Energy Savng for Automatc Tran Control n Movng Block Sgnalng Sytem Qng Gu, Xao-Yun Lu and Tao Tang Abtract Wth rapd development of the ralway traffc, the movng block gnalng ytem (MBS) method ha become more and more mportant for ncreang the track capacty by allowng tran to run n a horter tme-headway whle mantanng the requred afety margn. In th framework, the trackng target pont of the movng forward wth t leadng tran. Th paper focue on the energy avng trackng control of two ucceve tran n MBS. Nonlnear programmng method ued to optmze the energy avng peed trajectory of the. The real-tme locaton of the could be ntegrated nto the optmzaton proce. Due to mplcty, t can be ued for onlne mplementaton. Fnally, a moothng algorthm propoed to mprove the peed trajectory for rde comfort. The feablty and effectvene are verfed through mulaton. The reult how that the new method effcent on energy avng wth guaranteed rde comfort even when dturbance preent. Key word movng block, energy avng, ATP (Automatc Tran Protecton), ATO (Automatc Tran Operaton), trackng, tran peed trajectory, rde comfort, trajectory moothng W I. INTRODUCTION ITH afe, comfortable, punctual, and effcent feature, ma rapd trant ytem can brng tremendou convenence to daly lfe and an effectve oluton to modern traffc congeton problem. A ralway network could conume large amount of energy and contrbute gnfcantly n emon, to enure the punctualty and rde comfort of tran whle achevng energy-avng repreent an nteretng and challengng problem. In Fxed Block Sgnalng Sytem, Energy-avng on ralway ha been tuded for many year and got many effectve reult. The earlet and mot notceable work from the Schedulng Manucrpt receved Aprl 1, 11. Th work wa upported by the tate key laboratory of ral traffc control and afety (Bejng Jaotong Unverty) under the project RCSZZ1 and Natonal Natural Scence Foundaton of Chna No.3. Qng Gu wth tate key laboratory of ral traffc control and afety, Bejng Jaotong Unverty, Bejng,, Chna (phone:+5119; fax: +51519; e-mal: karengqq@ gmal.com). Xao-Yun Lu wth Calforna PATH, Inttute of tranportaton tude, Unverty of Calforna Berkeley. CA 9, USA (xylu@path.berkeley.edu). Tao Tang wth tate key laboratory of ral traffc control and afety, Bejng Jaotong Unverty, Bejng,, Chna (ttangr@bjtu.edu.cn). and Control Group (SCG) n North Autrala. Reearcher n SCG conducted theoretc reearch and project on tran energy-avng operaton. Mlroy, Lee and Tyler propoed energy-avng operaton model n [1]. They howed that the energy-avng control could be dvded n to four phae: tracton, peed holdng, coatng and brakng a llutrated n Fg. 1. Baed on that, many people nvetgated energy avng tratege, e.g. Chang and Wong appled dfferent algorthm to fnd coatng pont before the tran departure n fxed runnng dtance [, 3]. Snce MBS ha more mplementaton n modern day, reearch on drvng tratege n MBS wll be the trend n the future []. However, there ha not been much reearch n tran trackng control trategy n Movng Block Sgnalng (MBS). MBS wa propoed n [5] to reduce headway among ucceve tran. In MBS, two ucceve tran are eparated by a afety margn (a pre-determned dtance) and the requred brakng dtance of the. Durng the runnng proce, Automatc Tran Protecton (ATP) ytem calculate the brakng curve of the to guarantee the afety. At the ame tme, the follower could obtan the poton and peed of the leader. Therefore the peed trajectory of the follower could be optmzed wth repect to ome objectve functon. Fg.1. Speed curve of a typcal nter-taton run Th paper degn a new energy avng drvng tratege for tran trackng control. It could be mplemented by Automatc Tran Operaton (ATO) ytem or a the reference peed for drvng atance. A trajectory moothng algorthm propoed to mprove the rde comfort. The mulaton reult how that, compared wth the tradtonal approache, the new method gnfcantly more effcent on energy-avng wthout acrfcng the operaton tme when the runnng wthout nterference or only acrfcng lttle (due to moothng) operaton tme when the ha nterference.
Nomenclature: The followng notaton are ued throughout of the paper. t the tme parameter; S the poton of the head; leadng Sfollowng the poton of the head; Lz the ntantaneou dtance of two ucceve tran; Lt the length of the tran; Lafe the length of the afety margn; V followng (t) the ntantaneou peed of the ; a,b are ervce acceleraton and deceleraton of the tran; b the deceleraton n approxmate coatng phae; a 1, a, a 3 are retance coeffcent; before the departure 1 from the detnaton; p after the departure from the detnaton taton and the the wa delayed; S the poton of the detnaton taton; Ttackng the departure tme nterval; Tbp the tme whch the already ued; Ttackng the departure tme nterval of two ucceve tran; II. TRACKING INTERVAL MODEL IN MBS Under MBS, the trackng target pont of the move forward contnuouly a the travel. The ntantaneou dtance Lz of two ucceve tran expreed a: Lz Sleadng S followng (1) The dtance between two ucceve tran mut be larger than the afety margn at any moment even f the come to a udden halt, o we have Vfollowng Lz() t Lafe Lt, () b Baed on equaton (1) and equaton (), the relaton between the and hould atfy: Vfollowng Sleadng Lafe Lt Sfollowng, (3) b whch mple that the ntantaneou peed and poton of the hould atfy V b ( S S L L), () followng leadng followng afe t Vfollowng S followng Sleadng Lafe Lt. (5) b III. ANALYSIS AND MODELING OF NEW ENERGY SAVING TRACKING STRATEGY In MBS, the could get the peed and poton. Two problem hould be condered n peed trajectory degn for energy optmzaton. The frt how to modfy the runnng trategy for the real cenaro becaue, n ome crcumtance, t unneceary to go through all the four phae lted above. The econd how to etablh a mple model for eay onlne mplementaton. For the frt problem, the energy avng trategy could be acheved by arrangng the equence of the phae approprately. It known that ome runnng phae may not happen n ome crcumtance. On the other hand, f the ha a long top, the hould top to wat untl the leadng tran tart. To enure the new model to ft all runnng cenaro, the new trategy hould reflect all the cae. Snce the leadng tran poton wll be nvolved n the optmzaton of the peed trajectory, we can buld two model baed on dfferent phae of the (runnng or topped). For the econd problem, a quadratc programmng method ued to obtan the optmal peed trajectory due to the avalablty of everal effcent numercal method. Snce the coatng phae ha a varable deceleraton, t hard to repreent the runnng dtance wth repect to the deceleraton (control varable) and peed (tate varable). In order to mplfy the model, we replace the coatng phae wth a lowdown phae and call t the approxmate coatng phae n th paper. For energy avng, the deceleraton hould cloe to but not le than the mean deceleraton of the coatng phae, becaue the extra deceleraton would lead to gnfcant frcton force whch caue tear and wear to the brakng ytem. On the other hand, f the deceleraton too mall, the tracton ytem need to provde more tracton force to upport the tran, whch wll conume more energy. It therefore neceary to chooe an approprate value for a better trade-off. After analyzng the practcal data of coatng phae from Dalan Fat Track [], t can be oberved that the peed n coatng phae declne very lowly. Therefore, the peed-tme profle cloe to a traght lne and the lope of the lne the deceleraton n the coatng phae. We have ued the Leat-Square procedure to ft the peed-tme curve wth the reult hown n Table 1. From Table 1, t clear that the hgher the coatng tartng peed, the greater the deceleraton. In order to upply a mall tracton force to keep the tran movng n a contant deceleraton, -.1 m/ eem approprate. TABLE I MEASURED VALUE OF COASTING DATA Speed range (km/h) Slop (m/) Average Error (m) 37-31 -.17.7 1- -.15.31 3- -.17.3 5- -.13.3-59 -.37.9-1 -..31 For the two ucceve tran runnng on the track, aumng
two tuaton of the leader (runnng and topped), we degn correpondng drvng tratege for the. A. Problem Formulaton for Movng Leader Tran When the runnng, the new operaton trategy conted of four runnng phae: tracton, peed holdng, approxmate coatng and brakng. The ntal peed of each runnng phae v, (=1,, 3, ).The runnng dtance and tme of each phae are S, T, (=1,, 3, ) repectvely. It ealy known that v =v 3. In th paper, we ue knetc energy to meaure the energy conumpton of tran. The knetc energy dfference between v 1 and v, a well a T hould be mnmzed becaue the tracton and peed holdng phae are hghly energy conumng. Snce the approxmate coatng phae relatvely low energy conumng, t hoped that T3 can be longer ntead of T, whch could reduce the tme perod for tracton and peed holdng phae. where: penalty factor, ; v the tartng velocte of each runnng phae, Z, =1,,3,; The decon parameter here are v, v, T. B. Problem Formulaton for Stopped Leader Tran When the leader tran top, the dtance between t and the gettng horter and horter. However, the trackng tme between them unchanged. Therefore, the doe not need tracton phae any more. At the ame tme, f the ha a long top, the followng tran may need top to wat untl the re-tartng. Therefore, we remove the tracton phae from the trategy n the lat cae and add toppng phae to t a hown n Fg. 3. v v 1 v 3 v 1 v v 3 S S 1 S S3 F Fg.. Operaton trategy when the runnng There are two tuaton for tme and dtance contrant. Before the re-tart from the taton, the tme contrant Ttackng. And the dtance contrant the current dtance between thee two ucceve tran mnu the dtance of afety margn (Lafe). However, after the clear the taton, the dtance contrant the current dtance between the and the taton. Therefore, the tme contrant hould be changed accordngly. The tme contrant depend whether the delayed. If t not delayed, the tme contrant change to Ttackng- Tbp, where Tbp the runnng tme of the at trategy update. On the contrary, f t delayed, more paenger may wat at the taton. Therefore, there no need to apply the new trategy to the nce t ha to arrve at the detnaton a oon a poble. Baed on the analy above, the model a follow: 1 mn f m( v v1 ) ( T T3) () t.. v1 v v 3 v T Z, 1,, v v1 v3 v v (7) T T Ttrackng ptbp 1 a b' b v v1 v3 v v S T v ps ( L Lafe Lt) (1 ps ) SF a b' 1 v S Lafe Lt S L S F S 1 S S 3 Lafe Fg.3. Operaton trategy when the top The trackng nterval between two ucceve tran dvded nto phae: peed holdng, approxmate coatng, brakng and watng. The runnng tme and dtance of each phae are T and S, (=1,,), repectvely. The ntal peed of each runnng phae v, (=1,, 3, ). It known that v 1 =v. The tme and dtance contrant are the ame a thoe n (7). The new drvng trategy formulated a follow: mn f ( av 1 1 av 1 a3) S1 ( T1 T) () t.. v1 v v3 T Z, 1,, (9) v v3 v3 T T1 T Ttrackng ptbp 1 b' b 3 v v3 v3 S T1 v1 ps ( L Lafe Lt) (1 ps ) SF 1 b' b where: v the tartng velocte of each runnng phae, Z, =1,, 3; The decon parameter here are v 3, T 1. IV. SIMULATION AND DISCUSSION In th ecton, a mulaton ued to tet and verfy the new trategy. We ue the actual data to do the mulaton. The two ucceve taton are Tongj South Road Staton and Jangha Staton n Ma Trant Bejng Y Zhuang Lne. The dtance between them 55m. The length of tran (L t ) m, afety Lt S L
margn(l afe ) 5m, ervce trackng headway ( T trackng ), dwell tme (T dwell ), runnng tme n tme table 177, target peed (v 1 ) 1 m/, ervce acceleraton rate(a) 1m/, and ervce barkng deceleraton rate(b) 1 m/ wth b=-.1 m/. The mulaton update rate 1. We ue nteror-pont method to olve the model n Matlab. By applyng the tradtonal trategy, the peed curve hown n Fg. and Fg. 5. 1 1 From Fg., t can be oberved that the ha no coatng phae. Th becaue when the top, the n the peed holdng phae and even after the re-tartng, t tll n the ame phae. However, nce the delayed, more paenger may wat at the taton, whch requre that the arrve at the taton a oon a poble. Therefore, the coatng phae replaced by peed holdng phae. The runnng tme of the 175, earler than what wa cheduled. The total energy conumpton 15.9 kwh. 1 1 1 1 5 15 5 dance m Fg.. Ordnary operaton trajectory n the nner taton (v-) 1 1 1 1 5 15 5 dtance m Fg.. Followng tran trajectory when the ha a hort top under tradtonal trategy (v-) 1 1 1 tme Fg.5. Ordnary operaton trajectory n the nner taton (v-t) Under the normal crcumtance, ucceve tran depart every followng the peed trajectory hown n Fg and Fg 5. Wth tradtonal control trategy, no matter how the behave, the peed follow the curve hown n Fg. and Fg. 5 untl the contrant () volated. In uch a cae, the wll brake to top. In other word, wth th trategy, f the top due to ome nterrupton, the may tll accelerate or keep at a contant peed followed by breakng f the () atfed. Th caue the wate of energy. In the new trategy, the peed curve calculated onlne takng nto account the poton. Therefore, f the peed curve doe not match wth thoe depcted n Fg. and Fg 5, the wll avod unneceary tracton to reduce energy conumpton. Two mulaton cenaro have been preented below to how the effectvene on energy avng of the by applyng the new trategy even when the run abnormally. In the followng fgure, the red dotted lne the runnng trajectory of the and the blue old lne the trajectory of the. A. Leadng Tran wth Short Stop at Inner Staton When the ha a hort top at the poton of 19 meter for 35 econd, Fg. and Fg. 7 how the peed curve created by tradtonal control trategy. 5 15 5 3 tme Fg.7. Followng tran trajectory when the ha a hort top under tradtonal trategy (v-t) Fg. and Fg. 9 how the peed curve created wth the new trategy wth update rate 1. When the top, the acknowledged mmedately, whch ncorporated n peed curve degn of the next tep. It can be oberved that the tran only coat at begnnng. After the re-tart, the accelerate mmedately. After the top at the detnaton, the reduce to a lower peed and keep t untl the clear the detnaton. The total run tme of 15 whch later than cheduled. The total energy conumpton reduced to. kwh. Compared wth the tradtonal trategy, energy conumpton reduced to 1.% of the orgnal wth 5% tme delay, whch worthwhle. 1 1 1 5 15 5 dtance m Fg.. Followng tran trajectory when the ha a hort top
under new trategy (v-) 1 1 1 5 15 5 3 tme Fg.9. Followng tran trajectory when the ha a hort top under new trategy (v-t) B. Leadng Tran wth Long Stop at Inner Staton When the ha a long tme top at the poton of 19 meter for econd, Fg. and Fg. 11 how the peed curve created by tradtonal trategy. addton, the peed holdng phae (wth energy conumpton) n the front part replaced by an approxmate catng phae (lower energy conumpton) becaue the long top. Both mply energy avng. The runnng tme of the 9 veru 3. wth tradtonal trategy. However, the total energy conumpton reduced to. kwh. Compared wth the tradtonal trategy, energy conumpton reduced to.5% of the orgnal wth 11.% tme delay. Table how the comparon between the tradtonal and new tratege n dfferent cenaro. 1 1 1 1 1 1 5 15 5 dtance m Fg.1. Followng tran trajectory when the ha a long top under new trategy (v-) 1 1 5 15 5 dtance m Fg.. Followng tran trajectory when the ha a long top wth tradtonal control trategy (v-) 1 1 1 1 5 15 5 3 35 tme Fg.11. Followng tran trajectory when the ha a long top under tradtonal trategy (v-t) It noted that the top at 15 m for 35 econd, due to the long tme top. Moreover, nce the wa delayed. What can be acheved for the two tran run under the contrant o arrve at the next taton a oon a poble. Snce the accelerate mmedately after the re-tart, the tll ha a toppng phae, followed by acceleraton and then deceleraton before t arrve at the taton becaue of the dwell tme of the at the taton. The total runnng tme of the 5. wth energy conumpton 115.1kwh. Fgure 1 and 13 how the peed curve generated wth the new trategy. It can be oberved that there only one toppng phae for the ntead of two (v. Fg. and Fg. 11). Therefore, one acceleraton phae ha been avoded. In 5 15 5 3 35 tme Fg.13. Followng tran trajectory when the ha a long top under new trategy (v-t) TABLE II COMPARISON BETWEEN THE TRADITIONAL AND NEW STRATEGIES Short tme top Long tme top ordnary new ordnary new Energy Conumpton 15.9. 115.1. (kwh) Runnng Tme () 175 15 5. 9 V. FURTHER IMPROVEMENT FOR RIDE COMFORT Baed on the dcuon above, t known that the new trategy rather effectve on energy avng. However, the rde comfort may be deterorated due to non-mooth phae change. To mprove th, a mooth algorthm propoed below. In calculatng the onlne peed curve a above, we know the trend of the curve on both de of the phae changng pont. Therefore, ome moothng technque can apply around the phae changng pont for mooth tranton. Smooth tranton for peed trajectory degn wth pecewe nuodal functon were propoed n [7, ]. However, nce the tranton tme and dtance are too hort and fxed n tran control ytem, n th
paper, we propoe a technque for properly electng the parameter of the quadratc functon to acheve mooth tranton. v t t T v t T T Fg. 1. Smoothng tranton In Fgure 1, the red lne how the mooth tranton between two dfferent phae. We degn the followng moothng equaton: v () ( ) ub t A t B C (9) and the dervatve functon v a A( t B) () ub ub To enure the mooth tranton at both de, the followng boundary condton are mpoed: v ub (t )=v(t ), v ub (t e )=v(t e ) (11) a ub (t )=a(t ), a ub (t e )=a(t e ) (1) where: v ub (t) the peed n mooth curve of the tranton at tme t; v(t) the peed n the un-moothed trategy at tme t; t the tartng tme of the tranton; t the endng tme of the tranton. e A, B, C are parameter to be determned wth the boundary condton; a () ub t the acceleraton n mooth curve of the tranton at tme t, aub v ub ; at () the acceleraton n the un-moothed peed curve at tme t. After applyng the moothng technque to the peed curve n n Fg. 1 and Fg. 13, the reult are hown n Fg. 15 and Fg. 1. It can be oberved that the mooth caue a lttle delay. Th becaue the acceleraton durng the tranton maller than the one ued before. Therefore, the runnng dtance n the ame tme perod horter. Th mean that the ha to take longer tme to reach the next taton. The total runnng tme become 3 and energy conumpton. kwh wth gnfcant rde comfort mprovement. VI. CONCLUSION Th paper dcue energy avng trackng control for ucceve tran n Movng Block Sgnallng ytem (MBS). A new trategy propoed for peed trajectory degn and moothng technque ued to mprove the rde comfort. Snce the model mple to olve, the new trategy could be v e t e t mplemented onlne for Automatc Tran Operaton ytem (ATO). Smulaton how the feablty and effectvene of the new trategy on energy avng. Compared wth tradtonal trategy, the new trategy ha the ame effect on energy avng when the ha no nterrupton. More mportantly, the new trategy can gnfcantly reduce energy conumpton wth the cot a lttle bt tme delay when the ha a runnng nterrupton. At the ame tme, rde comfort can be guaranteed wth a lttle bt more cot on run-tme and energy conumpton a expected. 1 1 1 5 15 5 dtance m Fg.15. Smoothed trajectory when the ha a long top under new trategy (v-) 1 1 1 5 15 5 3 35 5 tme Fg.1. Smoothed trajectory when the ha a long top under new trategy (v-t) REFERENCES [1] G. H. Lee, I. P. Mlroy, A. Tyler "Applcaton of Pontryagn maxmum prncple to the em-automatc control of ral vehcle. Proceedng of Second Conference on Control Engneerng, Newcatle, 19. [] K. K. Wong and T. K. Ho, Dynamc coat control of tran movement wth genetc algorthm, Internatonal Journal of Sytem Scence,, 35(13-1): 35-. [3] C. S. Chang, and SIM, S. S., Optmzng tran movement through coat control ung Genetc Algorthm, IEE Proceedng-Electrcal Power Applcaton, 1997, 1(): 5 73. [] Pearon, L.V., "Movng Block Ralway Sgnallng," PhD the, Loughborough Unverty of Technology, UK 1973. [5] Q. Gu, T. Tang, Y. D. Song, A urvey on energy-avng operaton of ralway tranportaton ytem. Journal of Meaurement and Control,, Vol.3, No.7, pp.9-13. [] Z. Y. Yu, "Tran Operaton Expermental Report n Dalan Fat Track," techncal report, Bejng Jaotong Unverty. [7] X. Y.Lu, S. Shaldover, J. Hedrck, longtudnal tranton control for heavy-duty truck : between manual and automatc, Proc. 15th ITS World Congre, November 1-,, New York [] X. Y.Lu, S. Shaldover, J. Hedrck, Longtudnal tranton control for automated vehcle: between manual and automatc, ubmtted for publcaton