Page 670 - Mechatronics with Experiments

656 MECHATRONICS
4. when 90 ≤ ≤ 270, effective torque constant is less than ideal and negative. If
e
the normal position feedback and command polarity is used in the closed position
control loop, the motor will run away. In other words, the closed loop position
feedback control of the motor would be unstable.
At the most inner loop, voltage fed into each phase is controlled by the PWM amplifier
circuit in such a way that the current in each phase follows the commanded current. The
dynamic response lag between the voltage modulation and current response in the stator is
small but finite. This lag becomes an important factor at high speeds, since
−1
=tan ( ⋅ ) (8.198)
lag e m
where is the phase lag, is the electrical time constant of the current loop, and is
lag e m
the rotor speed. As the speed of the motor increases, the phase lag of the current control
loop can become significant. As a result, the effective angle between the field and armature
magnetic fields will not be 90 degrees. Therefore, the motor will be producing torque at a
lower efficiency. Keeping this in mind, if the time constant of the current loop ( ≃ L∕R)is
e
known approximately or estimated in real-time, the commanded current can be calculated
to make not a 90 degree phase with the rotor magnetic field vector but 90 degree plus the
anticipated phase lag. In other words, anticipating the phase lag, we can feed the command
signal with a phase lead to cancel out the phase lag due to the current regulation loop.
This is called phase advancing in the brushless drive commutation algorithm. This can
be accomplished in real-time by modifying the rotor position sensor signal as shown in
Figure 8.32.
Finally, the brushless commutation algorithm requires the absolute position mea-
surement of the rotor within one revolution. This is needed to initialize the commutation
algorithm on power-up. On power-up, incremental position sensors (i.e., incremental opti-
cal encoders) do not provide this information, whereas resolvers and absolute encoders do.
Over 70% of the brushless motors are used with incremental type encoders. Therefore, on
power-up a phase finding algorithm is needed to establish the absolute position information
when an incremental position sensor is used as the position feedback device.

Example: Drive Sizing Motor and drive (amplifier and power supply) sizes must
be matched in a well designed system. Let us assume that we have a motor size selected. It
is characterized by its torque capacity (peak and RMS: T max , T rms ), current to torque gain
(which is the same as back EMF gain: K = K ), winding resistance (R), and maximum
T E
operating speed (w ). Let us determine the required drive size.
max
The drive size determination means the determination of DC bus voltage (V )
DC,max
and current (i , i ) that the drive must supply.
max rms
Given motor specifications: T , T , K = K , R, w
max rms T E max
Determine matched drive size: i , i , V
max rms max
As a result, the maximum and RMS current requirements are calculated from,
i = T ∕K (8.199)
max max T
i = T ∕K (8.200)
rms rms T
The maximum DC bus voltage required at worst conditions, that is when providing maxi-
mum torque and running at maximum speed and neglecting the transient inductance effects,
di(t)
V DC = L ⋅ + R ⋅ i(t) + K ⋅ w(t) (8.201)
E
dt
V DC,max ≈ R ⋅ i max + K ⋅ w max (8.202)
E