A Time Delay System Case Study: Computer Integrated Manufacturing and Management System Robustness

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1 A Te Delay Syste Case Study: Copute Itegated Maufactug ad Maageet Syste Robustess Jozef B. Lewoc*, Ato Izwosk** Slawo Skowosk*** * BPBT Leade (Leadg Desge), ul Powst. Sl. 93/28, Woclaw, Polad ** Woclaw Uvesty of Techology, Wyb. Wyspaskego 27, Woclaw, Polad *** Woclaw Uvesty of Techology, Wyb. Wyspaskego 27, Woclaw, Polad Abstact: Thee s o cooly accepted appoach to selecto of a topology of a copute tegated aufactug ad/o aageet syste. The basc decsos ae udetake basg o the lkg of soe avalable hadwae, wthout ay cosdeato pad to ay chaactestcs of the topology. The pape poposes selecto of the topology basg o the syste obustess copaso, usg the μ fucto as the easue of obustess. Due to the fact that the systes ae of the te delay chaacte, calculato of μ s athe sple ad the ethod ay be used athe easly to solve the actual desg pobles. Copyght IFAC 2009 Keywods: Autoatc cotol, aufactug systes, aageet systes, copute tegated etepses, coucato systes, te delay systes, obustess, sgulaty.. INTRODUCTION The poble of the coucato eda (coucato etwok) topology dstbuted cotol/otog systes (e.g. those appled cotol ad otog of the wokg eda lage-scale aufactug etepses) s usually solved a athe abtay way. The coo opo s that soe kds of stadad local-aea etwoks of the cooedu type, lke Etheet (Csco Systes, 2006; NSF, 2002) ae the best possble soluto. Cosdeg that such appoach s hghly appopate, soe tals wee ade to select copute autoato syste topologes basg o the obustess. The fst case study attept was coected wth a copute-based oto of a bg theal powe plat (Izwosk 99a, Izwosk 99b). Whe desgg a ovel copute tegated aufactug ad aageet syste based o the Meda subsyste (Faask, 200, Izwosk 2006, Lewoc 2006), t was decded to use obustess ( the sese of autoatc cotol (Doyle, 982) ad ot of Atfcal Itellgece (AUAI, 2002; Coza, 997)), ad apply the vey basc obustess easue, the μ fucto defed fst by Doyle (982). The basc esults of the vey fst case study pefoed fo the Copute Itegated Maufactug ad Maageet (CIMM) systes (systes Meda) wee also publshed (Izwosk 2003a,b). The authos of the case studes etoed heeabove thought t ca be useful to peset soe oe geeal case of a copute autoato syste of topology selected o the bass of ts obustess. Howeve, the softwae tools developed fo the case study eabled to coduct soe oe geeal wok: to copae wokg eda cotol/aufactug systes of vaous topologes but teded to povde the sae sevces. The subject of the vestgatos ae the systes teded to oto ad cotol such vaables as the wokg eda (such as the electc powe, fuel gas, sold ad lqud fuels, cold ad hot wate, pocess stea, waste wate, waste gas, etc.) (the Systes). Afte Doyle (982), the stuctued sgula value fo the copesated plat subject to stuctued petubatos s used to aalyse the obustess of the pefoace of such plat. Such appoach has eabled to ake copasos of the Systes of dffeet topologes o soe atoal bass cotast to the abtay selectos ade by ost copute syste desges. Such appoach s hadly feasble fo geeal autoatc cotol systes because of vey sevee coputatoal pobles coected wth accuate coputato o eve wth appoxato of µ (Fu, 997). Howeve, sce the CIMM systes ude vestgato ay be aalysed as te delay systes, the appoach s feasble ad ay be useful. The pape pesets soe plots of the obustess easue adopted, the μ fucto, vesus the data tasfe cycle te. I accodace wth the expectatos, the obsolete sta topology featues wth uch hghe obustess values copaso wth the coo-edu (g o bus) topology, at least whe the fa copaso codtos ae appled. 2. CONFIGURATION OF THE SYSTEM Assug that the vaables a aufactug etepse cove those etoed the Itoducto of the peseted pape, the scheatc fuctoal stuctue of the Syste ay be peseted as Fg.. The poble s how to tecoect the cotolles dedcated to otog ad cotol of dvdual vaables ad the hghe level cotol ad otog syste povdg sevces to the Autoato

2 Depatet ad te-wokg wth the Copute Itegated Maageet syste of the etepse sce the Syste should be ecogsed as eedg co-opeato wth futue Copute Itegated Maufactug ad Maageet systes (Faask, 200, Izwosk 2006, Lewoc 2006). Actually, fo the pot of vew of data tassso ad obustess pled by that, thee ae two possble geeal aageets of the coucato syste tecoectg TO COMPUTER NETWORK OF THE ENTERPRISE the dvdual cotolles ad the cotol ad otog syste: the sta aageet whee all cotolles ae tecoected wth the hghe level syste va dvdual tassso lks (les) ad ay techage data wth the copute alost sultaeously ( the aco te) (see Fg. 2), ad the coo-edu data etwok aageet (see Fg. 3). The latte aageet ay be a bus wth pollg (e.g. RS 485, Modbus, Toke Bus) o a g (e.g. Etheet, Toke Rg, Poway). COMMUNI- CATIONS & MONITOR- ING SYSTEM VISUALISATION REPORT Vaable Vaable 2 Vaable 3 Vaable 4 Vaable 5 Vaable 6 Vaable Vaable PLANT UNDER MONITORING Fg.. Achtectue of the Syste Hgh level syste Hgh level syste Fg. 2. The Syste of the sta topology Fg. 3. The Syste of coo-edu topology

3 3. THE MODELS Fo the sta topology case, the odel of the cotol/otog loop s show Fg. 4.,, z z I ths case, the dstubace atx s gve by foula (2). R dag e s T d I ethe case, a sple tasfe fucto G(s) eetg the dead fo stablty defed by Doyle (982) s adopted. Whe a sple tegatg type acto of the plat s assued cofoty wth actual applcatos ay Autoato Depatets, G(s) ay be gve by the foula (3): k GR, k G R, k ; k,, (2) ; (3) z Fg. 4. Basc daga fo the sta topology Cosdeg the fact, that the Autoato Depatet (cluded the tasfe fucto G(s)) s able to obseve ad act o a lted set of the copoets of the z k vectos at oe te, t s possble to avod aalysg a hgh ube of vaables (exceedg seveal thousad ettes fo bg etepses (e.g. powe plats)). It ay be assued that all tasfe fuctos,,, ae of the pue te delay chaacte (the coucato syste toduces othg else tha te delays, beg a pue te delay syste; possble tassso eos ay be thought about as soe syste falues eedg sepaate aalyss). The dstubace atx s gve by (): s ( d ) S dag e () whee dj s a ultplcatve dstubace of the te delay type. Fo the coo-edu aageet case, the cotol loop daga s show Fg. 5 ad the equvalet daga Fg. 6. G R, G R, G R, Fg. 5. The coo-edu aageet: Basc daga Z Z G R, G R, Fg. 6. The coo-edu case: The equvalet daga Accodg to Doyle (982) ad Feees (999), the stuctued sgula value s defed by foulae (4) ad (5) fo the sta aageet case ad the coo-edu case, espectvely. ( G) ( S CM det 2 cos t,.., det S ( G) ( G 0),.., 2 cos t G 0) R : T z : The value of ω s deved, ethe case, fo the codto that ω = π/2t. To deve the foulae (4) ad (5), t was assued ( cofoty wth actual applcatos) that d = d, =,,. 4. ROBUSTNESS EVALUATION 4.. Assuptos coceg tassso delays To esue fa copasos, t was assued that the data ettes tastted va the coucato etwok have the sae data feld legths ( KB) whle the oveall data etty legths (cludg data ad cotol foato) ae (4) (5)

4 defed by elevat data tassso potocols. Ths eas, that fo the sta aageet case, the asychoous tasfe ode (oe stat bt, oe stop bt ad paty bt fo each 8-bt byte plus two bytes fo logtudal check su) s assued whle two sychosg octets (flags), ca 0% fo bt stuffg (seto/deleto of 0 afte a sees of fve s, to eable detecto of flags) plus 32 bts fo the edudacy check + 4 cotol octets ae assued fo the coo-edu aageet. S CM 4.2. Robustess evaluato cases Case. Ths case povdes the fa copaso of obustess fo the two coucato etwok aageet cases. The μ values (μ S fo the sta aageet ad μ CM fo the coo-edu aageet) vesus the data tasfe ate ae peseted Fgs. 7, 8 ad 9, fo = 2, 4 ad 8, espectvely. Fg. 9. μ values vesus tassso ate. Fa copaso. =8. CM (=0 7 b/s) CM S S Fg. 7. μ values vesus tassso ate. Fa copaso. = 2. S CM Fg. 0. μs values vesus low tassso ates; μcm = costat. The sta aageet opeatg at athe low tassso ates (seveal Kb/secod) s oe obust tha the cooode copetto opeatg at 0 Mb/secod (ad eve at hghe tassso ates). Ths eas, pactce, aothe poveet obustess due to the possblty to eploy coucato equpet opeatg at lowe tassso ates, that, at least theoy, should have tscally hghe hadwae obustess. The lowe lt of the pessble tassso ate s defed, of couse, by the equeets of the applcato fo the te esoluto. Nevetheless, eal Wokg Meda Egees Depatets, the equeets ae ot too sevee. Theefoe, t s feasble to eploy low o edu tassso ate equpet. Fg. 8. μ values vesus tassso ate. Fa copaso. =4. Wth the full tassso ate age vestgated, the sta aageet was uch bette the sese of obustess tha the coo-edu aageet. Case 2. I ths case, t was assued that the cooedu aageet opeated at the tassso speed of 0 Mb/secod ad the tassso ate the sta aageet was chaged the ego of seveal odes of agtude lowe. The plots of μ S vesus tassso ate ad μ CM (costat value) ae show Fg CONCLUSIONS Fo dstbuted copute cotol ad otog systes sla to the syste Meda descbed, the sta aageet s uch oe obust tha the cooedu oe, whe the fa copaso codtos ae appled. Fo the typcal ube of cotolles stalled, the sta aageet opeatg at the tassso ate of seveal thousad baud s oe obust tha the coespodg coo-edu aageet opeatg at 0 Mb/secod o at eve hghe tassso ates.

5 I spte of that t s athe dffcult to the copute o eve appoxate the μ fucto (Fu, 997; Feees, 999), the obustess evaluato ethods based o the vey tal obustess easue, the μ fucto defed aleady by Doyle (989), seas to be a teestg opto fo desgg the topology of dstbuted cotol systes sla to the syste Meda, whch ae te delay systes. The basc easo fo that s the fact that fo systes costtuted of pue te delay copoets, as s the case fo topology of copute systes, t s ot eeded to fd ege-values sce o the utay ccle, all values ae ege-values. Theefoe, the calculatos eeded to evaluate obustess ae sple ad staghtfowad (actually, the HP calculato was the oly coputg tool eeded to coduct all calculatos fo ths pape). Thus, due to the heet splcty, the ethod eables eally to elate the ethods used actual pactce, that ae athe abtay o, the best case, suppoted etely o the syste avalablty ad dvdual pefeeces of the syste desges. The esults obtaed fo the case studes fo the powe plat oto (Izwosk 99a,b) ad the Copute Itegated Maufactug ad Maageet systes (Izwosk 2006, Lewoc 2006) ay be athe easly tasfeed to oe geeal copute autoato systes. Ths s pled, aly, by the fact that the sae o sla coucato systes ae of fluece o the data tassso pocesses ad, cosequetly, o obustess of the syste ude vestgato. REFERENCES AUAI (2002). Avalable: Csco Systes (2006), Etheet Techologes. Avalable: cstwk/to_doc/eheet.ht Coza F. (997), Robustess aalyss of Bayesa etwoks wth local covex sets of dstbutos, Ucetaty Atfcal Itellgece, Moga & Kaufa, Sa Mateo. Doyle J.C. (982).Aalyss of feedback systes wth stuctued ucetates. Poceedgs of the Isttuto of Electcal Egees, Pat D, 29, Feees G. (999), A Pactcal Appoach to Robustess Aalyss wth Aeoautcal Applcatos, Kluve/Pleu. Faask L. et al. (200), Syste Meda a Step towad Copute Itegated Maufactug ad Maageet Systes, Modellg, Measueet ad Cotol (AMSE Pess), vol. 22, o. 3, pp Fu M. (997), The Real u s Hadly Appoxable, IEEE Tas. Auto. Cotol, vol. 42, o. 9, pp Izwosk A. ad Lewoc J.B. (99a), Qualty copaso fo bg powe plat copute otos: A case study, RCSDuH&RM, IMC/SERC/IEE/IEEE, Cabdge 99. Izwosk A., Lewoc J.B. (99b), Robustess Copaso fo dstbuted cotol systes of vaous topologes, DMCS (IFAC), Zuch Izwosk A., Lewoc J.B. ad Skowok S. (2003a), Robust Pefoace Case Study: Topology of Syste Meda, Cotol Applcatos of Optsato, IFAC, Vsegad. Izwosk A. ad Lewoc J.B. (2003b), Robustess Copaso of Etepse Eegy Dstbuto Systes of Vaous Topologes, I Robust Syste Desg (IFAC), Mla. Izwosk A., Lewoc J.B., Skowosk S. (2006), Developet of Copute Itegated Maufactug ad Maageet systes, I INCOM (IFAC), Sat Etee. Lewoc J.B., Izwosk A. ad Skowosk S. (2006), A LSIS Case Study: Copute Itegated Maufactug ad Maageet Systes, I ALSIS 06 (IFAC), Slja Le Helsk-Stockhol. NSF ad UCa, 2002, 0 Ggabt Etheet Use Cofeece. Avalable: