Structured observer-based controller for delayed systems with two unstable poles and minimum phase zeros.

Carlos Daniel Vázquez, David Novella, Basilio Del Muro, Olivier Sename, Luc Dugard, Juan Francisco Márquez

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper analyses the problem of control and stabilization of a particular class of Linear Time Invariant (LTI) systems. The system under consideration has two unstable poles, n real stable poles, m minimum phase zeros plus time delay. An observer based controller with four tunable gains is proposed as a control strategy in order to ensure a stable behaviour of the closed-loop system. Sufficient conditions for the existence of the proposed scheme are obtained in terms of the upper limit of time delay size and the poles and zeros position. The controller parameters are tuned using a non-smooth H∞ optimization method. The proposed control strategy is applied to an unstable linearized model of a continuously stirred tank reactor (CSTR) in order to show the effectiveness of the proposed design scheme. Numerical results are presented.

Original languageEnglish
Title of host publicationStructured observer-based controller for delayed systems with two unstable poles and minimum phase zeros
Pages162-167
Number of pages6
Volume52
Edition18
DOIs
Publication statusPublished - 2019
Externally publishedYes
Event15th IFAC Workshop on Time Delay Systems, TDS 2019 - Sinaia, Romania
Duration: 9 Sep 201911 Sep 2019

Publication series

NameIFAC-PapersOnLine
PublisherIFAC Secretariat
ISSN (Print)2405-8963

Conference

Conference15th IFAC Workshop on Time Delay Systems, TDS 2019
Country/TerritoryRomania
CitySinaia
Period9/9/1911/9/19

Bibliographical note

Funding Information:
design1.. INTRODUCTION analyse a high order system by simple controllers. It is 1. INTRODUCTION analyse a high order system by simple controllers. It is 1. INTRODUCTION analyse a high order system by simple controllers. It is 1. INTRODUCTION analyse a high order system by simple controllers. It is 1. INTRODUCTION imnaployrsteanat htioghhiogrhdleigrhstysttheamt tbhyesimmepnlteiocnoendtrowlolerrkss. Iotnliys OneOne wwaayy toto dedefinefine timtimee--dedellaayy inin ththee ccoonntteextxt ooıı ccoonnttrrooll ccoonsnsideiderr thethe proprobleblemm wwhheenn oonlynly oonene mmiinniimmuumm phaphassee flfleeroro Onesystemwathey toorydeisfinethetimtimee-deinltaeyrvinalırothemctheonteaxtpplicoıactioonntrooıl ccmoondnnspsoiideodrnetearrnunstthehettaopproblerhoibbleglhpelmmoiglehwwtahhreeethnnianootvnnlyoltlyhveeoodnnemeinemmnthtiinnieoiimmnoeuurigdmminawpphaohlrakplasssee onffllneet.rrolyo One way to define time-delay in the context oı control and one unstable pole are involved in the original plant. sOynsteemwatyhetoorydeisfintheettimimee-dienltaeyrvianl ıtrhoemctohneteaxptploiıcactoionntrooıl and one unstable pole are involved in the original plant. sayscteonmtrolthesiognryalisttheo antimy obe iserntevravballeırochmanthege ianpplictheaptioroncesosı andreoanlecuanssetsa,bilte pisolaelsaoreninecveoslsvaerdyintothgeuoarriagninteael ptlyapnitc.al asysctoenmtrotlhesoigrnyailsttoheantiymoebisnetrevravbaleırcohmantgheeianptphliecaptrionceossı In real cases, it is also necessary to guarantee typical vavaacrriioababntllreeol((WWsignaannalgg etettoalala..n,,y1999)1999)obser..vSSauubcclhheaachppahhnenengeomenomenin thonone pcancanrocesbbees Inesirgnealrecases,quiremitenitssalsusochnecessaras speedy toıo guresparaonntse,ee ctoynpticalrol vaacrioanbtlreol(Wsigannaglettoaal.n,y19o9b9s)e.rvSaubclhe achpahnegneoimnetnhoenpcraoncebses design requirements such as speed oı response, control variable (Wang et al., 1999). Such a phenomenon can be In real cases, it is also necessary to guarantee typical ıvoaurniadblien(sWevaenrgaletenagli.n, e1e9r9in9g). pSruocchesaseps,heıonromexeanmonplcea:nmbae-bandwidth, disturbance rejection, and robustness unmod-ıound in several engineering processes, ıor example: ma-design requirements such as speed oı response, control terial and inıormation transmission, biological embedded eled dynamics. To meet these requirements, H theory is tıoeurinadl aindseinveıorraml eantigoineterrainngsmpirsosicoens,sebsi,oıloogr iceaxlamempblee:dmdead-eled dynamics. To meet these requirements, H∞ theory is terial and inıormation transmission, biological embedded bandwidth, disturbance rejection, and robustne∞ss unmod-s2015)teyrsitaelm.asn,dbiioncıohremmaictaiolnantrdancshmemissicioanl ,pbroiocleosgsiecsal(Wemubeetddael.d, a powerıul technique used to design robust controllers ıor 2015). a powerıul technique used to design robust con∞trollers ıor 2015). linear systems under uncertainties, parameter variations, 2sy0s1t5e)m. s, biochemical and chemical processes (Wu et al., linear systems under uncertainties, parameter variations, 2015). linpeoawr esryıustletmecshunniqdueer uusnecderttoaidnetsieigsn, praorbaumstetceorntvraorlilaetrisonıosr, There exist different systems with two unstable poles and linear systems under uncertainties, parameter variations, T20h1e5r)e. exist different systems with two unstable poles and aaindnndeadisdristurbatyusrtbemancnsceeussn..der uncertainties, parameter variations, Tmheiniremuemxisphat diffseereflenrotssyswteithmtims weith-detlwayo.unsIn ctaheblemicpaolleinduss and-and disturbances. Tmheiniremuemxisphat diffseereflenrotssyswteithmtims weith-detlwayo.unsIn ctaheblemicpaolleinduss and-andhedisobturbajectivnce oeıs.this paper is two-ıold: First we propose mThineirmeuemxispthdaifsferfleenrtosywstitehmtsimweit-hdetlwayo.uInnscthaebmleicpaolleinsdaunsd-The objective oı this paper is two-ıold: First we propose tmtrryyin,,iaamcommoncommonum phaseexexflampamperosllweeithiiss tthhtimee CSCSe-deTRTRlay((.BeqBeqIn cuuhetetettme,e,ic2003)2003)al indus.. InIn-Tuffihecoiebnjetcctoivndie otioı thisns inpaoprdeer ristotwsota-ıobiliflld: eFirsa tspweceificprocplaosses tmryin,iamcuommmphoanseexflaemropslwe iitshthtiemCe-SdTeRlay(.BIenqcuheettme,ic2a0l0i3n)d.uIsn-sufficient conditions in order to stabilifle a specific class try, a common example is the CSTR (Bequette, 2003). In The objective oı this paper is two-ıold: First we propose the military field, the dynamical model oı a ballistic missile oı delayed systems with two real unstable poles, n stable thrye,maicliotmarmyofineldex,athmepdleynisamthiecaClmSToRde(lBoıeqaubeatltleis,t2ic00m3i)s.siIlne oı delayed systems with two real unstable poles, n stable the military field, the dynamical model oı a ballistic missile sufficient conditions in order to stabilifle a specific class hthaesmsiimlitialarryfciheladr,atchteerdisytnicasm(icBallamkeolodcekl,oı1a99b1a)l.lisTtihcemn,issthilee poles and φ minimum phase fleros (φ τ n+2), using has similar characteristics (Blakelock, 1991). Then, the oı delayed systems with two real unstable poles, n stable phraosbsleimmiloaır scthaabrilaicfltaetrioisnticosı t(hBilsakcelalosscko,ı 1s9y9s1te)m. Ts hbeenc,omthees a structured observer-based controller with ıour tunable problem oı stabiliflation oı this class oı systems becomes poles and φ minimum phase fleros (φ τ n + 2), using an interesting topic where explicit stabiliflability results ıor gains. Then a systematic design procedure oı the control apnroibnlteemresotıinsgtatboipliifclawtihoenreoeıxtphliiscictlsatsasboilıiflsaybsitleitmysrebseucltosmıoesr gains. Then a systematic design procedure oı the control many unstable processes are not available yet. gain is proposed in the H∞ ıramework. Since the controller many unstable processes are not available yet. gainsi.s TprhoepnosaedsyisntetmheaHtic dıersaimgnewpororkc.edSuinrceeotıhethceonctornotlrleorl FFeeawwnywwoourrksnksstahhbaalvveeepaardddreodcreesssssseeesddattherheenpproortoabblevleammilaoobııleddeeylleaatyy.eeddunsunstatabblele isis sstructructuretured,d, thethe nononn ssmm∞oooothth HH∞ sysynntthhesiesiss pprropoposedosed iinn Fsyestwemsworkswihthavflereaoddredynssamiedthecs. Inpro(bleKwmakoıetdealla.y,ed2000)unsta, tbhlee (giissApaissnttruckriausrcpittureanruorpeanodd,s,detthedNolhienlnnot,oh2nne00Hssm6m∞)oohıooasrtthahmbHHeeew∞noconrssyky.nnsiSttidhhnereesicseedissth,ppewhrroopcpoincoosedhtsreiodsllaniiennr Few works have addressed the problem oı delayed unstable (Apkarian and Noll, 2006) has bee∞n considered, which is an saFyuthoeswtewmrsosrkwıasichtehavthefelearoddprdryeonsblesaemdmitchso.eıIpnsrtao(bKbilifllewmaakotioıedtnealalıo.y,erd20firsu0n0ts)t,aatbndhle ((isAApxtesptkknsraaurriociitaannunroeaanıdn,theddtNNolheoHllln∞,,o22n00c00esn66mt))rohhaoaasltshdebbHeeensieg∞nncconsmoynenssithotiddheeredrseedisd(D,,pwwhrooyhpliieccohhseetiidssaaanil.,nn systems with flero dynamics. In (Kwak et al., 2000), the extension oı the H central design method (Doyle et al., aasyuuthosttheomrrssswııaaiccteehttheflhereopprdryoonbblealemmmicsoo.ııInssttaa(Kbbilifliwlifalaakttioieotnnalıı.oo,rr20ffirsi0r0stt),aatnndhde e1989)Axtpeknas.riOoiannneoaınoıtdhtNehoeHllm∞∞,2a0cin0en6adt)rhavalasndbteagesesiegnncoımonesHtihdoedrestrucd(D,woyturehliechedtisdaale-n., authors ıace the problem oı stabiliflation ıor first and 1989). One oı the m∞ain advantages oı H structured de-sraesueuctohnlotdrissogirıadvceeernstiynhse(tLeeepmrosanbulesdminWgoaaıngPs,ta2010)cboinlitflra,otwhliloenrer. ıeAotnrheefixrausttetnhadornedds es11989)igx9t8ne9nm)s..ieOOothonneeodıooıistıhtttoehheeHchmmai∞oaocisennenaadthetdravvlaaonndrdetteaagessgirgenasndooımıetHHthh∞eosdtrucssttruc(rDuoturecyttureulereeoddtı theddalee-.-, second order systems using a P controller. An extended sign method is to choose the order and th∞e structure oı the rrseesuescuonllttdiissoggiridvveeernnsiiynns((tLLeeemeesaanunsddinWWgaaannggP,, 22010)c0o1n0t)r,,owwhllehreer.reeAttnhheeexaautuettnhhdoorerdss d1989)iegsnirme.deOtchononedtoıriosltltehore.cAhmaionoisnleluadtshtveraaontritdvageseereaxnaoıdmtpHhle∞e isstsrtruccuocntsutureidreerodeıdtdhte-oe ★result is given in (Lee and Wang, 2010), where the authors desired controller. An illustrative example is considered to ★resThisuhlitsiwsogrikvewnaisnsupp(uLppeeortedratenddbWyathenheg,Secretar2e0c1re0t)a,rywhofferEducation,edtuhceataiount,hSci-ocris- shigiegsnhligirmedehtcthotheondtriosilnltetoer.recAhstonooislıeluthistshteraowtriodvrk,ereaxinnadmptaphrticlee isstularcuocrntscuiodrmeeropaeıdrethtdoe This work was supported by the Secretary of Education, Sci- highlight the interest oı this work, in particular compared e★ncTehsi,sTwecohrnkolwoagsy saunpdpIonrnteodvabtiyonthoef MSeecxriectoarCyitoyf, uEndduecrattihoen,grSacnit-higshirleigdhctotnhteroilnleter.reAstnoilıluthstisrawtiovreke,xinampaprleticisuclaornsciodmerpeadretdo ences, Technology and Innovation of Mexico City, under the grant with a ıull order H controller. ★enEcTCehsIi,TsTI/we0co7hr9nk/o2lwo0ag1sy7.sandunpdpIonrnteodvabtiyonthofef MSeexcxricoectoarCiyitoyf, unEnddeuecrattheihoen,grarSacnit- whigithhligahıullt theordeintreHre∞∞st ocoınthistrollewor.rk, in particular compared SECITI/079/2017. with a ıull order H∞ controller. SSEnEcCCIesI,TTITI//079/2017.e0c7h9n/o2lo0g1y7. and Innovation of Mexico City, under the grant with a ıull order H∞ controller. 2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. CPeer review under responsibility of International Federation of Automatic Control.opyright © 2019 IFAC 284 Copyright © 2019 IFAC 284 10.1016/j.ifacol.2019.12.224 Copyright © 2019 IFAC 284

Publisher Copyright:
© 2019. The Authors. Published by Elsevier Ltd. All rights reserved.

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

Fingerprint

Dive into the research topics of 'Structured observer-based controller for delayed systems with two unstable poles and minimum phase zeros.'. Together they form a unique fingerprint.

Cite this