Conferen ence ce on Decision cision and Contr ntrol ol 2018 18 WeB05 B05 Large-Scale Scale Systems ems Par aram ameteriza eterization ion of Al All State St te-Feedbac eedback k Retr etrof ofit it Co Contr ntroller ollers Dec. . 19th, h, 2018 18 Hampei mpei Sasa sahar hara, a, Takayuk yuki i Is Ishizak zaki, i, Jun-ic Ju ichi hi Im Imura Tokyo o tech., ., Japan an
Outl tline ine 1. Intr troduc oduction tion 2. Exi 2. xist sting ng Res esults ts on Ret etrof ofit it Co Contr trol ol - De Definitions itions - Ch Char arac acteriz terization tion of ret etrof ofit it co contr troll oller ers with th inter terconnec onnection tion si signal 3. Retr trof ofit it contr troller ollers s with thout out inter terconnec onnection tion si signal 4. Co Conclus lusion ion
Co Cont ntrol ol of of La Large-Sc Scale ale Sy Syst stems 1/16 16 contr ntrol ol of a comple mplex x large-scale scale sy syst stem em ? entir tire e model: el: unavaila ailable le partia tial model: del: avail ilable le des esign gn funda ndament mental al prob oblem em How w to to synth thesi esize e a c a contr trol oller ler wi with th th the e ac acce cess only y to to th the e par artia tial l model el informa ormati tion on?
Multi ltiple ple Oper perator tors 2/16 16 su suppose: pose: multiple tiple oper erato tors other her oper erator ors ? ? design sign independen pendently tly other’s control actions may vary ? funda ndament mental al prob oblem em (a (alt. t.) How w to to synth thesi esize e a c a contr trol oller ler th that t ca can dea eal with wi th th the e possibly var arying g en environment onment?
Exa xample: mple: Power er Syst stem em 3/16 16 ? - multiple ltiple ISOs Os (inde ndepend pendent ent system tem oper erator) tor) - too large e to capt ptur ure e the entir ire syste stem m model del - other r ISOs Os may chang nge their ir control ol polic licy Objectiv jective: e: impr mprove e the contr trol ol perform orman ance ce by attac achi hing ng (retr trof ofitting tting) ) a contr troll oller er only y wi with h the parti tial al model del
Retr etrof ofit it Contr trol ol 4/16 16 existing isting: : entir ire e system stem model del novel: el: local al model el inf nforma ormation tion ret etrof ofit it co cont ntrol ol [1 [1] - stabili bility ty assuri uring ng contr trol only ly with th the e local al model el [1] T. Ishiz izak aki, , T. Sadamoto amoto, , J. Imura, , H. Sandbe berg, , K. H. Johansson ansson, “Retrofit Control: Localization of Controller Design and Implementation,” Automa omatic tica, vol. . 95, pp. 336-346 346, , 2018. 18.
Retr etrof ofit it Contr trol ol 5/16 16 ret etrof ofit it co contr trol oller ler: : st stabilit ity y pres eser erving ving co contr ntroll oller er stability bility is preser served ed char aract acteriz erization tion under der an an as assumption tion [2 [2] gene neraliza alization tion: : remo moving ving the e assumption (today’s talk) [2] H. Sasahara , et al., “A Characterization of All Retrofit Controllers,” ACC , 2018.
Outl tline ine 1. Intr troduc oduction tion 2. Exi 2. xist sting ng Res esults ts on Ret etrof ofit it Co Contr trol ol - De Definitions itions - Ch Char arac acteriz terization tion of ret etrof ofit it co contr troll oller ers with th inter terconnec onnection tion si signal 3. Retr trof ofit it contr troller ollers s with thout out inter terconnec onnection tion si signal 4. Co Conclus lusion ion
Def efini inition tion: : Retr etrof ofit it Contr troll oller er 6/16 16 case 1: ca e 1: case 2: ca e 2: Env. is any element ment s.t. t. is stable le : the inter terconnected connected system em De Definition ition is called lled a retrof ofit it contr troll oller er if it stabili bilizes es the syste stem m for any s.t. t. is stable
Equ quiv ivalent alent Conditio dition 7/16 16 : inter ercon connection nection signals nals : measur surement ment, , contr ntrol The heor orem em is a r a ret etrof ofit it co contr troll oller er and an loop p transf ansfer er matrix rix : as assumed ed to to be sta e stable becau cause se : arbitr itrary ary co constr straine ained d Youl ula par arame ameteriza terization tion
Two Cla lasses sses of Retr etr. . Ctr trl. l. 8/16 16 : retr trof ofit it contr trolle ler linear ear, but rather ther gener eral al hard to to give e the solutions utions explicitly licitly Definition De ition 1. Ou Output put rectif ctifying ying retr trof ofit it contr ntroller oller 2. Input put rectif ctifying ying retr trof ofit it contr ntroller oller sim imple le struct uctur ure, , easy asy to o desi sign gn
Output tput Recti ectifying fying Retr etr. . Ctr trl. l. 9/16 16 Ou Output put Rectif ctifying ying Retr trof ofit it Contr troller oller （ ） Assu sumpti mption on can n be fed back Theo eorem em All outpu put t rectifying ctifying retr trof ofit it contr ntroller ollers s have e the st structu ucture : stabil biliz izes es (loca cally lly st stabilizing bilizing contr ntroller) oller)
Des esign ign Criteri iterion on 10/16 /16 resu sultant ltant con ontr trol ol system stem (Youla ula paramet ameter r w.r.t. .t. ) : affine ine funct nctions ions w.r.t. .t. des esign gn prob oblem: em: red educ uced ed to to an an unco constr train ained ed co convex x optimi timiza zation tion
Outl tline ine 1. Intr troduc oduction tion 2. 2. Exi xist sting ng Res esults ts on Ret etrof ofit it Co Contr trol ol - De Definitions itions - Ch Char arac acteriz terization tion of ret etrof ofit it co contr troll oller ers with th inter terconnec onnection tion si signal 3. Retr trof ofit it contr troller ollers s with thout out inter terconnec onnection tion si signal 4. Co Conclus lusion ion
Retr etrof ofit it Contr troll oller er w/ w/o 11/16 /16 The struct uctur ure provide vided d that Assu sumpti mption on can n be fed back What t if the assumption umption is not not sati tisf sfied? ied? How w to synthe thesiz size e a retr trofit it contr troller ler? Consider sider state te-feedbac edback retr trof ofit it contr trolle lers s without hout Main in idea: : regar arding ding the states tes actua tuated ted by the e inter er- connection nnection si signals als as s new inter terconnecti connection on si signals nals
Exa xample mple 12/16 /16 Example: mple: : inter ercon connecti nection on signal nal Suppose pose , the e direct ectly y affec ected ted st state te by y : : ( are e omitted) tted) 1. virtual tual inter erconnecti connection on signal gnal to the lower er dy dynam amic ics 2. design sign a retr trof ofit it contr trol oller ler for r the lower er dynamics amics
Exa xample mple 12/16 /16 Decompo compose se the state te by We consider sider the dynamics amics w.r.t. .t. regar arding ding as s a new w inter erconn connection ection si signal nal elimina minated ted
Exa xample mple 13/16 /16 Design ign a retr trof ofit it contr ntroller oller Dynam amics ics w.r.t. t. accor cording ding to the figur ure wher ere (the he previous ious case) e) the e sa same e st struct uctur ure It t has as bee een proven en th this s st structur cture e is a s also so nec eces essa sary ry
Par arameteriza ameterization tion 14/16 /16 Assumpti sumption on 1 canno nnot be fed d back Assu sumpti mption on 2 state te-feedbac eedback Theo eorem em All st state te-feedbac eedback retr trof ofit it contr ntroller ollers s have e the st structu ucture is a locally ally stabiliz ilizing ing contr trolle ler (for or the precise ecise statement, tement, see our r paper er)
Rough ugh Sketc etch h of Proof oof 15/16 /16 1) 1) linear ear equation ion in : the space ce of all real al rational tional trans ansfer er funct nctions ions is char aract acteriz rized ed by restricting stricting to be proper per, , we have e the e struct ucture 2) 2) let we can n show ow that is a locally ally stabiliz ilizing ing contr trolle ler
Outl tline ine 1. Intr troduc oduction tion 2. 2. Exi xist sting ng Res esults ts on Ret etrof ofit it Co Contr trol ol - De Definitions itions - Ch Char arac acteriz terization tion of ret etrof ofit it co contr troll oller ers with th inter terconnec onnection tion si signal 3. Retr trof ofit it contr troller ollers s with thout out inter terconnec onnection tion si signal 4. Co Conclus lusion ion
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