Page 665 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 651
ground voltage. In order to eliminate this problem, when H-bridges are controlled (i.e.,
by a microcontroller), either in software or hardware, a dead time (or delay) is introduced
between the ON to OFF command to one transistor and OFF to ON command to the other
transistor (this one is delayed in microsecond range) in order to avoid a short circuit. Most
microcontrollers have PWM output peripheral where this delay is programmable by writing
to a setup register associated with the PWM output channel.
If the top two transistors are both turned ON and the bottom two are turned OFF (or
the reverse; top two transistors are OFF, bottom two transistors are ON), the terminals of the
motor winding are effectively shorted without connection to the power supply, V (t) = 0.0.
t
This results in the so-called dynamic braking.
d (t)
V (t) = R ⋅ i(t) + (8.177)
t
dt
di(t)
̇
0 = R ⋅ i(t) + L ⋅ + k ⋅ (t) (8.178)
e
dt
di(t)
̇
− k ⋅ (t) = R ⋅ i(t) + L (8.179)
e
dt
Due to the back EMF voltage, there will be a current developed in the motor winding
(hence torque) in the opposite direction to the rotation speed. As a result, it will brake
(slow down) the motion. The generated current is approximately proportional to the speed,
hence the dynamic braking torque is large at high speeds and small at low speeds. One of
the transistors and the diode on the other side provides the conductive path. Let us assume
the top two transistors were turned ON, and the bottom two were OFF. Then for CW motion
of the motor, Q1 transistor and D2 diode provide the conductive path for current flow from
left to right across the motor. For CCW direction, Q2 diode and D1 transistor provide the
conductive path for current flow from right to left (opposite). Similar behavior occurs if the
bottom two transistors were ON and the top two transistors were OFF.
By controlling the current magnitude through the power transistors, the magnitude
of the torque is controlled. In very small size motors (fractional horsepower), linearly
operated transistor amplifiers are used. The pulse width modulation (PWM) circuit operates
the transistors in all ON or all OFF modes in order to increase the efficiency. The linear
amplifiers provide lower noise but are less efficient than the PWM amplifiers. The most
important difference between the linear mode and PWM mode of operating the power
transistors is the efficiency. Power loss at the transistor is approximately the voltage drop
across the transistor times the current it conducts,

P loss = V CE ⋅ i CE (8.180)

In the linear mode of operation, that is 50% turned ON, the voltage V across the transistor
CE
will be 50% of the supply voltage and the current will be the equal to the current amplification
gain of the transistor (between the base current and output current). Both values are finite
values, and there is significant power loss across the power transistor in linear operating
mode. In PWM mode, the transistors are always in one of two states: fully ON or fully
OFF. When the transistor is fully ON, voltage drop across the transistor is almost zero,
V ≈ 0.0, hence P = 0. When the transistor is fully OFF, the i is almost zero, hence
CE loss CE
hence P loss = 0. As a result, the PWM mode of operation of a transistor results in much
less power loss than the linear mode of operation. The only drawback of the PWM mode
of operation compared to linear mode of operation is that in PWM mode there will be
more noise in the current due to the switching frequency. Typical switching frequencies
for the PWM mode of operation for power transistors is in the range of 2–20 kHz. The
PWM switching frequency should be significantly larger than the desired current control