997 |
11 | 0.1 | 8.79996 |
12 | 0.11 | 9.67994 |
13 | 0.12 | 10.5599 |
⋮ | ⋮ | ⋮ |
1490 | 14.89 | 720.743 |
1491 | 14.9 | 720.743 |
1492 | 14.91 | 720.743 |
1493 | 14.92 | 720.743 |
1494 | 14.93 | 720.743 |
1495 | 14.94 | 720.743 |
1496 | 14.95 | 720.743 |
1497 | 14.96 | 720.743 |
1498 | 14.97 | 720.743 |
1499 | 14.98 | 720.743 |
1500 | 14.99 | 720.743 |
1501 | 15.0 | 720.743 |
Визуализация величины скольжения по времени:
Запуск модели с выключенной АБС
Изменение параметра модели:
Building...
Progress 0%
Progress 28%
Progress 100%
Progress 100%
Out[0]:
SimulationResult(
"stopping distance.main_out" => WorkspaceArray{Float64}("absbrake/stopping distance.main_out")
,
"slp" => WorkspaceArray{Float64}("absbrake/slp")
)
Выделение из переменной simout данных, описывающих тормозной путь и скольжение:
Out[0]:
2-element Vector{WorkspaceArray}:
WorkspaceArray{Float64}("absbrake/stopping distance.main_out")
WorkspaceArray{Float64}("absbrake/slp")
Определение данных из модели в соответствующие переменные:
Out[0]:
1501×2 DataFrame
1476 rows omitted
1 | 0.0 | 0.0 |
2 | 0.01 | 0.88 |
3 | 0.02 | 1.76 |
4 | 0.03 | 2.64 |
5 | 0.04 | 3.52 |
6 | 0.05 | 4.4 |
7 | 0.06 | 5.28 |
8 | 0.07 | 6.15999 |
9 | 0.08 | 7.03998 |
10 | 0.09 | 7.91997 |
11 | 0.1 | 8.79996 |
12 | 0.11 | 9.67994 |
13 | 0.12 | 10.5599 |
⋮ | ⋮ | ⋮ |
1490 | 14.89 | 795.675 |
1491 | 14.9 | 795.783 |
1492 | 14.91 | 795.891 |
1493 | 14.92 | 795.998 |
1494 | 14.93 | 796.105 |
1495 | 14.94 | 796.211 |
1496 | 14.95 | 796.316 |
1497 | 14.96 | 796.422 |
1498 | 14.97 | 796.526 |
1499 | 14.98 | 796.63 |
1500 | 14.99 | 796.733 |
1501 | 15.0 | 796.836 |
Визуализация величины скольжения по времени:
Сравнение результатов расчёта тормозного пути с АБС и без неё:
В данном примере было продемонстрировано моделирование анти-блокировочной системы. Сравнение результатов тормозного пути с АБС и без неё показало что торможение с АБС наиболее эффективно.
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