Wankun Zhou and Zhiqiang Gao Department of Electrical and Computer Engineering Cleveland State University, Cleveland, Ohio, USA

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1 6h IEEE Inernaional Conferene on Conrol Appliaions Par of IEEE Muli-onferene on Sysems and Conrol Singapore, -3 Oober 7 An Aive Disurbane Rejeion Approah o ension and Veloiy Regulaions in Web Proessing Lines Wankun Zhou and Zhiqiang Gao Deparmen of Elerial and Compuer Engineering Cleveland Sae Universiy, Cleveland, Ohio, USA uc. Absra In his paper, a unique disurbane rejeion onrol sraegy is proposed for a lass of ension and veloiy regulaion problems found in web proess lines. he proposed onrol sysem aively esimaes and rejes he effes of boh dynami hanges in he sysem and exernal disurbanes. Boh open-loop and losed-loop ension regulaion shemes are invesigaed. A ension observer is designed in order o failiae losed loop ension onrol in he absene of a ension ransduer. he performane of exising shemes and he proposed ones are ompared and he resuls show marked improvemens in raking and disurbane rejeion by he proposed soluions. Index erms-web ension Regulaion, ension Observer, Aumulaor, Web Span, Aive Disurbane Rejeion Conrol. I. INRODUCION eb ension regulaion is a raher ineresing and W hallenging indusrial onrol problem. Many ypes of maerial, suh as paper, plasi film, loh fabris, and even srip seel are manufaured or proessed in a web form. he qualiy of he end produ is ofen grealy affeed by he web ension, making i a ruial variable for feedbak onrol design, ogeher wih he veloiies a he various sages in he manufauring proess. he ever-inreasing demands on he qualiy and effiieny in indusry moivae researhers and engineers alike o explore beer mehods for ension and veloiy onrol. However, he highly nonlinear naure of he web handling proess and hanges in operaing ondiions (emperaure, humidiy, mahine wear, and variaions in raw maerials) make he onrol problem boh hallenging and simulaing. Aumulaors in web proessing lines are imporan elemens in web handling mahines as hey are primarily responsible for oninuous operaion of web proessing lines []. For his reason, he sudy and onrol of aumulaor dynamis is an imporan lass of problems [, 3], and is, herefore, he fous of his paper. A preliminary sudy on he modeling of aumulaors and he haraerisis of an aumulaor and is operaion are explained and given in [3]. Dynami behavior and onrol of he aumulaor arriage, web spans, and ension are disussed in []. Boh open-loop and losed-loop mehods are ommonly used in web proessing indusries for ension onrol purposes [4-8]. In he open-loop onrol ase, he ension in a web span is onrolled indirely by regulaing he veloiies of he rollers a eiher end of he web span. An inheren drawbak of his mehod is is dependeny on an aurae mahemaial desripion of he web ension as a funion of veloiies, where suh funion is generally highly nonlinear and highly sensiive o veloiy variaions. Sill, simpliiy of he onroller seems o ouweigh his drawbak in some appliaions. Closing he ension loop wih ension feedbak is a sraighforward soluion o improve auray and redue sensiiviy o modeling errors. I requires ension measuremen, for example, hrough a load ell, and he os and hardware omplexiy may be jusified by he resuling improvemens in ension regulaion. Some researhers [7, 8] have proposed o use observers in plae of ension measuremens, whih ould redue he hardware omplexiy and os. he rade-off is he inreased omplexiy in he onrol algorihm and is uning. In addiion, he disrepanies beween he esimaed and he aual ension will likely ause performane degradaion. he design of he observer also requires a fairly aurae mahemaial model of he ension dynamis, whih may no be available. Wih hese onsideraions in mind, i is no surprising o see ha mos of oday s ension feedbak loops employ ension measuremen. Conrol sysems will unavoidably enouner unerainies and his is pariularly rue for ension onrol appliaions, where operaing ondiions hange grealy. I is herefore paramoun ha he ension regulaion sheme mus be able o deal wih unexpeed variaions in boh inernal dynamis and exernal disurbanes. his led us o invesigae he use of disurbane rejeion ehniques. One lass of disurbane rejeion mehods is based on he onep of disurbane observer (DOB). Many forms of DOB have been proposed for various disurbane appliaions [9-3], bu he basi idea is o reje exernal disurbane under he assumpion ha he inernal dynamis is linear and ime invarian, and, for he mos par, given in a mahemaial model. he objeive of he researh desribed in his paper is o find a soluion for he web ension and veloiy regulaion ha an deal effeively wih he nonlinear, ime-varying, naure in mos appliaions. Equally imporan is suh soluion should no be dependen on he aurae plan model ha mos advaned onrol design assumes, for suh /7/$. 7 IEEE. 84

2 uc. assumpion simply does no hold in mos real world appliaions. One suh andidae is he Aive Disurbane Rejeion Conrol (ADRC), whih requires very lile informaion of he plan dynamis, is very easy o une, and has very good disurbane rejeion apabiliy [4-7]. ADRC onrollers are inherenly robus agains plan variaions and are effeive in a large range of operaions [8]. Iniial work in he appliaion of ADRC o web ension regulaion was evaluaed on a linear ransfer funion model of he ension loop [4]. Good performane was observed bu he onroller uses many nonlinear gain funions and is diffiuly o une, a problem resolved by he parameerizaion ehnique desribed in [6]. In his paper, he ADRC design mehodology is applied o a ruly nonlinear model of he ension dynamis, whih is used as he benhmark for omparison wih oher mehods. he remainder of he paper is organized as follows. he dynamis of he aumulaor arriage and he problem formulaion are disussed in Seion II. Proposed onroller design and observer design are given in Seion III. Simulaion resuls and he omparisons of four differen onrol shemes an be found in Seion IV. Finally, onluding remarks are inluded in Seion V II. PROBEM FORMULAION he mahemaial model of a web proess line and he exising onrol mehods are briefly reviewed in his seion. he aumulaor dynamis, as given in [3], is used as he es bed for he proposed mehod. A web proessing line layou inludes an enry seion, a proess seion and an exi seion. Operaions suh as wash and quenh on he web are performed in he proess seion. he enry and exi seion are responsible for web unwinding and rewinding operaions wih he help of aumulaors loaed in eah seions. A. Sysem Dynamis he dynamis of he arriage ension and he enry/exi rollers in aumulaor is shown as [3]: AE () = ( v () + ( v () v ()) () e p x () N x () = v () () (3) M v () = N () F () + u () M g d v e() = ( Bfve() + R ( r + δe() ()) + RKeue()) (4) v p() = ( B fvp() + R ( () r δ p()) + RK pu p()) (5) where v (),v e () and v p () are he arriage veloiy, exi-side and proess-side web veloiy, respeively. M is he mass of he arriage, x () is he arriage posiion, r is he desired web ension in he proess line and () is he average web ension. u (), u e () and u p () are he arriage, exi-side and proess-side driven roller onrol inpus, respeively. he disurbane fore, F d (), inludes friion in he arriage guides, rod seals and oher exernal fore on he arriage. K e and K p are posiive gains. δ e () and δ p () are he ension disurbanes on he exi side and proess line. he onsan oeffiiens in () o (5) are desribed in he Appendix. B. Design Objeives he ask a hand is o deermine a onrol law suh ha v (),v e () and v p (), whih are measured, as well as (), whih may or may no measured, all losely follow heir desired rajeories or values respeively. I is well known in web ransporing sysem ha disurbanes an propagae hrough he whole sysem. So he hallenge is o find a onroller ha has an inheren disurbane rejeion propery whih enables i o bring all four variables above o heir desired values onsisenly. he problem is hallenging beause: a) here is a srong oupling beween he arriage dynamis, srip ension dynamis and he roller dynamis. b) he ension dynamis are highly nonlinear and sensiive o veloiy variaions. ) he oeffiiens in () o (5) are highly dependen on he operaing ondiions and web maerial haraerisis, any hanges of whih may indue signifian variaions in sysem dynamis. d) here are exensive exernal disurbanes, whih propagae hrough he sysem whih ould make he sysem even unsable in some ases. C. Moivaion Sine he veloiies are onrolled in open-loop by feed forward and lassial PI onrol mehod, he indusrial onroller (IC) needs o reune when he operaing ondiions are hanged and exernal disurbane appears. In addiion, IC has a poor performane in he presene of disurbane. he Lyapunov based onroller () improves upon he indusrial onroller by adding auxiliary error feedbak erms o ge beer performane and disurbane rejeion. However, i is designed speifially o deal wih disurbanes, whih are inrodued in he model. And when unerainies appear in real appliaion, i may require re-design of he onroller []. Boh he IC and soluion are given in [] and hey are used as he basis for omparison in his paper. he imperaive in web proess regulaion is o find a soluion ha is ) no overly dependen on plan model; ) effeive in dealing wih unknown, nonlinear, and ime varying dynamis and exernal disurbanes; and 3) easy o undersand and deploy for he field engineers. Afer areful evaluaion of he haraerisis of he problem, we believe ADRC offers suh a soluion as i represens a ompleely differen design paradigm, where he inernal dynamis and exernal disurbanes are esimaed, no modeled, and ompensaed for in real ime. herefore, suh design is likely o be inherenly robus agains unerainies in he real world appliaions. 843

3 uc. In ension regulaion, we will explore boh open-loop and losed-loop opions. In he open-loop ase, he ension is no measured and is indirely onrolled aording o () by manipulaing he veloiy variables; in he losed-loop ase, a ension observer will be designed and used in he ension feedbak onrol. III. HE PROPOSED APPROACH In developing new soluions for his diffiul indusry problem, performane and simpliiy are sressed. ha is, he new onroller mus have a muh beer performane han he exising ones, and i should also be simple o design, implemen, and une. A key observaion in his researh is ha here are wo onrol problems o onsider: veloiy and ension. he hree veloiy loops are very similar in naure and finding a beer soluion would be a good firs sep. he ension problem is ruial beause of is imporane and is nonlinear dynamis. Based on he os and performane onsideraions, wo soluions will be explored: ) if he ension model in () is reliable, i an be well onrolled wih fas and aurae veloiy loops; ) indusry users are quie willing o insall ension sensors for dire ension feedbak onrol in reurn for beer ension performane. he veloiy onrol problem below will be addressed firs, followed by he soluions o he ension problem. A. A New Soluion o Veloiy Regulaion Veloiy regulaion in a proess line is one of he mos ommon onrol problems in he manufauring indusry. Sine mos proesses are well-behaved, a PID onroller is usually suffiien. he PID onroller is ypially uned by an experiened engineer. Oher ehniques, suh as pole-plaemen and loop shaping, ould poenially improve he performane over PID bu require mahemaial models of he proess. hey are also more diffiul o une one hey are implemened. By reformulaing he problem as ha of aive disurbane rejeion, an alernaive o PID and model based onrollers suh as, is desribed below. Noie ha he veloiy equaions (3)-(5) an be rewrien as v () = f () + bu () (6) v e() = fe() + bu e e() (7) v p() = fp() + bpup() (8) where f() = ( N() Fd() Mg) M f () = ( Bv() + ( ())) e f e R r f () = ( Bv () + ( () )) p f p R r b = [ b be bp] = [/ M RKe / RKp / ] (9) he plans in (6)-(8) are all of he form v () = f() + bu () () where v() is he veloiy o be onrolled, u() is he onrol signal, and he value of b is known, approximaely. f() represens he ombined effes of inernal dynamis and exernal disurbane. he key o he onrol design is o ompensae for f(), and he job will be muh simpler if is value an be deermined a any given ime. o his end, an exended sae observer [4-7] is employed. Wriing he plan in () in a sae spae form x = x + bu x = h () y = x Le x = v, x = f, where x is he augmened sae variable, and h = f. he sae spae of () is rewrien as x = Ax + Bu + Eh () y = Cx b where A=, B, C [ ], E = = = Now f an be esimaed using a sae observer based on he sae spae model (). A sae observer, referred o as linear exended sae observer (LESO), an be onsrued as o esimae boh x = v and x = f: z = Az+ Bu+ L( y yˆ ) (3) yˆ = Cz where L=[L L ] is he observer gain veor. By seing λ ( s) = si ( A LC) = ( s + ω o ) (4) ha is L =ω o, L =ω o, he observer an be easily uned wih a single uning parameer, ω o, making i araive as a praial soluion. Wih a funioning LESO, whih resuls in z v and z f, he onrol law will be as u = z + u b (5) ( ) ( ) / hus reduing he plan o v = f z + u u (6) A his poin, an unknown, nonlinear, and ime varying plan of () is redued o a linear one wih a pole a he origin. he onrol design is now sandardized o ha of a simply inegral plan, whih, for example, an be easily onrolled using a proporional erm u = k ( ) p r z (7) Seing k p = ω yields a losed-loop ransfer funion of ω Gl () s = (8) s + ω where ω is he desired losed-loop bandwidh and i an be used as he only uning parameer for he onroller. 844

4 uc. Remarks. Solving (3), (4) and (6) for z, he ransfer funion expression of z an be shown as ω o (9) z = ( sv( s) bu( s)) ( ) s + ω o. Subsiuing (5) ino (3), he onroller is simplified as z = L( y z) + kp ( r z) () u = ( kp ( r z ) L ( y z )) b 3. he unknown exernal disurbane and he inernal unerain dynamis are ombined reaed as a generalized disurbane. By augmening he observer an exra sae, whih an be aively esimaed and aneled ou he disurbane, hereby ahieving aive disurbane rejeion. 4. he proporional onroller in (7) an be replaed wih a more advaned design, suh as a nonlinear onroller, if neessary. 5. he uning parameers are ω o and ω. he only parameer needed from he plan is he approximae value of b in (). he above onroller-observer ombinaion in (3)-(7) is denoed as ADRC. he diagram for ADRC is shown in Figure. I is applied separaely o all hree veloiy loops. Figure ADRC-Based Veloiy Conrol B. ension Conrol Mehods Boh open-loop and losed-loop soluions o ension regulaion are disussed here. he former is simple and eonomi; he laer is more preise bu requires an addiional observer or a sensing devie for ension. Open-Loop ension Regulaion High qualiy veloiy regulaion allows he ension o be onrolled open-loop, if he model of he ension dynamis () is aurae. From (), he ension an be ompued as AE () = () + ( v () ( () ())) + ve vp d () x () N where () is he iniial value of ension. For he open-loop onrol, le he desired veloiies d d d v, ve and v, p be arefully hosen so ha () yields d () =, () For a given iniial ondiion () and a given ime onsrain,. hen, if all hree veloiy loops are well-behaved, he aual ension should be lose o he desired value. his mehod will be esed in simulaion in a laer seion. Noe ha, for his purpose, he desired veloiies mus saisfy he following ondiion d d ve () vp() d v () =, (3) N he above approah is a low os, open-loop soluion. As he operaing ondiion hanges, he ension dynamis () ould vary, ausing variaions in ension. For he ension is no measured, suh variaions go unnoied unil visible effes on he produ qualiy appear. o mainain aurae ension onrol, indusry users usually are willing o insall a ension sensor, whih regulaes he ension in a feedbak loop, as disussed below. Observer-based Closed-loop ension Regulaion A ension meer, suh as a load ell, an be used for losed-loop ension onrol. Bu i inreases he hardware omplexiy and os. herefore, implemening ension onrol wihou ension sensor would be benefiial from an eonomi poin. For his purpose, a ension observer is designed. Reall in (3)-(5), ension is oupled in veloiy loops, and we use an ADRC onroller o deouple he ension from he veloiy loops. Aually, ension is hrown ino f() par, whih is esimaed and aneled ou in LESO. Le us look a f() in hree veloiy loops, and we an find ou ha if he oher pars of f() are known, ension an be esimaed hrough equaion (9) and presened as: ˆ M () = ( f () ( Fd () M g)) N + M (4) ˆ () () () = ) e ( f B v + e f e R (5) r R ˆ () () () = ( f + B v + R ) (6) p p f p r R Wih a proper parameer seing, LESO an granee ha z v and z f. ha is o say, from LSEO, f (),f e () and f p () an be obained. Sine he oher pars in f() are all known in his problem, ension esimaion from hree veloiy loops an be alulaed based on (4)-(6). Figure An observer-based ension onrol sysem Finally, he ension observer is obained from he average of hree ension esimaions. () = ( () + e() + p()) (7) 3 he omplee blok diagram for he veloiy and 845

5 uc. ension onrol loops are shown in Figure. he simulaion resuls are revealed in he nex seion, where he proposed mehod is ompared o he wo previous mehods. IV. SIMULAION AND COMPARISON In his seion, four ypes of onrol sysems are ompared via simulaions, inluding: ) he ommonly used indusrial onroller (IC); ) he improved 3) he hree ADRC onrollers, desribed in (3)-(7), for he veloiy loops wih ension regulaed in open-loop (ADRC); and 4) he same ADRC veloiy onrollers wih an addiional ADRC onroller for he ension loop (ADRC). Noe ha in IC and ADRC, he ension is onrolled open-loop, while ADRC loses he ension loop wih a ension feedbak. relies on he ension esimaor for is losed-loop ension onrol. he omparison of hese onrollers is arried ou in he presene of disurbanes. In addiion, o demonsrae he feasibiliy of he proposed mehods, hey are implemened in disree-ime form wih a sampling period of ms. A. Simulaion Seup hree onrol shemes are invesigaed by onduing simulaions on an indusrial oninuous web proess line. he desired ension in he web span is 58 N. he desired proess speed is 3.3 m/s. A ypial senario of he exi speed and he arriage speed during a rewind roll hange is depied in Figure 3. Exi Vel.(m/se) Carriage Vel. (m/se) 6 4 B C A B C D E A D G -.5 E F ime se Figure 3 Desired exi speed and he arriage speed he objeive of onrol design is o make he arriage, exi veloiy, and proess veloiies losely rak heir desired rajeories, while mainaining he desired average web ension level. o make he simulaion resuls realisi, hree sinusoidal ension disurbanes are injeed in he veloiies loops. For he arriage veloiy loop, F d () in (3) is a sinusoidal disurbane wih he frequeny of.5hz and ampliude of 44N, and is applied only in hree shor speifi ime inervals: :3 seonds, 6:6 seonds, and 38:38 seonds as shown in Figure 4. For exi roller veloiy and proess veloiy loops, δ e () and δ p (), in equaion (4) and (5), respeively are he ension disurbanes added on F G hese wo veloiies loops. hey are also sinusoidal funions wih he frequeny of. Hz and he ampliude of 44N, and are applied hroughou he simulaion.. Amp:44N, Freq:.5Hz 5 Sinusoid Disurbane o Carriage wih Inervals :3 6:6 38: ime se Figure 4 Sinusoidal disurbane F d () added o he arriage B. Parameerizaion seup and uning Proedures Following he parameerizaion and design proedure desribed above, ω and ω o are he wo parameers need o be uned. As disussed in [6], relaionship beween ω and ω o is ωo 3 5ω. So we only have one parameer o une, whih is ω. he oher imporan parameer needed is he approximae value of b in (9). For his problem, he bes esimae of b in (9) is as follows b = [ b be bp] = [/ M RKe / RKp / ] = [ ], b = AE /5= A ohesive ADRC design and opimizaion proedure is given as follows: Sep : Design parameerized LESO and onroller where ω o and ω are design parameers; Sep : Choose an approximae value of b in differen plan, suh as b, b e,b p and b. Sep 3: Se ω o =5ω and simulae/es he ADRC in he simulaion or a hardware se-up; Sep 4: Inremenally inrease ω unil he noise levels and/or osillaions in he onrol signal and oupu exeed he olerane; Sep 5: If neessary, slighly inrease or derease he raion of ω and ω o. he parameers of he four onrollers are shown in able I. ABLE I: VALUES OF HE GAINS USED IN HE SIMULAION Veloiy Loops ension loop IC k ie =. k ip =. k pe =,k pp = γ 3 =, γ e =, γ p = ADRC ω =5, ω e =4, ω p =4, ADRC Same as ADRC ω = Here k pe, k pp, k ie and k ip are he gains for he IC. γ 3, γ e, and γ p are he gains for he. b, b e, and b p are speifi 846

6 uc. values of b in (9) for he arriage, exi, and proess veloiy loops, respeively. Similarly, ω o, ω oe and ω op are he observer gains in equaion (4); and ω,,ω e and ω p are he onroller gains (k p ) in equaion (8). b, ω, and ω o are he orresponding ADRC parameers for he ension plan in (). C. Simulaion Resuls and Comparison he veloiy and ension raking errors resuling form ADRC are shown in Figure 5. Obviously, he veloiy and ension raking errors are quie small, despie he fa ha he onroller is design no based on he omplee mahemaial model of he plan and here are signifian disurbanes in he proess. All he raios of raking errors o se poin are below.%. e v (m/se) e ve (m/se) e vp (m/se) e (N) x -4 Error of V x -3 Error of Ve x -4 Error of Vp Error of ime ( seond ) Figure 5 raking errors for Carriage Roller by ADRC he omparisons of IC, and ADRC are shown in Figures 6 and 7, in erms of he raking errors and onrol signals for he arriage veloiy loop. Noe ha he arriage veloiy errors indiae ha ADRC is muh beer han he oher wo mehods. e v e v e v 5 x Error Signals of Carriage Veloiy by IC,,ADRC x x ime (seond) IC ADRC Figure6 raking errors of arriage veloiy by IC, and ADRC U IC (N) U (N) U ADRC (N) 5 x 5 Conrol Signal for IC x 5 Conrol Signal for x 5 Conrol Signal for LADRC ime (seond) Figure 7 Conrol Signal for Carriage Roller by IC, and ADRC IC ADRC Similar haraerisis are also found in he exi and proess veloiy loops. For he sake of he lengh of his paper, hose resuls are no inluded here. Due o he poor resuls of IC, only, ADRC, ADRC are ompared in he ension onrol resuls in Figure 8. Noe ha, wih an open-loop ension onrol sheme, he seady sae error of ADRC is aused by he onsan sinusoid disurbanes added in he hree veloiy loops, whih ener ino he ension loop. Wih a dire ension measuremen and feedbak, he losed-loop ADRC ension onrol an resul in negligible ension errors. Furhermore, even in an open-loop onrol, ADRC has a smaller error han. his an be aribued o he high qualiy veloiy onrollers in ADRC. e (N) ADRC ADRC ADRC ADRC ime (seond) Figure 8 ension raking error by, ADRC,ADRC he veloiy and ension errors of all four onrol sysems are summarized in able II. Overall, hese resuls reveal ha he proposed ADRC onrollers have a disin advanage in he presene of sinusoidal disurbanes and a muh beer performane in ension onrol. 847

7 uc. ABLE II SIMULAION COMPARISON Roo Mean Square Maximum Error Error v v e v p (N) v v e v p IC 5.E E-3 8.5E-3 8.8E+4.E-4.E-3.E-3 7..E-4.7E-3.4E E 5.E-4 6.E-4. ADRC 8.E.5E-3.E-4 4..E.E.E-4.8 ADRC 7.E.3E-3.E-4.5E-.E.E.E-4.E-3 V. CONCLUDING REMARKS A new onrol sraegy is proposed for web proessing appliaions, based on he aive disurbane rejeion onep. I is applied o boh veloiy and ension regulaion problems. Alhough only one seion of he proess, inluding he arriage, he exi, and he proess sages, is inluded in his sudy, he proposed mehod applies o boh he upsream and downsream seions, overing he enire web line. Simulaion resuls, based on a full nonlinear model of he plan, demonsrae ha he proposed onrol algorihm resuls in no only beer veloiy onrol bu also signifianly less web ension variaion. he proposed mehod is promising beause: ) no deailed mahemaial model is required; ) zero seady sae error is ahieved wihou using he inegraor erm in he onroller; 3) muh beer ommand following is demonsraed during he ransien sage; and finally 4) exellen disurbane rejeion was ahieved. Appendix I: Plan Coeffiiens Values Desripions M 73 kg Mass of he arriage A m Cross seional area of web E 6.9 N/m Modulus of elasiiy R.54 m Radius of roller N 34 Number of web spans.54 kg-m Momen of ineria v f N-s/m Visous friion oeffiien B f.5-3 N-m-s Bearing friion oeffiien REFERENCES [].K. Seok, D.W. Chung, S.H.Song, e. al., A new approah o advaned old mill drive sysems, Conf. Pro. IEEE-IAS Annual Meeing, 997, pp [] P.R. Pagilla, I. Singh, and R.V. Dwivedula, A sudy on onrol of aumulaors in web proessing lines, Pro. of he 3 ACC, Vol.5, pp [3] P.R. Pagilla, S.S. Garimella, L.H. Dreinhoefer, and E.O. King, Dynamis and Conrol of Aumulaors in Coninuous Srip Proessing Lines, IEEE ransaions on Indusry Appliaions, Vol. 37,, pp [4] Yi Hou, Zhiqiang Gao, Fangjun iang, and Brian. Bouler, Aive Disurbane Rejeion Conrol for Web ension Regulaion, Pro. IEEE Conferene on Deision and Conrol, Vol.5, 4-7, De., pp: (N) [5]. Sakamoo, Analysis and onrol of web ension sysem, rans. Ins. Ele. Eng., apan, Vol. 7-D, No. 3, Marh 997, pp [6] D. ouve and D. Bui. Digial servo drives for maerial ension onrol and winding/unwinding appliaions, Pro. PCIM 96, pp [7] P.R. Pagilla, E.O. King, L.H. Dreinhoefer, and S.S. Garimella, Robus Observer-Based Conrol of an Aluminum Srip Proessing Line, IEEE ransaions on Indusry Appliaions, Vol. 36,, pp [8] M. D. Baumgar and L. Y. Pao Robus Lyapunov-Based Feedbak Conrol of Nonlinear Web-Winding Sysems, Pro. IEEE Conf. Deision and Conrol, Maui, HI, Deember 3, pp [9] E. Shrijver and. van Dijk, Disurbane Observers for Rigid Mehanial Sysems: Equivalene, Sabiliy, and Design, ournal of Dynami Sysems, Measuremen, and Conrol, vol.4, Deember, pp [] C.. Kempf and S. Kobayashi, Disurbane Observer and Feedforward Design for a High-Speed Dire-Drive Posiioning able, IEEE rans. Conrol Sysems eh., vol. 7, no. 5, Sepember 999, pp [] R. Bikel and M. omizuka, Passiviy-Based Versus Disurbane Observer Based Robo Conrol: Equivalene and Sabiliy, ournal of Dynami Sysems, Measuremen, and Conrol, vol., Marh 999, pp [] Y. Choi, K. Yang, W.K. Chung, H.R. Kim, and I.H. Suh, On he Robusness and Performane of Disurbane Observers for Seond-Order Sysems, IEEE rans. Auomai Conrol, vol. 48, no., February 3, pp [3] B.K. Kim, H.-. Choi, W.K. Chung, and I.H. Suh, Analysis and Design of Robus Moion Conrollers in he Unified Framework, ournal of Dynami Sysems, Measuremen, and Conrol, vol. 4, une, pp [4] Zhiqiang Gao and Yi Huang, ingqing Han, An Alernaive Paradigm for Conrol Sysem Design, Pro. of he 4h IEEE Conferene on Deision and Conrol, Orlando, FL, USA, Deember, pp [5]. Han, Nonlinear Design Mehods for Conrol Sysems, Pro. of he 4h IFAC World Congress, Beijing, 999. [6] Z.Gao, Saling and Parameerizaion Based Conroller uning, Pro. of he 3 Amerian Conrol Conferene, une 3, pp [7] Z. Gao, Aive Disurbane Rejeion Conrol: A Paradigm Shif in Feedbak Conrol Sysem Design, Pro. of he Amerian Conrol Conferene, Minneapolis, pp , 6. [8] Rober Miklosovi and Zhiqiang Gao, A Robus wo-degree-of-freedom Conrol Design ehnique and is Praial Appliaion, IEEE Indusrial Appliaion Soiey 4 Annual Meeing and World Conferene, O. 3-7,