(Solved): Table 1. Armature-controlled Dc Motor, Capstan, And Slide Parameters ð‘€ð‘ Mass Of Slide 5.693 K...
Table 1. Armature-controlled dc motor, capstan, and slide parameters
|
ð‘€ð‘ |
Mass of slide |
5.693 kg |
|
ð‘€ð‘ |
Mas of drive bar |
6.96 kg |
|
ð½ð‘š |
Inertia of roller, shaft, motor, and tachometer |
10.91 ∙ 10−3 kg.m2 |
|
ð‘Ÿ |
Roller radius |
31.75 ∙ 10−3 m |
|
ð‘ |
Motor damping from friction |
0.268 N.ms/rad |
|
ð¾ð‘š |
Torque constant |
0.8379 N.m/amp |
|
ð¾ð‘ |
Back emf constant |
0.838 V.s/rad |
|
ð‘…ð‘Ž |
Motor armature resistance |
1.36 Ω |
|
ð¿ð‘Ž |
Motor armature inductance |
3.6 mH |
The mathematical model of the system with disturbance is presented in (1) and (2).
|
ð‘£ð‘Ž = ð‘…ð‘Žð‘–ð‘Ž + ð¿ð‘Žð‘–ð‘Žâ€² + ð‘£ð‘ |
(1) |
|
ð‘‡ð¿ = ð‘‡ð‘š − ð‘‡ð‘‘ = ð½ð‘‡ðœƒâ€²â€² + ð‘ðœƒâ€² |
(2) |
where:
Total inertia ð½ð‘‡ = ð½ð‘š + ð‘Ÿ2(ð‘€ð‘ + ð‘€ð‘)
Back emf ð‘£ð‘ = ð¾ð‘𜔠Motor torque ð‘‡ð‘š = ð¾ð‘šð‘–ð‘Ž Load torque ð‘‡ð¿
Disturbance torque ð‘‡ð‘‘
- Based on Eqs. (1) & (2) and Table 1, derive the motor-slide transfer function, ðº(ð‘ ), where ð‘‰ð‘Ž(ð‘ ) and ð‘‹(ð‘ ) are the input and output respectively. Note: ignore disturbance torque ð‘‡ð‘‘.
- With the motor inductance ð¿ð‘Ž is ignored, repeat #2.
I need help solving questions 2 and 3 please.
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