Resistor
Electrical Systems and motors
𝑒𝑅 = 𝑖 ∗ 𝑅
Inductor
Back-EMF
𝑑𝑖
𝑑𝑡
𝑑𝑒𝑐 𝑖
=
𝑑𝑡
𝐶
𝑒𝑏 = 𝐾𝑚 ∗ 𝜔𝑚
Electromagnetic Torque
𝜏𝑚 = 𝐾𝑚 ∗ 𝑖
Capacitor
DC-Motor Scheme
𝑒𝐿 = 𝐿 ∗
𝑒𝑖𝑛 − 𝑒𝑟 − 𝑒𝐿 − 𝑒𝐵 = 0
Thermal Systems
Thermal Capacity
𝐶 = 𝜌 ∗ ∀ ∗ 𝐶𝑝
1
𝑞𝑜𝑢𝑡 (wall)
(𝑇 − 𝑇𝑎 )
𝑅
R (flat wall)
𝑑
𝐴∗𝑘
Rotational Systems
No-slip wheel on flat
No-slip wheel on wheel
𝑥 = 𝜃∗𝑟
𝜃1 ∗ 𝑟1 = 𝜃2 ∗ 𝑟2
Transient Response to a 2nd order system
Settling Time (Below)
Break away point: K = ….
𝑑𝑘
= 0, 𝑠 𝑣𝑎𝑙𝑢𝑒𝑠 𝑒𝑞𝑢𝑎𝑙𝑠 𝑏𝑟𝑒𝑎𝑘𝑎𝑤𝑎𝑦 𝑝𝑜𝑖𝑛𝑡
𝑑𝑠
Block Diagram Simplification (Closed feedback
loop)
Routh’s Conditions: All coefficients the same sign and no coefficient is zero.