Optimal Control of Dc Motor Using Performance Index of Energy

Transcription

1 American Journal of Engineering esearch AJE 06 American Journal of Engineering esearch AJE e-issn: p-issn : Volume-5, Issue-, pp esearch Paper Open Access Opimal Conrol of Dc Moor Using Performance Inde of Energy Arnisa Myrellari, Perika Marango, Margaria Gjonaj 3 3 Polyechnic Universiy of irana, Faculy of Elecrical Engineering, Deparmen of Auomaion, iranë,albania ASAC: DC moors are widely used in he mechanisms ha require conrol of speed. PID conroller are widely used for speed conrol. u hey aren suiable for high performance cases, because of he low robusness of PID conroller. Many researchers have been sudying various new conrol echniques in order o improve he sysem performance. In dynamic regimes, he conversion efficiency is diminished o abou half while during he saionary regime he efficiency is increased. he main drawback of hese drives is he obained diminished elecrical energy during he ransien regimes, i.e. saring, braking or reversing. he paper objecive is o validae a new conrol, opimal ype, which minimizes he consumpion of he necessary energy o perform a given sae rajecory. wo problems are presened in his paper: he problem formulaion and he energy saving conrol soluion, he numerical simulaion. he numerical resuls confirm he performances of he proposed conrol mehod. Keywords: opimal conrol, energy, DC Moor I. INODUCION he DC moors are comprehensively used in various indusrial applicaions such as elecrical equipmen, compuer peripherals, roboic manipulaors, acuaors, seel rolling mills, elecrical vehicles, and home appliances. Is applicaions spread from low horse power o he muli-mega wa due o is wide power, orque, speed ranges, high efficiency, fas response, and simple and coninuous conrol characerisics. he speed of DC moor can be changed by conrolling he armaure and field volages. he dynamic regimes of DC moor, such as saring and sopping, occur very ofen during normal work. hese frequen dynamic regimes diminish considerably he conversion s efficiency, which is higher in he saionary sae. he convenional conrol using P and/or PI conrollers or oher advanced echniques has as objecives a good dynamic behaviour and realizaion of he given rajecory wih a minimum error. here are heoreical resuls validaed by numerical simulaion concerning he energeic opimal conrol of DC and AC elecric drive sysems[7], which ake ino consideraion he minimizaion of he consumpion energy during he ransien periods, e.g. saring, sopping and reversing. he numerical resuls indicae he cerain possibiliies o decrease he consumpion energy [3,5]. here are many approaches regarding he conversion s efficiency. hus muli-objecive opimizaion mehods can be applied for he slow dynamic sysem or for saionary regimes. Also he differenial evoluion mehod could be applied for he case of seady-sae condiions. Loss minimizaion echniques and oher mehods are developed for AC. moors [7,8] or for real applicaion. aking ino consideraion hese requiremens and achivemens, an opimal conrol approach oriened o minimize he ependiure energy for a DC moor is developed in his paper. Using a model of a DC moor, an adequae performance funcional crieria, and opimal conrol heory [3], he non-recursive soluion of mari differenial equaion, iccai ype, MDE, is developed as opimal conrol law.hese approaches are based on very srong mahemaical insrumen, opimal conrol heory, being formulaed various problems as minimum ime or energy.obviously, here are consrains generaed by magniude limis for he elecric and mechanic parameers. he inroducion of he consrains ransforms he problem ino a nonlinear one. he soluion, assessed using numerical procedures, is applied o a DC moor. he numerical resuls confirm he uiliy as well as he properies of he soluion, high dynamic performances, wihou overshoos and good robusness. A schemeis proposed based on calculus of he opimal conrol law. w w w. a j e r. o r g Page 57

2 American Journal of Engineering esearch AJE 06 II. POLEM FOMULAION DC moor is a power acuaor which ransforms elecrical energy in o mechanical energy. DC moor is widely used in many indusrial applicaions where wide range of speed orque characerisics required. In his paper, he separaed ecied DC moor model is chosen according o his good elecrical and mechanical performances more han he oher DC moor models. A DC moor, conrolled by armaure volage, consan field is an invarianconrollable dynamic sysem described by he differenial equaions. d d b k i m J J J di k i u d L J L In he space sae he differenial equaions ge he form s A u Gw where he sae is given by i 3 he conrol problem consiss in finding of an admissible conrol, armaure volageu, which ransfers he sysem from he iniial sae o a desired sae i 5 in he fied ime, ɷ being he desired final speed, wih minimizaion of he consumpion energy. In order o minimize he consumpion energy, he inde performance crieria of energy in he form J - S - Q u u f 0 Is associaed o sysem, where weighing marices S and Q are posiive semidefined marices and is a posiive defined mari. he opimal conrol problem is: wih free end poin, fied ime and unconsrained. he resricions of he magniude for he conrol and sae could be solved by he adequae choice of he weighing marices. he direc minimizaion of drawn energy can be achieved by inroducing inpu power P u i u 7 in inde performance crieria 6. here are more power losses which are deerminaed by he angular speed: eddy curren losses p F k 8 F hyseresis power losses p k 9 H H viscous power losses p V b 0 also he oupu mechanic power has he form p O k H wherek F, k H, b are consan coefficiens. d 6 III. MEHODOLOGY he soluion of he problem eiss and is unique if he sysem is conrollable and compleely observable and he weighing marices carry ou he above condiions [,5].y using he variaional mehod, he Hamilonian ofhe opimal conrol problem is H, u,, g, u, f, u, Q u u λ being cosae vecor. herefore he following canonic sysem is obained w w w. a j e r. o r g Page 58

3 American Journal of Engineering esearch AJE 06 w w w. a j e r. o r g Page 59 0 w G A Q A 3 he well known boundary condiions resul from iniial sae 0= 0 ransversaliycondiion S 4 he soluion of he problem is given by * y u 5 where and y, he cos vecor being he soluion of he canonical Euler-Lagrange sysem. he opimal conrol law a any momen is * w K K P u 6 in which P - is he soluion of differenial mari equaion, iccai ype DME. he srucure of opimal conrol is as follow in Fig. Fig. Srucure of opimal conrol law he opimal conrol soluion 6 has hree componens: he sae feedback, he reference o achieve he desiredfinal sae, he compensaing feedforward of he perurbaion w effec, Fig.. he soluion is a nonrecursive one and can be compued for any value of, from iniial ime =0 o he final ime. IV. NUMEICAL ESULS he sysem was numerically simulaed using a discreized model and Malab/Simulink sofware. he sysem parameers are:.5 kw, 00rpm, 5A.he simulaion resuls are presened in Fig., Fig.3 and Fig.4 and concreely we have opimal conrol for speed, curren and volage of DC moorby acceping ha: =ɷ and =i. Fig.Opimal conrol law for speed

4 American Journal of Engineering esearch AJE 06 Fig.3Opimal conrol law for curren Fig.4Opimal conrol law for volage V. CONCLUSION In order o enhance he conversion efficiency of he DC drive sysems a new opimal conrol law, which minimizes he drawn energy, was developed. he soluion properies have been esed via simulaion, using MALA-SIMULINK. Wih respec o convenional conrol, he opimal proposed conrol for a DC drive sysem minimizes he drawn energy o perform a given rajecory. he reducion in he drawn energy leads o he decreasing of he energy ependiure.he main feaures of he proposed opimal conrol law are: he soluion of conrol is an analyical one, high dynamic performances, wihou overshoos and good robusness o he load variaion decreasing he drawn energy wih abou 6% o 0% for a dynamic regime as saring, sopping and reversing; he opimal conrol is linear and unconsrained being applicable only for linear drive sysems; volage, curren and speed limis can be mainained wihin sric limis by adequae choice of he weighing marices; he opimal conrol can be mied wih convenional conrol in he aim o assure he works, dynamic and seady sae regimes. EFEENCES []. Egami, H. Moria and. suchiya, Efficiency Opimized Model eference Adapive Conrol Sysem for a DC Moor, IEEE ransacions on Indusrial Elecronics, 37, 990, [] A.Myrellari, P. Marango, M.Gjonaj, Analysis and Performance of Linear Quadraic egulaor and PSO algorihm in opimal conrol of DC moor, Inernaional Journal of Laes esearch in Engineering and echnology,4, 06, [3] M. Ahans, P. L. Falb, Opimal Conrol: An Inroduciono he heory and Is Applicaions, New York: Dover Publicaions, 007 [4] Donald E. Kirk, Opimal Conrol heory An inroducion. Prenice Hall,970 w w w. a j e r. o r g Page 60

5 American Journal of Engineering esearch AJE 06 [5] Naidu. D. S, Opimal Conrol Sysem, CC Press LLC,003 [6] M. Ahans, P. L. Falb, Opimal Conrol: An Inroduciono he heory and Is Applicaions, New York: Dover Publicaions, 007, [7] Wai- Chuen Gun, obus and opimal conrol of AC machines, docoral diss, Hong Kong Universiy of Science and echnology, 00 [8] W.J. ook, J. Li, L. Xu, Z, Zhang, A new efficiency opimizaion mehod on vecor conrol of inducion moor,proc. IEEE Conf. Elecrical Machines and Drives, 005, w w w. a j e r. o r g Page 6