Compositional Specification of Functionality and Timing of Manufacturing Systems

Transcription

1 Compositionl Speifition of Funtionlity nd iming of Mnufturing Systems Brm vn der Snden, João Bstos, Jeroen Voeten, Mr Geilen, Mihel eniers, wn Bsten, John Jobs, nd mon Shiffelers Eindhoven University of ehnology, Eindhoven, he Netherlnds ASML, Veldhoven, he Netherlnds NO Embedded Systems Innovtion, Eindhoven, he Netherlnds Abstrt his pper introdues forml modeling pproh for ompositionl speifition of both funtionlity nd timing of mnufturing systems. Funtionlity spets n be onsidered orthogonlly to timing spets. he funtionl spets re speified using two bstrtion levels; high-level tivities nd lower level tions. Design of funtionlly orret ontroller is possible by looking only t the tivity level, bstrting from the different exeution orders of tions nd their timing. As result, ontroller design n be performed on muh smller stte spe ompred to n expliit model where timing nd tions re present. he performne of the ontroller n be nlyzed nd optimized by tking into ount the timing hrteristis. Sine forml semntis re given in terms of (mx, +) stte spe, vrious existing performne nlysis tehniques n be used. We illustrte the pproh, inluding performne nlysis, on n exmple mnufturing system. I. INODUCION One of the hllenges in the design of mnufturing systems is the development of supervisory ontrol omponents. Due to inresing omplexity of these systems, design of these omponents is beoming more diffiult. In suh systems, supervisory ontrollers ply role to gurntee funtionl orretness, for instne, to prevent unsfe behvior of the system suh s produt or robot ollisions in shred physil re. Besides funtionl orretness, the ontroller must lso optimize performne riteri suh s mximizing throughput or minimizing mkespn. In order to perform this optimiztion, the timing hrteristis of the system re neessry. In this pper, we introdue forml modeling pproh, shown in Fig. 1, to ddress both funtionlity nd timing spets of mnufturing systems in ompositionl wy. System opertions re modeled s so lled tivities. Ativities re speified s direted yli grphs, whih onsist of (1) set of tions exeuted on resoures, nd (2) set of dependenies mong the tions. Funtionl requirements relted to tivity sequenes re modulrly nd onisely speified using utomt. hese requirements n for instne enfore produt life yles nd ensure sfety [1]. he omposition of these utomt is hrterized using multiprty synhroniztion, where exeution of shred events mong different utomt is synhronous. he dvntge of multiprty synhroniztion is tht requirements n be dded in modulr wy, nd re respeted fter omposition. Fig. 1. Overview of the modeling pproh. Controller design is performed on the tivity level, bstrting from the internls (tions) of tivities. his mens tht t the ontroller level, there is no redundnt interleving from different exeution orders of fine-grined tions. Furthermore, we bstrt from the speifi timing of tions. As result, the stte spe of the ontroller is muh smller ompred to n expliit model where timing nd tions re present. Performne nlysis nd optimiztion of the supervisory ontroller requires the dynmi semntis (the timing behvior) of our modeling pproh. he dynmi semntis of tivities is expressed using mtries in (mx, +) liner lgebr (see for instne [2]). hese mtries bstrt from the internl grph struture, whih hs gin n dvntge in terms of slbility. Ativity sequenes re ptured by (mx, +) utomt [3], whih n lso be represented by (mx, +) stte spe. hese utomt ombine mtries with nondeterministi hoies, orresponding to hoies in the ordering of tivities. Finding throughput-optiml ontroller orresponds to finding n optiml repetble tivity sequene in the stte spe, whih n be found using existing optiml yle rtio lgorithms [4]. he modeling pproh presented in this pper n be tken s semnti underpinning, on top of whih domin speifi lnguge (DSL) is put, llowing system engineers to model omplete system. Our pproh is lredy in use within ASML 1, the world-leding mnufturer of lithogrphy 1

2 systems, to formlize the speifition of the produt hndling prt of their mhines. he DSL tht is put on top desribes the system in terms of resoures, tions, symboli positions of motors, nd tivities tht n be performed. he reminder of the pper is strutured s follows. Setion II desribes the modeling onepts, nd the stti nd dynmi semntis of both tivities nd tivity sequenes. Setion III illustrtes the use of the modeling pproh by n exmple mnufturing system. Both the tivities nd the llowed tivity sequenes re modeled onisely. he model is used to find throughput-optiml ontroller for the system. Setion IV desribes how the modeling formlism is being used in industry. elted work is given in Setion V, nd Setion VI onludes the pper nd desribes future extensions tht re urrently being investigted. II. MODELING CONCEPS In this setion, we introdue the forml semntis of our modeling pproh. First we fous on desribing ll possible mhine behviors. hen, we desribe tivities nd tivity sequenes tht llows to deribe useful behvior. We view the system s onsisting of set of peripherls. Eh of these peripherls n exeute tions. he omplete set of tions desribes ll behvior tht the mhine n exhibit. Peripherls re ggregted into resoures, whih n be limed nd relesed. As n exmple, onsider robot resoure tht n move produts. his robot hs number of peripherls tht n perform tions, suh s lmp tht n hold or relese produt, or robot motor to move the robot. In mnufturing systems there re often opertions of oordinted tions, tht desribe senrio of deterministi behvior. For instne, piking up produt nd pling it on nother proessing sttion, or performing fixed opertion on the produt. hese entire opertions re modeled s single tivities, onsisting of fixed set of tions nd dependenies mong them. A supervisory ontroller influenes the order in whih tivities n be exeuted, but not the order of tions in n tivity. Fig. 2 gives shemti overview of the modeling onepts nd the different lyers. In the reminder of this setion, we desribe the stti nd dynmi semntis of both tivities nd tivity sequenes. A. Stti Semntis he following sets define the bsi elements of our model: set A of tions, with typil elements A; set P of peripherls, with typil elements p P; set of resoures, with typil elements r. We ssume funtion : P, suh tht (p) is the resoure tht ontins p. Given the bsi elements of the lnguge, we now introdue the notion of n tivity, nd define its struture. As running exmple, we hve the three tivities shown in Fig. 3. Ativities re direted yli grphs (DAGs), onsisting of set of tions exeuted on resoures, nd dependenies mong those tions. Nodes refer to either n tion exeuted by peripherl, or lim or relese of resoure. In Fig. 3, nodes r3 r2 r1 b d e f r3 r2 r1 e b d f Fig. 2. Shemti overview of the onepts in our forml modeling pproh. he system is modeled using resoures onsisting of number of peripherls, whih n exeute tions. Ativities desribe deterministi opertions in the system. A supervisory ontroller ontrols the system by influening the order of tivity exeution. re nnotted with their mpping, nd the vlue in the node is the exeution time. he olors indite peripherl tions inluded in ertin tivity. Definition 1. An tivity is DAG (N, ), onsisting of set N of nodes nd set N N of dependenies. We write dependeny (, b) s b, We ssume mpping funtion M : N A P {rl, l}, whih ssoites node to either pir (, p) referring to n tion exeuted on peripherl; or to pir (r, v) with v {rl, l}, referring to lim (l) or relese (rl) of resoure r. Nodes mpped to pir (, p) re lled tion nodes, nd nodes mpped to lim or relese of resoure re lled lim nd relese nodes respetively. We ssume number of onstrints tht ensure tht tivities n be sttilly heked for proper resoure liming. hese onstrints re however not stritly neessry for timing nlysis. All nodes mpped to the sme peripherl re sequentilly ordered to void self-onurreny; Eh resoure is limed no more thn one; Eh resoure is relesed no more thn one; Every tion node is preeded by lim node on the orresponding resoure; Every tion node is sueeded by relese node on the orresponding resoure; Every relese node is preeded by lim node on the orresponding resoure; Every lim node is sueeded by relese node on the orresponding resoure. For eh tivity, we define the set of resoures it uses, whih is needed in the lter definition of sequening tivities. Definition 2 (esoures of Ativity). Given tivity At = (N, ), we define set (At) = {r ( n N M(n) = (r, l))}.

3 Fig. 3. Ativities At 1, At 2, nd At 3. Fig. 4. Ativity At 1 At 2 At 3. Multiple tivities n be omposed into ombined tivity using the sequening opertor. Given the set of shred resoures, it removes intermedite relese nd lim nodes on these resoures, nd properly links the dependenies. his form of sequening is similr to the notion of wek sequentil omposition [5], whih is lso defined reltive to dependeny reltion over set of tions. Definition 3 (Sequening Opertor). Given two tivities At 1 = (N 1, 1 ) nd At 2 = (N 2, 2 ) with N 1 N 2 =, we define At 1 At 2 s tivity At 1 2 = (N 1 2, 1 2 ). Let 1 2 = (At 1 ) (At 2 ) denote the set of resoures used in both tivities. Define the set of orresponding relese nodes in N 1, nd lim nodes in N 2 s rl 1 2 = {n 1 n 1 N 1 ( r 1 2 M(n 1 ) = (r, rl))}, nd l 1 2 = {n 2 n 2 N 2 ( r 1 2 M(n 2 ) = (r, l))} respetively. Ativity At 1 2 = (N 1 2, 1 2 ) is now defined s follows: N 1 2 = (N 1 N 2 )\(l 1 2 rl 1 2 ) 1 2 = {(n i, n j ) n i 1 n j n j rl 1 2 } {(n i, n j ) n i 2 n j n i l 1 2 } {(n 1, n 2 ) ( n rl rl 1 2 n 1 1 n rl ) ( n l l 1 2 n l 2 n 2 )}. Fig. 4 shows how tivities At 1, At 2, nd At 3, shown in Fig. 3, re omposed to tivity At 1 At 2 At 3 using the sequening opertor. Note tht the sequening opertor is ssoitive. B. Dynmi Semntis So fr, we hve desribed the struture of tivities nd the wy they n be omposed. In order to do performne nlysis, we need to introdue timing informtion. We do so on tion level, tivity level, nd tivity sequene level. Definition 4 (Exeution time of n tion). We ssume funtion : A 0 tht mps eh tion to its fixed exeution time. Definition 5 (Exeution time of node). We define funtion : N 0 tht mps eh node to fixed exeution time, given node n N in tivity (N, ): () if M(n) = (, p) (n) = for some A, p P 0 otherwise. We use (mx, +) lgebr to pture the dynmi semntis of tivities in onise wy. wo essentil hrteristis of the exeution of n tivity re synhroniztion; when node wits for ll its inoming dependenies to finish, nd dely; when n tion exeution strts, it tkes fixed mount of time before it ompletes. hese hrteristis orrespond well to the (mx, +) opertors mx nd ddition, defined over the set = { }. he mx nd + opertors re defined s in usul lgebr, with the dditionl onvention tht is the unit element of mx: mx(, x) = mx(x, ) = x, nd the zero-element of ddition: + x = x + =. Addition distributes over the mximum opertor: x + mx(y, z) = mx(x + y, x + z). o formlize synhroniztion we need notion of predeessor nodes. Definition 6 (Predeessor nodes). Given tivity (N, ) nd node n N, we define the set of predeessor nodes: P red(n) = {n in N n in n}. Sine tions re exeuted on resoures, we ssume resoure time stmp vetor γ :. he vetor represents the system stte in terms of resoure vilbility. Eh entry γ (r) orresponds to the vilbility time of the resoure r in the system. hese entries re used to determine when resoures re vilble, nd hene n be limed. All entries in the initil vetor re ssumed to be zero, to indite tht ll resoures re vilble upon strt of the system. Definition 7 (Strt nd ompletion time of node). Given tivity At = (N, ) nd resoure time stmp vetor γ, we n define the strt time strt(n) nd ompletion time end(n) for eh node n N: γ (r) if M(n) = (r, l) strt(n) = mx otherwise n in P red(n) end(n in) end(n) = strt(n) + (n). Ation n strt s soon s ll predeessor tions ompleted exeution. Note tht the strt nd end times for eh

4 node re uniquely defined, due to the struturl properties of tivities. his lso mens tht the dynmi semntis of n tivity At = (N, ) is uniquely defined by N,, nd timing funtion, Now, onsider resoure time stmp vetor γ s strting onfigurtion of the system. After exeution of tivity At = (N, ), we get new resoure time stmp vetor γ, where eh entry is defined s follows: γ (r) if r (At) γ (r) = end(n) if r (At) M(n) = (r, rl) for some n N. Sine (mx, +) lgebr is liner lgebr, it n be extended to mtries nd vetors in the usul wy. Given mtrix A nd vetor x, we use A x to denote the (mx, +) mtrix multiplition. Given m p mtrix A nd p n mtrix B, the elements of the resulting mtrix A B re determined by: [A B] ij = mx p ([A] ik + [B] kj ). For ny k=1 vetor x, x = mx i x i denotes the vetor norm of x. For vetor x, with x >, we use x norm to denote x x, the normlized vetor, suh tht x norm = 0. We use 0 to denote vetor with ll zero-vlued entries. Using this liner lgebr, we n pture the behvior of n tivity in (mx, +) mtrix. Consider tivity At, hrterized by (mx, +) mtrix M At. hen, given resoure time stmp vetor γ, the new vetor γ is given by γ = M At γ. An lgorithm for omputing the tivity mtries utomtilly n be found in [6, Algorithm 1]. Exmple 8 ((mx, +) hrteriztion). Consider tivity At 1, shown in Fig. 3, with () = 1, (b) = 2, () = 3 nd (d) = 1. Where = {r 1, r 2 }, (p 1 ) = (p 3 ) = r 1, nd (p 2 ) = r 2. We strt with resoure time stmp vetor γ = [r 1, r 2 ]. Now, the (mx, +) expressions relted to the ending time of the nodes re s follows: end(l(r 1 )) = γ (r 1 ) end(l(r 2 )) = γ (r 2 ) end() = mx(end(l(r 1 ))) + () = γ (r 1 ) + 1 end(b) = mx(end(l(r 2 ))) + (b) = γ (r 2 ) + 2 end() = mx(end(), end(b)) + () = mx(γ (r 1 ) + 1, γ (r 2 ) + 2) + 3 = mx(γ (r 1 ) + 4, γ (r 2 ) + 5) end(d) = mx(end(b)) + (d) = γ (r 2 ) + 3 end(rl(r 1 )) = end() = mx(γ (r 1 ) + 4, γ (r 2 ) + 5) end(rl(r 2 )) = end(d) = γ (r 2 ) + 3. he (mx, +) hrteriztion of end(rl(r j )) for ny r j n be written in the norml form r j = mx ri (γ (r i )+t i ) for some t i. Note tht t i = for ny r i \ (At 1 ). Written in norml form, we get: end(rl(r 1 )) = mx(γ (r 1 ) + 4, γ (r 2 ) + 5) end(rl(r 2 )) = mx(γ (r 1 ) +, γ (r 2 ) + 3). r 2 r 1 b d () Gntt hrt of At 1 given strting vetor γ = [0, 0]. r 2 r 1 b d (b) Gntt hrt of At 1 given strting vetor γ = [0, 1]. Fig. 5. Gntt hrts for At 1 given different strting resoure vilbility vetors. he (mx, +) hrteriztion of the tivity is [ ] 4 5 M At1 =. 3 Given γ, the new vetor γ is omputed s follows: [ ] [ ] 4 5 γ (r M At1 γ = 1 ) 3 γ (r 2 ) [ ] mx(4 + γ (r = 1 ), 5 + γ (r 2 )) mx( + γ (r 1 ), 3 + γ (r 2 )) [ ] γ = (r 1 ) γ (r. 2) For exmple, given strting vetor γ = [0 1], γ is omputed s: [ ] [ ] M A1 γ = 3 1 [ ] [ mx(4 + 0, 5 + 1) 6 = =. mx( + 0, 3 + 1) 4] Fig. 5 shows the Gntt hrts for At 1, for two different strting resoure vilbility vetors. hik edges re used to indite the time t whih resoures re limed nd relesed by the tivity. he light gry re denotes tht we hve to wit until the resoure beomes vilble, nd the light yellow res indite tht the resoure is limed but no tion is being exeuted on it. he timing semntis of n tivity sequene is defined in terms of repeted mtrix multiplition. Note tht lterntively, the timing n lso be omputed by first omposing ll tivities using the sequening opertor (Def. 3). he mtrix multiplition is however more effiient, sine eh tivity mtrix hs to be omputed only one. Lemm 9 ((mx, +) dynmis of n tivity sequene). Consider tivities At 1 nd At 2. hen M At1 At 2 = M At2 M At1. Fig. 6 shows the Gntt hrt indued by tivity sequene At 1 At 2 At 3. Note tht tivities re pipelined on the resoures. For instne, At 2 strts before At 1 is fully ompleted. C. Dispthing Ativities We use non-deterministi finite stte mhine (FSM) to model ll llowed (possibly infinite) tivity sequenes. hese

5 L CA U r 3 r 2 r 1 f b d e b h Z CL CL H CL Z CL Z Fig. 6. Gntt hrt of At 1 At 2 At 3 given strting vetor γ = [0, 0, 0]. tivity sequenes ensure tht funtionl requirements re met, for instne relted to enforing produt life yles nd ensuring sfety spets. Definition 10 (Ativity-FSM). An Ativity-FSM F on At is tuple L, At, δ, l 0 where L is finite set of lotions, At is nonempty set of tivities, δ L At L is the trnsition reltion, nd l 0 L is the initil lotion. Let l At l be shorthnd for (l, At, l ) δ. he timing of tivities n be dded to the Ativity- FSM by dding the (mx, +) mtrix of eh tivity to the orresponding edges. From this utomton (mx, +) stte spe n be generted for performne nlysis of the ontroller. Definition 11 (Normlized (mx, +) stte spe (dpted from [7])). Given Ativity-FSM L, At, δ, l 0, resoure set, nd (mx, +) mtrix set {M At At At}, we define the normlized (mx, +) stte spe C, o, s follows. Initil onfigurtion 0 = l 0, 0. Set C = L of onfigurtions onsisting of lotion nd normlized resoure vilbility vetor. A lbeled trnsition reltion C At C onsisting of the trnsitions in the set { l, γ, γ, At, l, γ norm (l, At, l ) δ γ = M At γ }. Eh stte l, γ refers to both n FSM lotion l, nd resoure vilbility vetor γ. Consider n edge l, γ, γ, At, l, γ norm. We strt from stte l, γ, nd exeute the senrio on the edge l, l in the FSM. γ denotes the trnsit time. he new stte is l, γ norm, where the new resoure time stmp vetor is omputed s γ = M At γ, whih is subsequently normlized. he stte spe reords only the normlized resoure vilbility vetors, sine only the reltive timing differenes ffet the future behvior, not their bsolute offset. Eh rehble yle in this stte spe llows for periodi exeution of the system. Eh edge on this yle is ssoited with trnsit time orresponding to the tivity durtion. Let the trnsit time of yle be the sum of the trnsit time vlues of its edges. hen the yle men is equl to its trnsit time divided by the number of edges in the yle. Both the best nd worst se performne of the system n be found by looking t these yles, using n mximum or minimum yle men lgorithm [4], [7]. IN COND DILL OU Fig. 7. Mnufturing system exmple (wilight system) with two robots nd two prodution stges. III. EXAMPLE: WILIGH SYSEM In this setion we show how the modeling pproh n be used to model nd nlyze mnufturing system. As n exmple we tke the wilight system shown in Fig. 7, where blls re proessed eh following given reipe. his mnufturing system is simplifition of the produt hndling model tht hs been reted t ASML, using similr kinds of peripherls nd resoures. A. Exmple Mnufturing System Our exmple system ontins four resoures. First, there re two robots to trnsport blls; the lod robot (L) nd the unlod robot (U). Eh robot hs homing position; L on the left orner, nd U on the right orner. he other two resoures re proessing sttions, the onditioner (COND) to ensure right bll temperture, nd the drill (DILL) to drill hole in bll. Both robots hve three peripherls; lmp (CL) to pik up nd hold bll, n -motor () to move long the ril, nd Z-motor (Z) to move the lmp up nd down. Sine eh robot n reh both proessing sttions, there is ollision re (CA). Both proessing sttions hve lmp peripherl. he onditioner hs heter (H), to het bll. he drill hs n -motor () to rotte the drill bit, nd Z-motor (Z) to move the drill bit up nd down. Eh bll proessed by the system follows the sme life yle. First, bll is piked up t the input buffer by the lod robot. hen it is brought to the onditioner nd proessed. Next, the item is trnsported by either one of the robots to the drill, where it is drilled. Finlly, the drilled bll is trnsported to the output buffer. B. Ativities In our system, there re two tivities tht proess blls: nd. For trnsporttion of the blls, there re two types of tivities: piking up bll by robot, nd relesing bll by robot on produt lotion. he omplete set of tivities is shown in ble I. Eh tivity is modeled formlly by speifying the tions involved nd the dependenies between these tions. As n exmple, onsider tivity L PikFromCond shown in Fig. 8, in whih the lod robot piks bll from the onditioner. In tivity L PikFromCond, we use the speil resoure CA to model the physil ollision re bove COND nd

6 ABLE I SE OF ACIVIIES FO OU EXAMPLE SYSEM. L PikFromInput L PutOn U PutOnCond L PutOnCond U PikFrom U PutOnOutput L PikFromCond U PikFromCond L PikFrom U PutOn Fig. 10. Produt lotion utomton. Fig. 8. Ativity L PikFromCond. DILL. As long s one robot hs limed this resoure, the other robot nnot enter. obots lwys return to their sfe home position before ending robot tivity. Using homing position gurntees sfety, but might not result in throughputoptiml system. More refined tivities llow more sheduling freedom by the ontroller, whih n be used to improve the mximl hievble throughput. We will not onsider suh refinements here. C. Allowed Ativity Sequenes Given the system tivities, we model whih tivity sequenes re llowed. his is done using set of requirements, modeled s utomt, where the trnsitions re lbeled with tivity nmes. Multiprty synhroniztion is used, where exeution of shred events is synhronous. his synhroniztion mehnism ensures tht fter omposition, eh requirement is still tken into ount. As mentioned before, eh tivity involves the trnsport or proessing of bll. In the model, we expliitly model the bll instnes in the system by dding n identifier i in the the tivity nme suffix. An infinite produt strem is simulted by using five bll instnes (see Fig. 9), indued by the resoure pity of the system (see lso [1]). Produts enter the system in the order indued by their indies. Given n tivity At involving produt nd set I of produt identifiers, we define set At = {At i i I}. For eh bll we model the lotion in the system nd the enbled tivities, shown in Fig. 10. For instne, if bll is t the drill (t), the system n perform the tivity on this bll, or pik it up by one of the robots. Eh bll is required to follow the sme life yle. his requirement is modeled using the utomton shown in Fig. 11. Fig. 11. Life yle utomton. Moves re expliitly enoded to ensure tht blls lwys move forwrd in the system. In this wy, we n find meningful miniml throughput gurntee in the nlysis step. Note tht there is still sheduling freedom whih robot is used to trnsport bll from the onditioner to the drill. his hoie might hve n impt on the overll system performne. o void bll ollisions, we dd lotion stte utomt, shown in Fig. 12. hese utomt ensure tht fter piking up bll by robot, it must first be relesed before the next bll n be piked. In the sme wy, we void putting two blls on the onditioner or the drill. Given the set of tivities, nd the requirements, we use supervisory ontroller synthesis [8], [9] to obtin n Ativity- FSM of ll llowed tivity sequenes. By using synthesis, the Ativity-FSM is gurnteed to be dedlok-free nd funtionlly orret with respet to the modeled requirements. he resulting Ativity-FSM fter synthesis is shown in Fig. 13. () Produt lotion COND (b) Produt lotion DILL () Produt lotion L (d) Produt lotion U Fig. 9. Produt order utomton. Fig. 12. Lotion stte utomt.

7 s4 L_PikPrdFromInput U_PikPrdFromCond L_PikPrdFromInput L_PikPrdFromInput U_PutPrdOnOutput s6 U_PikPrdFromCond s57 s60 s67 L_PikPrdFromInput L_PikPrdFromInput s71 s244 U_PutPrdOnOutput s41 U_PutPrdOn U_PutPrdOnOutput s39 s245 U_PutPrdOnOutput s46 U_PikPrdFromCond L_PutPrdOnCond s51 L_PikPrdFromInput U_PikPrdFrom L_PikPrdFromInput s47 s53 L_PikPrdFromInput L_PutPrdOnCond s35 s42 L_PikPrdFromInput U_PutPrdOn U_PutPrdOnOutput s61 s242 L_PikPrdFromInput s58 U_PutPrdOn s37 L_PikPrdFromCond s69 U_PutPrdOnOutput L_PikPrdFromInput L_PikPrdFromCond U_PutPrdOnOutput U_PikPrdFromCond s243 s44 U_PutPrdOnOutput L_PikPrdFromInput U_PutPrdOnOutput s65 L_PikPrdFromCond U_PutPrdOn U_PutPrdOnOutput s72 U_PutPrdOn s30 s33 L_PutPrdOn s38 L_PikPrdFromInput U_PutPrdOnOutput L_PikPrdFromInput s77 U_PutPrdOnOutput s68 s240 s36 L_PikPrdFromInput s79 U_PikPrdFrom s52 s241 s49 L_PikPrdFromInput U_PikPrdFrom L_PikPrdFromCond L_PikPrdFromInput L_PutPrdOnCond U_PutPrdOn s40 U_PutPrdOn U_PutPrdOnOutput U_PutPrdOnOutput s59 U_PutPrdOnOutput L_PikPrdFromCond s48 L_PikPrdFromCond L_PikPrdFromCond U_PutPrdOnOutput L_PutPrdOnCond s56 U_PutPrdOnOutput s34 L_PikPrdFromInput U_PutPrdOnOutput s45 s28 U_PikPrdFrom L_PikPrdFromInput L_PutPrdOn L_PikPrdFromInput L_PikPrdFromInput U_PutPrdOnOutput s43 L_PikPrdFromInput s24 s29 s70 U_PutPrdOnOutput U_PutPrdOn U_PutPrdOnOutput s239 s66 s238 L_PikPrdFromInput U_PutPrdOnOutput U_PutPrdOnOutput L_PikPrdFromCond U_PutPrdOnOutputL_PikPrdFromInput s31 L_PikPrdFromCond U_PutPrdOnOutput s75 s80 L_PikPrdFromCond s22 s78 L_PikPrdFromInput s32 L_PikPrdFromInput s23 s54 L_PikPrdFromInput U_PutPrdOnOutput U_PutPrdOnOutput L_PikPrdFromInput s84 s50 L_PikPrdFromInput L_PutPrdOnCond s27 s64 U_PutPrdOn U_PutPrdOn s237 U_PikPrdFrom L_PikPrdFromInput U_PutPrdOnOutput U_PutPrdOn s17 L_PikPrdFromInput U_PutPrdOnOutput U_PikPrdFrom s21 L_PutPrdOnCond U_PikPrdFrom s76 U_PikPrdFrom L_PikPrdFromCond U_PikPrdFrom s18 L_PikPrdFromCond U_PikPrdFrom s25 s236 L_PutPrdOnCond U_PutPrdOnOutput s85 s82 L_PikPrdFromInput L_PutPrdOnCond U_PikPrdFrom s62 s16 s55 s26 L_PutPrdOnCond L_PikPrdFromInput L_PutPrdOnCond U_PutPrdOnOutput L_PikPrdFromInput s74 U_PutPrdOn s19 s88 L_PutPrdOnCond U_PikPrdFrom U_PutPrdOnOutput U_PutPrdOnOutput L_PikPrdFromInput U_PutPrdOnOutput s235 U_PikPrdFrom s13 U_PutPrdOnOutput L_PikPrdFromInput s83 U_PutPrdOnOutput s14 L_PutPrdOnCond L_PikPrdFromInput L_PikPrdFromCond U_PutPrdOnOutput s63 s73 s86 L_PikPrdFromInput L_PutPrdOnCond U_PutPrdOnOutput s20 s233 s81 s89 L_PikPrdFromInput L_PutPrdOnCond L_PikPrdFromInput U_PutPrdOnOutput s11 U_PutPrdOnOutput L_PikPrdFromInput s15 s10 L_PikPrdFromInput L_PikPrdFromInput U_PutPrdOnOutput L_PikPrdFromCond U_PutPrdOnOutput U_PutPrdOnOutput s231 s5 U_PutPrdOn s7 U_PutPrdOn L_PikPrdFromInput L_PutPrdOn L_PutPrdOn U_PikPrdFrom s3 U_PikPrdFrom U_PutPrdOnOutput U_PikPrdFrom s229 L_PikPrdFromCond U_PutPrdOnOutput s224 L_PikPrdFromInput s227 L_PutPrdOnCond L_PikPrdFromInput s228 s199 L_PikPrdFromInput s8 L_PutPrdOnCond U_PutPrdOnOutput s198 s9 s195 U_PikPrdFrom s223 U_PutPrdOn U_PikPrdFrom U_PutPrdOnOutput U_PutPrdOnOutput L_PikPrdFromCond s211 L_PikPrdFromCond U_PutPrdOnOutput s217 s2 s225 U_PikPrdFrom L_PikPrdFromInput s220 L_PutPrdOnCond s222 s209 s215 L_PikPrdFromInput L_PikPrdFromCond U_PutPrdOnOutput L_PikPrdFromInput L_PikPrdFromCond U_PutPrdOn s213 U_PutPrdOn L_PikPrdFromInput U_PutPrdOnOutput U_PutPrdOnOutput L_PikPrdFromInput s203 s214 U_PutPrdOnOutput s210 U_PutPrdOnOutput L_PikPrdFromInput s216 s208 L_PutPrdOnCond s218 U_PikPrdFrom s1 s212 L_PikPrdFromInput s201 L_PikPrdFromInput L_PikPrdFromInput U_PutPrdOn s206 U_PutPrdOnOutput U_PutPrdOn s204 s197 U_PutPrdOnOutput L_PikPrdFromInput U_PutPrdOnOutput s202 L_PutPrdOnCond s205 s207 L_PikPrdFromInput L_PutPrdOnCond L_PutPrdOnCond s200 U_PutPrdOnOutput L_PikPrdFromInput s196 U_PikPrdFrom U_PutPrdOn s232 s221 s230 U_PutPrdOnOutput L_PikPrdFromCond s226 s234 U_PutPrdOnOutput L_PikPrdFromInput U_PutPrdOnOutput s219 s12 U_PikPrdFromCond L_PikPrdFromInput s192 L_PutPrdOnCond L_PikPrdFromInput L_PikPrdFromInput U_PutPrdOnOutput s153 U_PikPrdFrom s148 L_PutPrdOn s143 U_PutPrdOnOutput s87 s90 L_PikPrdFromInput L_PikPrdFromCond L_PutPrdOn U_PikPrdFromCond s91 s92 U_PikPrdFromCond L_PutPrdOn L_PikPrdFromInput U_PutPrdOnOutput U_PutPrdOn L_PikPrdFromInput s95 L_PikPrdFromInput s99 s94 U_PutPrdOn U_PutPrdOnOutput U_PutPrdOnOutput L_PikPrdFromInput U_PikPrdFrom L_PikPrdFromInput L_PutPrdOnCond U_PutPrdOnOutput s104 s103 s98 s97 L_PutPrdOnCond s105 s93 s101 s100 L_PutPrdOnCond L_PikPrdFromInput U_PutPrdOn U_PutPrdOnOutput L_PutPrdOnCond s107 U_PutPrdOnOutput L_PikPrdFromInput L_PikPrdFromInput U_PikPrdFrom L_PutPrdOnCond L_PikPrdFromInput L_PikPrdFromCond s112 U_PutPrdOn s108 s96 s102 s106 L_PikPrdFromInput U_PutPrdOn s114 s116 s111 U_PutPrdOnOutput s117 L_PikPrdFromInput s110 L_PikPrdFromInput s113 U_PutPrdOnOutput U_PutPrdOnOutput s115 U_PutPrdOn L_PutPrdOnCond L_PikPrdFromInput U_PikPrdFrom L_PikPrdFromInput L_PikPrdFromInput s118 s122 U_PutPrdOn L_PikPrdFromCond s120 L_PikPrdFromCond U_PutPrdOnOutput U_PutPrdOnOutput s141 L_PutPrdOnCond U_PutPrdOnOutput L_PutPrdOn U_PikPrdFromCond s179 s160 L_PikPrdFromInput s193 L_PikPrdFromInput U_PutPrdOnOutput U_PutPrdOn s189 U_PutPrdOn U_PutPrdOnOutput U_PikPrdFrom s140 s142 U_PutPrdOnOutput L_PutPrdOnCond s185 U_PikPrdFromCond L_PikPrdFromInput s188 s146 L_PikPrdFromInput L_PikPrdFromInput s152 U_PutPrdOnOutput s194 U_PikPrdFromCond s184 s172 L_PutPrdOn L_PikPrdFromInput L_PikPrdFromCond L_PutPrdOnCond U_PutPrdOnOutput s147 U_PutPrdOnOutput L_PikPrdFromInput U_PutPrdOnOutput U_PikPrdFrom L_PikPrdFromInput s191 U_PutPrdOnOutput L_PikPrdFromInput U_PutPrdOn s190 s144 s162 L_PutPrdOnCond U_PutPrdOnOutput s180 s150 L_PutPrdOn s181 L_PikPrdFromCond U_PutPrdOnOutput U_PikPrdFrom L_PikPrdFromInput L_PikPrdFromInput L_PutPrdOnCond s154 s145 L_PutPrdOnCond U_PikPrdFrom U_PutPrdOnOutput s187 U_PutPrdOn s173 s186 L_PutPrdOnCond s149 U_PutPrdOnOutput s157 s174 U_PikPrdFrom L_PikPrdFromCond L_PikPrdFromInput U_PikPrdFrom L_PikPrdFromInput s163 U_PutPrdOnOutput s183 s151 L_PikPrdFromCond U_PutPrdOn s182 L_PikPrdFromInput s164 L_PikPrdFromInput L_PikPrdFromInput s155 U_PutPrdOnOutput s167 U_PutPrdOnOutput U_PutPrdOn s176 U_PutPrdOnOutput L_PikPrdFromInput L_PikPrdFromCond U_PutPrdOnOutput s156 L_PikPrdFromInput L_PikPrdFromCond L_PikPrdFromInput s175 s168 s158 U_PutPrdOnOutput U_PutPrdOn U_PutPrdOnOutput s178 U_PutPrdOn s166 L_PikPrdFromCond s159 L_PikPrdFromInput s177 s165 U_PutPrdOnOutput s171 s170 s161 U_PutPrdOnOutput s169 s123 U_PutPrdOnOutput s124 s119 s126 s127 s125 U_PutPrdOnOutput U_PutPrdOnOutput s121 L_PikPrdFromInput L_PikPrdFromInput U_PikPrdFrom L_PikPrdFromInput s130 U_PikPrdFrom L_PikPrdFromCond L_PikPrdFromCond s128 U_PutPrdOnOutput L_PikPrdFromInput s134 U_PutPrdOnOutput L_PikPrdFromCond U_PutPrdOnOutput U_PikPrdFrom L_PikPrdFromInput s138 L_PikPrdFromCond s136 s139 s132 s135 L_PikPrdFromInputU_PutPrdOnOutput s137 s131 s129 U_PutPrdOnOutput U_PikPrdFrom s133 U_PutPrdOnOutput s109 Fig. 13. Synthesized Ativity-FSM for our exmple (245 lotions nd 510 trnsitions). he green yle is n optiml dispth sequene, the red yle is worst-se dispth sequene. Sine requirements re modeled in ompositionl wy, it is lso possible to use modulr synthesis tehniques [10], [11] for lrger ses. he result is set of supervisors tht work in onjuntion to enfore the omplete set of requirements. D. Anlysis o do performne nlysis, we ompute the mtries of the tivities nd then the normlized (mx, +) stte spe. his stte spe ontins 1633 sttes nd 2894 edges. o find the best-se throughput of the system, we use the yle nlysis lgorithm s desribed in Setion II-C. his lgorithm yields the optiml dispth sequene for stedy-stte behvior, shown in green in Fig. 13. E. Expliit Modeling using Finite Automt We hve lso modeled the exmple system expliitly using finite stte utomt with timing, to verify the benefit of our modeling pproh with respet to slbility. his benefit rises from the bstrtion of the tions in tivities. In the full model, there is expliit interleving of ll tions ontined in tivities. Note tht the full model ontins the sme shedules, sine we only unfold the interleving of lowlevel tions. Eh tivity is modeled s n utomton, nd instntited for eh ourrene in the Ativity-FSM with unique identifier. Per resoure we hve n utomton to pture the preedene onstrints mong tivities. For eh resoure, there is n utomton tht ensures orret liming nd relesing. In this model, lso multi-prty synhroniztion is used. As modeling tool we hve used CIF3 [12]. Explortion of the full stte spe rn out of memory fter n hour on n Intel E CPU nd 100GB of vilble virtul memory. We found out tht the full stte spe ontins t lest 5 million sttes. his shows the huge stte spe redution tht n be hieved by the (mx, +) stte spe, ompred to stte spe with full interleving of tions. he experiment shows the benefit of our forml modeling pproh, where nlysis n be done within few seonds. IV. INDUSIAL APPLICAION At ASML, the modeling formlism is used s semnti underpinning of DSL to express prt of the system behvior. he DSL llows domin engineers to desribe the system in terms of resoures, peripherls, tions, nd tivities. An importnt subset of the vilble tions re determined by symboli positions nd motion pths of robot resoures. For exmple, two robot rms hve been modeled tht hve 3 xes, round 50 symboli positions eh, nd round 300 motion pths between symboli positions resulting in lrge set of possible peripherl tions. Using this system model, vrious tivity sequenes n be nlyzed in terms of performne. Also, the impt of individul tion timings on mhine throughput is nlyzed. his timing nlysis is enbled by the (mx, +) semntis nd the vilble nlysis tehniques in this domin tht n esily be pplied to the system models. he urrent fous is on obtining omplete speifition for nominl behvior in the produt hndling prt of the mhine. here is forml speifition model of the produt logistis [1], tht n be linked to the system model. However, synthesis of the Ativity-FSM is not fesible due to slbility issues. herefore, n importnt urrent reserh topi is modulr synthesis of the Ativity-FSM to improve slbility. V. ELAED WOK Senrio-Awre Dt Flow (SADF) [7] hs similr seprtion of onerns with respet to funtionlity nd timing. his formlism uses the sme model of omputtion, (mx, +) lgebr, to perform throughput nlysis. Compred to SADF, our forml modeling pproh llows modulr speifition of both the tivities nd the requirements to be imposed on the ordering. Another dvntge of our pproh is the bility to synthesize the FSM ontining ll llowed tivity sequenes. hese two dvntges lso pply with respet to (mx, +) utomt. It is possible to onvert model in our formlism to n FSM-SADF model. As studied in [13], eh tivity n be mpped onto n SDF senrio, nd the Ativity-FSM orresponds to the FSM in FSM-SADF. Note tht n SDF senrio is more generl, sine it n lso ontin yles. Other well known formlisms used for modeling nd performne nlysis of mnufturing systems re timed utomt [14], timed Petri nets [15], nd job shop sheduling with preedene onstrints [16]. imed utomt extended with gme theory, timed gmes [17], llow synthesis of ontroller ensuring sfe behvior nd rehing finl stte eventully. imed Petri nets llow performne nlysis by ssoiting dely bounds with eh ple in the net [18]. In both forml models, speifition of timing nd funtionlity spets is not ompositionl. Insted, system with tions, tivities nd resoures is typilly speified s desribed in Setion III-E, whih supports the lim of similr type of

8 slbility issues. In job shop sheduling, finding n optiml ontroller is typilly onsidered s onstrint stisftion problem. Here, ll dependenies on job (tivity) level nd opertion (tion) level re enoded using onstrints. In this formultion, there is lso no seprtion of onerns with respet to funtionlity nd timing. Modeling system opertions s grphs is lso done in other domins. For instne in rel-time systems [19], where lso dedlines nd bounded inter-rrivl times of tions ply role. However, tivities re ssumed to be independent, whih mens tht there is no wy to speify dependenies mong the tivities, whih we do by mens of the Ativity-FSM. Our frmework lso resembles prtil-order utomt [20], where eh trnsition orresponds to set of prtil-ordered tres. In our se, eh tivity trnsition in the Ativity- FSM lso orresponds to DAG desribing multiple llowed tres. However, in prtil-order utomt, fter eh trnsition follows synhroniztion point, whih mens tht there is no wek-sequening. VI. CONCLUSION his pper introdues new forml modeling pproh tht llows ompositionl speifition of both funtionlity nd timing of mnufturing systems. In the pproh, behvior in the system is bstrted using the onept of tivities, nd the ontroller hoies reside on this bstrted level. his bstrtion leds to onise speifition, nd results in smller stte spe for synthesis nd nlysis, ompred to stte spe with full interleving of low-level tions. esoure mngement is hndled t the lower level, without expliit intertion with the ontroller. he semntis of the model re expressed in the (mx, +) domin, enbling the use of existing performne nlysis tehniques to find n optiml tivity ordering. Our pproh is illustrted on n exmple mnufturing system nd n industril se study is given. here re number of next steps to extend the pproh. First, we wnt to look into the extension of deling with exeptionl behvior nd externl disturbnes. In suh setting, the Ativity-FSM will need to be extended with unontrollble trnsitions tht pture this unontrollble behvior. Seond, speifition of funtionl requirements is now modeled diretly using utomt. In priniple however, there re mny other formlisms tht my be better suited to speify requirements. For exmple, extended finite utomt [21] n be used, where dt vribles re dded to finite utomt. his enbles the use of stte-bsed requirements [22], whih llows requirements to refer to sttes of other utomt. hird, in the industril use of the modeling formlism, there re slbility hllenges in synthesis of the Ativity-FSM. herefore, we re investigting severl pprohes to redue the stte spe tht needs to be explored using prtil order redution tehniques, nd the use of modulr synthesis tehniques. ACKNOWLEDGMEN his reserh is supported by the Duth ehnology Foundtion SW, rried out s prt of the obust Cyber-Physil Systems (CPS) progrm, projet number EFEENCES [1] B. vn der Snden et l., Modulr model-bsed supervisory ontroller design for wfer logistis in lithogrphy mhines, in 18th ACM/IEEE Int. Conf. on Model Driven Engineering Lnguges nd Systems, MoDELS 2015, Ottw, ON, Cnd, 2015, pp [2] F. Belli et l., Synhroniztion nd linerity: n lgebr for disrete event systems. John Wiley nd Sons, [3] S. Gubert, Performne evlution of (mx,+) utomt, IEEE rns. Autom. Control, vol. 40, no. 12, pp , De [4] A. Dsdn, Experimentl nlysis of the fstest optimum yle rtio nd men lgorithms, ACM rns. Design Automtion of Eletroni Systems, vol. 9, no. 4, pp , [5] A. ensink nd H. Wehrheim, Wek Sequentil Composition in Proess Algebrs. Springer Berlin Heidelberg, 1994, pp [6] M. Geilen, Synhronous dtflow senrios, ACM rns. Embed. Comput. Syst., vol. 10, no. 2, pp. 16:1 16:31, Jn [7] M. Geilen nd S. Stuijk, Worst-se performne nlysis of Synhronous Dtflow senrios, 2010 IEEE/ACM/IFIP Int. Conf. on Hrdwre/Softwre Codesign nd System Synthesis (CODES+ISSS), no. C, pp , [8] P. J. G. mdge nd W. M. Wonhm, Supervisory ontrol of lss of disrete event proesses, SIAM J. Control Optim., vol. 25, no. 1, pp , [9], he ontrol of disrete event systems, Pro. of the IEEE, vol. 77, no. 1, pp , [10] K. Shmidt nd C. Breindl, Mximlly permissive hierrhil ontrol of deentrlized disrete event systems, IEEE rns. Autom. Control, vol. 56, no. 4, pp , April [11] L. Feng nd W. Wonhm, Supervisory ontrol rhiteture for disreteevent systems, IEEE rns. Autom. Control, vol. 53, no. 6, pp , July [12] D. A. vn Beek et l., CIF 3: Model-bsed engineering of supervisory ontrollers, in ools nd Algorithms for the Constrution nd Anlysis of Systems, ser. Leture Notes in Comput. Si, E. Ábrhám nd K. Hvelund, Eds. Springer Berlin Heidelberg, 2014, vol. 8413, pp [13] J. Bstos et l., Modeling resoure shring using FSM-SADF, in 13. ACM/IEEE Int. Conf. on Forml Methods nd Models for Codesign, MEMOCODE 2015, Austin, X, USA, September 21-23, 2015, 2015, pp [14]. Alur nd D. L. Dill, A theory of timed utomt, heoretil Computer Siene, vol. 126, no. 2, pp , [15] B. Berthomieu nd M. Diz, Modeling nd verifition of time dependent systems using time petri nets, IEEE rns. Softw. Eng., vol. 17, no. 3, pp , Mr [16] A. Grrido et l., Heuristi methods for solving job-shop sheduling problems, in Pro. ECAI-2000 Workshop on New esults in Plnning, Sheduling nd Design, 2000, pp [17] G. Behrmnn et l., Computer Aided Verifition: 19th Int. Conf., CAV 2007, Berlin, Germny, July 3-7, Pro. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007, h. UPPAAL-ig: ime for Plying Gmes!, pp [18] H. Hulgrd nd S. M. Burns, Computer Aided Verifition: 7th Int. Conf., CAV 95 Liège, Belgium, July 3 5, 1995 Pro. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995, h. Effiient timing nlysis of lss of Petri nets, pp [19] M. Stigge et l., he digrph rel-time tsk model, in th IEEE el-ime nd Embedded ehnology nd Applitions Symposium, April 2011, pp [20] G. v. Bohmnn et l., esting Systems Speified s Prtil Order Input/Output Automt. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008, pp [21] M. Skoldstm, K. Åkesson, nd M. Fbin, Modeling of disrete event systems using finite utomt with vribles, in Deision nd Control, th IEEE Conf. on, De 2007, pp [22] J. Mrkovski et l., A stte-bsed frmework for supervisory ontrol synthesis nd verifition, in Deision nd Control (CDC), th IEEE Conf. on, De 2010, pp