Microsoft Word - KSR2014A433

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1 014 년도한국철도학회추계학술대회논문집 KSR014A433 강인제어기를이용한독립구동방식철도차량의주행성능개선 Runnng performance mproements of the ndependently rotatng wheel type ralway ehcle usng robust control 조연호 *, 이원상 *, 곽재호 ** Yonho Cho *, Wonsang Lee *, Jaeho Kwak * * Abstract The man method to accomplsh 100% low floor s usng ndependently rotatng wheel type boge. IRWs (ndependently rotatng wheels) hae ery small longtudnal creepages. So there s no lateral centerng force. For ths reason t cannot make huntng moton and extngush the unstable mode by selfexctaton. On the other hand IRWs type boge run on one sde of the ral because t does not hae selfcenterng force. If dsturbance or exctaton s appled the wear and the lateral forces grow worse for contnuous flange contact runnng. So many researches and attempts were accomplshed to mproe the demert of IRWs. Ths paper descrbes the robust control of the IRWs to mproe the runnng performance wth yaw torque. SMC (sldng mode control) s one of the ared state space model type non-lnear robust controls. Ths control logc s ery robust aganst model uncertanty and dsturbances. Keywords: low-floor tram, IRWs(ndependently rotatng wheels), Robust control. Sldng mode, Yaw moment 초록독립구동방식은전후방향크립력이미소하여횡방향복원력이발생하지않아이로인한사행동이없으므로자려진동에의한불안정성이제거된다는장점이있는반면에외력이가해진경우한쪽으로치우친상태에서복원이되지않아플렌지접촉현상이더욱빈번히발생하게되는단점을가지고있다. 이러한독립구동방식대차의단점을극복하기위해다양한시도가이루어지고있으며, 본논문에서는대차에요모멘트를발생시키거나횡방향제어력을작용하여안내력을발생시키는제어를통해독립구동방식대차의주행성능개선에대한연구를수행하였다. 특히모델불확실성이나외란에대한강건성을가지는강인제어기를적용함으로써제어성능과안정성을확보하고자하였다. 주요어 : 저상트램, 독립구동, 강인제어, 슬라이딩모드, 요모멘트 1. 서론최근국내여러도시에서도입을검토중인저상트램은 100% 저상화구현과급곡선주행성능개선을위해독립구동방식대차를적용하고있다. 독립구동방식대차는종방향크립력이매우적어횡방향복원력이거의발생하지않는다. 이러한특징인철도차량특유의불안정특성인사행동발생이없지만, 외란이나불균형조건에대하여한쪽레일에치우치게 교신저자 : 현대로템주행장치개발팀 (ycho@hyunda-rotem.co.kr) * 현대로템주행장치개발팀 ** 한국철도기술연구원무가선트램연구단

2 됨으로써오히려마모나횡압이증가할수있다. 이러한독립구동방식대차의문제점을개선하기위한많은연구가수행되어왔으며, 본논문에서도그러한노력의하나로서요토크와횡방향제어력에대한강인제어기를적용함으로써주행성능개선효과를확인할수있다.. 본론.1 운동방정식본논문에서는기존의논문에서무시되었던중력복원력에의한미소한종방향크리피지를추가하여모델링을수행하여보다현실적인주행특성확인이가능하다. F : mr FL FR NL NR FS WAk dh M : R ( F N ) R ( F N ) M M M dt R R R L L L L R S (1) () (1) 식과 () 식의뉴턴의운동방정식을기반으로각각의자유도별로방정식을유도할수있다. (3) 과 (4) 는강체윤축모델에대한선형운동방정식이고, (5)~(8) 의 4식은독립구동방식윤축의 4자유도에대한운동방정식이다. w f f r f my ( K ) y( C ) y f w 1 py 1 py a a f r 1 0 I a f y ( I f ) y ( f aw K b ) wz y px 1 1 r r a a f f 33 ( a C b ) px 1 1 (3) (4) w f f r f my ( K ) y( C ) y f (5) w 1 py 1 py a a f r0 1 I a f y ( I f ) y ( f aw K b ) wz y px 1 1 (6) r r a a f f 33 r r ( a C b ) f a f a px L 33 1R I f y r f f w1 1L L (7) I f y r f f (8) w1 1R R (9) 식에서와같이포화계수 alpha를도입하여보다현실적인휠 / 레일접촉특성을사용하여해석을수행하였다. 그리고, 플렌지접촉에대한접촉력을추가하여휠이플렌지접촉한계이상의변위가발생하지않도록하였다.

3 ( ) for for 3 F F R L jx jy,, j LR, j N K ( y ) for y r F 0 for y t K ( y ) for y r (9) (10) (11) 식부터 (14) 식은비선형독립구동방식윤축에대한운동방정식이다. w f f r f m y ( K ) y ( C ) y f F a a f r I a f y ( I f ) y ( f aw K b ) wz y px 1 1 r r a a w 1 py 1 py t1 f f r r ( a C b ) f a f a px L R I f y r f f I f y r f f w L L w R R Table 1 은해석에사용된파라메터를정리한표이다. (11) (1) (13) (14) Table 1. Parameter alues of ralway ehcle Symbol Value Unt Symbol Value Unt m w 800 kg L m m t 3,575 kg K px 1.e+7 N/m m c 11,970 kg K py 4.18e+6 N/m I wx 400 kg m K pz.093e+6 N/m I wy 4 kg m C px.77e+4 N s/m I wz 400 kg m C py 1.16e+4 N s/m I w1 100 kg m C pz 1.16e+4 N s/m I tx 1,500 kg m K sx 1.4e+5 N/m I tz 3,100 kg m K sy 1.4e+5 N/m I cz 164,000 kg m f 11.1e+6 N r.33 m f N m a m f 16 N λ f e+6 N b m W 5.6e+4 N b 1.11 m μ b m K r 1.617e+7 N/m L m δ m

4 . 제어기설계..1 슬라이딩모드제어슬라이딩모드제어는실용성이높은비선형제어이론으로인식되어있으나, 현장에서는 H 제어를이용한강인제어기를적용하기도한다. 구소련의연구자들에의해 1950년대등장하였다. 슬라이딩모드제어의가장큰특징은강인성에있다. 슬라이딩모드제어는시스템의구조를변경하여시스템의상태를슬라이딩평면에구속시킴으로써강인성을얻을수있는비선형제어기법이며큰의미에서는가변구조제어기이다. 모델의불확실성과외란이존재한경우에도제어시스템의상태를슬라이딩평면에있도록한다. 슬라이딩평면은페루프시스템의거동을결정하게된다... 슬라이딩모드제어기설계슬라이딩모드제어는기준모델설정후등가제어법칙으로절환면상에계의안정성보장되는등가제어법칙설계하여계의상태가절환면밖에있는경우슬라이딩조건에의해절환면에도달하도록절환제어법칙을설계하게된다. 제어입력은절환면에도달하기위한도달법칙과절환면에상태를유지하기위한등가제어법칙으로크게나뉠수있다. 오차가정의된상태에서오차정의를이용한절환면을지정하게된다. 절환면이지정되면등가제어법칙은리아프노프함수를이용한안정화법칙에따라결정되거나, 슬라이딩면존재조건에의해결정된다. 도달조건은등속조건, 지수접근, 제곱식접근, 일반해접근등이사용되며, 본연구에서는빠른도달이가능한지수법칙을사용하여제어입력을결정하였다. 상태공간에서의슬라이딩평면 () t 은아래와같이정의된다. () t Cx() t (15) 주어진상태방정식에대한등가방정식은 (16) 과같다. x t Axt B CB CAt I BCB CAxt 1 1 () () [ ()] [ n ] () (16) 슬라이딩모드제어는상태를슬라이딩면에도달한후슬라이딩면에고정시키도록한다. 이를위해제어입력은등가제어입력과비선형제어입력인도달법칙으로나뉘게된다. 또한일반적인슬라이딩모드제어의문제점인채터링을방지하기위해절환함수대신포화함수나한계함수로전환하여사용한다. ut () u () t u () t eq 1 () t unl () t ( CB) ( t) nl (17) (18)

5 ..3 슬라이딩모드제어결과아래의그림 1과 는슬라이딩모드제어의강인성을확인하기위해유전자알고리즘으로최적화된 PID 제어와 LQR제어에대한윤축의횡변위와요각도변위를비교한결과이다. wheelset lateral dsplacement(meter) 6 x 10-3 IRW wheelset 4dof model: Lateral dsplacement(r0=5m, V= 15km/h) Passe PID LQR SMC wheelset Yaw angle(degree) IRW wheelset 4dof model: Yaw angle (R0=5m, V= 15km/h) Passe PID LQR SMC tme(sec) tme(sec) Fg. 1 Lateral dsplacement of wheelset Fg. Yaw angle of wheelset 3. 결론 독립구동방식차량의주행성능개선을위해요모멘트를이용한제어기를구성하여주행성능개선효과를해석적으로확인하였다. 요모멘트를발생시키기위한요토크제어는 PID 제어와같은간략한제어기와더불어 LQR 과같은최적제어기, 슬라이딩모드와같은강인제어기를함께구성함으로써그특징을비교평가할수있었다. 특히슬라이딩모드제어는모델의불확실성이나외란에대하여도강인한제어특성을보이는것으로알려져있으며, 향후 H 제어와더불어모델에사용된다양한변수의불확실성에대한제어응답을확인해보도록하겠다. 참고문헌 [1] B. Lang and S. D. Iwnck (007), "An Expermental Study of Independently Rotatng Wheels for Ralway Vehcles", IEEE Proceedngs of Internatonal Conference on Mechatroncs and Automaton, [] T. X. Me and H. L (008), "Control Desgn for the Acte Stablzaton of Ral Wheelsets", Journal of Dynamc Systems Measurement and Control 130, [3] R. V. Dukkpat and S. Narayana Swamy (199), "Independently Rotatng Wheel Systems for Ralway Vehcles-A State of the Art Reew", Vehcle System Dynamcs 1, [4] R. M. Goodall and Hong L (000), "Sold Axle and Independently Rotatng Wheelsets - A Control Engneerng Assessment of Stablty", Vehcle System Dynamcs 33, [5] M. Gretzschel and L. Bose (00), "A New Concept for Integrated Gudance and Dre of Ralway Runnng Gears", Control Engneerng Practce 10, [6] T. X. Me, Z. Nagy, R. M. Goodall and A. H. Wckens (00), "Mechatronc Solutons for hgh speed ralway ehcles", Control Engneerng Practce 10, [7] V. Rose, L. Bao (007) Vbraton of

6 the plate wth a hole, Proceedngs of the 5th ASCE Internatonal Cl Engneerng Congress, New Orleans, LA, pp [7] T. X. Me and R. M. Goodall (003), "Practcal Strateges for Controllng Ralway Wheelset Independently Rotatng Wheels", ASME 15, [8] T. X. Me and R. M. Goodall (001), "Robust Control for IRW on a Ralway Vehcle Usng Practcal Sensors", IEEE Transactons on Control System Technology 9, 4, [9] A. Satoh and K. Tanfuj (00), "Comparson of Curng Characterstcs of Ral Vehcle wth Independently Rotatng Wheels between Steerng Methods", JSME 11th Proceedngs of transportaton conference 0-50, [10] R. Obata, K. Tanfuj, H. Soma and T. Masuda (006), "Curng Performance of a Ral Vehcle wth Independently Rotatng Wheels by Torque Dfference Control", JSME. C, 7, 716, [11] Y. Suda and S. Maeshro (1998), "Steerng Ablty of Self-steerng Truck wth Independently Rotatng Wheels n Tralng Axle", JSME, C, 64, 68, [1] M. Myamoto and T. Sato (001), "Study on the stablzaton of ralway ehcles wth ndependently rotatng wheels by control of steerng on wheelset (1 Axle traler boge)", JSME, 10th Conference of Transportaton 01-36, [13] T. Satou and M. Myamoto (00), "Study on the stablzaton of ralway ehcles wth ndependently rotatng wheels by control of steerng on wheelset (Model experment and a smulaton)", JSME 11th Conference of transportaton 0-50, [14] H. Yasuda and M. Myamoto (005), Study on the Stablzaton of Ralway Vehcles wth Independently Rotatng Wheels by Control of Steerng on Wheelset (Control of Front and Rear Wheelset Steerng), JSME Hokkado s 41st proceedngs of basc conference 047-1, [15] J. Perez, Jesus M. Bustura, T. X. Me and J. Vndas (004), Combned acte and tracton for mechatronc boge ehcle wth ndependently rotatng wheels, Annual Reew n Control 8, [16] J. L, R. M. Goodall, T. X. Me and H. L (003). Steerng Controllers for Ral Vehcles wth Independently Dren Wheel Motors, Electronc System and Control Dson Research, 4-6. [17] T. X. Me, R. M. Goodall and A. H. Wckens (00), Dynamc and Control Assessment of Ral Vehcle Usng Permanent Magnet Wheel Motor, Vehcle System Dynamcs Supplement 37, [18] Khaled E. Zaazaa and Bran Whtten (007), Effect of ndependently rotatng wheels on the dynamc performance of ralroad ehcles, ASME nternatonal Mechancal Engneerng Congress and Exposton, [19] H. Sugyama, R. Matsumura, Yoshhro Suda and Hdeak Ezak (009), Analyss of ndependently rotatng wheel system usng multbody dynamcs approach, ASME nternatonal Desgn Engneerng Techncal Conference and Computers and Informaton n Engneerng Conference-IDETC/CIE, 1-8. [0] Jnzh Feng, Jun L and R. M. Goodall (008), Integrated control strateges for ralway ehcles wth ndependently-dren wheel motors, Front. Mech. Eng. Chna,

Microsoft Word - KSR2012A062.doc

Microsoft Word - KSR2012A062.doc YWXY º º t rzyywxyhw]y Ÿk ƒ ƒ x Investgaton on Thermal Analyss Method of IPMSM for Ralway Vehcles ø ø ã ä ã äõ ã ä ã ä ú ã Chan-Bae Park *, Hyung-Woo Lee *, Jae-Hee Km *, Jun-Ho Lee *, Byung-Song Lee *