Fuzry Logic Controller

A New PI+D Type Hierarchical Fuzry Logic Controller Sezai Tokat, ibrahim Eksin. and Miijde Giizelkaya

appro.rinratc anv rcal continuous function on a compafi set rvirh arbirrary accuracy [a]. Thc information in a FL,y"*i, storcd in a knos,lcdgc basc. Thc knorvlcdgc bas" consists ofl rulc ba_sc and mcmbcrship functions n,hich cnable, *.11ng

Abstrac!- In this studt., a fu:zr'logic controllcr that uses thc intcgral acfion in a hierarchical manncr is considercd- Thc output of a conventional fuzzr. logic controllcr that uscs crror and dcrivativc of error as input variables is improved b.v using the second derivativc of error. An important fcaturc of the proposed controller is

vcry clcar starcmcnts froni ill dcfincd or complcx parametrrs

by using linguisric

is

simple structure. The simulations are pcrformed on linear and nonlinear plents. lt is shown that the new structure providcs an improvement in svstcm pcrformancc without inserting too much complcxih'. !ns[e-t

faTms- Fuzzv logic control; hicrarchiczl control; PID

control.

I.

-qroup,

controllcrs. Thc output signal of the controllcr is related o the time derivative and time integal of the controller input ind dircctly thc controller inpur isclf. The dcsigncr's task in ?lD control is to dcterminc which of thesc components should rc used in what portion and how thcy are to be connectcd I I ]. fhe main bcncfit of using PID type control is is casc of icsign. Parametcrs may be tuncd in a varicty of ways

input-output rclation of a convcntional PID controller is dircctly obtaincd by using a FLC strucurc [6] Threc input PID rypc FLCs arc dcsigtrcd in rhe litcrahre

I7). Howcvcr. FLC translatcs skillcd

lelayed linear systems and particularly complex or vague vstems that have no precisc mathcmatical models [2]. An

.

bcRcr controller performance is to incorporate human rtelligence into automatic control by developing fuzy logic i:-L) algorithms [3]. Fuzzy logic is first introduced in 1965 by Zadeh. tt is a eneral purpose, easy to implement and simplc to understand :rethod to realize nonlinear functions. FL systems are proved

rcduce thc complcxiry of a PID typc FLC [8].

[9] invcstigated one-, rwo- and thrce-inpirt PID type

and evaluatc thcm rvithout involving any

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FLCs

computer

simulations by defining proccss indcpendcnt crireria. ln

[0],

the numbcr of inpus arc reduced to fr,r'o by using a mathemaiical fusion of the input variables and the design is performcd through a phase diagram analysis. An optimal fuz4 PID controllcr is dcvclopcd in [2] by separating the PI and D parts. A simple PID type FLC using a single input variable with thrce rules and six design parame ters l5 proposcd in It l].The simplification is obrained as the

to

r\ll

'

opcrator

from the incrcasc of input parameters, different algorithms havc becn dcvelopcd for thc construction or tuning of frrzy systcms from numcrical data. There are differcnt ways to

Itemative that can be used to facc these problcms and to have

Manuscript reccivcd January 27. 2001. authors are with thc Concrol Enginccring Dcpannrnt, lsunbul :chnical Univcrsity, 806?6. lvlaslak, lsnnbul Turkcy. Enail: lstokat. cksin. .:aya )@clk.itu.cdu.tr (Corrcsponding author to providc phonq Mfijdc Gnzclkaya: +90-212i 5 3 500; fax: +90-2 I 2 -28535 86; c-mail: gkaya@ clk.iru.cdu.tr).

human

knowledgc into linguistic rules consisting from a condition and a conscqucnl part- Thcsc rulcs are formcd by considcring cach possiblc combination of propositions in the condition part. For threc input variablcs and if cach of them take oo m linguistic v-alues, than thc corrcsponding completc rule base contains m' diffcrcnt rulcs. This combinatorial explosion in the numbcr of fuzry rules involves a high design effort for rhe tuning of large numbcr of parametcrs, complicate thc gencration of an cffectivc and rcliable rule-base and is cxpensivc in terms of mcmory rcquiremenls and real-time computational cfTort [8J. To decrease the design effort arising

ncluding manual tuning, Zieglcr-Nichols tuning, loop .haping, analyicat methods, pole placement mcthod etc. Also heir simpliciry of operation, low cost, inexpcnsivc naintenance provides an cxtensive usage in industrial :utomation and process control systcms [2]. Howevcr, it has ,cen known that conventional PID conrrollcrs gcnerally do :ot work well for nonlinear systems, higher order and/or time

universal approximators which can be able

With their uniu.rs"l

is uscd for thc adaprarion of a convcnrional plD controller [5] whcrc a FLC is urilizcd on-linc bascd on crror signal (e) and is first dcrivativc (de) ro dcrerminc the controllcr paramercn This study is conccrned with thc sccond group in which, tbe

INTRoDUCTIoN

l/^)NE of the bcst known controllcrs uscd in practicc is thc \-,/ con vcn t iona I p roporti onal-intcgral {eri varivc ( Pl D) type

I be

rlariablcs.

approximarion propcrry and linguistic srrucrure, FL systems has found many succcslful industrial applicarions in tbc automar;c conrrol ficld rvith thc namc fuzzy logic controller (FLC). including complcx sysrem dynamics rhat could exhibit a highly nonlincar charactcr. Thcrc arc scvcral studics including FLC and plD subjects. Thcsc studics can bc classificd in tr,r'o main groups based on thc considcration of thc Fi-C part. ln the first rhe FLC

controllcr parametcrs containing mcmbership functions atc

q'7a

i

.it

{

II.

optimized via genetic algorithms both in [2' I l]' In [3], the proportional term in the convenrional PID controller is replaced with a two input PD rype FLCAlthough it iricreases the system performance, using the second derivative oferror (Ale) is expected to be inconvenient considering that it will increase the system input dimension, simulation time and system complexity [12]- Thus, most of the PID type FLC applications in the titerature are designed using e and Ae as input signals to avoid the increase of input dimension [3]. And generally PI or PD rype FLCs that are shown in Fig. I ,or their combinations are used as a controller' The rule base of the FLCs given in Fig- I are basically chosen as symmetric and the magnitude of the linguistic variables are proiortional with the distance from the diagonal of the linguistic ZE (zero) output as shown in Table l.

HIERARCHICAL FUZLY LoGIC coNTRoLLERs

The hierarclical FLC was first introduced and designed in [3]. ln this hierarchical srnrcture, the number of rules will increase linearly whereas it is e,xponential in conventional counterpart- In a hienrchical FLC structure the most influential parameters are chosen as the system variables in the first level, the next most important parameters are chosen as the sysrem variables in the second level, and so on as shown in Fig.2 [ia] where an n input fuzzy system is realized by an n-l rwo-input frzzy systems. In this hierarchy, the first level gives an approximate output which is then modified by the second level rule set. This procedure can be repeated in succeeding levels of hierarchy. The number of rules in a complete rule set is reduced towards a linear function of the

number

of

variables

by the hierarchy. Methods for

transforming hurnan experience or knowledge into the rule basc and database o{ a finzy inference system seek to generate the rule-base of a system by leaming all parameters of rhe system at once. Their success is limited and if there is a need to add or remove one of the parameters of the rule-base the the However, whole rule-base must be rebuilt

[5].

in

hierarchical structure, each input variable is used in a twoinput FLC and the knowledge can be easiiy rcdesigned rvhen adding or rcmoving an input variable.

(r) Fig. l. FLC slRlcturcs with two inpus: a) Pl t1pc. b) PD-type TAELE I RULE BASE OF r\ CONVENTIONAL FLC CONTROLLER

Ac

IV ZE

PS

PS

PB

PB

PB

NS

ZE

PS

PNI

Pltt

PB

NS

ZE

s

PS

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PB

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NNI

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ll E

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rvithout Hos'cvcr, in this study. thc A:c inlormation is usr"d dcsigncd is FLC PID'rypc Thc' incrcesing systcm complcxiry.

subjcct.

Thc transfer function of a conventional PtD controllcr can b!. wrirlcn &s

by dccompoSing thc tfrrcc input systcm into nvo dinrensional systcnrs FLCs in a tiiffcrcnt structurc by using thc hicrarchical

topic. ln Scction 2, thc hicrrrchical FLC structurc ts ln Sccrion 3' thc proposctj PID rypc FLC tvith

thc to applicd is hicrarchicll srructurc is givcn. Thc n$v algorithm comparco lrc lincar and a nonlincar plant and thc rcsult-s

intro'tuning of lkzy PID con(rolfcrs.' in Proc. !5'' tF.lC Tricnnio! lt'orll Congress' Barcclonr Spein. 1 l -16 Jull' 1002.

575

fl91 [20]

nol.

115-15.{, 1995.

F.6. Shinlcy, Procesr Contyol Systens+pplication, tlesign and tuning, ll'lcGnwHill. NcwYork. I 993. R.K illudi, end N. R. Pal, -A robusr sclf-tuning schcrrr for pl and pD typ< conrrollcrs,- IEEE Tronsactions on Fu=.r, Systems, vol. 7, no,l, p9.2-t6. t999-

IEEE Conference on Control Applications 2OO3

CCA

2OO3

June 23-75, 2003, Hotel Hilton, Istanbul, Turkey

ORGANIZATION SS/TS Chair Paul M. Frank

Technical Program Chair :Georgi M. Dimirovski

General Chair Olcyay Kaynak

Technical Program Co-Chairs DanielW. Repperger [N.& S. America) Kouhei Ohnishi (Asia-Pacific) Kurt Schlacher (EuroPe & Africa)

Advisory Committee Derek Atherton (UK) Tamer Basar (USA) Michel Grimble (uK)

Stephen Kahne (USA) C. Schrader (USA)

Leonhard Shaw (USA) Mark Spong [USA) Roberto Tempo (ltaly)

International Program Committee Pedro Albertos (ES) Famk Allgower (DE) lvlichael Athans (PT, US) John Baillieul (US) Sergio Bitanni (lT) lvlogens Blanke (DK) Seta BogosYan (TR) Jozsef Bokor (HU) Antonio tsraga (BR) Xi Ren Cao (HK, CN) Jose Sa da Costa (PT)

ian K. Craig (ZA) i\ntonio Dourado (PT) Nlchmet Onder Efe (US) Pcter Flcmins (UK) r\lexaneder Fradkov (RU) Katsuhisha Furuta (iP) Sanr Ge (SC)

Torkel Glad (SE) Luigi Glieilmo (lT)

John GraY (UK) Ivan Godler (JP)

Raymond Hanus (BE) Paul M.J. Van Den Hof (NL) Liu Hsu (BR) Enso lkonen (FI) Mo Jamshidi (US) KarelJezemik (SI) Yuanrvei Jing (CN) AMurrahman Kararnanc iogl u

(rR)

.

Uzay Kaymak {NL) Lazslo KeviczkY (HU) Andreas Kugi (DE)

Dimiter Lakov (BG) Jang ivli'ung Lee (KR) Lenart Ljung (SE) lv{ohamed Nlansour (CFl)

lvlanfr"'d lvlorari (C H)

Aminm lloshaior'(lL) Edoardo ivlosca (lL)

Kaddour.r\ajim (FR) Romeo Ortega (FR) Umit Ozguner (US) Markos Papageorgiou (GR) Rajni Patel (CA) Ron J. Panon (UK) AsiI Sabanovic (TR) Ricardo Sanz (ES) Jurek Sasiadek (Cr\) N{ichael Sebck (CZ) I{ebertt S i ra- Rarnirez ( lvf .X) Sigurd Skogestad (NO) ivlile Stankovski (ivlK) Pjotr Tatjc'r'ski (PL) Zoran Vukic (HR) ivl ionri r Vukobratovic (Y ti) Flarald \\ieber (DE) Xinghou Yu (AU) Cary G. Yen (US) Jun Zhao (CN)