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2 9 obus Cool of Nolea Sysems wh Hyseess Base o Play-Lke Opeaos Ju Fu, We-Fag Xe, Shao-Pg Wag a Yg J 3 The Depame of Mechacal & Iusal Egeeg Cocoa Uvesy The Depame of Mechaoc Cool, Behag Uvesy 3 Sae Key Laboaoy of Iegae Auomao of Pocess Iusy, Nohease Uvesy Caaa,3 Cha. Iouco Hyseess pheomeo occus all sma maeal-base sesos a acuaos, such as shape memoy alloys, pezoceamcs a mageoscve acuaos (Su, e al, ; Fu, e al, 7; Baks & Smh, ; Ta & Baas, 4). Whe he hyseess oleay pecees a sysem pla, he oleay usually causes he oveall close-loop sysems o exhb accuaces o oscllaos, eve leag o sably (Tao & Kokoovc, 995). Ths fac ofe makes he aoal cool mehos suffce fo pecso equeme a eve o be able o guaaee he basc equeme of sysem sably owg o he o-smooh a mul-value oleaes of he hyseess (Tao & Levs, ). Hece he cool of olea sysems pesece of hyseess oleaes s ffcul a challegg (Fu, e al, 7; Ta & Baas, 4). Geeally hee ae wo ways o mgae he effecs of hyseess. Oe s o cosuc a vese opeao of he cosee hyseess moel o pefom veso compesao (Ta & Baas, 4; Tao & Kokoovc, 995; Tao & Levs, ). The ohe s, whou ecessaly cosucg a vese, o fuse a suable hyseess moel wh avalable obus cool echques o mgae he hyseec effecs (Su, e al, ; Fu, e al, 7; Zhou, e al, 4; We & Zhou, 7). The veso compesao was poeee (Tao & Kokoovc, 995) a hee ae some ohe mpoa esuls (Ta & Baas, 5; Iye, e al, 5; Ta & Bea, 8). Howeve, mos of hese esuls wee acheve oly a acuao compoe level whou allowg fo he oveall yamc sysems wh acuao hyseess oleaes. Esseally, cosucg vese opeao eles o he pheomeologcal moel (such as Pesach moels) a flueces sogly he paccal applcao of he esg cocep (Su, e al, ). Because of mul-value a o-smoohess feaue of hyseess, hose mehos ae ofe complcae, compuaoally cosly a possess sog sesvy of he moel paamees o ukow measueme eos. These ssues ae ecly lke o he ffcules of guaaeeg he sably of sysems excep fo cea specal cases (Tao & Kokoovc, 995). Fo he mehos o mgae hyseec effecs whou cosucg he vese, hee ae wo ma challeges volve hs ea. Oe challege s ha vey few hyseess moels

3 44 ece Avaces obus Cool Novel Appoaches a Desg Mehos ae suable o be fuse wh avalable obus aapve cool echques. A he ohe s how o fuse he suable hyseess moel wh avalable cool echques o guaaee he sably of he yamcs sysems (Su, e al, ). Hece s usually ffcul o cosuc ew suable hyseess moels o be fuse o cool plas, a o exploe ew cool echques o mgae he effecs of hyseess a o esue he sysem sably, whou ecessaly cosucg he hyseess vese. Nocg he above challeges, we fs cosuc a hyseess moel usg play-lke opeaos, a smla way o L. Pal s cosuco of he Pal-Ishlsk moel usg play opeaos (Bokae & Spekels, 996), a hus ame Pal-Ishlsk-Lke moel. Because he play-lke opeao (Ekaayake & Iye, 8) s a geealzao of he backlash-lke opeao (Su, e al, ), he Pal-Ishlsk-Lke moel s a subclass of SSSL-PKP hyseess moel (Ekaayake & Iye, 8). The, he evelopme of wo obus aapve cool schemes o mgae he hyseess avos cosucg a hyseess vese. The ew mehos o oly ca pefom global sablzao a ackg asks of he yamc olea sysems, bu also ca eve ase pefomace ems of L om of ackg eo as a explc fuco of esg paamees, whch allows esges o mee he ese pefomace equeme by ug he esg paamees a explc way. The ma cobuos hs chape ae hghlghe as follows:. A ew hyseess moel s cosuce, whee he play-lke opeaos evelope (Ekaayake & Iye, 8) play a ole of bulg blocks. Fom a sapo of caegoes of hyseess moels, hs class of hyseess moels s a subclass of SSSL-PKP hyseess moels. I poves a possbly o mgae he effecs of hyseess whou ecessaly cosucg a vese, whch s he uque feaue of hs subclass moel efe fom he SSSL-PKP hyseess moel of geeal class he leaue;. A challege s aesse o fuse a suable hyseess moel wh avalable obus aapve echques o mgae he effecs of hyseess whou cosucg a complcae vese opeao of he hyseess moel;. Two backseppg schemes ae popose o accomplsh obus aapve cool asks fo a class of olea sysems pecee by he Pal-Ishlsk-Lke moels. Such cool schemes o oly esue he sablzao a ackg of he hyseec yamc olea sysems, bu also eve he ase pefomace ems of L om of ackg eo as a explc fuco of esg paamees. The ogazao of hs chape s as follows. Seco gves he poblem saeme. I Seco 3, we wll cosuc Pal-Ishlsh-Lke moel a exploe s popees. The eals abou wo cool schemes fo he olea sysems pecee by Pal-Ishlsh- Lke moel popose Seco 3 ae pesee Seco 4. Smulao esuls ae gve Seco 5. Seco 6 coclues hs pape wh some bef emaks.. Poblem saeme Cose a coolle sysem cossg of a olea pla pecee by a acuao wh hyseess oleay, ha s, he hyseess s pesee as a pu o he olea pla. The hyseess s eoe as a opeao w () = Pv [ ]() ()

4 obus Cool of Nolea Sysems wh Hyseess Base o Play-Lke Opeaos 45 wh v () as he pu a w () as he oupu. The opeao Pv [ ] wll be cosuce eal ex seco. The olea yamc sysem beg pecee by he pevous hyseess s escbe he caocal fom as k ( ) ( ) x () + ay( x (), x (),, x ()) = bw () () whee Y ae kow couous, lea o olea fuco. Paamees a a cool ga b ae ukow cosas. I s a commo assumpo ha he sg of b s kow. Whou losg geealy, we assume b s geae ha zeo. I shoul be oe ha moe geeal classes of olea sysems ca be asfome o hs sucue (Iso, 989). The cool objecve s o esg coolle v () (), as show Fgue, o ee he pla sae x () o ack a specfe ese ajecoy x (),.e., x () x() as. Thoughou hs pape he followg assumpo s mae. Fg.. Cofguao of he hyseec sysem Assumpo: The ese ajecoy T ( ) T ( ) T [,,, ] [ X, x ] Ω + wh Ω beg a compac se. 3. Pal-Ishlsk-Lke moel X = x x x s couous. Fuhemoe, I hs seco, we wll fs ecall he backlash-lke opeao (Su, e al, ) whch wll seve as elemeay hyseess opeao, ohe wos, he backlash-lke opeao wll play a ole of bulg blocks, he wll show how he ew hyseess wll be cosuce by usg he backlash-lke opeao a exploe s some useful popees of hs moel. 3. Backlash-lke opeao I, Su e al popose a couous-me yamc moel o escbe a class of backlashlke hyseess, as gve by F = α v ( cv F) + B v (3)

5 46 ece Avaces obus Cool Novel Appoaches a Desg Mehos whee α, c, a B ae cosas, sasfyg c > B. The soluo of (3) ca be solve explcly fo pecewse moooe v as follows α( v v )sg v αvsg v v αζ(sg v ) F = cv + F cv e + e B c e ζ () () [ ] [ ] v (4) fo v cosa a wv ( ) = w. Equao (4) ca also be ewe as α( v v ) αv B c αv αv cv + F cv e + e e e v > α F () = α( v v ) αv B c αv αv cv + F cv e + e e e v < α () [ ] ( ), () [ ] ( ), (5) I s woh o oe ha c B lm ( Fv ( ) cv) = + α c B lm ( Fv ( ) cv) = α v v (6) Hece, soluo F () expoeally coveges he oupu of a play opeao wh c B c B c B heshol = a swches bewee les cv + a cv. We wll cosuc α α α a ew Pal-Ishlsk-Lke moel by usg he above backlash-lke moel ex subseco, smla o he cosuco of he well-kow Pal-Ishlsk moel fom play opeaos, whch s ou movao beh he cosuco of hs ew moel ee. 3. Pal-Ishlsk-Lke moel We ow eay o cosuc Pal-Ishlsk-Lke moel hough a weghe supeposo of elemeay backlash-lke opeao F [ v]( ), a smla way as L. Pal (Bokae & Spekels, 996) cosuce Pal-Ishlsk moel by usg play opeaos. c B Keep = m a, whou losg geealy, se Fv ( () = ) = a c =, we α ewe equao (5) as F () ( B ) v v () e +, v > = B v + < v () e, v (7) whee s he heshol of he backlash-lke opeao. To hs e, we cosuc he Pal-Ishlsk-Lke moel by w () = p() F[ v]() (8)

6 obus Cool of Nolea Sysems wh Hyseess Base o Play-Lke Opeaos 47 whee p( ) s a gve couous esy fuco, sasfyg p ( ) wh p () <+, a s expece o be efe fom expemeal aa (Kasoskl skll & Pokovskll, 983; Bokae & Spekels, 996). Sce he esy fuco p( ) vashes fo lage values of, he choce of =+ as he uppe lm of egao he leaue s jus a mae of coveece (Bokae & Spekels, 996). Iseg (7) o (8) yels wv [ ]( ) ( B ) v pv () () p ()( e + ), v > = B v pv + p + e v < () () ()( ), (9) he hyseess (9) ca be expesse as w () pv ( B ) v p ()( e ), v > = + B v p + e v < ()( ), () whee p = p() s a cosa whch epes o he esy fuco p( ). Popey : Le v [ ]( ) ( B ) v p ()( e ), v > = B v p + e v < ()( ), () sasfyg p ( ) wh p () < +, he fo ay v () C ( pm, ), hee exss a cosa M such ha v [ ]( ) M. Poof: sce (7) ca be ewe as F () = v() + (, v) whee v (, ) ( B ) v e, v > = B v + < e, v Base o he aalyss (Su, e al, ), fo each fxe (, ), s always possble hee exss a posve cosa M, such ha v (, ) M. Hece v []() = pv () (, ) p () v (, ) M p ()

7 48 ece Avaces obus Cool Novel Appoaches a Desg Mehos By he efo of p( ), oe ca coclue ha M = M p( ). Popey : he Pal-Ishlsk-Lke moel cosuce by (9) s ae-epee. Poof: Followg (Bokae & Spekels, 996), we le σ :[, ] [, ] sasfyg σ () = a σ ( ) = be a couous ceasg fuco,.e. σ () s a amssble me asfomao E E a efe w [ v ] sasfyg w [ v ] = w[ v]( ), [, ] a v M [, ] whee v f f E epeses he ucao of v a, efe by v ( τ ) = v( τ ) fo τ a v ( τ ) = v( ) fo τ E, a wv [ ]( ) cosuce by (9). Fo he moel (9), we ca easly have wv [ σ ]() = w [( v σ)] = w [ v σ] = w [ v ] = wv [ ]( σ()) = wv [ ]() σ() f f σ() f σ() Hece fo all amssble me asfomao σ (), accog o he efo.. (Bokae & Spekels, 996), he moel cosuce by (9) s ae-epee. Popey 3: he Pal-Ishlsk-Lke moel cosuce by (9) has he Volea popey. Poof: s obvous wheeve vv, Mpm[, E] a [, E ], he v = v mples ha ( wv [ ]) = ( wv [ ]), so, accog o (Bokae & Spekels, 996, Page 37), he moel (8) has Volea popey. Lemma : If a fucoal w: Cpm[, E] Map([, E]) has boh ae epeece popey a Volea popey, he w s a hyseess opeao (Bokae & Spekels, 996). Poposo : he Pal-Ishlsk-Lke moel cosuce by (9) s a hyseess opeao. Poof: Fom he Popees, a Lemma, he Pal-Ishlsk-Lke moel (9) s a hyseess moel. emak : I shoul be meoe ha Pal-Ishlsk moel s a weghe supeposo of play opeao,.e. play opeao s he hyseo (Kasoskl skll & Pokovskll, 983), a ha backlash-lke opeao ca be vewe as a play-lke opeao fom a s oe ffeeal equao (Ekaayake & Iye, 8). Hece, he moel (8) s, wh a le abuse emology, ame Pal-Ishlsk-Lke moel. As a llusao, Fgue shows w () geeae by (9), wh v () = 7s(4)/( + ), wh Fv ( () = ) =. 6.7(. ) E p () = e (,5], B =.55, a pu E pm E 5 5 w() v() Fg.. Pal-Ishlsk-Lke Hyseess cuves gve by ()

8 obus Cool of Nolea Sysems wh Hyseess Base o Play-Lke Opeaos 49 emak : Fom aohe po of a aleave oe-paamec epeseao of Pesach opeao (Kejc, 996), he Pal-Ishlsk-Lke moel falls o PKP-ype opeao (Ekaayake & Iye, 8), as Pal-Ishlsk moel o Pesach moel. As a pelmay sep, he pape we exploe he popees of hs moel a s poeal o faclae cool whe a sysem s pecee by hs k of hyseess moel, whch wll be emosae he ex seco. egag hyseess pheomea whch k of sma acuao hs moel coul chaaceze, s sll uclea. The fuue wok wll focus o, whch s beyo of he scope of hs pape. To hs e, we ca ewe (9) o whee p = p() a v [ ]( ) s efe by (). w () = pv+ v [ ]() () emak 3: I shoul be oe ha () ecomposes he hyseess behavo o wo ems. The fs em escbes he lea evesble pa, whle he seco em escbes he olea hyseec behavo. Ths ecomposo s cucal (Su, e al,, Fu, e al, 7) sce faclaes he ulzao of he cuely avalable cool echques fo he coolle esg, whch wll be clea ex seco. 4. Aapve cool esg Fom () a Poposo we see ha he sgal w () s expesse as a lea fuco of pu sgal v () plus a boue em. Usg he hyseess moel of (), he olea sysem yamcs escbe by (), ca be e-expesse as x x = x = x k x = ay( x (), x (),, x ()) + bpv { ( ) v [ ]( )} T = a Y + b v() [ v] p b (3) whee x () = x(), Y Y Y Y k ( ) x () = x (),, x() = x (), a = [ a, a,, a ] T k, a bp = bp = [,,, ] T, a [ v]( ) = b[ v]( ). b Befoe peseg he aapve cool esg usg he backseppg echque (Ksc, e al, 995) o acheve he ese cool objecves, we make he followg chage of cooaes: z = x x ( ) α z = x x, =,3,, Whee α - s he vual coolle he h sep a wll be eeme lae. I he followg, we gve wo cool schemes. I Scheme I, he coolle s scouous; he ohe s couous Scheme II. (4)

9 43 ece Avaces obus Cool Novel Appoaches a Desg Mehos Scheme I I wha follows, he obus aapve cool law wll be evelope fo Scheme I. Fs, we gve he followg efos a () = a aˆ () φ() = φ ˆ φ() (5) M() = M Mˆ () whee â s a esmae of a, ˆ φ s a esmae of φ, whch s efe as φ : =, a ˆM s a b esmae of M. p Gve he pla a he hyseess moel subjec o he assumpo above, we popose he followg cool law v () = ˆ φ() v() ( ) ˆT ˆ () = a sg( ) + + α v c z z Y z D x ˆ( φ ) = ηv () z a ˆ( ) =ΓYz M () = γ z (6) whee c, η, a γ ae posve esg paamees, a Γ s a posve-efe max. These paamees ca pove a cea egee of feeom o eeme he aes of he aapaos. A α a he mplcα, =,3,, (6) wll be esge he poof of he followg heoem fo sably aalyss. The sably of he close-loop sysem escbe (3) a (6) s esablshe as: Theoem : Fo he pla gve () wh he hyseess (8), subjec o Assumpo, he obus aapve coolle specfe by (6) esues he followg saemes hol.. The esulg close-loop sysem () a (8) s globally sable he sese ha all he sgals of he close-loop sysem ulmaely boue;. The asympoc ackg s acheve,.e., lm[ x ( ) x( )] = ;. The ase ackg eo ca be explcly specfe by x () x() b T p a () Γ a () + φ() + M () η γ c Poof: we wll use a saa backseppg echque o pove he saemes a sysemacally way as follows: Sep : The me evave of z ca be compue as The vual cool α ca be esge as z = z + α (7)

10 obus Cool of Nolea Sysems wh Hyseess Base o Play-Lke Opeaos 43 α = cz whee c s a posve esg paamee. Hece, we ca ge he fs equao of ackg eo Sep : Dffeeag z gves The vual cool α ca be esge as Hece he yamcs s z = z c z z = z + α α 3 α = cz z + α z = c z z + z 3 Followg hs poceue sep by sep, we ca eve he yamcs of he es of saes ul he eal cool appeas. Sep : he -h yamcs ae gve by We esg he eal cool as follows: T ( ) = p + α + b z b v() a Y x [ v]() (8) v () = ˆ φ() v() ( ) ˆT ˆ () = a sg( ) + + α v c z z Y z M x ˆ( φ ) = ηv () z aˆ( ) =ΓYz M () = γ z (9) Noe ha bv p ( ) (9) ca be expesse as Hece, we oba bv () = b ˆ φ() v() = v() b φ() v() () p p p z c z z ˆ Y sg( z ) Mˆ [ v]( ) b ( ) v ( ) () T = a + b pφ To hs e, we efe he caae Lyapuov fuco as The evave V s gve by b T p V = z + a Γ a + φ + M () η γ

11 43 ece Avaces obus Cool Novel Appoaches a Desg Mehos b V z z MM T p = + a Γ a + φφ + η γ b T p ˆ ˆ a a φη φ η ˆ b b T p ˆ ˆ + a Γ Γ a φη + φ + η γ = cz γ cz + Γ ( ΓYz ) ( vz + ) z M+ z [ v]( ) + MM γ cz ( Yz ) ( vz ) M( z Mˆ ) (3) Equaos () a (3) mply ha V s oceasg. Hece, he boueess of he vaables z, z,, z, ˆ φ, â, ˆM ae esue. By applyg he LaSalle-Yoshzawa Theoem (Ksc, e al, 995, Theoem.), f fuhe follows ha z, =,,, as me goes o fy, whch mples lm[ x ( ) x( )] =. We ca pove he h saeme of Theoem he followg way. Fom (3), we kow () V() V( ) V() z = z s s c c b T p NocgV() = a () Γ a () + φ() + M () afe seg z() =, =,,,, hece η γ x () x() b T p a () Γ a () + ϕ() + M () η γ c (4) emak 4: Fom (4), we kow ha he ase pefomace a compuable explc fom epes o he esg paameesηγ,,c a o he al esmae eos a (), φ() M (), whch gves esges eough ug feeom fo ase pefomace. Scheme II I he cool scheme above, we oce ha he coolle, hee s sg( z ) ouce he esg pocess, whch makes he coolle scouous a hs may cause uesable chaeg. A aleave smooh scheme s popose o avo possble chaeg wh eso o he efo of couous sg fuco (Zhou e al, 4). Fs, he efo of sg ( z ) s ouce as follows: z, z δ z sg( z) = z z < δ + z + ( δ z ) (5)

12 obus Cool of Nolea Sysems wh Hyseess Base o Play-Lke Opeaos 433 whee esg paamee δ ( =,, ) s posve. I ca be kow ha sg ( z ) has ( + ) - h oe evaves. Hece we have whee, z δ sg( z) f( z) =, z < δ, z δ, f( z) =, z z δ < δ Gve he pla a he hyseess moel subjec o he assumpo above, we popose he followg couous coolle as follows: v () = ˆ φ() v() ( ) ˆT ˆ () = ( + )( δ) ( ) a ( ) + + α v c z sg z Y sg z M x ˆ( φ ) = ηv ()( z δ ) fsg ( z ) a ˆ( ) =ΓY( z δ) fsg( z) M () = γ( z δ ) f (6) whee, smlaly as Cool Scheme, c, η, a γ ae posve esg paamees, a Γ s a posve-efe max, a α a he mplcα, =,3,, (6) wll be esge he poof of he followg heoem fo sably aalyss. Theoem : Fo he pla gve () wh he hyseess (8), subjec o Assumpo, he obus aapve coolle specfe by (6) esues he followg saemes hol.. The esulg close-loop sysem () a (8) s globally sable he sese ha all he sgals of he close-loop sysem ulmaely boue;. The ackg eo ca asympocally each o. The ase ackg eo ca be explcly specfe by δ,.e., lm[ x () x()] = δ ; / b T p x () x() δ + () () φ() M() c a Γ a + + η γ (7) Poof: To guaaee he ffeeably of he esula fucos, z he Lyaouov fucos wll be eplace by ( ) + z δ f Seco 3. a z he esg poceue eale below wll be eplace by ( ) + z δ sg as (Zhou e al, 4). Sep : We choose a posve-efo fuco V as ( ) + V = z δ f ( z ), +

13 434 ece Avaces obus Cool Novel Appoaches a Desg Mehos a esg vual coolle α as c k z sg z sg z α = ( + )( δ ) ( ) ( δ + ) ( ) (8) wh cosa k sasfyg < k a a posve esg paamee c, he compue s 4 me evave by usg (7)(8), V z f z sg z z = ( δ) ( ) ( ) δ δ δ ( c + k)( z ) f ( z ) + ( z ) ( z ) f ( z ) (9) Sep : We choose a posve-efo fuco V as a esg vual coolle α as ( ) V = V + z δ f ( z ), = c+ k+ z sg z sg z α ( )( δ ) ( ) α ( δ ) ( ) (3) wh a posve esg paamee c, he compue s me evave, ( + ) δ δ + δ δ ( ) ( z δ) f( z) + ( z δ) ( z3 δ3 ) f( z) V c ( z ) f ( z ) k( z ) f ( z ) ( z ) ( z ) f ( z ) By usg equaly ab a + b, we have ( + ) ( δ) ( ) + ( δ ) 4k ( ) z δ f z + z δ z3 δ3 f z V c z f z z ( ) ( ) ( ) ( ) ( ) fo boh cases z δ + a z < δ +, we ca coclue ha ( + ) δ + δ 3 δ3 V c ( z ) f ( z ) ( z ) ( z ) f ( z ) (3) Sep : Followg hs poceue sep by sep, we ca eve he eal cool v () = ˆ φ() v() ( ) ˆT ˆ () = ( + )( δ) ( ) a ( ) + + α v c z sg z Y sg z M x ˆ( φ ) = ηv ()( z δ ) fsg ( z ) a ˆ( ) =ΓY( z δ) fsg( z) M () = γ( z δ ) f (3)

14 obus Cool of Nolea Sysems wh Hyseess Base o Play-Lke Opeaos 435 whee α ca be obae fom he commo fom of vual coolles + + α = ( c + k+ )( z δ ) sg ( z ) + α ( δ + ) sg ( z ), ( = 3,, ) wh posve esg paamees c. We efe a posve-efo fuco as b V = ( z ) f ( z ) + a Γ a+ + M + η γ ( + ) T p δ φ a compue s me evave by usg (3), (8), (3) a (3), b T p V = V + ( z δ) f( z) sg( z) z + a Γ a + φφ + MM η γ ( + ) T c z δ f z a Yz ( ) ( ) + Γ ( Γ a ˆ) bp ˆ φη ( vz + φ) z M+ z b[ v]( ) + MM η γ b + Γ Γ ( + ) T p c ( ) ( ) ( ˆ z δ f z a Yz a ) η ( + ) c( z δ) f( z) = ˆ φη ( vz + φ) + M ( γ z ˆ M) γ Thus we pove he fs saeme of he heoem. The es of he saemes ca be easly pove followg hose of he poof of heoem, hece ome hee fo savg space. emak 5: I s ow clea he wo popose cool schemes o mgae he hyseess oleaes ca be apple o may sysems a may o ecessaly be lme o he sysem (). Howeve, we shoul emphasze ha ou goal s o show he fuso of he hyseess moel wh avalable cool echques a smple seg ha eveals s esseal feaues. 5. Smulao esuls I hs seco, we llusae he mehoologes pesee he pevous secos usg a smple olea sysems (Su, e al, ; Zhou e al, 4) escbe by x () e x = a + bw() (33) x () + e whee w epeses he oupu of he hyseess oleay. The acual paamee values ae a =, a b =. Whou cool,.e., w () =, (33) s usable, because x () x () x () x () x = ( e )/( + e ) > fo x >, a x = ( e )/( + e ) < fo x <. The objecve s o cool he sysem sae x o follow he ese ajecoy x =.5s(.3 ). I he smulaos, he obus aapve cool law (9) of Scheme I was use, akg c =.9, γ =., η =., Γ =., ˆ() φ =.8 /3, M ˆ () =, x ˆ() = 3.5, v () =, B =.55,

15 436 ece Avaces obus Cool Novel Appoaches a Desg Mehos 6.7(. ) p () = e fo (,5]. The smulao esuls pesee he Fgue 3 s he compaso of sysem ackg eos fo he popose cool Scheme I a he sceao whou coseg he effecs of he hyseess. Fo Scheme II, we choose he same al values as befoe a δ =.35. The smulao esuls pesee he Fgue 4 s he compaso of sysem ackg eos fo he popose cool Scheme II a he sceao whou coseg he effecs of he hyseess. Clealy, he all smulao esuls vefy ou popose schemes a show he effecveess. Fg. 3. Tackg eos -- cool Scheme I (sol le) a he sceao whou coseg hyseess effecs (oe le) Fg. 4. Tackg eos -- cool Scheme II (sol le) a he sceao whou coseg hyseess effecs (oe le)

16 obus Cool of Nolea Sysems wh Hyseess Base o Play-Lke Opeaos Cocluso We have fo he fs me cosuce a class of ew hyseess moel base o play-lke opeaos a ame Pal-Ishlsh-Lke moel whee he play-lke opeaos play a ole of bulg blocks. We have popose wo cool schemes o accomplsh obus aapve cool asks fo a class of olea sysems pecee by Pal-Ishlsh-Lke moels o o oly esue sablzao a ackg of he hyseec yamc olea sysems, bu also eve he ase pefomace ems of L om of ackg eo as a explc fuco of esg paamees. By poposg Pal-Ishlsh-Lke moel a usg he backseppg echque, hs pape has aess a challege ha how o fuse a suable hyseess moel wh avalable obus aapve echques o mgae he effecs of hyseess avo cosucg a complcae vese opeao of he hyseess moel. Afe hs pelmay esul, he ea hs pape s beg fuhe exploe o eal wh a class of peube sc-feeback olea sysems wh ukow cool ecos pecee by hs ew hyseess moel. 7. Ackowlegeme Ths wok was suppoe by he NSEC Ga, he Naoal Naual Scece Fouao of Cha (649, 663), Docoal Fu of Msy of Eucao of Cha (433), a he Fuameal eseach Fus fo he Ceal Uveses (N484, N78). 8. efeeces Su, C. Y.; Sepaeko, Y.; Svoboa, J. & Leug, T. P. (). obus Aapve Cool of a Class of Nolea Sysems wh Ukow Backlash-Lke Hyseess, IEEE Tasacos o Auomac Cool, Vol. 45, No., pp Fu, J.; Xe, W. F. & Su, C. Y. (7). Paccally Aapve Oupu Tackg Cool of Iheely Nolea Sysems Poceee by Ukow Hyseess, Poc. of he 46h IEEE Cofeece o Decso a Cool, 36-33, New Oleas, LA, USA. Baks, H. T. & Smh,. C. (). Hyseess moelg sma maeal sysems, J. Appl. Mech. Eg, Vol. 5, pp Ta, X. & Baas, J. S. (4). Moellg a cool of hyseess mageoscve acuaos, Auomaca, Vol. 4, No. 9, pp Tao G. & Kokoovc P. V. (995). Aapve cool of Plas wh Ukow Hyseess, IEEE Tasacos o Auomac Cool, Vol. 4, No., pp. -. Tao G. & Lews, F., (). Es, Aapve cool of osmooh yamc sysems, New Yok: Spge-Velag,. Zhou J.; We C. & Zhag Y. (4). Aapve backseppg cool of a class of ucea olea sysems wh ukow backlash-lke hyseess, IEEE Tasacos o Auomac Cool, Vol. 49, No., pp We C. & Zhou J.(7). Decealze aapve sablzao he pesece of ukow backlash-lke hyseess, Auomaca, Vol. 43, No. 3, pp Ta X. & Baas J. (5). Aapve Iefcao a Cool of Hyseess Sma Maeals, IEEE Tasacos o Auomac Cool, Vol. 5, No. 6, pp

17 438 ece Avaces obus Cool Novel Appoaches a Desg Mehos Iye.; Ta X., & Kshapasa P.(5), Appoxmae Iveso of he Pesach Hyseess Opeao wh Applcao o Cool of Sma Acuaos, IEEE Tasacos o Auomac Cool, Vol. 5, No. 6, pp Ta X. & Bea O. (8). Fas Ivese Compesao of Pesach-Type Hyseess Opeaos Usg Fel-Pogammable Gae Aays, Poceegs of he Ameca Cool Cofeece, Seale, USA, pp Iso A. (989). Nolea Cool Sysems: a Iouco, e. Bel, Gemay: Spge-Velag. Kasoskl sk M. A. & Pokovsk A. V. (983). Sysems wh Hyseess. Moscow, ussa: Nauka. Bokae, M. & Spekels, J. (996). Hyseess a Phase Tasos, New Yok: Spge- Velag. Kejc P. (996) Hyseess, covexy a sspao hypebolc equaos, Gakuo I. Sees Mah. Sc. & Appl. Vol. 8, Gakkoosho, Tokyo. Ekaayake D. & Iye V. (8), Suy of a Play-lke Opeao, Physca B: Coese Mae, Vol. 43, No.-3, pp Ksc M.; Kaellakopoulos I. & Kokoovc P. (995). Nolea a Aapve Cool Desg. New Yok: Wley.

18 ece Avaces obus Cool - Novel Appoaches a Desg Mehos Ee by D. Aeas Muelle ISBN Ha cove, 46 pages Publshe ITech Publshe ole 7, Novembe, Publshe p eo Novembe, obus cool has bee a opc of acve eseach he las hee ecaes culmag H_/H_\fy a \mu esg mehos followe by eseach o paamec obusess, ally movae by Khaoov's heoem, he exeso o o-lea me elay sysems, a ohe moe ece mehos. The wo volumes of ece Avaces obus Cool gve a selecve ovevew of ece heoecal evelopmes a pese selece applcao examples. The volumes compse 39 cobuos coveg vaous heoecal aspecs as well as ffee applcao aeas. The fs volume coves selece poblems he heoy of obus cool a s applcao o oboc a elecomechacal sysems. The seco volume s ecae o specal opcs obus cool a poblem specfc soluos. ece Avaces obus Cool wll be a valuable efeece fo hose eese he ece heoecal avaces a fo eseaches wokg he boa fel of obocs a mechaocs. How o efeece I oe o coecly efeece hs scholaly wok, feel fee o copy a pase he followg: Ju Fu, We-Fag Xe, Shao-Pg Wag a Yg J (). obus Cool of Nolea Sysems wh Hyseess Base o Play-Lke Opeaos, ece Avaces obus Cool - Novel Appoaches a Desg Mehos, D. Aeas Muelle (E.), ISBN: , ITech, Avalable fom: hp:// ITech Euope Uvesy Campus STeP Slavka Kauzeka 83/A 5 jeka, Coaa Phoe: +385 (5) Fax: +385 (5) ITech Cha U 45, Offce Block, Hoel Equaoal Shagha No.65, Ya A oa (Wes), Shagha, 4, Cha Phoe: Fax:

19 The Auho(s). Lcesee IechOpe. Ths s a ope access acle sbue ue he ems of he Ceave Commos Abuo 3. Lcese, whch pems uesce use, sbuo, a epouco ay meum, pove he ogal wok s popely ce.