Par aram ameteriza eterization ion of Al All State St - - PowerPoint PPT Presentation

Par aram ameteriza eterization ion of Al All St State te-Feedbac eedback k Retr etrof

• fit

it Co Contr ntroller

• llers

Dec. . 19th, h, 2018 18 Hampei mpei Sasa sahar hara, a, Takayuk yuki i Is Ishizak zaki, i, Ju Jun-ic ichi hi Im Imura

Tokyo

• tech.,

., Japan an

Conferen ence ce on Decision cision and Contr ntrol

• l 2018

18 WeB05 B05 Large-Scale Scale Systems ems

• 1. Intr

troduc

• duction

tion

Outl tline ine

• De

Definitions itions

• Ch

Char arac acteriz terization tion of ret etrof

• fit

it co contr troll

• ller

ers with th inter terconnec

• nnection

tion si signal

• 3. Retr

trof

• fit

it contr troller

• llers

s with thout

• ut

inter terconnec

• nnection

tion si signal

• 4. Co

Conclus lusion ion 2.

• 2. Exi

xist sting ng Res esults ts on Ret etrof

• fit

it Co Contr trol

• l

Co Cont ntrol

• l of
• f La

Large-Sc Scale ale Sy Syst stems 1/16

16 entir tire e model: el: unavaila ailable le partia tial model: del: avail ilable le

?

des esign gn How w to to synth thesi esize e a c a contr trol

• ller

ler wi with th th the e ac acce cess

• nly

y to to th the e par artia tial l model el informa

• rmati

tion

• n?

contr ntrol

• l of a comple

mplex x large-scale scale sy syst stem em

funda ndament mental al prob

• blem

em

Multi ltiple ple Oper perator tors

2/16 16 su suppose: pose: multiple tiple oper erato tors

• ther

her oper erator

• rs

design sign independen pendently tly

• ther’s control actions may vary

?

How w to to synth thesi esize e a c a contr trol

• ller

ler th that t ca can dea eal wi with th th the e possibly var arying g en environment

• nment?

?

?

funda ndament mental al prob

• blem

em (a (alt. t.)

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

• l polic

licy Objectiv jective: e: impr mprove e the contr trol

• l perform
• rman

ance ce by attac achi hing ng (retr trof

• fitting

tting) ) a contr troll

• ller

er only y wi with h the parti tial al model del

Retr etrof

• fit

it Contr trol

• l

existing isting: : entir ire e system stem model del novel: el: local al model el inf nforma

• rmation

tion

ret etrof

• fit

it co cont ntrol

• l [1

[1]

• stabili

bility ty assuri uring ng contr trol only ly with th the e local al model el 4/16 16

[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

• matic

tica, vol. . 95, pp. 336-346 346, , 2018. 18.

Retr etrof

• fit

it Contr trol

• l

ret etrof

• fit

it co contr trol

• ller

ler: : st stabilit ity y pres eser erving ving co contr ntroll

• ller

er

5/16 16

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) stability bility is preser served ed

[2] H. Sasahara, et al., “A Characterization of All Retrofit Controllers,” ACC, 2018.

• 1. Intr

troduc

• duction

tion

Outl tline ine

• De

Definitions itions

• Ch

Char arac acteriz terization tion of ret etrof

• fit

it co contr troll

• ller

ers with th inter terconnec

• nnection

tion si signal

• 3. Retr

trof

• fit

it contr troller

• llers

s with thout

• ut

inter terconnec

• nnection

tion si signal

• 4. Co

Conclus lusion ion 2.

• 2. Exi

xist sting ng Res esults ts on Ret etrof

• fit

it Co Contr trol

• l

Def efini inition tion: : Retr etrof

• fit

it Contr troll

• ller

er

ca case 1: e 1: ca case 2: e 2:

is any element ment s.t. t.

De Definition ition

the syste stem m for any s.t. t.

Env.

: the inter terconnected connected system em is stable le

is called lled a retrof

• fit

it contr troll

• ller

er if it stabili bilizes es is stable

6/16 16

Equ quiv ivalent alent Conditio dition

: inter ercon connection nection signals nals : measur surement ment, , contr ntrol

The heor

• rem

em

is a r a ret etrof

• fit

it co contr troll

• ller

er an and

loop p transf ansfer er matrix rix : arbitr itrary ary

: as assumed ed to to be sta e stable

becau cause se

co constr straine ained d Youl ula par arame ameteriza terization tion

7/16 16

Two Cla lasses sses of Retr etr. . Ctr trl. l.

: retr trof

• fit

it contr trolle ler

• 1. Ou

Output put rectif ctifying ying retr trof

• fit

it contr ntroller

• ller
• 2. Input

put rectif ctifying ying retr trof

• fit

it contr ntroller

• ller

8/16 16 linear ear, but rather ther gener eral al

sim imple le struct uctur ure, , easy asy to

• desi

sign gn

De Definition ition

hard to to give e the solutions utions explicitly licitly

Output tput Recti ectifying fying Retr etr. . Ctr trl. l.

Ou Output put Rectif ctifying ying Retr trof

• fit

it Contr troller

• ller

Assu sumpti mption

• n

can n be fed back

Theo eorem em

All outpu put t rectifying ctifying retr trof

• fit

it contr ntroller

• llers

s have e the st structu ucture

（ ）

: stabil biliz izes es (loca cally lly st stabilizing bilizing contr ntroller)

• ller)

9/16 16

Des esign ign Criteri iterion

• n

(Youla ula paramet ameter r w.r.t. .t. ) : affine ine funct nctions ions w.r.t. .t.

des esign gn prob

• blem:

em: red educ uced ed to to an an unco constr train ained ed co convex x optimi timiza zation tion

resu sultant ltant con

• ntr

trol

• l system

stem

10/16 /16

• 1. Intr

troduc

• duction

tion 2.

• 2. Exi

xist sting ng Res esults ts on Ret etrof

• fit

it Co Contr trol

• l

Outl tline ine

• De

Definitions itions

• Ch

Char arac acteriz terization tion of ret etrof

• fit

it co contr troll

• ller

ers with th inter terconnec

• nnection

tion si signal

• 3. Retr

trof

• fit

it contr troller

• llers

s with thout

• ut

inter terconnec

• nnection

tion si signal

• 4. Co

Conclus lusion ion

Retr etrof

• fit

it Contr troll

• ller

er w/ w/o

11/16 /16 What t if the assumption umption is not not sati tisf sfied? ied? 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

• n si

signals nals

Assu sumpti mption

• n

can n be fed back The struct uctur ure provide vided d that How w to synthe thesiz size e a retr trofit it contr troller ler? Consider sider state te-feedbac edback retr trof

• fit

it contr trolle lers s without hout

Exa xample mple

12/16 /16 Suppose pose the e direct ectly y affec ected ted st state te by y : : Example: mple: , ( are e omitted) tted)

• 1. virtual

tual inter erconnecti connection

• n signal

gnal to the lower er dy dynam amic ics

• 2. design

sign a retr trof

• fit

it contr trol

• ller

ler for r the lower er dynamics amics : inter ercon connecti nection

• n signal

nal

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

Dynam amics ics w.r.t. t.

Design ign a retr trof

• fit

it contr ntroller

• ller

accor cording ding to the figur ure wher ere 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

(the he previous ious case) e)

Par arameteriza ameterization tion

Assumpti sumption

• n 1

canno nnot be fed d back

Theo eorem em

All st state te-feedbac eedback retr trof

• fit

it contr ntroller

• llers

s have e the st structu ucture is a locally ally stabiliz ilizing ing contr trolle ler 14/16 /16

Assu sumpti mption

• n 2

state te-feedbac eedback (for

• r the precise

ecise statement, tement, see our r paper er)

Rough ugh Sketc etch h of Proof

• of

15/16 /16 1) 1) linear ear equation ion in 2) 2) : 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 let we can n show

• w that

is a locally ally stabiliz ilizing ing contr trolle ler

• 1. Intr

troduc

• duction

tion 2.

• 2. Exi

xist sting ng Res esults ts on Ret etrof

• fit

it Co Contr trol

• l

Outl tline ine

• De

Definitions itions

• Ch

Char arac acteriz terization tion of ret etrof

• fit

it co contr troll

• ller

ers with th inter terconnec

• nnection

tion si signal

• 3. Retr

trof

• fit

it contr troller

• llers

s with thout

• ut

inter terconnec

• nnection

tion si signal

• 4. Co

Conclus lusion ion

Conc nclusi lusion

• n

16/16 /16

Than ank k you for your r kind d att tten ention tion

Retr trof

• fit

it Co Cont ntrol

• l

novel el co contr ntrol

• l th

theor eory for lar arge-scal cale e systems wh wher ere e multiple tiple oper erator tors

• st

stability ty pres eser erving ving

• si

simp mple e st struct ctur ure

• only wi

with th loca cal model el

Req equir uirement ement: