QUESTION 1 A motor is an electromechanical component that yields an angular displacement output for a voltage input, that is, a mechanical output generated by an electrical input. Figure (a), (b) and (c) below shows the motor's schematic, the block diagram and a typical equivalent mechanical loading on a motor, (0) Ra ww0000 - Part 2.. + Armature (0)| circuit (a) Tm(1) (1) fro Fixed field eeee Rotor T(0) (0) E() Dm G(s) (b) 0(x) where Ra and La are the resistance and inductance of the armature circuit, vb(t) is the voltage generated in the armature circuit. Tm(t) is the torque developed by the motor, Jm the equivalent inertia, Dm the equivalent viscous damping, ea(t) the input voltage, and m(t) the angular displacement output. Part 1. If given the torque T (t) = Ke (t)-K₂ de (t), where K, and K2 are two parameters of a motor, find dt differential equations to describe the relationship between input ea(t) and output 8(t) in time domain. Then derive a transfer function Om(s)/Ea(s) in the s-domain which models the motor. For the transfer function obtained in part 1, if a unit feedback is applied, find out the closed-loop system transfer function, and calculate the closed-loop system response to a step input ea(t)=1.3, given 0(s) if part 1 were 1 K₁ K2 Dm Jm 1. (Assume open-loop transfer function G(s) = - = E (s) s(s+2) unsuccessful)
QUESTION 1 A motor is an electromechanical component that yields an angular displacement output for a voltage input, that is, a mechanical output generated by an electrical input. Figure (a), (b) and (c) below shows the motor's schematic, the block diagram and a typical equivalent mechanical loading on a motor, (0) Ra ww0000 - Part 2.. + Armature (0)| circuit (a) Tm(1) (1) fro Fixed field eeee Rotor T(0) (0) E() Dm G(s) (b) 0(x) where Ra and La are the resistance and inductance of the armature circuit, vb(t) is the voltage generated in the armature circuit. Tm(t) is the torque developed by the motor, Jm the equivalent inertia, Dm the equivalent viscous damping, ea(t) the input voltage, and m(t) the angular displacement output. Part 1. If given the torque T (t) = Ke (t)-K₂ de (t), where K, and K2 are two parameters of a motor, find dt differential equations to describe the relationship between input ea(t) and output 8(t) in time domain. Then derive a transfer function Om(s)/Ea(s) in the s-domain which models the motor. For the transfer function obtained in part 1, if a unit feedback is applied, find out the closed-loop system transfer function, and calculate the closed-loop system response to a step input ea(t)=1.3, given 0(s) if part 1 were 1 K₁ K2 Dm Jm 1. (Assume open-loop transfer function G(s) = - = E (s) s(s+2) unsuccessful)
Introductory Circuit Analysis (13th Edition)
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![QUESTION 1
A motor is an electromechanical component that yields an angular displacement output for a voltage
input, that is, a mechanical output generated by an electrical input. Figure (a), (b) and (c) below shows
the motor's schematic, the block diagram and a typical equivalent mechanical loading on a motor,
(0)
R₂
0000
Armature (1)
circuit
(a)
Tm(1) (1)
fro
Fixed
field
elle
Rotor
Tm(1)
ein
E (s)
Dm
G(s)
(b)
0,(x)
(C)
where Ra and La are the resistance and inductance of the armature circuit, vo(t) is the voltage generated in
the armature circuit. Tm(t) is the torque developed by the motor, Jm the equivalent inertia, Dm the
equivalent viscous damping, ea(t) the input voltage, and Om(t) the angular displacement output.
Part 1.
If given the torque T (t) = Ke (t)-K₂
differential equations to describe the relationship between input ea(t) and output Om(t) in time domain.
Then derive a transfer function Om(s)/Ea(s) in the s-domain which models the motor.
Part 2..
For the transfer function obtained in part 1, if a unit feedback is applied, find out the closed-loop system
transfer function, and calculate the closed-loop system response to a step input ea(t)=1.3, given
0(s)
K₁ K2=Dm Jm=1. (Assume open-loop transfer function G(s)=-
if part 1 were
E (s)
unsuccessful)
de(t), where K, and K2 are two parameters of a motor, find
dt
=
1
s(s+2)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a4d4cdb-b4c3-4aa0-827f-b05a514fcbc6%2Ff401cb77-2d2d-4917-a05f-a7e73734d70e%2Fjnitbyj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:QUESTION 1
A motor is an electromechanical component that yields an angular displacement output for a voltage
input, that is, a mechanical output generated by an electrical input. Figure (a), (b) and (c) below shows
the motor's schematic, the block diagram and a typical equivalent mechanical loading on a motor,
(0)
R₂
0000
Armature (1)
circuit
(a)
Tm(1) (1)
fro
Fixed
field
elle
Rotor
Tm(1)
ein
E (s)
Dm
G(s)
(b)
0,(x)
(C)
where Ra and La are the resistance and inductance of the armature circuit, vo(t) is the voltage generated in
the armature circuit. Tm(t) is the torque developed by the motor, Jm the equivalent inertia, Dm the
equivalent viscous damping, ea(t) the input voltage, and Om(t) the angular displacement output.
Part 1.
If given the torque T (t) = Ke (t)-K₂
differential equations to describe the relationship between input ea(t) and output Om(t) in time domain.
Then derive a transfer function Om(s)/Ea(s) in the s-domain which models the motor.
Part 2..
For the transfer function obtained in part 1, if a unit feedback is applied, find out the closed-loop system
transfer function, and calculate the closed-loop system response to a step input ea(t)=1.3, given
0(s)
K₁ K2=Dm Jm=1. (Assume open-loop transfer function G(s)=-
if part 1 were
E (s)
unsuccessful)
de(t), where K, and K2 are two parameters of a motor, find
dt
=
1
s(s+2)
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