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(Solved): Table 1. Armature-controlled Dc Motor, Capstan, And Slide Parameters 𝑀𝑠 Mass Of Slide 5.693 K...


Table 1. Armature-controlled dc motor, capstan, and slide parameters

𝑀𝑠

Mass of slide

5.693 kg

𝑀𝑏

Mas of drive bar

6.96 kg

𝐽𝑚

Inertia of roller, shaft, motor, and tachometer

10.91 ∙ 10−3 kg.m2

𝑟

Roller radius

31.75 ∙ 10−3 m

𝑏

Motor damping from friction

0.268 N.ms/rad

𝐾𝑚

Torque constant

0.8379 N.m/amp

𝐾𝑏

Back emf constant

0.838 V.s/rad

𝑅𝑎

Motor armature resistance

1.36 Ω

𝐿𝑎

Motor armature inductance

3.6 mH

The mathematical model of the system with disturbance is presented in (1) and (2).

                                                               𝑣𝑎 = 𝑅𝑎𝑖𝑎 + 𝐿𝑎𝑖𝑎′ + 𝑣𝑏

(1)

                                                            𝑇𝐿 = 𝑇𝑚 − 𝑇𝑑 = 𝐽𝑇𝜃′′ + 𝑏𝜃′

(2)

where:

Total inertia 𝐽𝑇 = 𝐽𝑚 + 𝑟2(𝑀𝑠 + 𝑀𝑏)

Back emf 𝑣𝑏 = 𝐾𝑏𝜔 Motor torque 𝑇𝑚 = 𝐾𝑚𝑖𝑎 Load torque 𝑇𝐿

Disturbance torque 𝑇𝑑

  1. Based on Eqs. (1) & (2) and Table 1, derive the motor-slide transfer function, 𝐺(𝑠), where 𝑉𝑎(𝑠) and 𝑋(𝑠) are the input and output respectively. Note: ignore disturbance torque 𝑇𝑑.
  2. With the motor inductance 𝐿𝑎 is ignored, repeat #2.

I need help solving questions 2 and 3 please.



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