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6.3.2 Feed-Forward Loops
As described in the previous paragraph, the main driving force in a PID
loop is the proportional term. The other two correct static and dynamic
errors associated with the closed loop.
Taking a closer look at the desired and actual motion parameters and at the
characteristics of the DC motors, some interesting observations can be made.
For a constant load, the velocity of a DC motor is approximately proportional
with the voltage. This means that for a trapezoidal velocity profile, for
instance, the motor voltage will have also a trapezoidal shape (Figure 6.3-5).
Figure 6.3-5 — Trapezoidal Velocity Profile
The second observation is that the desired velocity is calculated by the
trajectory generator and is known ahead of time. The obvious conclusion is
that we could take this velocity information, scale it by a K
it to the motor driver. If the scaling is done properly, the right amount of
voltage is sent to the motor to get the desired velocities, without the need
for a closed loop. Because the signal is derived from the velocity profile
and it is being sent directly to the motor driver, the procedure is called
velocity feed-forward.
Of course, this looks like an open loop, and it is (Figure 6.3-6). But, adding
this signal to the closed loop has the effect of significantly reducing the
"work" the PID has to do, thus reducing the overall following error. The PID
now has to correct only for the residual error left over by the feed-forward
signal.
Trajectory
Generator
Kvff
Motion Controller
Figure 6.3-6 — PID Loop with Feed-Forward
Desired Velocity
Motor Voltage
Servo Controller
e
Kp
∫
e
Ki
de
Kd
dt
Time
factor and feed
vff
Motor
Driver
Encoder
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