A Decision Support System for Safe Switching Control

Transcription

1 6th WSEAS Internatnal Cnference n CIRCUITS, SYSTEMS, ELECTRONICS,CONTROL & SIGNAL PROCESSING, Car, Egypt, Dec 29-31, A Decsn Supprt System fr Safe Swtchng Cntrl F. N. KOUMBOULIS, M. P. TZAMTZI, M. G. SKARPETIS Department f Autmatn Halks Insttute f Technlgy Psahna, Eva GREECE Abstract: - In the present wrk a Decsn Supprt System (DSS) s desgned, that ams t supprt decsn makng wth regard t the selectn f the apprprate cntrl desgn apprach fr nnlnear plants. Mre specfcally, the desgned DSS supprts decsn makng cncernng several aspects f desgnng safe swtchng cntrllers. Decsns are based n the avalable nfrmatn abut the plant s descrptn and characterstcs, as well the avalable epermental data. Key-Wrds: -Decsn Supprt System, Safe Swtchng, Cntrl Desgn 1 Intrductn Decsn makng regardng the selectn f the cntrl desgn apprach whch s apprprate t be appled fr each ndustral plant s a cmple task, snce t has t cnsder a number f factrs, as fr eample the characterstcs f the plant, the desred desgn gal, the prerequstes fr the applcatn f each cntrl apprach, as well as ts perfrmance characterstcs, the requred data, etc. The decsn shuld be based n any avalable theretcal r epermental nfrmatn abut the plant, takng nt accunt the degree f assurance and/r accuracy f each nfrmatn, as well as the ptental presence f errneus data. In ther cases the avalable data may appear t be ncnsstent t each ther, whch mples that part f the avalable nfrmatn shuld be dscarded. These, n cnjunctn wth the fact that ndustral prcesses are characterzed by cmple behavr, nnlneartes, lack f analytcal mdels and parameter uncertanty, cmplcate sgnfcantly decsn makng regardng the desgn and develpment f effcent ndustral autmatn systems. In practce such prblems are slved by eperts wh reckn tgether the avalable data t prpse a sutable cntrl apprach. Decsn supprt systems (DSS) are sftware tls whch am t supprt r even replace human epert decsn makng [1]-[8]. The three man appraches t develp decsn supprt systems are [4]: a) the data drven appraches, as fr eample the prncpal cmpnent analyss and the partal least square, whch are dmensnalty reductn technques, b) the analytcal appraches, as fr eample parameter estmatn and bserver based methds and c) the knwledge based appraches ([9]-[18]), as fr eample epert systems, machne learnng, etc. As referred n [4], an epert system s a sftware system that captures human epertse fr supprtng decsn makng. Thus, epert systems are partcularly suted fr cases where the avalable nfrmatn s uncertan r ncmplete, as well as fr cases where cmple decsns are requred, whch may depend n several factrs. Swtchng cntrl s a supervsry cntrl scheme used t cntrl nnlnear plants, whse range f peratn s large enugh t make nadequate cntrl by a sngle feld cntrller ([19]- [22]). A swtchng cntrl scheme cnssts, n general, f a set f feld cntrllers, each desgned t acheve specfc perfrmance requrements fr a lmted range f peratn f the nnlnear plant, as well as a supervsry cntrller that mplements the swtchng lgc, that s t perfrms swtchng between the feld cntrllers, as the plant s nput/utput trajectres mve between dfferent areas f peratn. Safe swtchng s a swtchng cntrl scheme that ams t acheve safe transtns between dfferent peratng ranges f a gven plant ([22]-[25]). Ths may be acheved usng several cntrl appraches, whch share a cmmn characterstc: they use cmmn cntrllers fr transtns between neghbrng peratng areas, that s cntrllers that acheve desred perfrmance characterstcs smultaneusly fr tw r mre neghbrng peratng areas. The man representatve f the afrementned safe swtchng appraches s the Step-Wse Safe Swtchng (SWSS) fr nnlnear plants wth unknwn descrptn, that was frst ntrduced n [22]. Hwever, there s a number f

2 6th WSEAS Internatnal Cnference n CIRCUITS, SYSTEMS, ELECTRONICS,CONTROL & SIGNAL PROCESSING, Car, Egypt, Dec 29-31, appraches that have been develped t cntrbute twards safe swtchng [22]-[31]. These appraches dffer wth respect t the requred characterstcs f the plant s mdel, the requred a prr nfrmatn abut the plant, the desgn gal, etc. The selectn f the apprprate safe swtchng cntrl apprach s a cmple task, that requres epert evaluatn f the avalable theretcal and/r epermental data. In the present wrk a DSS s desgned, that supprts decsn makng regardng the desgn and applcatn f safe swtchng cntrllers. The prpsed DSS s desgned as a rule-based epert system (see [1]), whch may be mplemented n a varety f hgh level prgrammng sftware tls, as fr eample Matlab. The desgned DSS emphaszes n the case f sngle nput sngle utput (SISO) systems. Hwever, ts desgn may be etended fr the case f multvarable systems. It s als mprtant t nte that the DSS presented n the fllwng sectns s a generc tl, that may be easly appled fr a varety f ndustral cntrl plants. Mrever, t can be embedded as an ndependent sftware unt wthn a supervsry scheme fr Safe Swtchng Cntrllers ([25]). 2 Safe Swtchng Cntrl Appraches As already mentned, the Step-Wse Safe Swtchng (SWSS) algrthm fr nnlnear plants wth unknwn descrptn was frst ntrduced fr the SISO case n [22]. In the fllwng the man gudelnes f ths algrthm are presented. Cnsder a sngle nput-sngle utput prcess, where y and u dente the utput and the nput f the prcess, respectvely. Let L= { = [ Y, U], = 1,, μ} dente a set f plant s nmnal peratng pnts (pnts f the nput-utput space where the prcess may settle at steady state), where YU, are the nmnal utput and nput values, respectvely. Let als the plant s descrptn be apprmated by a set S, = 1,, μ f lnear mdels, determned thrugh dentfcatn abut the nmnal peratng pnts. Fr each we determne, usng eclusvely epermental data, the s called target ( O ) and tlerance ( O ) peratng areas [22], whch are epermental apprmatns f the neghburhd f valdty f each lcal lnear mdel S. The nmnal peratng pnts are selected dense enugh t satsfy the fllwng requrements [22]: O O + 1, O1 O2 O1, O μ 1 O μ O, μ O 1 O O, O O+ 1 O, = 2,, μ 1. The abve cndtns cnsttute an epermental frmulatn f the dense web prncple [22], accrdng t whch the set f lnear mdels S, = 1,, μ descrbes satsfactrly the prcess behavur. Fnally, cnsder that fr each par (, + 1 ) f adjacent peratng pnts, there ests a cmmn cntrller C, + 1, that satsfes a set f desred desgn requrements smultaneusly fr bth lnear mdels S and S + 1. Then, the SWSS algrthm ntrduced n [22] rchestrates apprprate swtchng between the set f cmmn cntrllers C +, = 1,, μ 1, as the prcess trajectres, 1 mve between adjacent target peratng areas. The man characterstcs f ths algrthm are summarzed as fllws: a) The SWSS apprach s based n the applcatn f cntrllers that cmmnly acheve the requred perfrmance smultaneusly fr adjacent nmnal peratng pnts. b) Cntrller swtchng s allwed t take place nly when the prcess has reached an peratng pnt. Ths requrement s strct but avds undesrable effects that may cme frm swtchng whle mvng e.g. nstablty. Thus, the mtn between any tw dfferent peratng pnts s perfrmed by mvng n a step-wse manner between peratng areas f an apprprately selected sequence f adjacent nmnal peratng pnts. c) The plant s lnearzatns and the crrespndng peratng areas are determned usng eclusvely epermental data. In [22] the target and tlerance peratng areas f each peratng pnt are determned usng emprcal rules. Hwever, t has been prven n [24], that fr the case f frst rder nnlnear plants, the range f these areas can be determned usng epermental plant data and Input t State Stablty Lyapunv thery, s as t guarantee safe transtns durng SWSS. The etensn f these results fr hgher rder systems s currently under nvestgatn. The SWSS algrthm f [22] s appled fr the case when the plant s nnlnear mdel s unknwn. Hwever, n several ndustral applcatns, a nnlnear mdel may be derved based n knwn physcal laws. In ths case SWSS may be als appled. Hwever, n ths case the lnear mdels S, = 1,, μ may be derved usng lnearzatn, nstead f dentfcatn. Mrever, the crrespndng areas f peratn may be determned analytcally usng the lcal stablty prpertes f the nnlnear plant. The applcatn f SWSS fr knwn frst-rder nnlnear plants has been studed n [23].

3 6th WSEAS Internatnal Cnference n CIRCUITS, SYSTEMS, ELECTRONICS,CONTROL & SIGNAL PROCESSING, Car, Egypt, Dec 29-31, Its etensn fr hgher rder plants s currently under nvestgatn. As already mentned, ne f the man characterstcs f SWSS s the applcatn f cmmn cntrllers, whch acheve desred clsed-lp perfrmance characterstcs fr tw r mre neghburng lnearzatns f the plant. Cmmn cntrllers may als be used t acheve safe swtchng fr anther class f ndustral plants, whse descrptn has the frm f a mult-lnear mdel. A mult-lnear mdel s cnsttuted by a set f mdels and a set f swtchng cndtns that gverns the plant s transtn frm ne lnear descrptn t anther. Swtchng can be actvated by envrnmental factrs, by cntrl cmmands r by changes n the mde f peratn f the prcess. Fr eample, n the case f a wheeled mble rbt, swtchng between dfferent dynamc mdels ccurs when the mtn f the wheels changes frm rllng t sldng. Typcal eamples f such systems nclude batch prcesses, pwer systems, relay systems, transmssn and stepper mtrs, nternal cmbustn engne cntrl, cnstraned rbtcs, etc. The applcatn f a cmmn cntrller C, + 1 t the multlnear mdel S, = 1,, μ shuld acheve: a) satsfactry perfrmance f the crrespndng clsed-lp system wthn the range f valdty f each lnear mdel S and S + 1 and b) safe and satsfactry perfrmance f the crrespndng clsed-lp system fr all transtns between the tw mdels S and S + 1. A generc heurstc algrthm has been ntrduced n [26] fr the dervatn f cmmn PI cntrllers fr mult-lnear plants. Ths algrthm, whch may be easly etended fr ther classes f cntrllers, s als sutable fr the desgn f cmmn cntrllers fr nnlnear plants whse descrptn s apprmated by a mult-lnear mdel. Cmmn cntrller desgn may als be treated as a rbust cntrl prblem. In the feld f rbust cntrl, a varety f cntrl desgn prblems have been slved. A case f specal nterest fr the cntrl f ndustral prcesses s that f rbust dynamc cntrllers, as fr eample PI r PID cntrllers, whch may be desgned t serve a varety f desgn requrements. Other nterestng cases fr cntrl prblems n ndustral envrnment are rbust cntrllers desgned t acheve nput/utput decuplng and/r dsturbance rejectn fr uncertan systems subject t cnstrants, as the case f uncertan sngular systems. T treat the prblem f desgnng cmmn cntrllers as a rbust cntrl prblem, a number f rbust cntrl methds may be prpsed (see [27]- [31]). All these wrks present rbust cntrl technques fr lnear systems wth nnlnear uncertan structure, wthut requrng any lmtatn r specfcatn (cntnuty, bundness, smthness, etc.) n the structure f the uncertanty. Mrever, these rbust cntrl appraches may cver the case f slwly varyng uncertan parameters, fact that makes them partcularly suted fr the desgn f cmmn cntrllers t be appled wthn a SWSS framewrk. The prpsed rbust cntrl appraches serve the fllwng desgn requrements: a) Rbust cmmand fllwng wth PI ([28]) r PID ([30]) cntrllers. b) Rbust ple assgnment wth dynamc cntrllers ([29]). c) Rbust eact mdel matchng wth dynamc cntrllers ([27]). d) Rbust dsturbance rejectn fr generalzed state space systems wth statc cntrllers. e) Rbust npututput decuplng fr generalzed state space systems wth statc cntrllers ([31]). The selectn f the apprach t be used shuld be perfrmed based n the characterstcs f the prcess, the desred requrements fr the clsed-lp system, as well as the structure f the cntrller t be appled. As t fllws frm the prevus dscussn, selectn f the apprprate safe swtchng cntrl apprach, as well as selectn f the apprprate cmmn cntrller desgn apprach requres epert knwledge, n rder t dentfy the plant characterstcs whch are crtcal fr the cntrller selectn, based n any avalable theretcal and/r epermental nfrmatn abut the plant. Mrever, the DSS shuld dentfy ptental ncnsstences between the avalable nfrmatn, as fr eample the case when the knwn mdel plant s ncnsstent wth the epermental data, whch mples that the avalable epermental data cannt be reprduced by the knwn mdel plant. 3 Decsn Supprt System The desgned DSS s a rule-based decsn supprt system cnsttuted by three typcal cmpnents [1]: the rule base, the nference engne and the user nterface. The rule-base cmprses a set f rules n the frm f a generc IF cndtn THEN actn structure. Each rule requres specfc data abut the plant and s actvated whenever these data are avalable. The actvatn f the apprprate rule based n the avalable data s perfrmed by the nference engne. The user nterface prvdes a graphcal nterface thrugh whch the peratr f the DSS answers a questnnare and prvdes any avalable theretcal and epermental nfrmatn abut the plant. The fllwng subsectns present the man characterstcs f the DSS. Subsectn III.A

4 6th WSEAS Internatnal Cnference n CIRCUITS, SYSTEMS, ELECTRONICS,CONTROL & SIGNAL PROCESSING, Car, Egypt, Dec 29-31, presents the rules f the DSS n a data-cndtnactn frm, whle Subsectn III.B prvdes clarfcatns n these rules. Subsectn III.C cmments n the determnatn f uncertantes, whch s requred at several actns actvated by the DSS rules. 3.1 DSS Rules In the fllwng the rules that determne the functnalty f the DSS are presented. Each rule n a data-cndtn-actn structure. The data feld s the dstngushng characterstc f ts rule. The nference engne actvates the rule whse data feld cncdes wth the avalable t the DSS nfrmatn abut the plant. The cndtn felds f each dente the set f cndtn whch are tested by the rule. Whenever a cndtn s fund t be true, the DSS prceeds wth the eecutn f actn descrbed n the crrespndng actn feld. The DSS cmprses the fllwng seven rules. RULE Mdel f the plant Cndtn 1.1: The plant s descrbed by a multlnear mdel Actn 1.1: Apply the heurstc cmmn cntrller desgn technque fr mult-lnear mdels. Desgn cmmn cntrllers fr grups f tw r mre adjacent lnear systems. Cndtn 1.2: The plant s descrbed by a nnlnear mdel Actn 1.2: Apply SWSS fr knwn nnlnear mdels. RULE Mdel f the plant 2.2 Operatng curve f the plant, derved frm epermental data. Cndtn 2.1: The epermental peratng curve cncdes wth the peratng curve derved frm the plant s mdel. Actn 2.1: Apply SWSS fr knwn nnlnear mdels. Cndtn 2.2: The epermental peratng curve devates mderately frm the peratng curve derved frm the plant s mdel. Actn 2.2: Determne parametrc uncertantes n the plant s mdel, s as t derve an uncertan descrptn f the plant, whch s cnsstent wth the epermental peratng curve. Apply SWSS fr knwn nnlnear mdels. Determne the crrespndng lnearzatns as uncertan lnear systems. Apply rbust cntrl technques t desgn cmmn cntrllers fr neghbrng uncertan lnearzatns. Cndtn 2.3: The epermental peratng curve devates sgnfcantly frm the peratng curve crrespndng t the knwn plant s mdel. Actn 2.3: Ignre the whle plant s mdel r thse parts f the mdel that are respnsble fr the ncnsstency between the epermental and the theretcally derved peratng curve. Perfrm dentfcatn t derve the plant s mdel r the afrementned mssng parts. Apply SWSS fr nnlnear systems wth unknwn descrptn. RULE Mdel f the plant 3.2 Operatng curve f the plant, derved frm epermental data 3.3 Epermental measurements f the plant s varables Cndtn 3.1: The epermental peratng curve cncdes wth the peratng curve derved frm the plant s mdel. Actn 3.1: Ignre the avalable measurements f the plant s varables and apply SWSS fr knwn nnlnear mdels. Cndtn 3.2: The avalable measurements f the plant s varables are cnsstent wth the avalable plant s mdel. Hwever, the epermental peratng curve devates frm the peratng curve crrespndng t the knwn plant s mdel. Actn 3.2: Perfrm addtnal eperments t determne the peratng curve. Use these eperments t determne uncertantes n the plant s mdel. Cndtn 3.2.1: The addtnal eperments succeed t determne an uncertan descrptn f the plant, whch s cnsstent wth the epermental peratng curve. Actn 3.2.1: Prceed as n Actn 2.2 Cndtn 3.2.1: The addtnal eperments fal t determne an uncertan descrptn f the plant, whch s cnsstent wth the epermental peratng curve. Actn 3.2.1: Prceed as n Actn 2.3 RULE Part f the plant s mdel avalable thrugh mdelng based n knwn physcal laws. 4.2 Part f the plant s mdel avalable thrugh dentfcatn Actn 4.1: Cnsder the plant s mdel as knwn

5 6th WSEAS Internatnal Cnference n CIRCUITS, SYSTEMS, ELECTRONICS,CONTROL & SIGNAL PROCESSING, Car, Egypt, Dec 29-31, and apply Rule 1. RULE The plant s mdel s avalable thrugh dentfcatn Actn 5.1: Apply SWSS fr plants wth unknwn nnlnear mdels. RULE A set S, = 1,, μ f uncertan lnear mdels fr whch cmmn cntrllers shuld be desgned Cndtn 6.1: The feld cntrllers are PI cntrllers. Actn 6.1: Apply the rbust cntrl apprach f [28] Cndtn 6.2: The feld cntrllers are PID cntrllers. Actn 6.2: Apply the rbust cntrl apprach f [30] Cndtn 6.3: The feld cntrllers are dynamc and the desgn gal s ple assgnment. Actn 6.3: Apply the rbust cntrl apprach f [29] Cndtn 6.4: The feld cntrllers are dynamc and the desgn gal s eact mdel matchng. Actn 6.4: Apply the rbust cntrl apprach f [27] Cndtn 6.5: The mdels S are multvarable systems and the desgn gal s I/O decuplng. Actn 6.5: Apply the rbust cntrl apprach f [31] Cndtn 6.6: The mdels S are multvarable systems and the desgn gal s dsturbance rejectn. Actn 6.6: Apply the rbust cntrl apprach f rbust dsturbance rejectn fr multvarable systems. RULE A set S, = 1,, μ f lnear mdels (nt uncertan) fr whch cmmn cntrllers shuld be desgned Cndtn 7.1: The lnear mdels S, = 1,, μ are nt uncertan mdels. Actn 7.2: Desgn cmmn cntrllers usng a heurstc search algrthm (see [26]). If ths algrthm fals, then prceed wth rbust cntrl appraches as n Rule Clarfcatns n the DSS Rules In the fllwng several clarfcatns are presented, regardng the functnalty and the mplementatn f the DSS rules. Rule 1: Rule 1 s appled when the plant s mdel s knwn, whle there are nt avalable any epermental data. Then the cntrl desgn apprach s selected based eclusvely n the characterstcs f the knwn mdel. Mre specfcally, f the plant s descrbed by a mult-lnear mdel S = { Sj, j = 1,, m}, then cmmn cntrllers are desgned fr each par f adjacent lnear mdels belngng t S, usng the heurstc cmmn cntrller tunng technque prpsed n [26]. Tw lnear mdels S and S k f S are cnsdered t be adjacent, f there ests ptental swtchng events that drve the plant frm descrptn S t descrptn S k. Cnsder nw tw pars ( S, S k) and ( Sk, S l) f adjacent lnear mdels n S and the crrespndng cmmn cntrllers C k, and C kl,. Cntrller C k, s appled befre any swtchng event between S and S k, whle cntrller C kl, s appled befre any swtchng event between S k and S l, n rder t guarantee safe transtns. If the plant s descrbed by a knwn nnlnear mdel, then SWSS fr knwn lnear mdels s appled [23]. The set f lnear mdels that apprmate the plant s behavr are determned usng lnearzatn. Cmmn cntrllers may be desgned usng the afrementned heurstc technque, r even rbust cntrl technques. Fnally, ths apprach eplts the knwledge f the plant s mdel t determne analytcally the peratng areas arund each nmnal peratng pnt, nsde whch safe transtns may be guaranteed by the step-wse safe swtchng algrthm. Rule 2: Rule 2 s appled when besdes the plant s mdel, there s avalable an epermental peratng curve. Then, befre selectng the cntrl apprach, the DSS checks the cnsstency between the plant s mdel and the epermental peratng curve. Mre specfcally, the DSS cmpares the peratng curve, derved theretcally usng the knwn plant s mdel, wth the epermentally derved peratng curve. The cmparsn may be perfrmed usng an apprprate measure functn. Wthut lss f generalty, let assume that the theretcally derved peratng curve s gven by a functn y= ( u). The measure that determnes the devatn between the theretcal and the epermental peratng curve s defned as

6 6th WSEAS Internatnal Cnference n CIRCUITS, SYSTEMS, ELECTRONICS,CONTROL & SIGNAL PROCESSING, Car, Egypt, Dec 29-31, M E u u 2 2 = ( 2 1) + + ( N ), where E = ( u1) yu ( u 1 2) yu ( u ) 2 N y u N, dentes the Eucldean nrm, u 1,, u N s an 2 apprprate samplng f the cntrl varable and dentes the utput value f the crrespndng peratng pnt ( u, y u ) n the epermental peratng curve. The measure f devatn M s cmpared wth three threshld values h 1, h 2 and h 3, that crrespnd t nsgnfcant, mderate and sgnfcant devatn, respectvely. When the tw curves cncde, whch mples that the devatn measure M s smaller than the threshld value h 1, the cntrl desgn prceeds as n Rule 1, cnsderng the plant s mdel t be knwn. In case the range f devatn between the theretcal and the epermental curve s mderate, whch mples that h1 < M < h2, the DSS determnes parametrc uncertantes n the plant s mdel, s as t derve an uncertan descrptn f the plant, whch s cnsstent wth the epermental peratng curve (see Subsectn III.C). Then, SWSS fr knwn nnlnear mdels, s appled, wth the cmmn cntrllers beng desgned applyng rbust cntrl technques, snce the plant s lnearzatns are uncertan lnear systems. In case the range f devatn between the theretcal and the epermental curve s sgnfcant, that s M h2, then the DSS dscards the plant s mdel and prceeds wth dentfcatn, t derve a new mdel fr the plant, based n epermental data. In ths case the cntrl desgn s perfrmed usng the SWSS algrthm fr unknwn mdels. In sme cases, the devatns may be due t a specfc part f the knwn mdel. Then, the DSS may dscard nly the specfc part, whle keepng the rest equatns f the knwn plant s mdel. Rule 3: Ths rule s appled when the avalable data cmprse a plant s mdel, an epermental peratng curve, as well as measurements f all r sme f the plant s nput, utput and state varables. Befre selectng the cntrl apprach, the DSS checks cnsstency between the plant s mdel and the epermental peratng curve, fllwng the steps prevusly descrbed fr Rule 2. When cnsstency s establshed, the DSS dscards the measurements f the plant s varables and the cntrl desgn prceeds as n Rule 1, cnsderng the plant s mdel t be knwn. If the epermental peratng curve s ncnsstent wth the avalable plant s mdel y u (mderate r sgnfcant devatns), then the DSS prceeds wth checkng cnsstency f the plant s mdel wth the avalable measurements f the plant s varables. Ths s acheved by perfrmng smulatn f the plant s mdel usng as nput, the values f the cntrl varable whch are avalable frm epermentatn. Then epermental state and utput values are cmpared wth thse derved thrugh smulatn. Mre specfcally, let dente a state r utput varable f the plant and let dente the crrespndng measurements. Then, the measure f devatn between the smulated and the epermental values s determned by 2 2 M = E ( k 2 1) + + ( kn ), where E = ( k ) ( k ) ( k ) ( k ) [ k ( N) k ( N ) and k,, 1 k N apprprate nstants f tme. The measure f devatn M s cmpared wth an apprprate threshld value h. If M h fr all measured utput and state varables, then the mdel s cnsstent wth the epermental measurements, whle the DSS suggests the eecutn f addtnal eperments n rder t determne the peratng curve, as well as uncertantes n the plant s mdel (see Subsectn III.C). In case ths fals t succeed, the DSS dscards the plant s mdel and prceeds, as n Rule 2 wth dentfcatn and applcatn f the step-wse safe swtchng algrthm fr plants wth unknwn descrptn. Otherwse the DSS prceeds as n Actn 2.2. If M > h fr at least ne measured varable, then the mdel s ncnsstent wth the bth the epermental peratng curve and the measurement data. Then the DSS dscards the plant s mdel and prceeds, as n Rule 2, wth dentfcatn and applcatn f the step-wse safe swtchng algrthm fr plants wth unknwn descrptn. Rule 4: Ths rule s vald fr the case where sme part f the plant s mdel s avalable thrugh the mplementatn f knwn physcal laws, whle the rest part s determned thrugh dentfcatn, whle n epermental data are avalable. In ths case, the DSS cnsders the plant s mdel t be knwn, and prceeds as n Rule 1. Rule 5: Ths rule s vald fr the case where the whle mdel f the plant s derved thrugh dentfcatn. In ths case the DSS prpses the applcatn f the step-wse safe swtchng algrthm fr plants wth unknwn mdels. Rules 6 and 7: These rules cncern the selectn f the apprprate desgn apprach fr cmmn

7 6th WSEAS Internatnal Cnference n CIRCUITS, SYSTEMS, ELECTRONICS,CONTROL & SIGNAL PROCESSING, Car, Egypt, Dec 29-31, cntrllers. Whenever the lnearzed mdels f the plant are subject t uncertanty (see fr eample Actns 2.2 and 3.2.1), rbust cntrl appraches are appled, accrdng t Rule 6, whch selects the apprprate apprach based n the desred desgn gal, the structure f the feld cntrllers and the structure f the lnear mdels. If the lnearzed mdels are nt subject t uncertanty, heurstc cntrl desgn technques are preferred. In case the heurstc algrthm fals t determne cmmn cntrllers, the DSS actvates Rule 6 t prpse a rbust cntrl apprach. 3.3 Determnatn f Uncertantes As t was referred n the prevus subsectn, when the plant s mdel s nt cnsstent wth the epermentally derved peratng curve, whle the devatn between the epermental and the theretcal peratng curve s fund t be mderate, the DSS prceeds wth the determnatn f parametrc uncertantes n the plant s mdel. Ths mples that the DSS determnes ranges f uncertanty fr specfc parameters f the mdel, s that the derved uncertan mdel s cnsstent wth the epermental peratng curve. Mre specfcally, cnsder, wthut lss f generalty that the theretcally peratng curve s epressed by an equatn f the frm y = ( u; λ), where λ = [ λ1,, λ p ] a vectr f physcal plant parameters. Fr each parameter λ there are avalable nfrmatn cncernng ts physcal nterpretatn. Mrever, there may be avalable nfrmatn cncernng physcal cnstrants that may be mpsed n ts value, as well as a nmnal value λ n,. The range f uncertanty fr each parameter λ s determned by slvng the prblem f mnmzng the measure f devatn M, wth respect t λ. In case cnstrants are knwn fr the values f the parameters λ, the crrespndng prblem s epressed as a mnmzatn under cnstrants prblem. Let λm = λ1, m λ p, m dente the value f λ, that mnmzes M. Then, the range f uncertanty f each parameter λ s determned as [ λn,, λ m, ]. In case there s nt avalable a nmnal value fr the parameter λ, the range f uncertanty s determned as [0, λ m, ]. The derved uncertan mdel s cnsdered t be cnsstent wth the epermental peratng curve prvded that the value f M crrespndng t λ m s smaller than h 1. 4 Cnclusn A DSS, that supprts decsn makng regardng the desgn and applcatn f safe swtchng cntrllers fr nnlnear plants, has been desgned. The prpsed DSS s desgned as a rule-based epert system, whch may be mplemented n a varety f hgh level prgrammng sftware tls, as fr eample Matlab. The desgned DSS emphaszes n the case f SISO systems. Hwever, ts desgn may be etended fr the case f multvarable systems. Ths DSS s a generc tl, that may be easly appled fr a varety f ndustral cntrl plants. Aknwledgment The present wrk s c-fnanced by the Hellenc Mnstry f Educatn and Relgus Affars and the ESF f the Eurpean Unn wthn the framewrk f the Operatnal Prgramme fr Educatn and Intal Vcatnal Tranng (Operatn Archmedes-I ). References: [1] K. J. Åström, J. J. Antn and K.-E. Årzén, Epert cntrl, Autmatca, vl.22, n. 3, pp , [2] R. Kulhavý, A develper s perspectve f a decsn supprt system, IEEE Cntr. Syst. Mag., pp , Dec 2003 [3] S. Guerlan, D. E. Brwn and C. Mastrangel, Intellgent decsn supprt systems, IEEE Inter. Cnf. Syst. Man Cybern. 2000, vl. 3, pp , [4]. V. Urakul, C. W. Chan, P. Tntwachwuthkul, Artfcal ntellgence fr mntrng and supervsry cntrl f prcess systems, Engneerng Applcatns Artfcal Intellgence, vl. 20, pp , [5] J. Sebestyénvá, Case-based reasnng n agentbased decsn supprt system, Acta Plytechnca Hungarca, vl. 4, n. 1, pp , [6] M. L. Dnnell, Autmated assstance f system cntrl-related decsn makng n cmple real-tme envrnments: desgn and analyss prblems, 5th Internatnal Sympsum n Intellgent Cntrl, pp , [7] D Bünz and K. Gütschw, CATPAC An nteractve sftware package fr cntrl system desgn, Autmatca, vl. 21, n.2, pp , [8] R. Strrup and A. J. Chpperfeld, Hybrd cntrl and evlutnary decsn supprt wthn a sustanable envrnment, 2002 IEEE

8 6th WSEAS Internatnal Cnference n CIRCUITS, SYSTEMS, ELECTRONICS,CONTROL & SIGNAL PROCESSING, Car, Egypt, Dec 29-31, Int. Symp. Intellgent Cntrl., Vancuver, Canada, pp , [9] P. Ettlert, M. Valečkvá, M. Kárný and I. Puchr, Twards a knwledge-based cntrl f a cmple ndustral prcess, Amercan Cntr. Cnf., Chcag, Illns, pp , [10] A. J. Krjgsman, H. M. T. Breders, H. B. Verbruggen and P. M. Brujn, Knwledgebased cntrl, 27th Cnf. Decsn Cntrl, pp , Austn, Teas, [11] N. H Ozgur and M. K. Stenstrm, KBES fr prcess cntrl f ntrfcatn n actvated sludge prcess, J. f Envrn. Eng., vl. 120, pp , [12] V. G. Mudgal, K. M. Passn and S. Yurkvch, Ruled based cntrl fr a fleblelnk rbt, IEEE Trans. Cntr. Sys. Tech., vl. 2, n. 4, pp , [13] K. E. Smny, N. K. Lh and R. E. Haskell, An applcatn f epert herarchcal cntrl t pecewse lnear systems, 28th Cnf. Decsn Cntrl, pp , Tampa, Flrda, [14] H. T. Nguyen, V. Krenvch and Q. Zu, Interval-valued degrees f belef: Applcatn f nterval cmputatns t epert systems and ntellgent cntrl, Int. J. Uncertanty, Fuzzness, Knwledge-Based Systems, vl. 5, pp , [15] X.-S. Chen, Q.-L and S. M. Fe, Supervsry epert cntrl fr ball mll grndng crcuts, Epert Systems wth Applcatns (2007), d: /j.eswa [16] Pang, Grantham K. H., An epert system fr CAD f multvarable cntrl systems usng a systematc desgn apprach, Amercan Cntr. Cnf. 1982, vl. 24, pp , [17] J. H. Taylr and D. K. Frederck, An epert system archtecture fr cmputer-aded cntrl engneerng, Prceedngs f the IEEE, vl. 72, n. 12, pp , [18] T. L. Trankle, P. Sheu and U. H. Rabn, Epert system archtecture fr cntrl system desgn, Amercan Cntr. Cnf. 1982, vl. 23, Part 1, pp , [19] A. Lenessa, W.M. Haddad, V. Chelabna, Nnlnear system stablzatn va herarchcal swtchng cntrl, IEEE Trans. n Autm. Cntrl, vl. 46, pp , 2001 [20] M.W. McCnley, B.D. Appleby, M.A. Dalheh, E. Fern, A cmputatnally effcent Lyapunv-based schedulng prcedure fr cntrl f nnlnear systems wth stablty guarantees, IEEE Trans. n Autm. Cntrl, vl. 45, pp , 2000 [21] E.F. Csta, V.A. Olvera, Gan scheduled cntrllers fr dynamc systems usng sectr nnlneartes, Autmatca, vl.38, pp , 2002 [22] F.N. Kumbuls, R.E. Kng, A. Stathak, Lgc-Based Swtchng Cntrllers A stepwse safe swtchng apprach, Infrmatn Scences, vl. 177, pp , 2007 [23] F.N. Kumbuls, M.P. Tzamtz, Twards Analytc Slutns f Step-Wse Safe Swtchng fr Knwn Affne-Lnear Mdels, Int. Cnf. n Numercal Analyss and Appled Mathematcs 2007 (ICNAAM 2007), Crfu, Greece, Sep [24] F.N. Kumbuls, M.P. Tzamtz, On the Stablty f the Step-Wse Safe Swtchng Cntrl Apprach, submtted [25] F.N. Kumbuls, M.P. Tzamtz, Supervsry Scheme fr Stepwse Safe Swtchng Cntrllers, submtted [26] F. N. Kumbuls, "On the heurstc desgn f cmmn PI cntrllers fr mult-mdel plants", 10 th IEEE Internatnal Cnf. n Emergng Techn. and Factry Autmatn (ETFA 2005), Italy, pp , 2005 [27] F. N. Kumbuls, M. P. Tzamtz, M. G. Skarpets, Rbust Eact Mdel Matchng fr SISO Systems va Fnte Precsn Dynamc Output Feedback, 14 th Med. Cnf. n Cntrl and Autm (2006), Italy, [28] F. N. Kumbuls, M. G. Skarpets, M. P. Tzamtz, Rbust PI Cntrllers fr Cmmand Fllwng wth Applcatn t an Electrpneumatc Actuatr, 14 th Med. Cnf. n Cntrl and Autm. (2006), Italy, 2006 [29] F.N. Kumbuls, M.P. Tzamtz, M.G. Skarpets, Fnte Precsn Cntrllers fr Rbust Ple Assgnment f Lnear Systems wth Nnlnear Uncertan Structure, 11th IEEE Int. Cnf. n Emergng Techn. and Factry Autm., Czech Republc, 2006, pp [30] F.N. Kumbuls, M.G. Skarpets, M.P. Tzamtz, Rbust PID Cntrller Desgn wth Applcatn t a Flght Actuatr, 32nd Annual Cnf. IEEE Industral Electr. Sc. (IECON'06), Pars, France, 7-10 Nv. 2006, pp [31] F.N. Kumbuls, M.G. Skarpets, M.P. Tzamtz, Rbust Input Output Decuplng fr Sngular Systems wth Nnlnear Uncertan Structure Presentatn, Eurpean Cntrl Cnf., Ks, Greece, 2007