Page 755 - Mechatronics with Experiments

PROGRAMMABLE MOTION CONTROL SYSTEMS 741
Approach 2: Tension Control with Electronic Gearing Electronic gearing
refers to a position servo controlled motion where the desired motion command is generated
based on a gear ratio multiplied by a master (reference) motion source. In this case, the
master is the nip roller speed. In software, we monitor the motion of nip roller at the servo
loop update rate, and command the desired motion to the unwind roll proportional to the
master motion speed. The proportional value is the gear ratio defined in the software.
The key difference in this approach is that the variation in tension is not allowed to
get too large as seen by the feedback loop. The gear ratio in software is updated based on
the tension error. The tension error is passed through a PI control algorithm, and the result
is the updated gear ratio. The feedback loop sees much smaller tension error levels. Hence,
it can have larger gain and larger acceleration/deceleration rates without causing closed
loop stability problems. Notice that the gear ratio initial starting value must be accurate for
this approach to be more accurate than the first approach. This can be obtained by either
directly sensing the roll diameter at the beginning of a cycle or always starting with a known
diameter known in advance or entered by the operator as setup information.
Control Algorithm for Tension Control Using Electronic
Gearing
Initialize once:
{Define/Input/Read} tension loop polarity (unwind/
rewind) sign = +1 or -1
{Define/Input/Read} desired tension:
Td = ....
{Define/Input/Read} nip roll diameter
d1 = ....
{Define/Input/Read} current unwind/rewind roll diameter
d2 = .....
Calculate initial gear ratio: z = (d_1 / d_2)
Initialize the parameters of the tension control
algorithm (PI in this example):
z_ I = 0.0
Kp = 0.01
Ki = 0.001
End_Initialize

Update Periodically: (i.e. every 10 msec)
Read tension sensor: Ta
Tension error: e_T = Td-Ta
Integral portion of control dz_i = dz_i +
sign * Ki * e_T
Proportional portion of control dz = sign * Kp *
e_T
P + I portion dz = dz + dz_i
Calculate the new gear ratio z = z + dz
Update the gear ratio ‘z’ in the electronically geared
motion between master and slave axes.
EndUpdate

10.6.3 Smart Conveyors
Conveyors are one of the most common mechanical systems used in industrial automation.
They can be considered “the work-horse” of mass production. A typical conveyor runs at