First-order response и time constant
Цель: Изучить тему «First-order response и time constant» и закрепить её практическими заданиями и самопроверкой.
2 акад. часа чтение и разбор теории, решение задач, работа со схемой или виртуальным стендом и проверка понимания.
Основной материал
Many process responses approximate first-order: after step input output approaches new steady state exponentially. Time constant tau characterizes speed. At t=tau response reaches about 63.2 % total change; at 3tau ~95 %, 4tau ~98 %.
Physical meaning
Tank temperature changes slowly because stored thermal energy must change. Level changes because material accumulates. Sensor thermowell adds its own time constant on top of process.
Практическая работа
Step causes final temperature change from 20 to 100 °C. If tau = 10 min, estimate temperature after 10 min assuming first-order no dead time: 20 + 0.632*(80) ≈ 70.6 °C.
Самопроверка
• Что означает tau?
• Сколько % response after one tau?
• Почему storage increases tau?
• Может ли sensor add tau?
• Когда first-order approximation useful?
Что нужно запомнить
- Many process responses approximate first-order: after step input output approaches new steady state exponentially.
- At t=tau response reaches about 63.2 % total change; at 3tau ~95 %, 4tau ~98 %.
- Tank temperature changes slowly because stored thermal energy must change.
- Sensor thermowell adds its own time constant on top of process.
- Step causes final temperature change from 20 to 100 °C.