New Mathematical Models and Control Strategies for Rotary Printing

New Mathematical Models and Control Strategies

for Rotary Printing Presses and Related Web Handling Systems Günther Brandenburg*

*Technische Universität München, Germany

(Tel:++49 89 289 15195; e-mail:[email protected])

Abstract: Advanced models for the control of rotary printing presses and related plants are presented. The model representing micro slip of the moving web between rollers with stiction and Coulomb friction is extended to macro slip. The mathematical description of color register errors is extended to doubling errors. New types of cutting register errors are defined taking into con-sideration printing and non-printing nips. This leads to a new two-variable-control of web force and cutting register error, which re-duces the amount of paper waste considerably. The results have been experimentally confirmed with a commercial printing press.

1. INTRODUCTION

The most important requirement for the web transport in ro-tary color printing presses is, that four or more colors must be congruently superimposed with high accuracy. Therefore the single drive technology of the printing cylinders was only in-troduced about 15 years ago, c.f. Brandenburg et al. (1999). In comparison, with virtually all other production lines, where printed information need not be considered, the change to the new technology had already been completed in the seventies of the last century. In printing presses the former mechanical line shaft has currently been replaced by the electronic line shaft consisting of electronically synchronized, high dynamic and high accurate speed and angle controlled AC motors with digital control. This new technology provides the opportunity to develop advanced control strategies which in turn lead to a demand of enlarged process models. On the basis of the state of the art before 2000, cf. Branden-burg, Tröndle, Wolfermann et al. (1971-2000), this paper presents a survey on new mathematical models and a new cut-off register control method, which have been developed by the author during the last ten years in the course of a co-operation with one of the most important manufacturers of rotary printing presses in the world. The paper is organized as follows. In Section 2 the well-known dynamic behavior of a moving web with “micro slip” on a roller is extended to the case of “macro slip”. Section 3 discusses doubling errors in printing presses, and in Section 4 the so-called partial cutting register errors are introduced. This leads directly to Section 5, where a new two-variable control of web forces and partial cut-off register errors is explained. Selected papers of other authors on printing presses and various other problems of web handling systems are briefly discussed in Section 6. The author apologizes to the reader that most formula symbols must be found in the Appendix, because of the confined length of the paper. The following definitions are given in advance: For linearization ( , ) ( ) ( , )u x t u x u x t is

introduced, with

( , )u x t variable

( )u x steady state of u

( , )u x t small deviation from steady state u

lim( )t

u u t

new steady state after a transient.

2. WEB DYNAMICS WITH STATIC AND DYNAMIC FRICTION

Fig.1. Roller with micro slip (a) and with macro slip (b) 2.1 Driven rollers with micro slip In many parts of plants with moving webs electrically driven draw rollers are applied in order to control the

area of slip R

area of ad-hesion R

αRβ

αγ

(a)

23F

12F

cv

αγ

23F

12F

cv

area of slip

R R

R

(b)

Preprints of the 18th IFAC World CongressMilano (Italy) August 28 - September 2, 2011

Copyright by theInternational Federation of Automatic Control (IFAC)

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Fig. 2. Three-roller system (a) and block diagrams repre-senting micro slip (b) and macro slip (c); 12 23E E E

tension in the web. As was shown by Brandenburg (1971) and (1976) a roller which is threaded through a web im- presses its circumferential velocity cv to the web in an area

of adhesion at the input (Fig. 1a). If 23 12F F is assumed

in the adjacent down stream free web section an area of slip due to variable strain in the web develops, where the Euler-Eytelwein equation 23 12( ) / ( ) exp ( )F t F t t is valid

and where the web velocity v differs from cv , cv v . For

this type of slip the expression “micro slip” is coined. In the 3-roller-system of Fig. 2a in steady-state the conti-nuity equation yields the well-known relation

3 23 23 23

2 12 12 12

1 1 / 1 /( )

1 1 / 1 /( )c F e

c F e

v E F A E

v E F A E

(1)

if the web material is assumed to be elastic and Hooke´s law can be applied. On the other hand, the equation

3 23 23 23

1 01 01 01

1 1 / 1 /( )

1 1 / 1 /( )c F e

c F e

v E F A E

v E F A E

(2)

also holds for this system. This equation is independent from 2cv . Hence any change of the speed 2cv leads only to

a transient, but not to a sustained deflection of 23 , 23 or

23F . This phenomenon has been observed very often in

web sections with dry paper and is named “self compensation”. The dynamic behavior of the process quantities of Fig. 2a and Fig. 2b can be described through the linearized continuity equation (see Brandenburg and Tröndle, 1975 and Brandenburg et al., 2008)

1,

11, , 1

0

( ) ( )1( , ) ( ) ( )

n nl

cn cnn n E n En

v t v tx t dx t t

v t v

(3) where 1n and n signify subsequent rollers. In transient

condition the strain is assumed to be dependent on the coordinate x (in transport direction of the web) and time t

due to a variable elasticity modulus ,E x t and a variable

cross section ,eA x t , which are travelling with the paper

web through the printing press after a reel change. The so-called transport disturbance in section 1,n n is defined as

1, 1,1,

1,

( , ) ( , )( , ) en n n n

Tn nn ne

A x t E x tz x t

EA

, (4)

and the transport-dependent strain in this section ist

1, 1, 1,( , ) ( , )Tn n n n Tn nx t z x t . (5) Correspondingly the force dependent strain is defined to be

1, 1,1, 1,

1, 1,

( ) ( )( ) n n n n

Fn n Fn nn n e n n

F t F tt

F A E

. (6)

Then the total strain in section 1,n n is

1, 1, 1,( , ) ( ) ( , )n n Fn n Tn nx t t x t . (7)

In steady state the total strain equals the force dependent strain

1,1, 1,

1,

n nn n Fn n

e n n

F

A E

. (8)

From (3) the force-dependent strain 1,Fn n in section

1,n n can be derived to be

11, 2, 1 1, 2, 1 1

1,

1

1cn cn

Fn n Fn n n n n n TEnn n

v vz

T s v

.

(9)


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Fig. 3. Step responses with micro slip. Left: Measurement. Right: Simulation. Web forces (a, b) and partial register errors (c, d) In this equation 1TEnz is the transport disturbance at the in-

put of roller 1n . At the input of a roller n

1 1 1 11

01

n nT s T s eE ETEn TE

e

A Ez e z e

EA

(10)

holds, 1TEz being the transport disturbance at the input of

roller 1 . For the transport of 1TEz to roller n the dead time

11 12 23 1, 1,... ... nn i i n n

lT T T T T

v (11)

is necessary. Furthermore, the expression

1, 2, 11

1cnn n n n

cn

v

v

(12)

is valid. If the rollers 1, 2, ... , n are assumed to be printing units,

the color register error 1nY at the input of roller n is

11 1( ) ( ) ( )nT sn En E

vY s s e s

s

. (13)

It can be shown that, in contrast to (13), the relation

1

1

1

*1 1, 01 1, 01

1, 01

1, 01

1, 01 1

( ) ( ) ( ) ( )

( ) ( )

( )( )

n

n

n

T sn Fn n F n n TEn

n n T s

e n n e

T s cnn n TE

vY s s e s z s

s

F s F se

v A E A E

s v se z s

v

(14) holds for the so-called partial cutting register error between the printing unit 1 and a non-printing roller n (see Section

Fig. 4. Step responses with macro slip ( 6 1k ). Left:

Measurement. Right: Simulation. Web forces (a, b) and partial register errors (c, d)

Fig. 5 Step responses with macro slip ( 6 1k ). Left:

Measurement. Right: Simulation. Web forces (a, b) and partial register errors (bc d) 4). The block diagram of Fig. 2b can be constructed with the help of these equations and represents the present state of the art. By comparing the simulated and the measured step responses of Fig. 3, the correctness of the theory is satisfyingly confirmed – in spite of the high contents of harmonics in the signals which have been measured with a modern printing press with 9 nips ( 56 12 67 23,F F F F ).

2.2 Driven rollers with macro slip If 23 12F F is assumed and 23F is increased and reaches

the value of 23 12/ expF F the region of micro slip on

Fig. 1a has extended to the whole angle of wrap, ,

and the region of adhesion becomes zero, 0 . A further

differential increase of 23F leads to complete slipping

between web and roller, Fig. 1b. For this type of slip the expression “macro slip” is coined. Then the ratio of web forces is constant, according to the Euler-Eytelwein equa-tion

23 232 2

12 12 2

( ) ( ) 1exp[ ( 1)]

( ) ( ) t

F t F tsign const

F t F t k , (15)


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and the roller velocity 2 ( )cv t is without influence. Two

different cases have to be taken into account:

122

23

122

23

1

1 .

Fk the roller drives the web

F

Fk the web drives the roller

F

(16)

As is shown in Brandenburg (2003) the following equations are valid now for the system of Fig. 2a

0112 01 1

23

13 3 123 12 2

( )( ) ( )

( ) 1

1 ( ) ( )( ) ( )

TEe

e G c cTE

F sz s

F s A EA E T s v s v s

z sv

(17)

12 2 23( ) ( )F s k F s , (18)

with

13 2 12 23GT k T T . (19) In contrast to micro slip only one common time constant

13GT is valid for both sections of the web with macro slip.

For the register errors the following equations hold (see Brandenburg, 2003):

12 12* 312 23 23 01 23 01 1

( )( ) (1 ) ( )T s T s c

F F F F TE

v svY s T s e e z

s v

(20)

13 13 3*

13 23 01 23 01 1cT T s

F F F F TE

v svY s e e z

s v

.

(21) With these equations the block diagram of Fig. 2c can be constructed. At the transition point from micro to macro slip the system switches its structure. Göb and Hahn (2009) have extended the Euler-Eytelwein equation and achieve a smooth transition. Evaluating Fig. 4a and Fig. 4b as well as Fig. 5a and Fig. 5b one is surprised that the simulated and the experimental curves, which were measured with a modern printing press, coincide very well. Measured step responses like these indicate significantly that macro slip of a driven roller occurs. If, however, an air cushion is entrained between roller and web these curves will change its shape completely (see, e.g., Ducotey, 1998).

3. DOUBLING BETWEEN PRINTING UNITS

First the principle of operation of a commercial printing-press is explained. The simplified scheme of Fig.10a is

used. The paper web is unwound from the reel 0 (W) and fed to nip 1 via a dancing roller by which the force 01F is

impressed to the web. Nip 1 represents the four printing units, which successively print the colors black, cyan, ma-genta and yellow. The wet web leaving nip 1 is dried in the drier T and cooled in the chilling unit 2 (KE) consisting of several chill rolls threaded by the web. Nip 3 (WE) repre-sents the drawing roller of the turn over device where the paper is longitudinally cut into two or more separate rib-bons of which one or more can be turned through turn bars. Then these ribbons are gathered one above the other to form a package of several layers which are led to a former, where they are folded in length direction. Finally they are cut by a cross cutter, nip 4 (MZ), which consists of a cut-ting cylinder and a cutting blade. In adjoining sections, not depicted in Fig. 10a, the product is finished for dispatch.

Though doubling mainly has occurred in presses with long mechanical line shafts, it is casually also found in modern machines with electronic line shafts. Doubling or “ghost-ing” can occur either within a printing unit or between two printing units. Only the latter is explained here using Fig. 6. The mathematics can be found in Brandenburg (2000).

An offset printing unit consists of a plate cylinder and a blanket cylinder which are coupled mechanically. The im-age on the plate cylinder (PZ) is transferred to blanket cyl-inder (GZ) which prints the image on the paper. In Fig. 6 the points 1a, 1b (say cyan) and 2a (say magenta) represent the same point of the image to be printed.

Point 1a is printed at time aptt 1 and transported with the

running web (Fig. 6a). After half a turn of the rollers, point 1b is transferred from PZ 1 to GZ 1 and half a turn later, at

1p bt t , printed on the paper (Fig. 6b). When 2a is printed

by unit 2 at 2p at t point 1a should have reached the posi-

tion 12x l . But due to disturbances in web strain a differ-

ence between both points may exist. This is the color regis-ter error 12Y (Fig. 6c). When at time 1s at t point 1a

reaches the nip of unit 2, it transfers color to the blanket cylinder by ink splitting. This “ghost point” is transported with GZ 2 and is printed a second time at dtt . At this

point of time point 1b should have reached GZ 2. But a dis-tance 12E , denoted as doubling error (Fig. 6f), may exist

due to disturbances in the web. An important result is: Variations of web strain lead to color register errors and additionally splitting of color causes doubling errors.

The essential linearized model equations, c.f. Brandenburg (2000), are

1212 2 1( ) [ ( ) ( )]T s

E E

vY s s e s

s (22)

and

1212 2 1( ) (1 )[ ( ) ( )]uT s T s

E E

vE s e s e s

s . (23)


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Fig. 6. Color register error 12Y and doubling error 12E between printing unit 1 and 2

The combination of both equations yields

12 12( ) (1 ) ( )uT sE s e Y s (24)

with 2 /UT , being the steady-state angular veloc-

ity of the cylinders. If the strain does not depend on x , the strain Ei at the input of a roller can be replaced by

1,i i which is the strain in the upstream “free web” section.

In Fig. 7 the block diagram is shown. In order to confirm the theory, measurements have been carried out (see Fig. 8)

by applying an aperiodic displacement x to printing unit

2, thus artificially generating a register error 12Y and a

doubling error 12E . A comparison of the measured to the

simulated curves proves the correctness of the theory with surprising accuracy.

Often doubling is induced through periodic signals, i.e. os-cillations of the cylinders. The mathematical model clearly shows that oscillation frequencies of which are whole-

number multiples of the rotational frequency,

/ / 2o u uf kf k T k with 1, 2, ... ,k n , (25)


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Fig. 7. Block diagram of register error 12Y and doubling er-

ror 12E .

cannot lead to periodic doubling errors, because they add to zero, due to the upper dead time block in Fig. 7. But they induce periodic register errors.

4. PARTIAL REGISTER ERRORS

4.1 Statement of the problem

In a printing press the paper web is exposed to numerous periodic and non-periodic disturbances. The paper absorbs water and color in the printing nips and expands. In the dryer the web contracts again, and it will experience further dimensional changes on the rollers of the chilling unit due to cooling. These and other various influences lead to in-creasing and decreasing position changes of the printed im-ages relatively to the position of the blade of the rotating cutting cylinder at the end of the press (nip 4 on Fig. 10a). At this point a significant “total” cutting register error (TCRE) occurs, as the paper adds up the many “partial” cutting register errors (PCRE) during its travel through the printing press.

It would be advantageous, therefore, to control one or even several PCREs before a big TCRE at the cutting cylinder has been built up. Optical sensors can be provided in cer-tain sections of the printing press to detect these errors, e. g. at nip 3 in Fig. 10a. A mathematical model of the PCRE has been derived which has led to a completely new control scheme which considerably reduces the rate of waste paper in heat set commercial presses for illustration printing and for letter press printing (Brandenburg et al., 2004).

(a) Register displacement m of DW 2, (b) strain and force,

(c) simulation of register and doubling error m , (d) meas-

ured register error m , (e) measured doubling error m , (d)

comparison of simulation and measurement.

Fig. 8. Doubling between printing units (DW) 1 and 2 due to displacement of printing unit DW 2.

4.2 Mathematical model

In Fig. 9a-d nip 1 is a printing unit whereas nip 2 and 3 in Fig. 9a-c are assumed to be electrically driven, non-printing drawing rollers. Nip 1 prints point 1a, which may denote the cutting line between two images, at time 1P at t . In steady-state this point passes the position 1Mx l of sensor S1 at time 1B at t and is measured by S1. In transient mo-tion, however, point 1 would not reach this position: A PCRE *

12MY occurs in section 1-2, (Fig. 9b) which can be calculated by an algorithm implemented in the sensor. Af-ter having passed nip 1 the PCRE has changed to be *

13MY at the position 12 2Mx l l and is measured by the sensor S2 at time 1B at kt (with k accounting for the position of sensor S2).

If we assume now that nip 3 in Fig. 9d is a cutting cylinder the TCRE 13Y would occur there at 1C at t .

If not only the singular point 1a is considered, but all suc-cessive points which are printed by nip 1, the PCRE at a position 1,i i iMx l l becomes a continuous function of

time, * *1 1 ( ).M i M iY Y t For details of the mathematics see

Brandenburg et al., (2004 a, b) and (2006). If the sensor is mounted next to a nip k the PCRE can be calculated to be

,*, ,

( )( ) ( ) ( ) k q kT s ck

k q k Ek E k q

v svY s s s e

s v

. (26)


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x

2 3S1 S2

l + l12 2Ml1M l12

t = tC1a

vc1 vc2 vc3

11a

l + l12 23

Y13

x

1 2 3

1a

S1 S2

l + l12 23

l + ll1M l12

*YM13

vc1 vc2 vc3

x

2 3S1 S2

l23

12 2Ml1M l12

l2M

t = tp1a

vc1 vc2 vc3

11a

l + l12 23

l12

l1M

x

2 3S1 S2

l + l12 2Ml1M l12

t = tB1a

vc1 vc2 vc3

1

1a

*YM12

volume

l + l12 23

(a)

(d)

(c)

(b)

t = ktB1a

Fig. 9. Definition of partial and total cutting register error.

The subscript q k denotes the number of the nip which *

,k q kY refers to. The time constant ,k q kT is

,,

k q kk q k

lT

v

. (27)

If the strain does not depend on x , in (26) Ei at the in-

put of a roller can be replaced by 1,i i which is the strain

in the upstream web section. In contrast to the PCRE the TCRE is given through

,

, ,( ) ( ) ( ) k q kT sk q k Ek E k q

vY s s s e

s

. (28)


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The difference between the PCRE *,k q kY

and the TCRE

,k q kY is that the PCRE is related to a sensor at a static posi-

tion, whereas the TCRE is related to the rotating blade of the cutting cylinder. That is why ckv appears in (26).

5. TWO-VARIABLE CONTROL OF WEB FORCES AND CUT-OFF REGISTER ERRORS

5.1 Conditions of the printing press

Equation (26) shows that the PCRE *,k q kY

can be influ-

enced through the circumferential velocity ckv of that

roller where the PCRE is measured. In case of 3k and 1k q , (26) reads as

13* 313 3 1

( )( ) ( ) ( ) T s c

E E

v svY s s s e

s v

. (29)

It may be assumed that the strain in section 0-1 as well as the strain in section 2-3 are solely functions of time t and not of position x , because the actual printing process is virtually completed, and the paper is dry when it has left nip 2. In section 0-1 the unwound paper is also dry. Hence

1 01E and 3 23E is valid, and with (14) the equation

13

13

13

* 313 23 01 23 01 3

23 01

23 01

323 01 1

T s cF F F F TE

T s

e e

T s cF F TE

vvY e z

s v

F Fe

v A E A E

s ve z

v

(30)

is obtained. Equ. (11) yields the expression

12

3 223 12 23 12 2

23

3 212 23 12 1

23

1( )

1

1( )

1

c cF F F m TE

T sc cF F m TE

v vz

T s v

v ve z

T s v

.

(31)

Due to the influence of humidity and, above all, of the high temperature in the dryer the steady-state strain 12 is de-

pendent on the position, i.e. 12 12 ( )x . Therefore, the

mean value 12 12m F has been introduced in (31).

Furthermore, the temperature- and humidity-dependent dy-namic part 12 ( , )x t is assumed to be very slow compared

to the force dependent strain 12 ( )F t and hence is neg-

lected.

The aim is to control independently the PCRE *13Y and the

force 23 23 23 23e FF A E . Mean values 23eA of cross section

and 23E of Young’s modulus are assumed. The equations

(30) and (31) clearly show that the variables *13Y and 23F

are coupled to each other because 3cv appears in (31) and

23 2( )F cf v appears in (30). In order to achieve a stable

system, a non-interacting two-variable control has to be de-signed. Two manipulated variables are required. It has been shown in Brandenburg et al. (2006), that 3cv and 2cv are

appropriate, the latter by reason of the fact, that self com-pensation of 23F is virtually prevented because of plastic

deformation of the hot paper in web span 1-2. Furthermore it has been shown that the influence of 12F is allowed to

be cut off for control design purpose, as is indicated in the block diagram of Fig. 10b. This simplifies the design of the control. 5.2 Design of the two-variable control

Two controllers together with decoupling networks can be found, by applying Föllinger (1985), in such a way, that

two uncoupled closed control loops for 23F and *13Y result

which can be separately optimized. The calculated decoup-ling transfer functions (see Brandenburg et. al., 2004 a, b and 2006), can be simplified in such a way that the cross coupling, which is inherent to the mechanical system to be controlled, is compensated for through the correspondent cross structure - with opposite signs - on the controller side. In Fig. 10c the resultant control loops are depicted, with the decoupling elements on the mechanical level of the system. However, these elements can only be realized on the elec-tronic level of the drives controls (Fig. 10d). In doing so the dynamic performance of the actuators, i.e. the speed and angle controlled AC motors with subordinate current controls, has to be taken into account. The closed-loop speed control of drive i can be approximately written as

1

1i

e iiw e i

GT s

. (32)

Experiments have shown that the open mechanic integrator

231/( )T s of Fig. 10c, which has to be emulated in the drive

electronics, causes instability of the system, because this in-tegrator can never be tuned with sufficient accuracy. Slowly increasing errors would arise which drive the sys-tem into instability. Replacing this integrator through a first-order time lag guarantees stability:

23 23

1 1

1T s T s

. (33)


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DE four printing units KE chilling unit MZ cutting cylinder T dryer W unwinder WE draw roller of turner bars

Fig. 10. Rotary offset printing press with decoupled control of web force 23 23FF and cutting register errors *13Y and 14Y

5.3 Experimental results The new control scheme could be implemented and tested with a commercial offset press of type ROTOMAN pro-duced by manroland, Augsburg (Germany). MATLAB/ SIMULINK proved to be an efficient tool to simulate the press as a system of eight nips similar to Fig. 10. The chill-ing unit (nip 2) was modeled as a dead time element, be-cause the areas of adhesion by far exceed the areas of slip on the rollers (c.f. Brandenburg , 1971). According to the measured frequency responses the belt driven roller masses of the chilling unit (nip 2) and of the turner bar unit (nip 3) together with the appertaining motors can be modeled as

elastic two-mass systems. In both cases the closed-loop current controls were approximated through a first-order lag analog to (32), and the speed control loops were opti-mized without consideration of the influence of the web forces acting as load torques on the motors (c.f. Kessler et al., 1984). The speeds of the other nips were assumed to be ideally impressed. The control was implemented on the real time rapid prototyping system SIMULINK/xPC Target. For the data transfer between sensors and actors RS232 inter-faces and CAN buses with a cycle time of 3.2 ms were used.


8628

Fig. 11. Reference step response of tensile force 23F (a)

Fig. 12. Reference step response of the partial cutting register *

13Y (b)

Fig. 13 Reel change on the run: Tensile forces (a) and partial cutting register errors (b) without control

Fig. 14. Reel change on the run: Tensile forces (a) and par-tial cutting register errors (b) with non-interacting control

Reference Step Responses The measured reference value step response of the tensile

force 23F in Fig. 11a shows that the influence of 2cv on

12F is very small. This performance justifies the assump-

tion of constant strain 12F in paragraph 5.1. The deflection

of the controlled PCRE *13Y (Fig. 11b) is negligible which

underlines the perfect functioning of the decoupling net-

works. The reference value step response of the *13Y in Fig.

12b is nearly without influence on the controlled tensile

force 23F (Fig. 12a).

Disturbance Responses When an automatic reel change occurs in the uncontrolled

system, the tensile forces 12F and 23F as well as the PCREs

*12Y and *

13Y experience high deviations as Fig. 13 shows.

The tolerance band of 0.4 mm is clearly and permanently

exceeded. With the new non-interacting control shown in

Fig.14a the controlled force 23F is driven back to its old

reference value and the controlled PCRE *13Y exceeds the

tolerance band only during 2.8 s (Fig. 14b). This corre-sponds to 20 copies of waste paper at the speed of

14.31 25000 /v ms ex h . This is a considerable im-

provement compared to the former state of the art of cutting register controls. 5.4 Extensions of the Controls

If *13Y is controlled only, it may happen that the steady-state

TCRE 14Y assumes higher values than in case of the uncon-

trolled plant. It is essential, therefore, to directly measure the TCRE of the outer paper ribbon of the complete multi-


8629

layer package as close as possible to the cutting cylinder.

Then a closed loop control for 14Y is superimposed to the

control of *13Y (see Fig. 10e). By this method the best result

in reduced waste paper is achieved. Additionally the

PCREs *,k q kY

of the other ribbons of the package should be

separately controlled. Various controls of this kind have been successfully investigated in experiments (see also, e.g., Güth et. al., 2003). Furthermore, instead of the chilling unit (nip 2 in Fig. 10a) the four printing units together (nip 1) can serve as manipu-lated variable. A decoupling is possible also in this case, as has been shown by simulations and experiments. The functioning of the non-interacting control has been demonstrated at the rated machine speed of

10.3 / 60000 /v m s ex h . 6. DISCUSSION OF SELECTED PUBLICATIONS ON MISCELLANEOUS PROBLEMS OF WEB HANDLING SYSTEMS Galle (2007) and Schnabel (2007 and 2009) have presented important contributions on the decoupling of controls in successive web spans of rotogravure presses. Schnabel in-tegrates visco-elastic web properties into a non-linear model for start-up processes of a press, using the results of Tröndle (1973), who was the first in this area and who in-troduced also the continuity equation of continuum me-chanics into the theory of moving webs. Göb and Hahn (2010) continue similar investigations. A new system of cutting register control for newspaper printing presses has been described by Güth et. al. (2003). The brightness distribution of an image passing a sensor is compared to the reference brightness distribution in steady state, which is calculated from the pre-press stage. The dif-ference controls a register roller. Very often plants with moving webs suffer from periodical disturbances, e.g. due to unwinders running out of true. Höger and Liepert (2003) have developed a learning device to compensate for periodical disturbances with constant frequencies, whereas Wolfermann (2003) suggests Artifi-cial Neuronal Networks which are adaptive to unknown and variable frequencies. Nearly every web handling system needs pivoting rollers in order to correct the lateral position of the web. Branden-burg (2010 and 2011) has derived a simplified mathemati-cal model which describes the lateral dynamics of webs, which can be approximated by a “harp” of threads. An important publication on printing press technology must not be forgotten in this context, namely Glöckner (1998). In his dissertation he recorded his experience gained by life-long experimental investigations of printing presses.

Decoupling is an important issue with various other types of web handling plants where high dynamic tension con-trols are necessary. Knittel (see Knittel et al., 2007 and 2010) devotes his research activities to the application of robust design with H strategies to tension controls of sys-tems with moving webs on a high level of modern control theory. Wolfermann (1995) has developed decentralized control methods, where a large-scale system is divided into several smaller subsystems, which can be separately optimized. State controllers with Luenberger observers are applied. These methods have been successfully implemented in a coater in order to reduce paper breaks and to improve the product quality (Mair and Hackl, 2007). Oedl (2005) re-ports a significantly improved performance in thin film production lines by using these successive decentralized controls in combination with direct drive technology. In his dissertation Patri (2003) summarized the most important research results of the “Munich School of Web Handling” and developed Model Reference Adaptive Control (MRAC) methods, thus making an important step into the direction of self optimization of large scale web systems. SUMMARY In rotary color printing presses four or more colors must be congruently superimposed with high accuracy. The single drive technology with speed and angle controlled AC motors of the printing and cutting cylinders and also of the drawing rollers, has offered the possibility of advanced control strate-gies for web forces and for the cutting register, which re-quired new mathematical models. A survey of these subjects is given, based on investigations during the last ten years, which have led to an improved performance of standard ro-tary printing presses for illustration and letterpress printing. Furthermore, a short discussion of a number of selected pa-pers referring to other problems with moving webs lead to be-lieve that digital control will introduce more electronic intel-ligence into these large scale systems in the future. In the area of printing presses this depends, to which extent electroni-cally supplied information will replace printed information. The author would like to express his appreciation to the re-sponsible persons of manroland, Augsburg (Germany), who provided him with the unique opportunity of fundamental investigations with industrial rotary printing presses. He is also much obliged to Dr. A. Klemm and Dipl.-Ing. S. Geißenberger, his temporary co-authors, for carrying out measurements and simulations as well as for fruitful dis-cussions and a successful co-operation during many years.


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REFERENCES Brandenburg, G.(1971) Über das Verhalten durchlaufender

elastischer Stoffbahnen bei Kraftübertragung durch Coulomb'sche Reibung in einem System angetriebe-ner, umschlungener Walzen. Dr.-Ing.-Dissertation. TH München 1971.

Brandenburg, G. and H.-P. Tröndle (1975). Das Verhalten durchlaufender elastischer Stoffbahnen bei ortsabhän-giger Verteilung von Elastizitätsmodul, Querschnitt und Dichte. Siemens Forschungs- und Entwicklungs-berichte, Jg. 4 no. 6, pp. 359-367.

Brandenburg, G. (1976a). New mathematical models for web tension and register error. Proc. 3. Int. IFAC Conf. on Instrumentation and Automation in the Pa-per, Rubber and Plastics Industries. PRP 3, Brussels 1976, pp. 411-438.

Brandenburg, G. (1976b). Verallgemeinertes Prozessmo-dell für Fertigungsanlagen mit durchlaufenden Bahnen und Anwendung auf Antrieb und Registerregelung bei Rotationsdruckmaschinen. Fortschrittberichte der VDI Zeitschriften, Reihe 1, Nr. 46. Düsseldorf, VDI-Verlag 1976.

Brandenburg, G., S. Geißenberger et al. (1999). Multi-motor electronic line shafts for rotary offset printing presses - a revolution in printing machine techniques. IEEE/ASME Transactions on Mechatronics, Vol. 4, no. 1, pp. 25-31.

Brandenburg, G. (2000). Dynamisches Verhalten von Dub-lier- und Registerfehlern bei Rollenoffset-Druckma-schinen. In: Tagungsband SPS/IPC/DRIVES, Nürn-berg 2000, pp. 698-715, Hüthig-Verlag, Heidelberg.

Brandenburg, G., S. Geißenberger and A. Klemm (2002). Einfluss von Transport- und Leitwalzen mit Gleit-schlupf auf die Bahndynamik von kontinuierlichen Fertigungsanlagen der Metall, Kunststoff-, Papier- und Druckindustrie. In: Tagungsband SPS/IPC/ DRIVES, Nürnberg 2002, pp. 679-690, Hüthig-Verlag, Heidel-berg.

Brandenburg, G., S. Geißenberger and A. Klemm (2003). Einfluss von Klemmstellen mit Gleitschlupf auf Zug-kräfte und Registerfehler von durchlaufenden Bahnen in kontinuierlichen Fertigungsanlagen. In: Tagungs-band VVD 2003, Fachtagung Verarbeitungsmaschi-nen und Verpackungstechnik 2003, pp. 391-411, Technische Universität Dresden.

Brandenburg, G., S. Geißenberger and A. Klemm (2004a). Entkoppelte Regelung von Bahnzugkraft und Schnitt-registerfehlern bei Rollendruckmaschinen mit elektro-nischer Welle. In: VDI/VDE Tagung Elektrisch-mechanische Antriebssysteme, pp. 273-285 Fulda 2004.

Brandenburg, G., S. Geißenberger and A. Klemm (2004b). Schnelle Schnittregister- und Bahnzugkraftregelung für Rollendruckmaschinen. Tagungsband SPS/IPC/ DRIVES, Nürnberg 2004, pp. 435-447

Brandenburg, G., S. Geißenberger and A. Klemm (2006). Non-interacting control of web forces and cut-off reg-ister errors in rotary printing presses with electronic line shafts. EPE Journal, Vol. 16, no 2, pp. 38-55.

Brandenburg, G., A. Klemm and J. Seebauer (2008): Onli-

ne-Rekonstruktion von Elastizitätsmodul-Änderungen der Papierbahn in Rollendruckmaschinen. In: Ta-gungsband SPS/IPC/ DRIVES, Nürnberg 2008, pp. 461-473. VDE-Verlag, Berlin, Offenbach

Brandenburg, G. (2010). Vereinfachtes Prozessmodell für das Seitenkantenverhalten durchlaufender, elastischer Bahnen. In: Tagungsband SPS/IPC/ DRIVES 2010, Nürnberg 2010, pp. 95-110

Brandenburg, G. (2011). Lateralverhalten elastischer Bah-nen vereinfacht modelliert. To appear in: atp Automa-tisierungstechnische Praxis 2011, Heft 4 (Teil 1) und Heft 5 (Teil 2)

Ducotey, K. S. and J. K. Good (1998). The effect of web permeability and side leakage on the air film height between a roller and web. Journal of Tribology,Vol. 20, pp. 559-565.

Föllinger, O. (1985). Regelungstechnik. Hüthig-Verlag Heidelberg.

Galle, A. (2007). Regelungstechnische Untersuchung der Bedruckstoffförderung in Rollendruckmaschinen. Dr.-Ing. Dissertation TU Chemnitz. http://archiv. tu-chemnitz.de/pub/007/0159.

Glöckner, E. (1998). Untersuchungen zum Papierverhalten in Zeitungsdruckmaschinen zur Qualitätssteigerung bei Mehrbahnbetrieb und für Bahnspannungsregelung. Dr.-Ing.-Dissertation, TU Chemnitz 1998.

Göb, M. and I. Hahn (2009). Simulation des Bahnspan-nungsverhaltens in bahnverarbeitenden Maschinen un-ter Berücksichtigung von Klemmstellen mit Dehn- und Gleitschlupf. In: Tagungsband SPS/IPC/ DRIVES, Nürnberg 2009, pp. 359-367, VDE-Verlag, Berlin, Of-fenbach .

Göb, M. and I. Hahn (2010). Identifikation des Material-verhaltens in kontinuierlichen Fertigungsanlagen. In: Tagungsband SPS/IPC/ DRIVES, Nürnberg 2010, pp. 75-83, VDE-Verlag, Berlin, Offenbach.

Güth, R., J. C. Mengiesen and C. Munz (2003). Bildba-sierte Schnittlageregelung in der WIFAG evolution 471 und 371. Evolution, WIFAG Informationsbulletin no. 36, pp. 4-13, Bern (CH).

Höger, W. and K. Liepert (2003). Kompensation periodi-scher Störungen bei Antriebssystemen mit schwin-gungsfähiger Mechanik. In: Tagungsband SPS/IPC/ DRIVES 2003, Nürnberg 2003, pp. 767-777, VDE-Verlag, Berlin, Offenbach.

Kessler, G., G. Brandenburg, W. Schlosser and W. Wol-fermann (1984). Struktur und Regelung bei Systemen mit durchlaufenden elastischen Bahnen und Mehrmo-toren-Antrieben. Regelungstechnik (32) H. 8, pp. 251-266.

Knittel D., D. Henrion, M. Millstone and M. Vedrines (2007). Fixed-order and structure H control with model based feed-forward for elastic web winding systems (invited session). IFAC Conference in Large Scale Systems (LSS), Poland.

Knittel D., J. Frechard and M. Vedrines (2010). Multi-objective optimization for manufacturing process de-sign: application in roll-to-roll systems. Third Interna-


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Mair, B. and Ch. Hackl (2007). Optimierung der Bahn-spannungsregelung durch dezentrale Regelsysteme auf der Basis von moderner Mikroelektronik und intelli-genter Software zur Steigerung der Produktionssicher-heit und Produktivität von Papierstreichanlagen. www.pts-paper.de/forschung.html.

Oedl. G. Tension control at thin film production lines (2005). In: Proc. of the 8. Int. Conf. on Web Handling IWEB05, pp. 239-253. Oklahoma. USA.

Patri, T. (2003). Regelung von kontinuierlichen Fertigungs-anlagen. Fortschritt-Berichte VDI Reihe 8 Nr. 1009. VDI-Verlag, Düsseldorf.

Schnabel, H. (2007). Neue Techniken zur Registerregelung in wellenlosen Tiefdruckmaschinen. In: Tagungsband SPS/IPC/ DRIVES 2007, Nürnberg 2007, pp. 607-615, VDE-Verlag, Berlin, Offenbach.

Schnabel, H. (2009). Entwicklung von Methoden zur Re-gisterregelung in Abhängigkeit der Bahnzugkraft bei Rollen-Tiefdruckmaschinen. Dr.-Ing. Dissertation TU Darmstadt. Sierke-Verlag, Göttingen 2009.

Tröndle, H.P. (1973). Zum dynamischen Verhalten trans-portierter elastischer und visko-elastischer Stoffbah-nen zwischen aufeinanderfolgenden Klemmstellen. Dr.-Ing. Dissertation. TU München 1973.

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APPENDIX (NOMENCLATURE)

eA cross section of the web

1, ( , )en nA x t cross section dependent on position x

and time t in section 1,n n

eA steady-state value of eA , assumed as con-

stant along the whole web length

eEnA cross section eA at the input of nip n

E elasticity modulus or doubling error

1, ( , )n nE x t elasticity modulus dependent on position

x and time t in section 1,n n

1,n nE steady-state value of 1, ( , )n nE x t , not con-

stant along the whole web length

EnE elasticity modulus at the input of nip n

12E doubling error between printing units 1

and 2, see equations (23), (24) and Fig. 7

1,n nF web force in section 1,n n

o uf kf whole number multiple of uf ,

1, 2, ...,k n

uf revolution frequency of a roller

e iG transfer function

nk force transmission ratio

1nl free web length between nip 1 and n

1,n nl free web length between nip 1n and

n PCRE partial cutting register error s Laplace operator t time TCRE total cutting register error

e iT equivalent time constant of closed loop

speed control of drive i

13GT time constant between nip 1and 3 with

macro slip of nip 2

1,n nT time constant between nip 1n and n

1,nT time constant between nip 1 and n

uT revolution time of a roller

v mean value of web transport velocity

cnv circumference velocity of nip n

x position

1nY color register or cutting register error be-

tween printing nips 1 and n *

1nY partial cutting register error between nips

1 and n TEnz transport disturbance at the input of nip

n angle of the thread angle of the area of adhesion

1,n n angle of the area of micro slip

En strain at input of nip n

1,n n total strain in section 1,n n

1,Fn n force dependent strain in section

1,n n

1, 1,n n Fn n steady-state strain in section 1,n n

1,Tn n transport dependent strain in section

1,n n

1,n n stress in web section 1,n n

angular velocity i actual value of angular velocity (speed) of

drive i

iw reference value of angular velocity

(speed) i


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New Mathematical Models and Control Strategies for Rotary Printing

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