Elastic web processing lines : optimal tension and velocity closed loop bandwidths
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1 Elasi web proessing lines : opimal ension and veloiy losed loop bandwidhs Dominique KNIEL, Prof Web Handling Researh Group, Universiy of Srasbourg, Frane kniel@unisra.fr 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel
2 Ouline Inroduion & moivaion Roll-o-Roll sysems Modelling Conrol sraegy Influene of he maser roller posiion Referene raking performanes Disurbane rejeion Parameri robusness Influene of he ension and veloiy losed loop bandwidhs Conlusion 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel
3 Inroduion Roll-o-Roll sysems Roll-o-Roll experimenal plan a Universiy of Srasbourg Goal of his plan: o o move he web a he expeed speed o o mainain he web ensions in a small range 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 3
4 Inroduion Problem formulaion Roll-o-Roll sysems usually onain a large number of auaors he ension onrol requires an adequae posiion of he maser roller he maser roller imposes he web speed of he proessing line he oher auaors ensure web ension onrol Problem saemen : Where is he opimal maser roller posiion, in order o respe he sysem requiremens? Wha is he influene of he maser roller posiion on he web ensions in he proessing line? Influene of he ension and veloiy losed loop bandwidhs? 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 4
5 Roll-o-roll sysems Modelling A dediaed sysem model has been developed for his sudy 7 driven rollers, 6 idle rollers having load ells Inpus : u i Conrol signal of he driven roller in Web ension a sysem enrane ou Web speed a sysem exi ou Web ension a sysem exi Oupus : i Web ensions Ω i Driven roller roaional speed 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 5
6 Roll-o-roll sysems Modelling of Roll-o-Roll sysems Web speed of he k h roller (assuming no slippage) : d J k k R k k k Cm C f d ( ) Web srain beween wo onseuive rollers: Lk d d k k k k k Linearizaion of he ension equaion around a working poin v : L k d d k ( ES ) ( k k ) ( k k 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel ) 6
7 Firs ase: Downsream web ension onrol Modelling of Roll-o-Roll sysems Roll-o-roll sysems R u J K R L L E L J R J f J R L E L L E J R J f 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel
8 Seond ase: Upsream web ension onrol Modelling of Roll-o-Roll sysems Roll-o-roll sysems 8 R u J K R J f J R L E L L E L J R J f J R L E L AIMCAL Web Coaing & Handling Conferene Europe D. Kniel
9 Roll-o-roll sysems Conrol sraegy Speed onrol (C v : IP onroller : does no inrodue a zero in he losedloop ransfer funion) ension onrol (C : PI onroller) 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 9
10 Roll-o-roll sysems Conrol sraegy deenralized onrol sraegy wih he maser driven roller in seond posiion 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel
11 Roll-o-roll sysems Conroller synhesis Global sysem subsysem Conroller C is auomaially opimized (in Malab) M : desired losed loop model (gives he ension-loop bandwidh) W p, W u, W : frequeny filers 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel
12 INFLUENCE OF HE MASER ROLLER POSIION
13 Influene of maser roller posiion Referene raking performanes Simulaion wih a web ension referene variaion (sep) : Web ensions lose o he maser roller have beer performanes Performanes derease for web ensions far from he maser roller 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 3
14 Influene of maser roller posiion Referene raking performanes Bode diagram of he hree onfiguraions : Solid lines : dire ransfer funion ref i -> i Dashed lines : oupling ransfer funion ref i -> j 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 4
15 Influene of maser roller posiion Disurbane signal omposed of four sinus Fundamenal : eenriiy Harmonis : non-irulariy Disurbane rejeion his disurbane signal is hen added on several ensions in order o es he disurbane rejeion propery of he hree onfiguraions 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 5
16 Influene of maser roller posiion Disurbane rejeion Disurbane on in Configuraion wih he maser roller in seond posiion is he wors ase he wo oher onfiguraions give beer resuls 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 6
17 Influene of maser roller posiion Disurbane rejeion Disurbane on S5 Web ensions lose o he maser roller have beer performanes 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 7
18 Influene of maser roller posiion Web elasiiy variaions : Parameri robusness Configuraion wih he maser roller in sixh posiion is no robus o web elasiiy variaions Configuraion wih he maser roller in seond posiion is he mos robus o elasiiy variaions he observed resuls are onfirmed by he sysem ransfer funion 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 8
19 Influene of maser roller posiion Summary Maser roller in nd posiion 4h posiion 6h posiion H norm for E H norm for E / 5 8 H norm inrease(%) 8% 7% 37% 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 9
20 Influene of maser roller posiion Summary Summary of he omparison beween he 3 onfiguraions Maser roller in Mean of referene raking error Disurbane rejeion Robusness regarding E ariaions Seond Posiion Fourh Posiion Sixh Posiion AIMCAL Web Coaing & Handling Conferene Europe D. Kniel
21 Influene of he ension and veloiy losed loop bandwidhs
22 Influene of he veloiy losed loop bandwidh ime domain simulaion A lower bandwidh of he speed loop filers he ension referene variaion 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel
23 Influene of he veloiy losed loop bandwidh Frequeny domain omparison Bode diagram of he losed loop sysem Wih lower rossover frequeny of speed loop he maximum singular value is lower 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 3
24 Inermediae roller ension. Inermediae roller ension. Inermediae roller ension. Inermediae roller ension. Inermediae roller ension. Inermediae roller ension. Influene of he ension and veloiy losed loop bandwidhs ime domain omparison Web ension : for losed loop ension bandwidh 5 rad/s and E nom ime (s) ime (s) ime (s) veloiy bandwidh : 5 rad/s 3 rad/s 5 rad/s For E nom / : ime (s) ime (s) 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel ime (s) 4
25 Inermediae roller ension. Inermediae roller ension. Inermediae roller ension. Inermediae roller ension. Influene of he ension and veloiy losed loop bandwidhs ime domain omparison Web ension : for losed loop veloiy bandwidh 3 rad/s and E nom ime (s) ime (s) ension bandwidh : 5 rad/s For E nom / : rad/s ime (s) ime (s) 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 4 3 5
26 Conlusion Maser roller posiion depends on he plan requiremens : Web ensions lose o he maser roller have beer performanes he maser roller should be hosen in he area where he web ensions have o follow he referene wih an higher preision o guaranee a beer robusness o web elasiiy variaions, he maser roller should be loaed lose o he unwinder ension and veloiy losed loop bandwidhs have o be hosen arefully: ension bandwidh < veloiy bandwidh robusness o web elasiiy variaions : redued veloiy bandwidh Appliaion his sudy has been validaed on he nonlinear model of an indusrial roll-o-roll sysem 6 AIMCAL Web Coaing & Handling Conferene Europe D. Kniel 6
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