Fuzzy speed control of belt conveyor system to improve energy efficiency

Transcription

1 5h Inernaional Power Elecronics and Moion Conrol Conference, EPE-PEMC 22 ECCE Europe, Novi Sad, Serbia Fuzzy speed conrol of bel conveyor sysem o improve energy efficiency L.B. Risić, M.Z. Bebić, D.S. Jević, I.D. Mihailović, S.Ž. Šakić 2, N.T. Rašić, B.I. Jefenić Faculy of Elecrical Engineering, Universiy of Belgrade, Belgrade, Republic of Serbia, drives@ef.bg.ac.rs 2 Universiy of Prisina in Kosovska Mirovica Faculy of Technical Sciences, Kosovska Mirovica, Republic of Serbia, sakic@ef.rs Absrac The paper presens a conrol sraegy for he sysem of bel conveyors wih adjusable speed drives based on fuzzy logic conrol. The proposed conrol srucure is developed and esed on he deailed mahemaical model of he drive sysem wih he rubber bel. The presened algorihm is implemened on he new variable speed bel conveyor sysem wih remoe conrol on an open pi mine. Resuls of measuremens on he sysem are used o compare he proposed algorihm wih anoher approach o opimum speed deerminaion based on he mehod of sequenial quadraic programming. I is proved ha boh soluions provide minimum of elecrical energy consumpion of he drive under given consrains. Keywords Conveyors, Opimal conrol, Mining indusry. I. INTRODUCTION Elecrical energy consumpion is increasing globally in order o keep improving our qualiy of life. Energy efficiency is oday one of he key elemens in energy policy of all developed counries in he world, because i conribues o he improvemen of economy globally and exends he lifeime of convenional energy sources, since he greaes par of oal elecrical energy is generaed by fossil fuels. According o available daa presened in [], abou 87% of oal energy is generaed by fossil fuels, of which 28% comes from coal. The growing demand for coal producion leads o increased amouns of coal and overburden o be ranspored wihin he mine wih he sysems of bel conveyors. The lengh and he capaciy are increasing causing he insalled power of hese sysems o increase, consequenly requiring energy efficiency improvemen. I has been esimaed ha he widespread energy efficiency improvemen wih he exising echnologies can save 2% of he global energy demand, and anoher 2% can be saved by prevening wase of energy, i.e., by various conservaion mehods []. In various branches of indusry where bulk maerials are produced or used, various ypes of bel conveyors (BCs) are used for he ranspor of maerials. Coninuous mining is used in large open pi mines (OPM), mos ofen in mines where coal is excavaed for use in hermal power plans. The mechanizaion in hese ypes of mines is organized ino sysems, such as an ECS (excavaor - bel conveyor - spreader) for excavaing overburden, or an ECSY (excavaor - bel conveyor -sock yard) for excavaing coal. The BCs which are placed nex o he excavaor are called bench conveyors and heir ask is o receive he maerial from he excavaor. The BC which ransfers he maerial ino he spreader is called he dump-side conveyor and BCs which connec he bench and dump-side conveyors are called connecing conveyors. In recen imes, very long BCs have been buil wih lenghs of several dozen kilomeers. Due o he lengh of he roue and he necessiy o shif he roue regularly as a resul of he echnological demands a sysem of several BCs, i.e. BC saions are formed. BC saions are placed along he envisaged roue so ha maerial is ransferred from BC o BC several imes unil i reaches he final desinaion. The insalled power of hese BCs is large and each raionalizaion of energy consumpion can provide significan savings, which is naurally of significan ineres for a user [2-3]. This can be saisfied wih drives which enable coninuous speed conrol. This paper invesigaes he possibiliy o improve energy efficiency of he BC sysem in an OPM, which ranspors overburden from he excavaor o he spreader wih he sysem of five BCs. Conrolling hese kinds of sysems, due o heir size and lengh, requires a very reliable srucure of communicaion, for he exchange of informaion beween he BC saions hemselves, as well as beween he BC saions, excavaor and spreader. II. ENERGY SAVING WITH VARIABLE SPEED BELT CONVEYORS Modern bel conveyor sysems are highly sophisicaed sysems which can be realized wih remoe conrol from he conrol cenre of he OPM. Remoe conrol makes full use of advances in modern echnologies o increase safey, reliabiliy and produciviy levels. Conrol of he BC sysem as a whole in he view of improved energy efficiency is possible only if he remoe conrol is uilized. Bulk maerial ranspored by a BC can be disribued along he lengh of he bel in various ways depending on how he maerial is deposied ono he conveyor. The quaniy of maerial which is ranspored wihin a uni of ime, or he average capaciy, can be expressed wih he general formula: T Q = A() v() d T () The insananeous quaniy of bulk maerial which is being ranspored using a BC depends on he operaional mode of he sysem wihin which he BC is used. In a large number of cases, his quaniy is variable and mos ofen he insananeous cross secion area of maerial on /2/$3. 22 IEEE DS2a.9-

2 he bel is less han he raed value. Since BC ofen operaes a a decreased capaciy, he same quaniy of maerial can be ransferred in wo ways: wih a consan raed speed (v r ) and smaller cross secion of maerial on he bel (A()), or wih raed cross secion area of maerial (A r ), bu a a lower han raed speed (v()), as shown in Fig.. I has been shown [4], ha mos ofen in pracice A()<A r, meaning ha if he speed is modified according o (2), he BC could operae a a lower han raed speed. A() v () = vr (2) A Fig. Two BCs in a series connecion - cross secion of maerial on a bel Operaion of conveyor a lower han raed speed would naurally lead o a decrease in he amoun of energy needed o conduc ranspor [2-4]. The needed force F for ranspor a quaniy of mass m of maerial is given in (3), where g is graviaional acceleraion and f is fricion coefficien. F() v = m g f() v (3) Fricion is generally a funcion of speed. The dependency of fricion on speed depends on he ype of moional resisance, i.e., from he consrucion of he ransporaion device, in our case of he BC. To esablish his dependency, one can measure he power for operaing he BC wih no load P nl a a consan speed of v, which can be expressed using (4), where m b is equivalen mass of a bel. Pnl () v = mb g f() v v (4) The dependency of no load power on speed is pracically linear for he considered sysem of BCs according o he measuremens presened in [5], which means ha in hese cases fricion does no depend on speed. Tha could be expeced because he maximum speed is a relaively small 5.8 m/s, all bearings on he BC are rolling-elemen ype and a he ime when he measuremens were aken he equipmen was brand new. Under he assumpion ha he cross secion area of maerial on he bel is he same along he enire lengh of he conveyor, he speed is consan and fricion does no depend on speed, he necessary power P for driving a BC wih a lengh L is given in (5), where γ is specific mass of maerial. P = ( mbm + mb ) g f v = ( A L γ + mb ) g f v = ( Av ) L γ g f+ m b g f v (5) cons Due o he conservaion of capaciy and regarding (2), he firs addend in (5) corresponds o he power necessary for ranspor of maerial is consan. The second erm corresponds o he power for overcoming moional r resisances of an empy ransporer which depends on he speed. Therefore, if he speed is adjused according o (2) for he ranspor of a cerain quaniy of maerial, savings of energy will be achieved based on he decreased power necessary for driving he bel. This confirms he expeced savings of energy for ranspor of bulk maerial wih reduced speed. However, due o he complexiy of he mechanics of driving a loaded bel, i should be expeced ha he load will cause an increased coefficien f which can reduce he effec of decreased power wih decreased speed. Addiionally, uneven disribuion of maerial along he lengh of BC cerainly affecs he drive power. III. ALGORITHM FOR GENERATING REFERENCE SPEED OF BELT CONVEYOR DRIVE Speed conrol of a BC requires informaion abou he quaniy of maerial which is deposied ono he bel, meaning he insananeous capaciy mus be known. The insananeous capaciy is: dv () Q () = = A () v () = A () vcons A () (6) d The speed of he bel ono which he maerial is deposied should be modified in accordance wih (2) in order o achieve he defined crieria of speed conrol. However, he insananeous capaciy changes quie frequenly and sporadically. This means ha he speed should be increased and decreased in he same manner as he insananeous capaciy changes. These dynamic processes would be unfavorable for he mechanical assemblies of a BC, especially for he bel, and could lead o increased energy consumpion. Because of he fac ha he insananeous capaciy changes, and hose changes canno be prediced, he conrol algorihm mus be such ha he bel speed is adjused o he condiions a he beginning of he conveyor, i.e., a he locaion where he insananeous capaciy is measured. The algorihm for generaing he reference speed of he bel drive is defined as follows:.the heoreical bel speed is calculaed on he basis of he equaion (2), and can be expressed as is special case when a BC in he sysem of BCs is considered: Ain() v() = vin() (7) Ar In (7) A in () and v in () are he insananeous value of cross secion of incoming maerial and he insananeous speed of he previous bel. The acual reference speed of he bel drive v ref () is calculaed on he basis of (7) according o (9) under he condiions defined by (8): dv () and v( ) vref ( ) ε, (8) d vref () = c ( v () vref ()) d+ vref ( ) (9) where is he momen when boh condiions defined by (8) are acquired, c and ε are consans wih dimensions [s - ] and [%v r ] respecively, while dv /d is ime derivaive of heoreical bel speed wih he dimension of [%v r /s]. 2. When he condiions from (8) are no fulfilled, i.e. DS2a.9-2

3 dv () < and v( ) vref ( ) < ε () d he acual reference speed is deermined on he basis of (), vref () = vref ( 2) k ( 2), () where 2 is he momen when a leas one of he condiions from (8) ceases o be valid and k is deceleraion. During he period when he quaniy of maerial coming ono he conveyor increases, he reference speed of he drive is deermined according o (9), and a ha ime he drive acceleraes. The consan c deermines he dynamic of reference speed. In his manner he cross secion of he maerial on he speed conrolled bel increases, meaning i graviaes owards A r. When he quaniy of incoming maerial decreases, he reference speed is calculaed on he basis of he relaion (), i.e., he speed decreases wih a deceleraion k. The speed adjusmen range is limied, minimum speed should be 5% of he raed speed; he maximum speed is se a - 25%, dependan on he capaciy of excavaor and working condiions. The consan k deermines he deceleraion of he drive which mus conform wih he dynamic characerisics of he drive. An abrup deceleraion unfavorably affecs all mechanical assemblies, couplings, bearings, he bel, ec. BC drives wih a roue which does no raverse an incline use braking wih a resisor and chopper in he DC circui. An abrup deceleraion would lead o he acivaion of he elecric braking sysem whereby he braking energy would unnecessarily ransform ino hea wihin he resisors. Due o aforemenioned reasons, a he opimal value of he consan k, he orque of he bel drive moor is equal o zero. As he condiions under which he bel deceleraes are no always he same, due o various quaniies of maerial on he bel, variable moional resisances as a resul of weaher condiions, and he condiion of equipmen, k should be variable o provide deceleraion wih drive orque nearly zero (bu no negaive). I can be deermined using he expression (2), derived from he Newons law, Tl () k () = JΣ () (2) where J Σ () is he oal ineria referred o moor shaf, including he effec of maerial mass. In accordance wih DIN22 sandard, T l can be expressed as Tl() = Tl + Tl( mbm) (3) where T l is consan par of he oal load orque and T l (m bm ) is a par which is a funcion of mass of he maerial on he bel and consequenly ime dependan. Similar can be derived for he oal momen of ineria of he loaded bel conveyor, JΣ() = JΣ + JΣ( m bm ) (4) where J Σ is a consan par of he oal momen of ineria and J Σ (m bm ) is a par proporional o mass of he maerial on he bel and is also ime dependan. The consan par of he load orque, as well as he consan par of he momen of ineria, can be calculaed wih sufficien accuracy. The values can also be updaed from ime o ime o accoun for changes in he sysem of BCs, due o changes of lengh or changes in condiion of he equipmen. However, componens of load orque and momen of ineria remain unknown since hey are funcions of mass of maerial on he bel and exernal condiions. This leads o inaccurae calculaion of k and inappropriae deceleraion of a BC. To overcome he difficulies in accurae calculaion of k, he auhors of he paper propose differen mehodology o develop he algorihm for generaing he reference speed of he bel, which relies on variables presen in he sysem and will no depend of exernal condiions. IV. FUZZY LOGIC CONTROL Convenional realizaion of conrol is based on mahemaical model of he conrolled objec, while his is no required for fuzzy conrol. If he mahemaical model of he conrolled objec is very complex or undefined, alhough he conrolled objec has deermined performance, a conrol sraegy should be conduced in accordance wih principles of he sysem operaion. These sysems are herefore considered as inelligenly driven. Fuzzy logic based inelligen conrol has been successfully employed in he large number of scienific and engineering applicaions, as well as numerous commercial applicaions and indusrial sysems. In his paper, a knowledge based conrol algorihm, called fuzzy logic conrol (FLC) is proposed o solve he minimizaion problem, i.e. o drive he sysem wih minimum elecrical power meaning o convey he maximum cross secion of maerial a opimum speed. FLC generaes opimum speed reference wih deerminaion of acceleraion and deceleraion under all previously explained consrains. As shown in [2], he srucure of he model of BC is known, bu he parameers of he model are changing under various exernal condiions and heir values canno be precisely known a any insan. The auhors' experience and knowledge are embedded in he linguisic rule based descripion of he conrol sraegy. The FLC is used as a scheme o ranslae expers' knowledge ino a form convenien for PLC implemenaion of conrol sraegy o find he opimal soluion, ye wihou informaion abou exernal facors which can affec he sysem's deceleraion. Fuzzy conrol was found o calculae acceleraion and deceleraion, based on measuring hree values: speed of previous BC, cross secion of incoming maerial, and he drive orque. The block diagram of he algorihm for generaing he reference speed of BC wih FLC is shown in Fig. 2. As i can be seen from Fig. 2, he FLC has wo inpus: according o ( n) = v( n) vref ( n ) (5) and he drive orque Te. The ask of mainaining he orque of he moor a a zero value during periods of deceleraion is now provided by he FLC. Therefore, he deceleraion is achieved while avoiding all he problems caused wih he parameers variaion due o exernal condiions. The FLC is wih single oupu N(). I is based on Mamdani's reasoning mehods, developed using Fuzzy Logic Toolbox [6] and inegraed ino Malab Simulink dynamic model of BC, which is presened in [2]. Membership funcions for he inpu are given in Fig. 3, membership funcions for he inpu Te are given in Fig. 4, and membership funcions for he oupu N() are given in Fig. 5. DS2a.9-3

4 z vin () Ain () A r v () v + Te N( ) v r + c P 2 T s z v ref Fig. 2. Algorihm for generaing he reference speed of he bel wih FLC.5 - μ NB NM ZE PM PB Fig. 3. Membership funcions for inpu variable Fig. 4. Membership funcions for inpu variable Te. Fig. 5. Membership funcions for oupu variable N(). The oupu variable N() is incremen of he reference speed, generaed from fuzzy rule base given in Table I. Values for inpu and oupu variables are normalized wih base values seleced in accordance wih raed parameers of moor and he bel conveyor, given in he Appendix. TABLE I FUZZY RULES Te N ZE PS PM PB NB ZE NS NM NB NB NM ZE ZE NS NM NB ZE ZE ZE ZE ZE ZE PM ZE PB PB PB PB PB ZE PB PB PB PB In he process of fuzzificaion, he universe of discourse for linguisic variables, Te and N() is mapped in he [-, ] inerval and divided ino fuzzy ses: negaive (N), negaive big (NB), negaive medium (NM), zero (ZE), posiive small (PS), posiive medium (PM), and posiive big (PB). The MIN MAX mehod is used for fuzzy rules processing, while he cenre of graviy mehod is used for defuzzificaion. Considering Table I, hree regions can clearly be disinguished and described wih fuzzy rules as follows: - If (Te is N) hen (N() is ZE) - meaning ha if drive orque approaches zero, he reference speed incremen mus converge o zero in order o avoid acivaion of elecrical braking; - If ( is ZE) hen (N() is ZE) - meaning ha if he required change of reference speed is small (zero), hen no change of he oupu value (reference speed incremen) is needed, regardless of drive orque value; - If ( is PM) hen (N() is PB) or If ( is PB) hen (N() is PB) - meaning ha if incoming maerial on he bel is increasing, he BC drive mus achieve proper acceleraion in order o avoid spillage of maerial over he bel. The desired performance of he sysem was accomplished wih only five fuzzy ses per variable. This reduces he size of able of fuzzy rules. Disribuion of fuzzy ses depends on he requiremens of he sysem. Also i provides adequae conrol sensiiviy. For he inpu variable Te, a single fuzzy se N denoes braking which should be avoided. When orque is close o zero, high conrol sensiiviy is required, herefore narrow fuzzy ses are defined. For any posiive value of he Te, when he inpu variable is posiive, he FLC gives big value a he oupu in order o avoid spillage of maerial on he bel. For small variaions of inpu variable, i.e. small variaions of maerial cross secion a he inpu of he BC (A in ), he sysem has no sudden change of he oupu variable, which is provided wih he adequae uning of he ZE fuzzy ses. The shape of generaed conrol funcion is given as a surface in Fig. 6. This form is suiable for implemenaion in PLC as look up able wih inerpolaion beween he calculaed poins. The described algorihm wih FLC for generaing he speed reference is developed and esed on he deailed mahemaical model of he drive sysem wih he rubber bel [2, 5]. The resuls of measuremens of he implemened algorihm on he dump-side conveyor on he new variable speed BC sysem wih remoe conrol on an OPM are presened in Fig. 7. The speed is adjused in he range from 6% o % of he raed speed, as he user demanded. DS2a.9-4

5 Cross secion [%] Speed [%] Torque [%] N() Te Fig. 6. The shape of generaed conrol funcion N() Time [min] Time [min] A 4ou Time [min] Fig. 7 Characerisic values of he dump-side BC: implemenaion of he algorihm for generaing he reference speed of he bel wih FLC (speed conrol in he range of 6% o % v r) When maerial is deposied o he beginning of he bel a a consan speed (v cons ), hen he cross secion area of maerial a he ransfer poin is proporional o he insananeous capaciy of he maerial which is being deposied. In his case, he capaciy which is obained in his manner is proporional o A in (). If i is no he case, i.e. he maerial is deposied o he beginning of he bel a a speed which is no consan, bu is he resul of he algorihm presened in Fig. 2, hen he cross secion area of maerial a he ransfer poin mus be calculaed in accordance wih he conservaion of capaciy, as in (6), for he ransfer poin beween wo BCs, (i-) and i-h, (where i=5, i.e. i-=4), A 5in v 5ref v 5 T e5 A( i ) ou() A() i in () = v( i ) (). (6) v()() i According o (2), he cross secion a he end of he (i-) bel mus be deermined. Calculaion is conduced by monioring he movemen of maerial along he bel over ime. This can be performed by dividing he bel ino secions of consan lengh. The lengh of hese secions is deermined so ha a consan cross secion of maerial can be observed along is enire lengh. The cross secion area of maerial on one such secion is enered ino he memory, i.e., regisry. The regisries are organized in a series so ha a he sampling insan he earlier recorded values are shifed ino he nex regisry and new value is enered ino he firs regisry [5]. The cross secion value of incoming maerial o he dump-side BC (A 4ou ) is herefore calculaed, no measured. Discreizaion of he inpu maerial cross secion a he ransfer poin beween wo BCs influences all oher characerisic values of BC, which are archived wih SCADA and presened in Fig. 7. I has been shown by experimenal resuls presened in Fig. 7 ha he conrol sraegy wih FLC adjuss he speed of he loaded BC in accordance wih he quaniy of maerial on he bel, in order o achieve energy saving in normal operaion. Variable acceleraion and deceleraion is performed in such a way o cause minimum sress of mechanical assemblies and he bel. I can also be noiced from presened resuls ha he cross secion of maerial on he bel is someimes greaer han % which is he maximum heoreical value. Even when he value of he cross secion reaches 6% of he heoreic value, ranspor can sill be conduced wihou spillage [7]. V. COMPARISON BETWEEN DIFFERENT APPROACHES TO OMTIMUM SPEED DETERMINATION A funcion of mechanical power of bel conveyor drive is developed based on DIN 22 mehodologies for moional resisances calculaion. I is presened in [8] as a new energy model, which lumps all he parameers ino four coefficiens, θ, θ 2, θ 3 and θ 4. The procedure for leas square (LSQ) based off - line parameers esimaion has been applied o indenify coefficiens of energy model of he observed BC. The required speed has also been deermined using he mehod of sequenial quadraic programming, wih he goal o reduce he elecrical energy consumpion under defined consrains of he sysem. The resul achieved in his way, has been compared wih he resul of he applied algorihm wih FLC. Mechanical power of he BC drive as a funcion of capaciy and speed, for he defined operaing condiions, i.e. energy model is given wih (7), T v T PT,v ( ) = θ T v+ θ2 v+ θ3 + θ4 T+ (7) v 36. where P [W] is mechanical power, v [m/s] is speed and T [/h] is mass flow, T [/h] = γ[/m 3 ] Q[m 3 /h]. Mechanical power in seady sae operaion of he considered dump-side conveyor is calculaed for differen values of inpu variables, i.e. capaciy and speed. Based on achieved resuls, he parameer esimaion scheme presened in [8] has been applied providing he following values of energy model coefficiens: Θ [p.u.] = [.36 DS2a.9-5

6 ] T. All variables are normalized wih base values seleced in accordance wih raed parameers of moor and he BC, given in he Appendix. Seady sae characerisics for P av = f (v, Q = cons), given in Fig. 8, are calculaed wih he esimaed parameers θ, θ 2, θ 3 and θ 4, for differen values of capaciy Q (from.5 o [p.u.]), by varying speed in he range of v = [.4,...,][p.u.]. For speed values less han.4 p.u., he relaion (7) is inappropriae, herefore, differen funcional dependency for P av = f (v, Q) has o be esablished. Noneheless, he performed analysis does no apply in his range. Two more characerisics, P av = f (v, A max ) and P av min = f (v, Q), are also presened in he same figure. The presened resuls clearly show ha he characerisic for P av min is o he lef of he characerisic P av = f (v, A max ). Consequenly, he considered BC will no be able o operae a speed which provides minimum energy consumpion, because i will cause he spillage of maerial over he bel. Due o his reason, he BC can operae only wih speeds equal or higher han he speeds deermined by he characerisic P av = f (v, A max ). Hence, he rue minimum of energy consumpion will no correspond o he absolue minimum of average mechanical power (P av ), bu o he average mechanical power, which is deermined in accordance wih he consrain of maximum capaciy. Bel conveyors in OPMs always work in he sysem wih excavaors and spreaders for he purpose of maerial handling, so heir energy efficiency is affeced by many consrains which exis a he equipmen or sysem level. In pracice, many bel conveyors are working wih reduced capaciy, even wih empy bels, due o problems which may occur during he sysem operaion. The paper deals wih he opimizaion problem which is dedicaed o opimize he bel conveyor speed under a reduced capaciy and under defined sysem consrains, in order o minimize elecrical energy consumpion. Hence, he analyical expression for elecrical energy consumpion is employed as he objecive of his problem for minimizaion. The bel speed is wihin is defined limis, as well as maximum mass per uni of bel lengh. They form he consrains of his problem. As addiional consrain, he range for ime derivaive of speed is also inroduced. This especially refers o deceleraion coefficien which has o mee hree requiremens: firs, o provide he maximum cross secion of maerial wihou spillage over he bel; second, o fulfill echnical crierion k() k max ech = 3.5 [%v r /s] in order o keep mechanical ensions wihin defined limis; hird, o be variable o provide deceleraion wih drive orque nearly zero (bu no negaive), as defined in (). Therefore, he opimizaion problem is formulaed as follows, j= N el ( j j ) = ( j j) s j= η min W v,q : j N P v,q subjec o : 5. vmax vj vmax Δv vj vj linear consrains min Δvmax s s s M' M' nonlinear consrains Lj Lmax (8) where η is he overall efficiency of he driving sysem, s is sampling ime, Q in = [Q in,...,q inn ] is acquired from file which is recorded on he real sysem and M' L [kg/m] = γ Q in / (3,6 v) is mass of maerial per uni of bel lengh. The resuls of measuremens of he implemened algorihm wih FLC, which are presened in Fig. 7, are recorded for he same values of inpu variable Q in. The soluion of he opimizaion problem is he opimum speed v op = [v op,..., v opn ] for he given value of he inpu capaciy of maerial, which provides he operaion of BC wih minimum energy consumpion, i.e. wih maximum energy efficiency under defined linear and nonlinear consrains. The minimum and maximum speed of he bel, as well as minimum and maximum ime derivaive of he bel speed presen linear consrains, while maximum mass of maerial per uni of bel lengh presens nonlinear consrain. Pav [p.u.] Fig. 8 Characerisics for P av = f (v, Q = cons) The required soluion is obained by applying he fmincon funcion of MATLAB Opimizaion Toolbox [9], which finds a minimum of a consrained nonlinear mulivariable funcion based on SQP algorihm (sequenial quadraic programming). In he considered case, consans η, T max = γ Q max and M' Lmax are he acual values of he analyzed sysem of BCs. The lower limi of bel speed is se on 6% of v r, while he upper limi is se o % of v r. Sampling rae for he inpu variable Q in is s = s. Maximum values for acceleraion and deceleraion coefficiens are equal and se o 3.3 % v r / s, in accordance wih recommendaions given in []. The resul for he opimum speed obained as he soluion of he described opimizaion problem, v op, is in excellen agreemen wih he resul of measuremen for he fuzzy speed conrol of BC, v ref, as presened in Fig Time [s] Fig. 9 Reference speed obained wih algorihm wih FLC, v ref, ogeher wih opimum speed obained wih fmincon funcion, v op v op v ref DS2a.9-6

7 Presened ime diagrams also confirm ha he variable deceleraion in he case of fuzzy speed conrol does no exceed he maximum value and saisfies all hree defined requiremens. Therefore, i is proved ha he proposed algorihm wih FLC provides operaion wih minimum energy consumpion, in he exising operaing condiions and under defined sysem consrains. VI. CONCLUSION The paper presens a novel conrol sraegy for he sysem of bel conveyors wih adjusable speed inducion moor drives based on a principle of minimum energy consumpion. Fuzzy logic conrol is used for generaing he reference speed. The proposed conrol sraegy wih FLC is implemened on he new sysem of bel conveyors wih remoe conrol on an OPM and resuls of measuremens of BC characerisics values are presened in he paper. The presened resuls are furher compared wih resuls of he oher approach o opimum speed deerminaion. According o his approach, resuls for he opimum speed of BC are obained off - line for he same incoming maerial, i.e. for he same inpu variable Q in, applying he mehod of sequenial quadraic programming and using he new idenified funcion for average power of BC drive. I is proved ha opimum speed is deermined wih boh approaches, providing he minimum of elecrical energy consumpion under given consrains of he considered sysem of bel conveyors. ACKNOWLEDGEMENT The paper is he resul of research on he Projec TR 336, which is financially suppored by he Minisry of Educaion and Science. APPENDIX Moor daa: Operaing volage: 69 V; Winding connecion: ; Power: kw / 995rpm; Duy: S, ED %; Efficiency: 96.5%;Power facor:.837; Curren: 36 A; Torque: 96Nm BC daa: Bel widh 2mm; Number of drives 4; Type of drives: frequency converer wih DTC; Maximum lengh 3.25km; Raed speed 4.65 m/s; Raed capaciy of 66m 3 /h Sysem of BCs daa: Number of bel conveyors: 5; Toal insalled power 2 MW; Curren lengh: 7.5 km REFERENCES [] B. Bose, "Global Warming: Energy, Environmenal Polluion, and he Impac of Power Elecronics," IEEE Indusrial Elecronics Magazine, vol. 4, pp. 6-7, 2. [2] B. Jefenić, L. Risić,M. Bebić, S. Šakić, I. Mihailović, D. Jević, "Opimal Uilizaion of he Bulk Maerial Transporaion Sysem based on Speed Conrolled Drives," XIX Inernaional Conference on Elecrical Machines ICEM 2, Rome, Ialy, 2, pp. -6. [3] B. Jefenić, I. Mihailović, M. Bebić, L. Risić, D. Jević, N. Rašić, S. Šakić, "Energy efficiency in ransporaion of bulk maerial wih frequency conrolled drives," 4h Inernaional Power Elecronics and Moion Conrol Conference EPE-PEMC 2, Ohrid, Macedonia, 2, pp. T [4] Werner Daus, S. Körber, Norber Becker, "Raw Coal Loading and Bel Conveyer Sysem a he Nochen Opencas Mine," Braunkohle Surface Mining, vol. 5, p. 2, 998. [5] L. B. Risić and B. I. Jefenić, "Implemenaion of Fuzzy Conrol o Improve Energy Efficiency of Variable Speed Bulk Maerial Transporaion," IEEE Transacions on Indusrial Elecronics, vol. 59, pp , 22. [6] Sivanandam S.N., Sumahi S., Inroducion o Fuzzy Logic using MATLAB: Springer, 27. [7] Jefenić, B.,Bebić, M.,Risić, L.,Šakić, S., "Design and Selecion of Bel Conveying Equipmen & Sysems," in Design and Selecion of Bulk Maerial Handling Equipmen and Sysems : Mining, Mineral Processing, Por, Plan and Excavaion Engineering. vol. I, J. Bhaacharya, Ed., I ed Kolkaa: Wide Publishing, 22, p [8] S. Zhang and X. Xia, "Modeling and energy efficiency opimizaion of bel conveyors," Applied Energy, vol. 88, p., 2. [9] Opimizaion Toolbox User s Guide For Use wih MATLAB, Version 2. Available: [] Y. Pang and G. Lodewijks, "Improving energy efficiency in maerial ranspor sysems by fuzzy speed conrol," 3rd IEEE Inernaional Symposium on Logisics and Indusrial Informaics (LINDI), 2, 2, pp DS2a.9-7