Page 754 - Mechatronics with Experiments

740 MECHATRONICS
2. Dancer arm based tension sensor results in lower loop gain since the same change
in web in-feed and out-feed will result in smaller tension variations. This effectively
reduces the loop gain of the closed loop system and instability problems are less
likely to occur. The potential problem with this method is the inertia and spring
effect of this type of tension sensor. The dancer mechanism has some inertia. It also
usually has a preloaded spring. As the dancer moves under the web tension, it may
tend to oscillate. The oscillations are more significant during high acceleration and
deceleration. Therefore, the oscillations of the dancer arm itself causes fluctuations
in actual tension. It may also excite natural resonance of the web and result in large
oscillations. The only solution would be to move the web in such a way that the
dancer arm is not displaced too fast, which means the variation in web in-feed and
out-feed rate must be very slowly varying.
We will consider two different control ideas which differ only in their control algo-
rithms. In both approaches, we use the same nip roller drive and tension transducer. Let us
assume that the nip roller is commanded to run at a certain speed with predefined accelera-
tion and deceleration rates. The only difference is in the way we control the unwind/rewind
roll in order to regulate the tension. All of the following ideas are identically applicable to
both unwind and rewind application with the only exception being polarity difference. A
tension control algorithm for unwind tension control problem can be applied to a rewind
tension control problem by changing the sign of the output of the tension control loop output.

Approach 1: Tension Control with Adjusted Velocity Command – web tension control
by controlling the roll drive with inner velocity servo loop and outer PI tension
servo loop.
Approach 2: Tension Control with Electronic Gearing – web tension control by
controlling the unwind/rewind roll drive with inner position loop commanded by
electronic gearing, and outer tension loop which modifies the electronic gear ratio.

Approach 1: Tension Control with Adjusted Velocity Command The
traditional approach is to control the rewind/unwind roll motor using two closed loops: (i)
inner loop is a velocity PI type-loop (compare desired velocity and measured velocity and
command the amplifier based on velocity error) which presumably makes the motor track
the commanded velocity within its bandwidth capability; (ii) outer tension PI-loop which
generates the commanded velocity based on the tension loop error.
This approach has two limitations:
1. closed loop stability problem due to large loop gain,
2. slow acceleration/deceleration rate limitation.

Let us explain these limitations by focusing on the tension control loop control sys-
tem. Figure 10.15 shows the closed loop of the tension control from a different perspective.
The key observation to be made in this block diagram is that the loop gain from web tension
error to roll speed change is large. In other words, small changes in in-feed and out-feed
rates will result in large tension errors, and that in turn will result in large commands and
possibly transient oscillation on the roll speed. Both of the above mentioned limitations are
the result of large loop gain. Large loop gain not only causes stability problems, but also the
acceleration/deceleration rates must be slow enough to avoid large oscillations. Large accel-
eration/deceleration rates will require large changes in commanded speed, which means
large changes in tension. This means that the system will not be able to accurately regulate
tension (keep tension error small) under large accelerations/deceleration cases of motion.