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# (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 ð½ð‘š Inertia of roller, shaft, motor, and tachometer 10.91 âˆ™ 10âˆ’3 kg.m2 ð‘Ÿ Roller radius 31.75 âˆ™ 10âˆ’3 m ð‘ Motor damping from friction 0.268 N.ms/rad ð¾ð‘š Torque constant 0.8379 N.m/amp ð¾ð‘ Back emf constant 0.838 V.s/rad ð‘…ð‘Ž Motor armature resistance 1.36 Î© 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 âˆ’ ð‘‡ð‘‘ = ð½ð‘‡ðœƒâ€²â€² + ð‘ðœƒâ€² (2)

where:

Total inertia ð½ð‘‡ = ð½ð‘š + ð‘Ÿ2(ð‘€ð‘  + ð‘€ð‘)

Back emf ð‘£ð‘ = ð¾ð‘ðœ” Motor torque ð‘‡ð‘š = ð¾ð‘šð‘–ð‘Ž Load torque ð‘‡ð¿

Disturbance torque ð‘‡ð‘‘

1. Based on Eqs. (1) & (2) and Table 1, derive the motor-slide transfer function, ðº(ð‘ ), where ð‘‰ð‘Ž(ð‘ ) and ð‘‹(ð‘ ) are the input and output respectively. Note: ignore disturbance torque ð‘‡ð‘‘.
2. With the motor inductance ð¿ð‘Ž is ignored, repeat #2.

I need help solving questions 2 and 3 please.

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