4 Chopper-Controlled DC Motor Drive

4 Chopper-Controlled DC Motor Drive
• Chopper: The variable dc voltage is controlled
by varying the on- and off-times of a converter.
• Fig. 4.1 is a schematic diagram of the chopper.

• Its frequency of operation is
f
1
+ t
c =
=
(ton
off )
1
T
and its duty cycle is defined as
d
=
t
T
on
• Assuming that the switch is ideal, the
average output is
t
V
on
dc = Vs
=
T
dV
s
• varying the duty cycle changes the output
voltage.

• The duty cycle d can be changed in two ways:
(i) varying the on-time (constant switching
frequency).
(ii) varying the chopping frequency.
• Constant switching frequency has many
advantages in practice.

4.3 Four-Quadrant Chopper Circuit
• Fig. 4.2 is the chopper circuit with transistor
switches.

• Fig. 4.3 is first-quadrant operation.

• Fig. 4.4 is first-quadrant operation with zero
voltage across the load.

• Fig. 4.5 voltage and current waveforms in
first-quadrant operation.

• Fig. 4.6 second-quadrant operation

• Fig. 4.7 voltage and current waveforms in
second-quadrant operation.

• Fig. 4.8 Modes of operation in the third
quadrant.

• Fig. 4.9 waveform in third-quadrant operation

• Fig. 4.10 Waveforms in fourth-quadrant
operation.

4.4 Chopper for inversion
• Converter: DC ⇒ DC (different voltage)
• The chopper is the building block for that:
AC ⇒ DC ⇒ DC(different voltage)

4.5 Chopper with other power devices
• MOSFETs, IGBTs, GTOs, or SCRs are
used for different power level.
• The MOSFET and transistor choppers are
used at power levels up to 50kW.

4.6 Model of The Chopper
• The transfer function of the chopper is
G
r
K
(s) =
r
sT
1+
2
where K r = V s /V cm , V s is the source voltage,
and V cm is the maximum control voltage.
• Increasing the chopping frequency decreases
the delay time, and its becomes a simple gain.

4.7 Input to the chopper
• The chopper input: a battery or a rectified ac
supply.
• Fig. 4.11 is the chopper with rectified circuit.

• Its disadvantage: it cannot transfer power from
dc link into ac mains.
• Fig. 4.12 Chopper with regeneration capability

• The generating converter has to be operated
at triggering angles greater that 90.

4.8 Other Chopper Circuits
• Fig. 4.13 one- and two-quadrant operation.

4.9 Steady-state analysis ...
• 4.9.1 Analysis by averaging
• The average armature current is
I
av
Vdc
− E
=
R
a
where V dc = dV s
• The electromagnetic torque is
T av = K b I av = K b (dV s -K b w m )/R a (N·m)

• The normalized torque is
T
en
=
T
T
av
b
/ V
/ V
b
b
=
K
b
(dV
K
s
b
− K
I R
b
a
b
ωm
) /
/ V
b
V
b
=
dVn
− ω
R
an
mn
,
p.u.
I
R
where R
b a
an = , p.u. V
s
V
n = , p.u. ω
m
mn = , p.u.
b
Vb
ωb
• 4.9.2 Instantaneous steady-state computation
(including harmonics)
• The equations of the motor for on and off times
(continuous current conduction)
di
V E R i L
a
s = + a a + a
dt
di
0 = E + R i L
a
a a + a ,
dt
,
0
dT
≤
≤
t
t
V
≤
≤
dT
T
ω

• Fig. 4.15 The waveform of applied voltage
and armature current.

• The solutions of the above equations:
t
V E
i (t)
s − T
(1 e a T
) I e a
a = − + a0 , 0 < t <
R
i
a
(t)
= −
a
E
R
a
(1 − e
−
1
t
−
T
a
) +
I
a1
e
where T a = L a /R a (Armature time constant)
t 1 = t - dT
• By using boundary condition
I
a1
=
V (1 − e
s
R
a
(1 − e
−dT / T
−T / T
a
a
)
)
−
E
R
−
1
t
−
T
a
a
t
,
I
dT
a0
≤
=
t
≤
V (e
s
R
a
dT
dT
(e
dT / T
T / T
a
a
−1)
−1)
−
E
R
a

• The critical duty cycle: the limiting or
minimum value of duty cycle for
continuous current; I a0 equates to zero.
• The relevant equations for discontinuous
current-conduction mode
V
s
=
E
+
R
a
i
a
+
L
di
dt
di
0 = E + R i L
a
a + a , dT ≤ t ≤ tx
dt
with i a (t x + dT) = 0; i a (0) = 0
a
a
,
0
≤
t
≤
a +
dT
dT

• Hence,
i
a
I
a1
(t
x
=
Vs
−
R
a
+ dT) = −
E
(1 − e
E
R
a
−dT /
(1 − e
Ta
t
−
T
x
a
)
) +
• tx is evaluated from (4.25) and the above
eqs. as
tx = Ta
loge[1
+
I
a1
R
E
a
]
I
a1
e
t
−
T
x
a

• The solution for the armature current in
three time segments is
V E
i (t)
s −
(1 e a
a = − ), 0 < t <
R
i
a
(t)
=
I
a1
e
a
(t−dT)
−
T
a
−
−
t
T
E
R
a
(1 − e
dT
(t−dT)
−
T
ia (t) = 0, (tx
+ dT) < t <
a
),
T
dT
≤
t
≤
t
x
- dT

4.10 Rating of the device
• The rms value of the power switch current
I
t
=
2
max
I
2T
(T + dT) =
1+
d
2
max
• The average diode current
I
1−
d
= ( ) ⋅
2
d I max
⋅ I

• Transistor and diode currents for motoring
operation in the continuous-conduction mode.

4.11 Pulsating Torque
• The average of the harmonic torque is zero.
• High-performance applications require the
pulsating torque to be minimum.
• The applied voltage is resolved into Fourier
components as
V
where
= V +
∞ a ∑ n=1
A
sin(nω
a (t)
n c t n )
dT
V a = Vs
= dV
T
A
n
2V
=
s
nπ
s
nω
dT
sin
c
2
ω
θ
c
n
2π
= 2πf
c =
T
π nωcdT
= −
2 2
+
θ

• The armature current is expressed as
i
a
A
(t) = I
n
av +
∞
∑n
= 1 sin(nωct
+ θn
− φ
Zn
Va
− E
Iav
Zn
= R
Ra
−1
R
φ cos {
a
n =
}
2 2 2
R + n ω L
where
= a c a
a
c
2
a
n
)
+
jnω
L
• The input power is
P
i
=
V
a
⎧V aI
⎪
= ⎨
⎪+
V
⎩
a
(t)i
av
a
+ I
(t)
av
∑
∞
n = 1
sin(nω
t + θ
∞ An
∑ = ω + θ − φ +
∞
n 1 sin(n ct
n n)
∑n
=
Z
n
A
n
c
n
)
1
A
(
Z
2
n
n
sin(nω
c
t + θ
n
)sin(nω
c
t + θ
n
− φ
n
⎫
⎪
⎬
)) ⎪
⎭

4.12 Closed-loop operation
• Fig. 4.20 is the closed-loop speed-controller
dc motor drive.

• The current controller can be
(i) Pulse-Width-Modulation (PWM) controller
(ii) Hysteresis controller
Fig. 4.21 shows on- and off-time for PWM

• Fig. 4.22 is the implementation of PWM
current controller.

• Fig. 4.24 shows hysteresis-controlled operation
a
*
a
i ≤ i − ∆i,
set v =
*
a
a
V
i a ≥ i + ∆i,
reset va
=
s
0

• Fig. 4.23

• Fig. 4.25 is realization of hysteresis controller.