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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1 Power Electronics No. 9: Rotation speed control of DC motor using step-down converter Takeshi Furuhashi Furuhashi_at_cse.nagoya-u.ac.jp

Transcript of Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2...

Page 1: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

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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

Page 2: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

2

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]

Page 3: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

La Ra

ia

vD vω

ia

vD

ωvviRtiL Daaa

a −=+  d  d  

3

DC motor symbol Equivalent circuit of DC motor

Differential equation of the electrical circuit of a DC motor

Page 4: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

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

Page 5: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

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

Page 6: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

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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]

Page 7: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

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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

Page 8: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

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.

Page 9: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

D

Tr

RB

La

ia

Ra

9

 

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]

Page 10: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

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

Page 11: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

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

11

P1A       

Micro computer program

3 V

3 V

If vcom >= vtri then

vP1A = 0 If vcom < vtri then

vP1A = 6[V]

Page 12: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

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t

vtri vcom 3

-3

[V]

What the micro-computer does.

Tr : ON OFF     ON        OFF      ON

vPWM

0

[V]

6

Page 13: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

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

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

Page 14: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

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

vD

VE

(-3V)

(+3V)

(-3V)

(+3V)

50RS

Page 15: Power Electronics No. 9: Rotation speed control of DC motor ...ω-+ 10k 10k 100k 0.1µF R 2 R 1 VR 2 C1 OP 1 D DCM 1 DCM 2 2k VR 1 STEP 7. Circuit construction practice Construct the

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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