Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2...
Transcript of Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2...
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Power Electronics No. 9: Rotation speed control of DC
motor using step-down converter
Takeshi Furuhashi Furuhashi_at_cse.nagoya-u.ac.jp
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N S
Permanent magnet
Coil
I [A]
B [T] La Ra
Equivalent circuit of a DC motor
ia
vD vωArmature electro-motive force[V]
vω = Κe ω :armature electro-motive force Ke : counter emf constant ω =2π n
Armature current[A]
(Armature coil)
(Field magnet)
(Armature current)
(Leakage flux)
Armature resistance[Ω] Armature inductance[H]
La Ra
ia
vD vω
ia
vD
ωvviRtiL Daaa
a −=+ d d
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DC motor symbol Equivalent circuit of DC motor
Differential equation of the electrical circuit of a DC motor
La Ra
ia
vD vωωvviR
tiL Daaa
a −=+ d d
0 that assumed isit ,0at ,(constant)
==
=−
a
D
itEvv ω
circuit electrical an of constant time
:
exp1
τ
τ ⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛−−=t
RE
a
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−−= tLR
REi
a
a
aa exp1
L
+ RL C
47µF D 510
RB
Tr 2SA950
vo E
iL
E Vo
iL
Equivalent circuit of a step-down chopper
D
L Re2
E Va
ia
Equivalent circuit of a step-down chopper and DC motor
D
La Ra
DC motor
E
Tr 2SA950
D 510 RB
Transistor drive circuit
Transistor drive circuit
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E
Tr 2SA950
D 100 RB
Rdet vdet
ia [A]
t [µs]
Experiment on the time constant of an electrical circuit of a DC motor
Armature resistance: Ra= 1.25 [Ω] Resistor for detecting armature current: Rdet= 1.2 [Ω]
0
0.5
1
1.5
0 200 400 600 800 1000
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛ −−=
τ0
0 exp1 ttIia
ia
La Ra
At t = 0.2 [ms], step voltage was applied to the DC motor. The rotor axis of the DC motor was locked to make vω = 0.
Driving circuit of transistor
Experimental waveform
Approximated waveform
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛ −−−=
] [ 120] [ 200exp1 35.1 t
µs µs
Approx. 120 [µs]
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( )det
det
RRL
RRL
a
a
+=
+=
τ
τ
E
Tr 2SA950
D 100 RB
Rdet vdet
ia
La Ra
Experiment on the time constant of electrical circuit of a DC motor
Armature resistance: Ra= 1.25 [Ω] Resistor for detecting armature current: Rdet= 1.2 [Ω]
Driving circuit of transistor
[mH] 3.0 ][ 5.2s][ 120
=
Ω×≈ µ
Tr 2SA950
510RB
D
DCM1
DCM2 6V
ia
PWM waveform generator vPWM
fsw = 3 [kHz] fsw = 20 [kHz] fsw = 50 [Hz]
ia
vPWM
10 [msec]
ia
vPWM
40 [µsec]
ia
vPWM
0.4 [msec]
The amount of ripple is small.
Armature current is intermittent.
Armature current is continuous, and contains a large amount of ripple.
D
Tr
RB
La
ia
vω
Ra
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La = 0.3 [mH] Ra = 1.3 [Ω]
τ = Ra / La = 0.23 [ms]
Armature resistance: Ra
Tsw << τ
Tsw = 0.08 [ms] → fsw = 12.5 [kHz]
ω
Tr 2SA950
510RB
VE D
DCM1
DCM2
Drive of DC motor using step-down chopper
510R1
LED1
PIC16F615 PIC12F615
P1A
A1 A0
0.1µFCS
A1 A0 = 10: Mode for driving DC motor P1A = 12.5kHzPWM output
A2
10
vcom
vPWM
PIC12F615
A2 A1 A0
PIC12F615 PIC12F 615
vPWM
Triangular wave generator
vcom
vtri
A/D converter.
VDD
VSS
Program for generating PWM waveform
(A1 A0 = 10 : mode for driving DC motor, fPWM =12.5kHz)
vcom
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P1A
Micro computer program
3 V
3 V
If vcom >= vtri then
vP1A = 0 If vcom < vtri then
vP1A = 6[V]
12
t
vtri vcom 3
-3
[V]
What the micro-computer does.
Tr : ON OFF ON OFF ON
vPWM
0
[V]
6
ω
-
+ 10k
10k 0.1µF100k
R2
R1
VR2 C1
OP1
D DCM1
DCM2
2kVR1
STEP 7. Circuit construction practice Construct the DC motor speed control system below. The source voltage of the op-amp should be set at ±3 [V].
6V
3V
LED1
(A1 A0 = 10)
3V PIC16F615 PIC12F615 PIC12F615
P1A
A2 A1 A0 1µFCS
-vωcom vcom
vω
510 RB
Tr 2SA950
50RS
Separate the battery for the chopper circuit from that for the op-amp and the micro controller. This will free the op-amp and mi-con from noise generated by the chopper circuit and motor
STEP 7. Problem 1 Answer questions (a) and (b) on the next page regarding why motor speed vω increases when voltage command vcom increases.
ω
Tr 2SA950
510RB D
DCM1
DCM2
2kVR1
6V
3V
vPWM
(A1 A0 = 10)
3V PIC16F615 PIC12F615 PIC12F615
P1A
A2 A1 A0 1µFCS
vcom
vω
vD
VE
(-3V)
(+3V)
(-3V)
(+3V)
50RS
t
t
vtri vcom
vPWM
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STEP 7. Problem 1 (continued) The figure below shows how the PWM waveform is generated. The output voltage of micro-computer vPWM is determined according to the difference between triangular waveform vtri and command voltage vcom. (a) In which periods is transistor Tr turned on/off? (b) If vcom increases, 1) is the average voltage across diode vD higher or lower? 2) does motor speed vω go up or down?
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-3
[V]
[V]
0
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