Comparison between proportional, integral, derivative controller and fuzzy logic approaches on controlling quarter car suspension system

* Co esponding au ho : ahme m.ka [email protected] Compa ison be ween p opo ional, in eg al, de i a i e con olle and uzzy logic app oaches on con olling qua e ca suspension sys em Ahme Mehme Ka adeniz1,*, Amma Alsabbagh1, and D .Geza Husi1 1Uni e si y o Deb ecen, Depa men o Mecha onics, 4028 Deb ecen O eme o u ca 2.-4., Hunga y Abs ac . De eloping and cons an ly changing echnologies, e o s o achie e maximum e iciency wi h minimum uel consump ion, as well as he de elopmen o com o and sa e y sys ems, ha e become e y essen ial opic in ca manu ac u ing and design. Whe eas com o and secu i y we e no gi en a high impo ance in he i s p oduced ca s, hey a e indispensable elemen s o oday's au omobiles. Since public anspo a ion uses oad in la ge scale, he need o sa e y and epose is also inc easing. Nowadays, ehicles ha e be e secu i y and com o sys ems, which eac e y quickly o all kinds o loads and di e en cases o d i ing (b aking, accele a ion, high speed, co ne ing), whe e he i es can keep he oad a i s bes , u ilizing an ad anced suspension sys em. In his s udy, a qua e -ca model was ul illed using LabVIEW (Labo a o y Vi ual Ins umen a ion Enginee ing Wo kbench) so wa e. The con ol o his model has been ealized by applying wo di e en con olle s. PID (p opo ional, in eg al, de i a i e) con olle which is a common and con en ional con ol me hod and he Fuzzy Logic con olle which is conside ed as an expe sys em ha is becoming mo e and mo e widely used. In bo h con ol app oaches, con olling he suspension sys em was achie ed success ully. Howe e ; I has been de e mined ha con olling he sys em using Fuzzy Logic con olle ga e be e dynamic esponse han applying he PID con olle o he qua e ca suspension model ha has been used in he di ec ion o his s udy. 1 In oduc ion In ecen yea s, imp o ing o ehicle suspension sys ems has been an in ensi e esea ch and de elopmen opic. These s udies a e ca ied ou in wo di e en o ms, scien i ic and comme cial. Comme cial wo k is ca ied ou by ehicle and pa s manu ac u e s aiming o enhance he quali y o hei p oduc s. Scien i ic s udies a e ca ied ou by esea che s, i concen a es mo e on con olling he sys em in o de o p o ide au oma ic con ol o ehicle suspensions elying on he new de elopmen s o ac ua o s, senso s and low cos elec onics. The ea u es expec ed om a good suspension sys em make suspension con ol mo e in e es ing. The desi ed ea u es a e:  Adjus men o body mo emen : Ideally, a suspension should p o ec he body om oad i egula i ies and om i egula i ies caused by ine ia a he s a , s op and du ing co ne ing.  Adjus men o he suspension mo emen : Ex eme e ical mo emen o he wheel will cause he i e o be in an imp ope posi ion wi h espec o he oad, which will also esul a poo oadholding. In o he wo ds, he su ace be ween he i es and he oad should be maximized in o de o inc ease he engine e iciency.  Fo ce dis ibu ion: P ope i e and oad con ac mus be p o ided on all ou wheels o ensu e a good oadholding and handling. These ea u es o e lap each o he acco ding o he oad and ehicle si ua ion, he e o , adi ional suspension sys ems canno p o ide all hese ea u es. A design ha educes he sideways il o he o so, o ins ance, will ha e oo much s i ness, which cause he ib a ions om he oad o be ansmi ed o he ehicle body. This can be shown on he qua e ca model in which he single wheel is conside ed. The ampli ude o he ans e unc ion, which ela es he e ical changes on he cu e o he changes in he e ical eloci y o he ehicle body, is seen. The s aigh line is he answe o he adi ional ehicle suspension sys em. The e a e wo esonance s a es. Lowe one; he ib a ions o he body (sp ing mass), and he o he one; ha is ela ed o he ib a ions o he wheel hub (unsp ing mass). Imp o ing he low equency cha ac e is ics o he suspension may be possible by inc easing he damping cons an o he suspension. The do ed line indica es he case whe e he damping cons an is inc eased en imes. The esponse a low equencies can be imp o ed by shi ing he esonance egion. No e ha he esonance ampli udes o he body and he wheel inc ease while he gain a high equencies dec eases. © The Au ho s, published by EDP Sciences. This is an open access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License 4.0 (h p://c ea i ecommons.o g/licenses/by/4.0/). MATEC Web o Con e ences 184, 02018 (2018) h ps://doi.o g/10.1051/ma eccon /201818402018 Annual Session o Scien i ic Pape s IMT ORADEA 2018 The simple qua e ca model men ioned abo e clea ly demons a es he dilemma be ween low and high- equency d i ing com o . Fu he mo e, he con ol o he side il o he nose and he ea pa will be a unc ion o he in e ac ion be ween each suspension [1]. 2 Qua e Ca Model The qua e ca model, which is one o he mos p e e ed, mos use ul and simples ca models, is shown in Fig. 1. The pa ame e s o he model used in his s udy a e ob ained by ex ac ing he ma hema ical model o he sys em and using he e e ence [2]. The ib a ions o a ehicle subjec ed o a e ical axis o as esul om dynamic beha iou s can be modelled as M1 and M2 double masses. M1 ep esen s qua e o he o al mass o he ehicle, and M2 ep esen s he mass o he wheel o he ehicle. The equa ions o he qua e ca suspension model a e shown in he bo h equa ions 1 and 2: uxxKxxbxM  )()( 2112111  (1) uxwkxwb xxKxxbxM   )()( )()( 2222 2112122   (2) 2.1. Modelling Qua e Ca Suspension Sys em LabVIEW (Labo a o y Vi ual Ins umen a ion Enginee ing Wo kbench) allows modelling o sys ems ha can be exp essed as ma hema ical equa ions using block diag ams. The modelling in he LabVIEW en i onmen using he equa ions o he qua e ehicle suspension model is shown in Fig. 2. The pa ame e s and alues used du ing his modelling a e shown in Table 1. Table 1. Sys em Pa ame e s Pa ame e Value Uni M1 2500 Kg M2 320 Kg K1 80000 N/m K2 500000 N/m b 1 b2 350 N.s/m 15020 N.s/m As minimising he ib a ion is one o his esea ch mos signi ican aims, con olling he e ical mo emen and o cing i o goes o ze o is wha is impo an . Fo non- eedback sys ems, he desi ed pa ame e canno be con olled o only he open-loop esponse, which is he uncon olled esponse o he sys em, can be ob ained. Fig. 3 shows he open loop esponse ob ained o he qua e ca suspension sys em. As shown in Fig. 3, i has an oscilla ed dumbed beha iou because i has no eedback no con olle (open loop esponse). 2.2. Con olling Sys em U ilizing PID PID con ol is a p opo ional in eg al plus de i a i e con olle whose ans e unc ion is: sK s K KsG d i pPID )( (3) Fig. 1. Qua e Ca Suspension Sys em. Fig. 2. LabVIEW Model o he Sys em. Fig. 3. Open Loop Response o he Sys em. 2 MATEC Web o Con e ences 184, 02018 (2018) h ps://doi.o g/10.1051/ma eccon /201818402018 Annual Session o Scien i ic Pape s IMT ORADEA 2018 PID con olle is conside ed as one o he simples con olle s, easy o be applied and i does no equi e high pe o mance mic op ocesso s [5]. The PID gains can be ob ained using many di e en me hods like ze o-pool cancela ion, Ziegle -Nichols, and ial and e o . In his pape , T ial and e o me hod has been used in o de o une he PID con olle . Kp, Ki, Kd gains a e called p opo ional PID gain, in eg al PID gain, and de i a i e PID gain, espec i ely. E o signal is he inpu o p opo ional, de i a i e and in eg al gains o he PID con olle o ob ain desi ed ou pu . The block diag am o he LabVIEW PID con olle wi h he subsys em which ep esen s qua e ca suspension sys em o his s udy model is shown in Figu e 4. Whe e he PID (p opo ional, in eg al, de i a i e) con olle is applied o he qua e ca suspension sys em as se ies wi h a eedback. Table 2 shows he alues used o PID pa ame e s which a e Kp, Ki, Kd gains. Table 2. PID Pa ame e s PID Pa ame e es Values Kp 146975.92 Ki 890807. 1099 Kd 956.8692 Fig. 5 shows he ob ained esul when he PID con olle is applied wi h he pa ame e s gi en in Table 2. Looking a his esul , we can see ha he sys em espond is ze o a e 1 second. The se ling down o he sys em o ze o means ha he ib a ions along he e ical axis in he ehicle will no a ec he passenge s. 2.3. Con olling Sys em U ilizing Fuzzy Logic Fuzzy logic, unlike classical logic, does no ha e sha p dis inc ions. Tha is, one le el does no only ha e only 0 o 1 alues, bu i can also ha e alues in be ween. NB (nega i e big), NS (nega i e small), Z (ze o), PS (posi i e small), PB (posi i e big) le els, which a e commonly used in uzzy logic con olle s. Fuzzy Sys em Designe is used o ans e hese le els o he LabVIEW en i onmen . Wi h Fuzzy Sys em Designe , he membe ship unc ions o he sys em we e de ined using he able 3, which was c ea ed by expe s and he alues o membe ship unc ions can be de e mined. A e he decisions, he con ol model is designed wi h he uzzy logic con olle in LabVIEW. The uzzy logic con olle model designed o his sys em is shown in Fig. 6. Since iden i ica ion o membe ship unc ions he uzzy logic con olle is impo an , he ype, numbe and no maliza ion ac o s o he membe ship unc ions should be ca e ully de e mined a his s ep. In his s udy, he gene al apezoidal membe ship unc ion was chosen howe e , only he Z membe ship unc ion was chosen as he iangula membe ship unc ion because i is desi ed o be highly sensi i e o make he e o goes o ze o as p ecise as possible. In he no maliza ion p ocess, he inpu unc ion is kep in he ange o -1 o +1. The ule ables ha show he ela ionship be ween he inpu and ou pu in he con ol wi h he uzzy logic con olle a e impo an ac o s. The ule able used o his s udy is shown in Table 3 and membe ship unc ions a e shown in Fig. 7 on Fuzzy Sys em Designe [3,4]. Table 3. Rule Table du / u NB NS Z PS PB NB NB NB NB NS Z NS NB NB NS Z PS Z NB NB Z PS PB PS NS NS Z PB PB PB Z Z PS PB PB In o de o e alua e he pe o mance o he uzzy logic con olle designed in acco dance wi h he ules and membe ship unc ions speci ied in Table 3 and Fig. 7, i is necessa y o compa e he ou pu alues wi h he desi ed alues. The closed-loop esponse o he sys em con olled using he uzzy logic con olle o his s udy is demons a ed in Fig. 8. The choosing o he con olle o be applied in o de o con ol any sys em is pe o med as a esul o compa ing he esponses o he speci ied con olle s o his sys em. Fig. 9 shows he esponse o bo h con olle s o his sys em. The beha iou o he ehicle's suspension sys em wi hou any con olle is shown in he open loop esponse in Fig. 3. To conclude om his, he uncon olled ehicle Fig. 4. Con olling he suspension sys em using PID Fig. 5. The sys em esponse o he PID con olle Fig. 6. Con olling he sys em using Fuzzy Logic 3 MATEC Web o Con e ences 184, 02018 (2018) h ps://doi.o g/10.1051/ma eccon /201818402018 Annual Session o Scien i ic Pape s IMT ORADEA 2018 suspension sys em is no desi able conside ing ma e ial li e and passenge heal h and sa e y. A con ol me hod 2.4. Compa ison o PID and Fuzzy Logic should be selec ed o emo e such undesi able si ua ions and de eloped in such a way ha he con ol pa ame e s a e applied o he sys em o p o ide he op imum le el. The con ol me hod ha should be applied o he qua e ca suspension sys em will be cla i ied by compa ing he esul s ob ained in his s udy. As can be seen o m ig. 9, he esponse using uzzy logic con olle is ee ime less downshoo han he u ilizing PID (abou 4 cen ime es downshoo u ilizing uzzy logic con olle agains 13 cen ime es downshoo using PID con olle ). Mo eo e , con ol he qua e suspension sys em akes abou hal o consumed ime by PID o each he s eady s a e ( he uzzy logic con olle leaded he sys em o each he s able s a e in app oxima ely 0.75 second, while he PID con olle ook a ound 1.5 seconds o make he qua e suspension sys em each he s eady s a e). 3 Conclusions The pe o mance o he PID and Fuzzy Logic con olle s o he qua e ca suspension sys em was es ed. The model used in his s udy is aken om [1]. Fuzzy Logic and PID con olle s we e applied o he sys em sepa a ely and he ob ained esul s we e compa ed wi h each o he . In his compa ison, i has been obse ed ha he Fuzzy Logic con olle gi es be e esul s han he PID con olle o he con ol o he designed model in espec o bo h ime ha was aking o each he s eady s a e, and in espec o o e shoo and downshoo , which means, ha he uzzy logic con olle was able o educe he oscilla ion ampli ude o he sys em and enhance he sa e y o mechanical pa s o he ehicle as well as he passenge sa e y. Acknowledgmen The publica ion is suppo ed by he EFOP-3.6.1-16-2016- 00022 p ojec . The p ojec is co- inanced by he Eu opean Union and he Eu opean Social Fund. Mo eo e , hanks o Adewale O iyomi Oseni o being encou aging, suppo ing, and making his wo k mo e e icien and easie . Re e ences 1. R.K. Pekgöz, M.A. Gü el, M. Bilgehan, M. Kısa, Ac i e Suspension o Ca s Using Con olle Op imized by Gene ic Algo i hm, In . J. o Eng. and Appl. Sci. (IJEAS) 2, Issue 4 27-37, (2010) 2. h p://c ms.engin.umich.edu/CTMS/index.php?exam ple=Suspension§ion=Sys emModeling, ( e ie ed on 25.11.2017) 3. J. Jan zen, Founda ions o uzzy con ol, Chiches e , England; Hoboken, NJ: John Wiley & Sons, 2007. 4. N. E. I. S. U. Manual, NI Educa ional Labo a o y Vi ual Ins umen a ion Sui e II Se ies (NI ELVISTM II Se ies) Use Manual, (2009) 5. Amma Alsabbagh, Pé e T. SZEMES, Abdulkade Baki, B ushless DC Mo o Modeling Using Bond G aph Me hod and Con ol using LabVIEW. (RIim) Recen Inno a ion in Mecha onics. Vol. 5, No 1, 2018. Fig. 9. Compa ison o PID and Fuzzy Logic Con olle s. Fig. 7. Membe ship Func ions ‘u’, ‘  u’, ‘ou pu ’. Fig. 8. The sys em esponse o Fuzzy Logic con olle 4 MATEC Web o Con e ences 184, 02018 (2018) h ps://doi.o g/10.1051/ma eccon /201818402018 Annual Session o Scien i ic Pape s IMT ORADEA 2018