Page 753 - Mechatronics with Experiments

PROGRAMMABLE MOTION CONTROL SYSTEMS 739
From master axis position sensor

Controller
Drive: power supply + amplifier
Trajectory PID: θ Power Encoder Motor Tension
generator PID: V Commutation PID: PI sensor
stage
d
≈ (.)
PI : T dt
+ _
T
T cmd
mea
FIGURE 10.15: A servo control loop to control tension in the web. There are two different
common implementations: (i) No master axis speed is provided. The commanded speed of this
axis is modified (increased or decreased) based on the tension control loop: i.e.,
̇ = ̇ +Δ ̇ (T − T ). (ii) a master axis speed is provided and the gear ratio between
cmd cmd0 cmd0 d a
the master axis and this (slave) axis is modified based on the tension control loop: i.e.,
= z ⋅ ̇ , z = z +Δz(T − T ).
̇ cmd master 0 d a

In general, the production rate dictates the line speed at which the web must be
moving nominally. While the web is moving, the tension of the web must also be measured
and corrections must be made to the feed in order to maintain the desired tension. In order
to both control the speed and tension on a web, there needs to be two actuation sources:
one to set the nominal line speed, the other to track the first nominally but to maintain the
desired tension.
Consider that the web speed is set by the nip roller (or similar mechanism) which
is specified by the required process speed. The unwind/rewind roll speed needs to be
adjusted in order to maintain the desired tension while the web is being moved. In unwind
applications, if the tension is less than the desired tension, the unwind roll speed needs to
be decreased. The opposite is true in the rewind applications. That is, if the tension is less
than the desired tension, the rewind roll speed needs to be increased. This is referred to as
the polarity of the tension control loop.

ΔV = (sign) ⋅ k ⋅ (T − T ) (10.13)
d
a
where the sign is (+1) for unwind applications, and (−1) for rewind applications. The
polarity is defined as the sign (positive or negative) ratios of the change in the tension to
the required change in the speed of the drive used to control the tension. The polarity of
unwind and rewind tension control are opposite (10.14).
The differences between using a strain-gauge based tension sensor versus a dancer
arm based tension sensor are as follows:

1. Strain-gauge based tension sensor results in larger loop gain since small changes in
web in-feed and out-feed results in large tension changes compared to the dancer arm
based tension sensor. On one hand, if the web is too stiff, the loop gain as a result of
small differences in in-feed and out-feed web may be so large that large oscillations
and closed loop instability may occur. With sufficiently flexible web, on the other
hand, this method would provide the fastest closed loop response. The web stiffness
and tension sensor sensitivity combination must be carefully judged to determine
whether they will result in good tight closed loop performance with large loop gain
or they will result in too large loop gain that will create instability problems.