AN IMPROVED FRICTION SLIDING MODEL FOR WEB HANDLING SYSTEMS. APPLICATION TO THE CONTROLLER PARAMETRIZATION

Copyright (c) 2005 IFAC. All rights reserved 16th Triennial World Congress, Prague, Czech Republic


       
 

 

 

 
   !"##$%  







   
 
 




   
  ! "! #    $
$%
&
'((
(
))

*
+
%  ,! -
$
  

.
! ! /.
*0
 

1
$ 
*
   
 !2  3!"4 # 4 # 

$

$%&
'((
(
+

+



                 

                                              

                                                                                             
             

                       4- 5
6
0
 !                  " #$%&'( %#

  

         
               -!6 
 /88/0               $     

         ,       9    1
     -!6 
 /88/0 &    ,                                  

       2+:   -!6 
 /88/0                      

                        *     
      

)                     *      
           

                                                                    

     

            

                  + ,   -    ./0 1                       234  1
 5    

217

                                 

,   + /                                             9             *    ;             <                = + >      /

(<
2 !
$
!! -        

.3 "    - 73 "  73 0  .3 73  .3 " /73  73 "  -/0 

= 9
-
 !&      73   3         -!6 
 /88/0   7 3  ?3   3 -. 3  . 3 " 0  > 3 , 3   $ -90    3     >3,3       

         $       #     ?3   3                   

+2
# 5%&?2 #4









4
4 !!
@>A

 
<&     ,       -/0          -90       '     ?3D3            73         -90           -!6 
 /88/0 C  - 0  -  0 C  =-  0 , D  C -;0 


    

,    +          ."              *          -   0     @           .  .      7                             

  

D  F . 79 . 8 E   ,

E

F






8
E C
E
F
7*


.*


7


.


7(


.(


7


.


70
E 9 . " ?*      9   /   


."

7"

7/

.9

.;

7<

7;

79




8





 


 


+

+

+

, A

/

A 7
7$


G                    8      8
                                           @                  

,

,


B ." A./

.
$


               

  ,          

                  . - 0 > . - 0 > 8  *    -<0   - 0   8 - 0  8




7
./


B .9A.; /

4
# (1?&'2 #4 (%#$%2

A .8
$


. / &  +            -!6 
 /88/0                   

                 

;

 9
! !
 !& 5           

           

    "0
    :3;
8    .  

        
   8 .       -"0 8      C                  8        /0
    ;
8                       

 

5%&?2 
 %# %.
&1? %#
#& 2 & #4 %. 1? )?G

G -/88/0                

       '                                                               *    

    (              

218

            ->0 -H0  -J0    

  



 .

 A  



!


 . 9            !     

      .@<  .@'<                         .         .8      

-"90

)                -G  /88/0                                5        
        G -/88/0                F@<     "         8            D    F-0  

           

               

    

  '       

           


-=0    @    < !  @    <            ?  ->0  -H0                                     

           ->0

 -H0   I   !        

F@< B F - F@#*<0  K 5
@0    !  .@  <   G @    <    H

-";0      
E
  
E
        .      -  "0   ! 

 <  ! @  <    @  < 

->0

        <   !   -"<0      -J0       F             -G /88/0                                -J0            G  -   
 /88"0
                     E 
                       +   G      -   
 /88"0     

                       -H0      .  .8    -  "0    -     0 -"=0



  . -   0  . - 0  0   - 0    - 0 /

-H0   -    0                 C  2     

   !            - !   0! -J0                                           

 -G  /88/0                             . .  . @ <  .  8 

     -     0 /   -     0   

             *  .  -"/0      .8 -    B 0  . -    B 80                 5

. 9     

 -     0 

-"/0

              




 .@    <  .@  < !@

.@  <  @ .   <    

  

 .  -  A  0

-""0

   

 - 0



.    . - 0   

-"80

            .  .

219

         -"=0                               -!6 
 /88/0 -!  
 /8890
                           

  

            B <88 D9  B "=8 5 B 9 D/    B 8/=    B "88  =

                     

           

            

                            %        

              

    

       

       

 *   
B 8/<  *            *           9,     5D         
 * <

$%G' (%#$%2 ) 1%' 2 & #4


<
$$
$
5
-
3!
4!                <                            . <                                       ;                          <        

   "<8>                   F                  -

. =0 web velocity and velocity reference

4

velocity (m/s)

3 2

without sliding velocity reference with sliding

1 0 -1 14. 9

1.5 1

14.9 5

15

15.0 15. 5 Time(s) 1

15.1 5

web tension before and after the master traction roll 25ith d ith t lidi

0.5 web velocity velocity reference

0 2

4

6

8 10 12 Time (s)

14

16

Tension (N)

velocity (m/s)

   

                                         

   -M  
 "JJJ0 -+ 
 /88/0 .             "&%.  /&%.        1
 2+:     *       -!6 
 /88/0 -N 
 /8890 -!  
 /8890                                   1
   D!D           ;               9,         

       -         F0
 *                           web velocity and velocity reference 2

-0.5 0

'&C %. 2 & #4 %(('$$?#(?

18

web tension before and after the master traction 25

20

without sliding velocity reference with sliding

15 10

Tension (N)

20

10 5 0 0

5 14. 9

Tu Tw w tension reference

15

2

4

6

8 10 Time (s)

12

14

14.9 5

15

15.0 15. Time(s) 5 1

15.1 5

. <             16

18

. ;               

220

    4-0 "

 "                 

8H

+     .8 B . 

4

8= 8; 8/ 8 ";J

";J<

"<

"<8<  -0

"<"

%                    )         C            )                      

"<"<

. =      F     

                              5               ,    -
G0   -+      /8890 - /88/0

&0 !$!
5
$
5
$!
$$!
                     .8
 .
   K        

 " .8

*        - 0   .

G0 I4J!
$
5
-
$!
8
 .                                              

>

(<
!$ !
$

45- 
4 .                    

              .8 -        .     0 . >    *      

  *            

   





     







(%#(2' %#

)                        5                '                P       

             9,                                                                                         *             I     







      -DO0

-
D %0 8888; 888=H 8HH=> =H=>








(!#%)2?&45?#





      .  5  $        I  Q)        * R -?$    8" G 89J<0





. >                  

             % -      .8   0           -*     0    -
D %0  

         

$?.?$?#(? G  
 $ -/88/0 5T   P V P X      T     


L !$M!
!!!
$!45! ;   # 

221

+  +
 + ?  -/88/0 5         

,,

    !
!
!$!
!5  ,5  
F 
1
 J
F
=!!  @*<
7 5
 5!
! PJ
J   !
!
 ! $$3!
!
! 7$3!
!
!
7 5 !  ! 5!3
R(
:$
+
44
(0#( I & & -"JJ"0 &       *  
      -/88/0      ,      +&   2     :
  $ G -/8880      

        N C & !  5  5  -/8890  ,  

,,

       ,    I             IIOS(
1!
[ ! M &  ! 4  -"JJ<0 $    /!
: '   $  # M  
44
+#+((

(  '-"JJ=0 ?

    :
 /5O
5     .       [ 4  5 M 4 1  -"JJJ0
       !
!
! : 5 5
$
;++    "9<,"=J !  & & 4 ? 2 -/88/0 $              !
!
!$! !5  !  & ? 2  & 4 1 !6 -/8890            

  

 1
   .! !
!
! -
44!
9J-"0  ""9,"/8 !6 1 & !  5  5   4
 -/88/0 5            
.! !
! ! - 
.5! - "8-/0  "J>,/8H +     
 M  M! ! M 2\  -/8890 )

    ,    23 ^ 2+:D25  

*     ?  ( (   ?((P89 ( 


++?#& N

. H    9,     5D  

222