Power Electronics
No. 9: Rotation speed control of DC
motor using step-down converter		Takeshi Furuhashi	Furuhashi_at_cse.nagoya-u.ac.jp1

(Armature coil)	
Coil	

(Field magnet)	
Permanent magnet	

Armature resistance[Ω]	
Armature inductance[H]	

La

Ra

B [T]	iaS	N	

I [A]	(Leakage flux)	

(Armature current)	

vD

Armaturecurrent[A]	

vω

Armatureelectro-motiveforce[V]	

Equivalent circuit of a DC motor	 vω = Κe ω :armature electro-motive force
Ke : counter emf constantω =2π n	 2LaRaiaiavD

DC motor symbol	vDvωEquivalent circuit of DC motor	 

Differential equation of the electrical circuit of a DC motor	 	  d	  iaLa+ Raia = vD − vωd	  t3

LaRaiavDvω	  d	  iaLa+ Raia = vD − vωd	  tvD − vω = E (constant),at t = 0, it is assumed that ia = 0⎛ Ra ⎞ ⎞E ⎛⎜
ia = ⎜1 − exp⎜⎜ − t ⎟⎟ ⎟⎟Ra ⎝⎝ La ⎠ ⎠=E ⎛⎛ t ⎞ ⎞⎜⎜1 − exp⎜ − ⎟ ⎟⎟	  Ra ⎝⎝ τ ⎠ ⎠	  	  τ : time	  constant 	  of 	  an	  electrical	  circuit

Tr2SA950

RB510

ERa
DC	motor	

DE

ERB510DTransistor drive
circuit	 iaVa

DTransistor drive
circuit 	 Tr2SA950

La

Equivalent circuit of a step-down
chopper and DC motor	 

LRe2iLC
47µF+RLvoE

L

iL

D

Equivalent circuit of a step-down
chopper	 

VoExperiment on the time constant of an electrical circuit of a DC motor	 

ERB
100

La

Ra

Tr 2SA950

D⎛⎛ t − t 0 ⎞ ⎞ia = I0 ⎜⎜1 − exp⎜⎟ ⎟⎟⎝ τ ⎠ ⎠⎝Rdet	 v

det	Driving circuitof transistor	 

1.5⎛⎛ t − 200 [µs ] ⎞ ⎞⎜
= 1.35 ⎜1 − exp⎜ −⎟ ⎟⎟⎝ 120 [µs ] ⎠ ⎠⎝ia [A]	
Experimentalwaveform	 

1At t = 0.2 [ms], step
voltage was applied tothe DC motor.
The rotor axis of theDC motor was locked
to make vω = 0.	 

Armature resistance: Ra= 1.25 [Ω]	 
Resistor for detecting armature current: Rdet= 1.2 [Ω]	 

iaApproximated waveform	 

0.500200

400

600

Approx. 120 [µs]

800

1000

t [µs]	
6Experiment on the time constant of electrical circuit of a DC motor	 Ra

Tr 2SA950

ERB
100

Driving circuitof transistor	 

DLa

Armature resistance: Ra= 1.25 [Ω]	 
Resistor for detecting armature current: Rdet= 1.2 [Ω]	 

iaRdet	 v

det	L
τ=Ra + Rdet
L = τ (Ra + Rdet )≈ 120 [ µs] × 2.5 [Ω]= 0.3 [mH]7

Tr
2SA9506VRB
510
PWM waveformgenerator	

Armature current isintermittent.	

ia
DCM1
D

DCM2vPWM

Armature current is
continuous, and contains alarge amount of ripple．	

The amount of ripple
is small.	

iaiaia

vPWM

vPWM

vPWM

10 [msec]fsw = 50 [Hz]0.4 [msec]
fsw = 3 [kHz]40 [µsec]
fsw = 20 [kHz]

Ra

TrRB

La
Armature resistance: Ra	 iaDvω

Tsw <<τ 	 

La = 0.3 [mH]Ra = 1.3 [Ω]τ = Ra / La = 0.23 [ms]Tsw = 0.08 [ms]→ fsw = 12.5 [kHz]9Tr
2SA950

RB

DCM1
ω

D510

VE

DCM2

P1A

PIC12F615
PIC16F615
PIC12F615
A2vcom

A1 A0CS
0.1µF

R1510

vPWM
LED1

A1 A0 = 10: Mode for driving DC motor	
P1A = 12.5kHzPWM output	

Drive of DC motor using step-down chopper	 

10Micro computer
program	

（A1 A0 = 10 : mode for driving DC motor, fPWM =12.5kHz）

Program for generating
PWM waveform	

P1A

VDD

3V

PIC12F
PIC12F615615
vcom

If vcom >= vtri thenvP1A = 0A/D
converter.	 

If vcom < vtri thenvPWM

vP1A = 6[V]vtri

Triangular wave generator	 
3V

A2

A1

A0VSS

vcom
11

What the micro-computer does.	
[V]

vtrivcom

3t-3

[V]

vPWM

60
Tr : ON OFFONOFFON	
12

STEP 7. Circuit construction practice Construct the DC motor speed control systembelow. The source voltage of the op-amp should be set at ±3 [V]．

Separate thebattery for thechopper circuitfrom that for the
op-amp and themicro controller.
This will free theop-amp and micon from noise
generated by thechopper circuitand motor	 

Tr2SA950

DRB 5106V

DCM1
ω
DCM2LED1vω

P1A

3V
R1 10k

3V

VR12k-vωcom

R210k

VR2

C1100k

0.1µF

PIC12F615
PIC16F615
PIC12F615-	+	 OP1

A2 A1 A0RS50CS1µFvcom（A1 A0 = 10）	

STEP 7. Problem 1Answer questions (a) and (b) on the next page regarding why motor speed vω increases when voltage commandvcom increases.

(+3V)	

Tr 2SA950

VERB

6V510

DvD

DCM1ω
DCM2(-3V)	
(+3V)	RS50
P1A3V
PIC12F615
PIC16F615
PIC12F615

3V

VR12k

A2 A1 A0CS
1µFvcom(-3V)	（A1 A0 = 10）	vPWMvωSTEP 7. Problem 1 (continued)	 
The figure below shows how the PWM waveform is generated. The output voltage of micro-computervPWM is determined according to the difference between triangular waveform vtri and command voltagevcom.
(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?
[V]
3

vtri

vcom

t-3

[V]

vPWM

60t15