Power Electronics No. 9: Rotation speed control of DC motor ... ¯â€°-+ 10k 10k...

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Transcript of Power Electronics No. 9: Rotation speed control of DC motor ... ¯â€°-+ 10k 10k...

  • 1

    Power Electronics No. 9: Rotation speed control of DC

    motor using step-down converter

    Takeshi Furuhashi Furuhashi_at_cse.nagoya-u.ac.jp

  • 2

    N S

    Permanent magnet

    Coil

    I [A]

    B [T] La Ra

    Equivalent circuit of a DC motor

    ia vD vω

    Armature 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

    ωvviRt iL Daaaa −=+  d  d  

    3

    DC motor symbol Equivalent circuit of DC motor

    Differential equation of the electrical circuit of a DC motor

  • La Ra

    ia vD vω

    ωvviRt iL Daaaa −=+  d  d  

    0 that assumed isit ,0at ,(constant)

    ==

    =−

    a

    D

    it Evv ω

    circuit  electrical  an  of  constant  time    

     

    :

    exp1

    τ

    τ ⎟ ⎟ ⎠

    ⎞ ⎜⎜ ⎝

    ⎛ ⎟ ⎠

    ⎞ ⎜ ⎝

    ⎛−−= t

    R E

    a

    ⎟ ⎟ ⎠

    ⎞ ⎜ ⎜ ⎝

    ⎛ ⎟⎟ ⎠

    ⎞ ⎜⎜ ⎝

    ⎛ −−= t L R

    R Ei

    a

    a

    a a 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

  • 6

    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

    ⎟⎟ ⎠

    ⎞ ⎜⎜ ⎝

    ⎛ ⎟ ⎠

    ⎞ ⎜ ⎝

    ⎛ −−= τ 0

    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]

  • 7

    ( )det

    det

    RRL

    RR L

    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

    510 RB

    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

    Ra

    9

     

    La = 0.3 [mH] Ra = 1.3 [Ω]

    τ = Ra / La = 0.23 [ms]

    Armature resistance: Ra

    Tsw

  • ω

    Tr 2SA950

    510 RB

    VE D

    DCM1

    DCM2

    Drive of DC motor using step-down chopper

    510 R1

    LED1

    PIC16F615 PIC12F615

    P1A

    A1 A0

    0.1µF CS

    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

    11

    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

    2k VR1

    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 1µF CS

    -vωcom vcom

    510 RB

    Tr 2SA950

    50 RS

    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

    510 RB D

    DCM1

    DCM2

    2k VR1

    6V

    3V

    vPWM

    (A1 A0 = 10)

    3V PIC16F615 PIC12F615 PIC12F615

    P1A

    A2 A1 A0 1µF CS

    vcom

    vD VE

    (-3V)

    (+3V)

    (-3V)

    (+3V)

    50 RS

  • t

    t

    vtri vcom

    vPWM

    3

    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?

    15

    -3

    [V]

    [V]

    0

    6