PLC control solution for rolling machines with
loading changes of the moment of inertia
Milan Adžić *, Evgenije Adžić**, Vladimir Katić**
* Polytechnic School of Engineering, Subotica
** Faculty of Technical Sciences, Novi Sad
*adzicm@vts.su.ac.rs
** evgenije@uns.ac.rs, katav@uns.ac.rs
Abstract—Unrolling and rolling machines for tape materials
represents specific problem in electric drives such as metal
rolling mills, paper mils, wire, textiles and plastic
production plants. The main task for this drives is to achieve
the desired constant tension of materials in all operation
modes even during acceleration and deceleration
independently of the actual rolling drum diameter. The
drive moment of inertia varies especially due to the drum
diameter changes. Because of the extreme demands such are
wide working speed range and wide load variation from one
side and necessary high dynamic from the other side,
control solutions for the rolling drives are very complex,
especially in cases of high speeds of modern production
lines, high ratio of maximal and minimal drum diameter
and when indirect measurement of material tension is
applied. Due to the wide range of drum diameter changes,
drive motors also works in field weakening region. There
are two conventional field weakening methods used
depending on the motor electromotive force and drum
diameter. The paper describes control solution with
programmable logic controller (PLC) that covers both
regulation methods, with an indirect measuring method for
material tension, also concerning the moment of inertia
changes based on estimated drum diameter, which provides
fast dynamic tension control during stationary operation, as
in acceleration and deceleration phases. The paper specially
addresses the control algorithm problems which are used
for deriving solutions for specific PLC.
Keywords— Winder drives, DC machine, Sensorless tension
control.
I.
INTRODUCTION
In industrial plants there are two construction solutions
for rolling drives: rolling drive with auxiliary roller and
axle roller. Unrolling drives solutions essentially are no
different from the rollers. In drives with auxiliary roller
power is transferred to the main roller by friction force of
auxiliary drive, which is the main limiting factor in this
solution. In this case the control principle is relatively
simple, because all relevant mechanical variables in the
stationary state does not depend on the diameter of the
roller. Due to the more rigorous technological
requirements, and because of its simple mechanical
construction, axle rollers are most widely used in practice,
where the machine torque is transmitted directly to the
shaft of the roller. In this case, change of the roller
diameter should take into account in the control algorithm.
Figure 1 shows a simplified structure of an axle roller with
the diagram presenting the change of mechanical variables
with the diameter of the roller. The usual requirements for
a constant line speed and the material tension force, leads
to the fact that the winding power P = Fv is constant in
the whole range of driving motor speed.
Figure 1. Characteristic diagram of change of mechanical variables
with the diameter of the roller.
Figure 2. Speed/torque characteristics with speed and torque limit for
axle roller.
Needed motor operation area in the reference frame of
torque and rotational speed is therefore limited with
constant power hyperbole curve, maximum speed and
maximum torque value, as it is shown in Figure 2.
Consequently, for better motor utilization control
algorithm usually combine the speed regulation in the area
of constant torque and constant power. In the case of the
drive with DC motor with separate excitation, it is
performed by applying standard controlled thyristor
network driven rectifiers, one for a armature voltage
variation and the other to vary the excitation voltage.
Rolling drive controller have a task to maintain constant
tension force in the material, regardless of the changes in
diameter, and the mechanical losses, both in steady state
and dynamic states during drive acceleration and
deceleration. Because of the roller diameter variations
there is also change of the drive moment of inertia, which
further complicates the problem. Tension force regulation
can be derived directly by its measuring or by reserve
material loop installation, or indirectly when it is
performed on the basis of a mathematical model of the
drive. Modern PLC devices are able to perform required
control algorithm, so this paper describes its application
for roller drive control implementation in steel rolling
plant. Based on the given values of tension, line speed and
acceleration, algorithm calculates the required value for
rotor current necessary for their maintaining. Especially,
the paper gives emphasis to the problems which lead to
synthesis of software solution.
II. OPERATION PRINCIPLE
The control principle is resulting from the mechanical
equations of the drive and the equation of the DC motor
with separate excitation. For tension force following
relations are valid:
F
2M P UI E

 
 I  k1 I
D
v
v
v
D
(1)
from which the following relations for motor rotor current
and the roller diameter yields:
FD
k1
60v
D
N
I
(2)
(3)
where the symbols are in accordance with Figure 1 and 2.
From these relations the following possibilities for
indirect control of the tension force can be derived:
 by motor power P, and
 using the motor rotor current, I.
Power regulation is realized so it is indirectly calculated
as P=UIη, and then it is used as the feedback variable for
outer control loop, as it is shown in Figure 3.
Calculation of the reference power wp is performed
proportional to the line speed v. In addition, it is possible
to perform compensation of losses, which are independent
and dependent on the rotational speed, as well as
compensation for acceleration and deceleration. However,
this method does not give good results at high values of
modern production line speeds, where it is usually used a
different method that is based on calculating the required
values of motor rotor current [1], [2]. In that case there are
used two methods for field weakening:
 depending on the value of electromotive force e, and
 depending on the actual value of the diameter, D.
Figure 3. Control algorithm with control of motor power.
A. Field weakening in function of electromotive force
In this method, the field weakening is performed
independently of the roller control, i.e. on standard way as
a function of the electromotive force value or motor rotor
voltage. The advantage of this method is that motor
operate with the maximum excitation till nominal speed,
which provides better utilization of the motor, a smaller
rotor current value and less consumption of a reactive
power from the grid. Reserve in the rotor current in low
speed range can be utilized for additional tight straining of
the line.
Figure 4 shows a block diagram of roller drive
regulation with field weakening in function of the
electromotive force value e. Set point for the rotor current
wi for maintaining a constant tension force is calculated
from the value of mechanical torque ∑m divided by the
value of flux in the machine φ. The flux value until
reaching nominal motor speed is equal to the nominal
value φ=1
flux is lower than the nominal value φ<1. Flux value is
obtained by dividing values of electromotive force e or the
rotor voltage value with motor rotational speed n. The
actual value of the roller diameter d, is also indirectly
determined as the ratio of line speed and the rotational
speed value n.
Torque required for the stationary operation mode mf is
calculated as the product of the reference tension value wf
and the actual value of the diameter d. Required
acceleration torque is calculated based on the value of the
line acceleration dv/dt, actual value of the diameter d and
technological parameters such as width b and specific
mass of the material in the rolling drive ρ.
Compensation of the mechanical losses is performed by
non-linear function of the rotational speed, and it is added
as correction factor to the reference value of total rotor
current wi.
Especially if desire is to perform relief of the speed
regulator for rectifier in the rotor circuit, it is possible to
generate its reference value wn based on actual values of
line speed and diameter d.
block diagram of this method is considerably simplified
compared to the previous method, because there is no
need to calculate division for finding the motor flux and
multiplication to calculate the torque in the stationary
state.
Figure 4. Control algorithm for roller the field weakening of function
of the electromotive force.
v
n
e
wf
Line speed
Motor speed of rotation
Electromotive force
Tension reference
ma
mf
m
iv
wn
wi
Speed reference
Rotor current reference
1
2
d
b
Actual diameter
Width
Specific mass
3
4
5
dv
dt
Line acceleration
6
Acceleration torque
Stationary moment
Cumulative moment
Current for compensation of
losses
Diameter calculator
Acceleration torque
calculator
Compensation of losses
Divided torque and flux
Računar momenta zatezanja
Computer flux
Flux calculator
Motor flux
7
Speed calculator


B. Field weakening of function of the roller diameter
In this method, the value of electromotive force is
maintaining proportional to the value of line speed v, by
changing the excitation current value. In this case, in the
entire regulated speed range, rotor current value in the
stationary state without considering mechanical losses is
proportional to the tension force wf, and flux value φ
proportional to the actual value of the diameter.
The principle of this method is shown in block diagram
in Figure 5. Apart from the advantage that tension
reference value wf can be directly applied as the current
reference wi, other benefits are based on the fact that the
variation range of the rotor current is less comparing with
previous method and that, instead of the flux value φ to
calculate the required acceleration torque ma, actual
diameter d can be taken. It can be done only if the range of
diameter change corresponds to a range of motor speed
changes in the field weakening region. Due to this control
Figure 5. Control algorithm for roller the field weakening of function
of the roller diameter.
Apply the same labels as in Figure 4
mv
Torque for compensation of 8
losses
wiF Field current calculator
9
Nelinearan član
nonlinear
Δφ controller
The
Current reference correction is obtained as the ratio
between correction torque ∑m and actual diameter value
d. Correction torque represents the sum of the required
acceleration torque ma and torque of the losses mv. Other
functions for calculating the actual diameter d, the torque
for acceleration ma and losses mv are the same as in
previous method. Motor flux value φ should be
proportional to the actual value of the diameter d, so the
excitation current iF must be set by a nonlinear inverse
magnetizing curve. Besides, it is useful to correct motor
flux φ by Δφ using the appropriate superior regulator for
maintaining a proportional relationship between
electromotive force e and a line speed value v.
III. CONTROL FUNCTIONS
All control functions associated with roller drive is
carried out with the programmable logic controller, from
PLC family SIMATIC S300 [5]. The basic PLC
configuration is equipped with multiple input/output cards
for processing digital and analog signals and terminals for
setting, adjusting and controlling the parameters, as in this
case, it manages a pair of roller and unroller drive and also
rolling appartment with three presses.
Control algorithm for the roller and unroller drive is
performed by the same functional blocks, shown in the
Figure 6. Functional blocks includes the described field
weakening method in the function of actual value of the
diameter, and whose performance is described below
through the presentation of some selected functions.
Another described method certainly can be done with
minimal changes.
Figure 6. Functional block for control algorithm for roller.
A. Diameter calculator
Figure 7 presents a block diagram of the diameter
calculator which performs its calculation based on the
equation (3) including the line speed and the roller motor
speed. On the same figure functional block diagram of the
implemented algorithm for diameter calculation is given.
The block input values are normalized and can be of
different polarity because rolling drive can change
direction. Any possible glitches in the calculated diameter
value are avoided applying the speed increase limiter,
which also serves to remember the achieved diameter in
the cases of line material breaking or stagnation. Besides,
the calculated diameter value is limited between the
minimum (Dmin) and maximum (1) allowable values.
B. Acceleration torque calculator
Figure 8, shows a acceleration torque computer block
diagram, which is the most important part of the rolling
drive controller because it compensates the changes in the
drive moment of inertia. Based on the normalized
diameter value d, line material width b and an acceleration
value dv/dt, it determine a normalized torque required for
acceleration ma. Torque value ma is derived based on the
following equation:
Ma 
2
J 0  J B  dN
60
dt
(4)
where N is the rotational speed of the roller, J0 is a
moment of inertia of empty cylinder and JB is cylinder
moment of inertia specified by relation:
JB 
D
32
B
4
 Dmin
4

(5)
where are: ρ - the specific mass of the line material, B –
material width and Dmin diameter of the rolling cylinder.
Normalizing the variables from the previous relation
one can get the relation for acceleration torque in the
following form:
d
d

ma  k1  min  k2b d 3  k3 min
d

 d
dv
 dv
  j0  jB   ma
dt
dt
 dv


 dt
(6)
where j0 and jB are the components of the empty cylinder
and winded cylinder at the time of acceleration. Schematic
and functional block diagram in Figure 8 have been
synthesized based on this relation.
Figure 9 shows the typical trend of changes in
components j0 and jB with change in diameter. By default
maximum acceleration torque is obtained at maximum
diameter. Figure 10 gives a characteristic diagram of a
rotor current changes wi with the changes in diameter at
field weakening region (in function of the diameter). In
field weakening method
in the function of the
electromotive force, presented diagram is valid only at the
maximum line speed.
Figure 7. Diameter calculator.
Figure 10. Characteristic diagram of a rotor current changes in function
of the diameter for field weakening method of function of the roller
diameter.
C. Compensation of losses
Figure 8. Acceleration torque calculator
Figure 11. Compensation of losses.
Figure 9. Typical trend of changes in components j0 and jB with
change in diameter.
Figure 11 illustrates a block for losses compensation.
Good approximation of the losses can be done with two
components, one constant and the second linearly
dependent on the rotational speed value. The constant
component must have proper polarity and be equal to zero
at the rest. For a better approximation components
dependent on the higher-order of rotation speed can be
introduced. In field weakening method in the function of
diameter losses compensation are added to the motor
torque, while in the field weakening as a function of
electromotive force they are added to the rotor current
reference.
D. Tension force reference
In the field weakening as the function of actual
diameter tension force reference wf is directly used for
setting the reference values for rotor current wi (Fig. 12).
In other field weakening method which is the function of
electromotive force, required torque for material
tightening mf is calculated by multiplying the tension
force reference value wf with an actual diameter d.
IV. CONCLUSION
Application of PLC devices provides a simple solution
for complex problems such as changing the rolling drive
moment of inertia. Their use offers great opportunities at
the facilities where it is necessary to perform complex
mathematical calculations (the position control in optimal
time interval, speed reference setting based on the
complex algorithms, regulation of minimal tension
moment, regulation and positioning of flying shears). As a
final result in this case mechanical performance in terms
of uniform material tension are improved.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
Figure 12. Generation of reference values for rotor and excitation
current.
[7]
[8]
Arne Buxbaum, Günter Cerny, Egon Nähring, “Die neue Haspelund Wickelerregelung im Bausteinsystem LOGIDYN”, Tech.
Mitt. AEG-TELEFUNKEN, vol. 72, pp. 55–62, 2/3 1982.
K. Senger, “Vollelektronische Haspelregelung”, Tech. Mitt. AEGTELEFUNKEN, vol. 60, pp. 383–386, 6 1970.
Eckart Raatz, “Regelungs- und Steuermgssysteme für Antriebe in
der Grundsofftindustrie”, Tech. Mitt. AEG-TELEFUNKEN, vol.
69, pp. 50–65, 2 1979.
E. Emilius, J. Liedke, “Gleichstromantriebe für die Draht- und
Kabelindustrie”, Siemens Zeitschrift, vol. 52, pp. 372-375, 6 1978.
Arne Buxbaum, Klaus Schierau, Berechung von Regelkreisen der
Antriebstechnik, AEG-TELEFUNKEN Aktiengesellschaft, Berlin
und Frankfurt, 1980.
Jürgen Langhoff, Eckart Raaatz, Geregelte Gleichstromantriebe,
Elitera-Verlag, Berlin, 1977.
P. C. Sen, Thyristor DC drives, John Wiley and sons, New York,
1981.
Hans Berger, Automating with STEP7 in STL and SCL –
Programmable Controllers SIMATIC S7-300/400, MCD Verlag,
Erlangen, 2000.