Page 692 - Mechatronics with Experiments

678 MECHATRONICS
As a result, the current vector does not change in sudden jumps, but instead it is smoothly
changed. Resonance is greatly reduced, and resolution is sharply increased, because there
are many more equilibrium points as the current is ratioed between multiple phases.
Microstepping is usually performed with two bidirectional phases. These two phases have
similar torque equations as a brushless DC motor. Let us assume that the phase current-
torque gain is a sinusoidal function of the rotor position, . The two phases are 90 degrees
r
apart. Further, let us assume that the current to each phase is controlled with a sinusoidal
function in order to implement the microstepping mode of current control. The phase
current and torque relationships are,

T = K ⋅ i ⋅ sin( ) = Ki cos( ) ⋅ sin( ) (8.268)
a
r
a
r
c
where
i (t) = i ⋅ cos( (t)) (8.269)
a
c
T = K ⋅ i ⋅ cos( ) = Ki (−sin( )) ⋅ cos( ) (8.270)
c
r
r
b
b
where
i (t) = i ⋅ (−sin( (t))) (8.271)
b
c
T total = T + T = Ki sin( − ) (8.272)
r
a
b
c
where is the real position and is the commanded position, i , i are currents in phase
r c a b
a and b, K is a proportionality constant. In equilibrium, these two positions are identical,
= , so the total torque equation becomes:
c
r
T = Ki sin( − ) = 0 (8.273)
total c r
◦
and when − = 90 , the torque is maximized for a given current.
c
c
The step motor torque is developed as the rotor is forced to move away from the
equilibrium position for a given state of winding current. The equilibrium position is the
one that minimizes the magnetic reluctance (maximizes the inductance). When the rotor is
at the exact position that minimizes the reluctance, the torque is zero. The holding torque
is developed as the rotor position deviates from the ideal position due to load or current
commutation in the windings.
Example: Unipolar Integrated Circuit (IC) Drive for Step Motors An
integrated circuit (IC) drive which can be used to drive a unipolar stepper motor is shown
in Figure 8.55. The SLA7051M (by Philips Semiconductors) integrates two blocks of
Figure 8.48, the translator and the power switch set. The translator section is made of a
low-power CMOS logic circuit and handles the logic for sequencing, direction, full and
half step operation. The translator decides on the firing sequence of windings for full step
(AB, BC, CD, DA in forward or reverse direction) or for half step (A, AB, B, BC, C, CD,
D, DA in forward or reverse direction) as a function of the input signals at the terminals
STEP (also named Clock), FULL/HALF, CW/CCW. At each low to high transition of the
STEP input signal, the translator checks the state of FULL/HALF pin to determine if full
step mode or half step mode is commanded (high for full step, low for half step mode), and
the CW/CCW input to determine the direction command. Then it decides which one or two
of the windings to be fired according to the sequence defined above (AB, BC, CD, DA or
A, AB, B, BC, C, CD, D, DA).
The PWM current controlled power stage uses FET output and can handle up to
2 A and 46 V per phase. The maximum current is controlled by the reference voltage and