Fault Diagnosis and Safety Design of Automated Steering Controller and Electronic Control Unit (ECU) for Steering Actuator

Transcription

1 CALIFORNIA PATH PROGRAM INSTITUTE OF TRANSPORTATION STUDIES UNIVERSITY OF CALIFORNIA, BERKELEY Fault Diagnoi and Safety Deign of Automated Steeing Contolle and Electonic Contol Unit (ECU) fo Steeing Actuato Han-Shue Tan, Fanping Bu, Shiang-Lung Koo, Wei-Bin Zhang Califonia PATH Reeach Repot UCB-ITS-PRR-5-7 Thi wok wa pefomed a pat of the Califonia PATH Pogam of the Univeity of Califonia, in coopeation with the State of Califonia Buine, Tanpotation, and Houing Agency, Depatment of Tanpotation, and the United State Depatment of Tanpotation, Fedeal Highway Adminitation. The content of thi epot eflect the view of the autho who ae eponible fo the fact and the accuacy of the data peented heein. The content do not neceaily eflect the official view o policie of the State of Califonia. Thi epot doe not contitute a tandad, pecification, o egulation. Final Repot fo RTA 64A8 Novembe 5 ISSN CALIFORNIA PARTNERS FOR ADVANCED TRANSIT AND HIGHWAYS

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3 Fault Diagnoi and Safety Deign of Automated Steeing Contolle and Electonic Contol Unit (ECU) fo Steeing Actuato Pat I epot fo Development of Peciion Docking Function fo Bu Rapid Tanit Han-Shue Tan, Fanping Bu, Shiang-Lung Koo and Wei-Bin Zhang. Intoduction BRT ha demontated it effectivene to be a potion of the backbone of an integated tanit netwok. It ha become an effective mean fo attacting non-taditional tanit ide and theefoe can help to educe uban tanpotation need and taffic congetion. Many Califonia tanit agencie ae planning to deploy BRT and have conideed the ue of dedicated lane fo BRT to be a vey attactive option a it i le affected by automobile taffic and theefoe can povide ail-like quality of evice. In 999, Caltan geneated a Caltan Action Requet (CAR) to equet paticipation in the Bu Rapid Tanit Poject with VTA and othe local tanit povide. The futue of BRT in Califonia, a enviioned by Caltan, would include a ytem of coodinated tanit infatuctue, equipment, and opeation that will give pefeence to bue on local uban tanpotation ytem and the High Occupancy Vehicle (HOV) lane at congeted coido. The goal of the BRT evice i to attact ide fom ingle-occupancy vehicle, which could eult in congetion elief without majo infatuctue expanion. In the long-tem, the popoed poject may integate the cuently epaate local tanpotation ytem and tanit evice (offeed by multiple tanit agencie in a egion) to povide expe tanit evice enabled by inteconnectivity between local ytem and the State highway HOV ytem. Unde the Caltan Action Requet, a BRT eeach pogam i etablihed. One of the element of thi pogam i Development of Peciion Docking Function fo Bu Rapid tanit (named Peciion Docking o BPD fom heeon). Peciion docking -- an innovative technology that enable bu to pefom ail like level boading ha hown geat potential fo allowing fat boading and alighting and theefoe educing the total tip time and impoving evice eliability and quality fo BRT ytem. The bu peciion docking eek to achieve, with the help of electonic guidance technologie, a high docking accuacy and conitency that allow fat loading and unloading of paenge with pecial need. In addition to the potential of eving a a majo component of an advanced bu top, uch an automation capability would alo educe the kill and taining equiement on the bu dive a well a the te aociated with achieving the high accuacy by the dive. In addition to peciion docking, electonic guidance technologie alo uppot a numbe of citical function fo BRT and tanit application. Once a bu i intumented with electonic guidance, it can povide lane ait along dedicated BRT lane. In the application whee dedicated lane

4 ae not available, lane ait can facilitate efficient opeation at Queue Jump Lane and can ignificantly benefit Bu Pioity Sytem. Electonic guidance can alo uppot application at a bu depot whee BPD technology can be ueful a a component of the concept of Advanced Maintenance Station. PATH ha demontated peciion docking function on automobile. The objective of the BPD poject i to develop and enhance the peciion docking ytem fo eal-wold bu opeation. At the poject ealy tage, Caltan and PATH have decided to develop and demontate automated BRT uing thee automated bue (Demo 3). Becaue of the ynegy of thee two pogam, and due to the afety citical natue of peciion docking/lane ait function, PATH and Caltan have detemined to focu thi poject to afety deign of peciion docking ytem. The two poject will complement each othe and the mutual goal i to acceleate the deployment of peciion docking/lane ait technologie. Thi final epot the fault analyi of peciion docking ytem and afety deign of the afety citical element fo peciion docking ytem. The epot include thee Pat, including: Pat I povide a deciption of the Peciion Docking Sytem and epot analyi fo fault diagnoi and afety deign of automated teeing contolle and Electonic Contol Unit (ECU) fo teeing actuato. It alo epot a demontation PATH conducted duing the National Intelligent Vehicle Initiative demontation oganized by the US Depatment of Tanpotation Joint Pogam Office. Pat II epot an analyi and deign fo a eliable diect dive fo the teeing wheel column of bue. Pat III epot powe ytem eliability. The epot below i the Pat I epot: Fault diagnoi and afety deign of automated teeing contolle and Electonic Contol Unit (ECU) fo teeing actuato.. Deciption of Peciion Docking Sytem Bu docking ytem povide a pecial function unde lane-ait Bu contol ytem. The ytem employ almot identical vehicle component fo the geneal lane ait capabilitie. In the oftwae aea, except fo the cetain docking contol algoithm pecific and the docking accuacy equiement, thoe of the peciion docking ytem may not be too much diffeent fom thoe fo the lane-ait contol ytem. A typical bu docking ytem include the following baic element and function: Lateal guidance ytem In pinciple, any lateal guidance technologie (uch a GPS, DGPS/INS, machine viion, electonic make ytem, magnetic tape, magnetic make, tanponde, etc.) can be a candidate fo peciion docking a long a it

5 atifie the eliability and accuacy equiement fo the pecific peciion docking application. Magnetic guidance ytem i choen fo thi tudy becaue of it high eliability unde almot all opeational cenaio a well a poviding accuacy to within a centimete. A typical lateal guidance ytem may involve infatuctue uppot, eno, ignal poceing and validation. Steeing actuato ytem The teeing actuato ytem fo an automated teeing contol vehicle can be any actuato that can change o modify the teeing mechanim o that the tee wheel follow peciely the deied teeing command. The powe component can be hydaulic mechanical o electical. It can be diectly intalled a a pimay teeing mechanim o it can be an add-on device that dive though the exiting teeing ait ytem. Howeve, the equiement fo the teeing actuato do depend on the above ytem deign configuation. Futhemoe, highe peed opeation often demand highe bandwidth while low peed equie moe powe. A decouple-able tand-alone intelligent evo contol ytem i a pefeed teeing actuato configuation. In uch famewok, the actuato can then be teated a a component fo the peciion docking ytem and help to educe the oveall deign complexity. Lane-keeping and tanition contol ytem Lane-keeping and automatic/manual tanition contol ae the heat of the peciion docking contol ytem. It fulfill the deign equiement and take into account the following facto: teeing actuato and mechanim, eno accuacy and impefection, vaiou peed and oad geomety, fault detection and ignal poceing, dive intenion and intevention, vehicle dynamic and envionmental uncetaintie, high peed bandwidth and low peed nonlineaity. The deign of obut and extemely eliable teeing contol and tanition ytem ae key tak fo the peciion docking ytem. Dive vehicle inteface (DVI) ytem Since peciion docking ytem application equie mooth intefacing with dive. A uitable inteface between the automated contol ytem and dive i eential. The inteface ytem can be eithe complicated o imple. A complicated tanition may equie the dive to eithe follow cetain tict opeational pocedue o obeve cetain tanitional ule befoe tanition. A imple, tanpaent but effective inteface with the dive i almot alway a bette choice. Howeve, a imple DVI often equie athe complicated tanitional oftwae to mooth out all uncetaintie both in the contol ytem and fom the dive. Fault detection and management ytem The fault detection and failue management ytem ae the cucial component in any automated vehicle ytem. It complexity inceae a the complexity of the ytem inceae. In the peciion docking ytem deigned unde thi poject, all component failue ae included in the deign, although the deign itelf may not be compehenive due to the limited eouce and time. Aociated longitudinal contol and ening ytem (if applicable)

6 The longitudinal contol i geneally not equied in a peciion docking ytem. Howeve it can help the bu to top moothly at any pedetinated location with high accuacy. Theefoe an aociated longitudinal contol ytem will be a good optional contol ytem that uppot the peciion docking opeation. One cautionay note: Any poible ingle point failue hould have edundancy to potect the ytem afety and integity. Howeve uch afety citical opeational deign i not implemented fo thi tet ytem due to the eouce limitation a well a the fact that it deign pupoe i fo tudie and not fo field opeational tet. Figue.. depict the majo component fo the PATH Peciion Docking Sytem uing magnetic make lateal guidance ytem. A een in thi figue, the majo component ae: font and ea magnetomete a the main lateal eno, yaw gyo and peed a auxiliay eno, add-on DC moto on the teeing column a the teeing actuato, compute with all the ignal poceing, contol algoithm, and DVI contol a the intelligent cente of the ytem, and button and witche, dive indicato, ound, paenge diplay and indicato a the DVI ytem. Figue.. PATH Peciion Docking Sytem Component Diagam Figue.. illutate the ytem block diagam of the PATH Peciion Docking ytem. It include hadwae, oftwae with vaiou function. The hadwae conit of vaiou witche, teeing DC moto, vehicle eno, compute, diplay and audible unit. The oftwae conit of vaiou oftwae dive, teeing actuato algoithm, lateal contol

7 algoithm, and DVI contol. The teeing actuato contol algoithm povide function uch a elf-calibation, tight poition evo, vaiou mode tanition and fault detection. The lateal contol algoithm include lane-tacking contol, tanition contol, tajectoy planning, mode witching and failue detection and fault mode contol. The DVI contol tack the contol tate, dive eaction, and povide appopiate inteface fo manual, automated, and tanition contol. It alo include waning and emegency uppot. Figue..3 how the oftwae achitectue of the PATH Peciion Docking ytem. The coe of the oftwae achitectue i a public ubcibed databae (db_lv). All input/output dive povide and inteface with the databae. All application oftwae made it deciion baed on the eal-time databae infomation. The lateal contol conit of the following block: vehicle I/O (eno input), lateal contol (eno ignal poceing and vaiou lateal contol), docking longitudinal contol (algoithm intefacing with the longitudinal hadwae fo pecie topping), docking coodination, (coodinate longitudinal and lateal contol), teeing actuato (teeing hadwae dive), teeing inne loop (teeing evo and it aociated intelligence), DVI input and output. Figue.. PATH Peciion Docking Sytem Block Diagam

8 Figue..3 PATH Peciion Docking Softwae Achitectue. Development of the bu docking ytem The tak involved in the development of the bu docking ytem ae lited a follow: Sytem Deign o Define and tadeoff pefomance equiement o Flow down component equiement fom ytem pefomance equiement o Define and deign ytem configuation Hadwae and Softwae Development o Intall magnetomete and deign and veify ignal poceing fo lateal ening accuacy and eliability

9 o Intall teeing actuato and develop hadwae dive o Intall yaw ate gyo o Integate longitudinal eno, Jbu, and contol Analyi o Develop appopiate bu vehicle model o Pedict ytem pefomance and evaluation o Develop dive model and chaacteitic fo tanition Contol Algoithm Development o Deign teeing actuato evo contol to account fo vaiou uncetaintie and non-lineaity; deign appopiate component-level intelligence to elieve lateal contol complexity o Deign high pefomance lateal lane-tacking contolle o Deign high eliable tanition contol with on-demand capability o Deign DVI contol inteface that uppot tanpaent dive/automated ytem tanition Safety Deign o Deign and evaluate the obutne popetie fo the ytem opeation o Deign failue detection fo all ub-ytem o Develop failue mode contol o Evaluation poible edundancy and thei effect and limitation The baic peciion docking ytem deign involve fou majo development aea: lateal ening ytem, teeing actuato, contol algoithm, DVI deign and failue mode contol. Subection.3,.4,.5 and.6 will focu on the lateal ening ytem, teeing actuato inne loop contol deign and peciion docking contolle deign. DVI and failue mode will be dicued in the Section 3..3 Magnetic Make Lateal Sening Sytem.3. Intoduction The development of a eliable and accuate lateal efeencing ytem i cucial to the ucce of the lateal guidance ytem fo peciion docking. Fo the Automated Peciion docking ytem, the accuacy equiement fo the lateal ening ytem i diectly popotional to the equied docking accuacy epecially along the docking platfom. The lateal ening accuacy equiement wa et to be bette than centimete fo the docking accuacy tageted to be bette than the ame value. The aumption i that the intallation and meauement accuacy ae andomly and evenly ditibuted along the coect poition. PATH ha popoed and developed a lateal efeencing and ening ytem that i baed on the magnetic make embedded in the oad cente to povide the lateal poition and oad geometic infomation. The Bu teeing guidance ytem baed on uch technology povide the contol ytem with the following two fundamental piece of infomation: the vehicle poition with epect to the oadway, and the cuent and futue oad

10 geomety. Two aay of magnetomete, one located behind the font bumpe and the othe at about 5 mete behind the font eno, wee ued to imultaneouly obtain font and ea lateal offet meauement. Extenive development and expeiment have been pefomed on magnetic make-baed lateal ening ytem fo many PATH vehicle equipped with automated teeing contol. The vat knowledge available about thi lateal ening technique wa one of the pimay eaon that thi technology wa fit choen to uppot the Peciion Docking teeing guidance ytem. Othe poitive chaacteitic of thi lateal ening technique include good accuacy (bette than one centimete), high eliability, inenitivity to weathe condition, and uppot fo binay coding. The equiement of modifying the infatuctue (intalling magnet) and the inheent look-down natue (the eno meaue the lateal diplacement at location within the vehicle phyical boundaie, veu look-ahead ability) of the ening ytem ae two known limitation of thi technology. The pinciple idea fo thi ening ytem i taightfowad. Magnetic make ae intalled unde the oadway delineating the cente of each lane o any othe appopiate line fo the pecific application. Magnetomete mounted unde the vehicle ene the tength of the magnetic field a the vehicle pae ove each magnet. Onboad ignal poceing oftwae calculate the elative diplacement fom the vehicle to the magnet baed on the magnetic tength and the knowledge of the magnetic chaacteitic of the make. Thi computation i deigned to be inenitive to the vehicle bouncing (e.g., heave and pitch) and the eve-peent natual and man-made magnetic noie. Futhemoe, the oad geometic infomation can be encoded a a equence of bit, with each bit coeponding to a magnet. The polaity of each magnet epeent eithe (one) o (zeo) in the code. In addition to the lateal diplacement meauement and oad geomety peview infomation, othe vehicle meauement uch a yaw ate, lateal acceleation, and teeing wheel angle may alo be ued to impove the pefomance of uch a lateal guidance ytem..3. Magnetic Noie Effect Fou majo noie ouce ae uually peent in the magnetic ignal meauement in a typical vehicle opeational envionment: eath field, local magnetic field ditotion, vehicle intenal electomagnetic field, and electical noie. The mot fequent extenal ditubance i the eve-peent eath pemanent magnetic field, which i uually on the ode of.5 Gau. The value of the eath field meaued by the magnetomete on the vehicle depend on the location of the vehicle on eath a well a the altitude and oientation of the vehicle. Although the eath magnetic field uually change lowly, hap tun and evee baking can quickly change the field meauement along the vehicle axe. The mot eiou noie poblem ae caued by local anomalie due to the peence of oadway tuctual uppot, einfocing eba, and the feou component in the vehicle o unde the oadway. Undegound powe line ae anothe ouce of uch local field ditotion. Reba o tuctual uppot uually ceate a hap change in the backgound

11 magnetic field and ometime i difficult to identify. Mot ignal poceing algoithm will have ome difficulty ecoveing fom uch hap ditotion. The feou component in the vehicle, on the othe hand, can be iolated a long a thei location ae fixed with epect to the magnetomete, o ae located at a ignificant ditance fom the eno. A thid ouce of noie come fom the altenating electic field geneated by vaiou moto opeating in the vehicle. Thee moto may include altenato, fan, electic pump, compeo and othe actuato. Howeve, thei effect vay accoding to the moto otational peed and ditance fom the magnetomete. The highe the moto pm o the fathe it i placed away fom the magnetomete, the le the eultant noie. Sometime modet change in eno placement can alte the ize of uch ditubance. The lat common noie ouce aie fom the electonic noie in the meauement ignal itelf. Such noie can be ceated by the voltage fluctuation in the electical gounding o fom the powe ouce. It can alo be a eult of poo wiing inulation againt electomagnetic ditubance. Uually, the longe the wie, the highe uch noie. Although low-pa filteing can educe the magnitude of uch ditubance, noticeable degadation of the magnetic eno ignal poce algoithm occu when uch noie level exceed.4 Gau. Digital tanmiion of magnetic field meauement o local embedded poceo i two poible appoache that can ignificantly educe uch noie..3.3 Magnetic Sening Algoithm One of the impotant attibute of the lateal ening ytem i it eliability. Cuently, thee exit eveal algoithm deigned to detect the elative poition between the make and eno (magnetomete), a well a to ead the code embedded within a equence of thee make. Thee magnetic make detection and mapping algoithm have been expeimented with by PATH. The fit i called the peak-mapping method that utilize a ingle magnetomete to etimate the make elative lateal poition when the eno i paing ove the magnet. The econd algoithm i the vecto atio method that equie a pai of magnetomete to ample the field at two location. It etun a equence of lateal etimate in a neighbohood uounding, but not including the peak. The thid i the diffeential peak-mapping algoithm that compae the magnetic field meauement at two obevation point to eliminate the common-mode contibution and econtuct a functional elationhip between the diffeential eno eading and the lateal poition uing the knowledge of the eno geomety. The peak-mapping algoithm wa elected fo the peciion docking poject becaue it ha been poven effective ove a wide ange of peed and ha been widely applied in many expeimental application conducted by PATH. In the Bu opeational envionment, the magnetic field map can deviate quite ignificantly fom the theoetical dipole equation pediction becaue of the maive amount of feou mateial fom the bu body tuctue located jut above the magnetomete. Numeical mapping ceated by empiical data gatheing (calibation) i ued to ceate the aociated invee map. Figue.3. and.3. how the font and ea magnetic table fo the 4 bu, epectively. The figue conit of table of the

12 even magnetomete tating fom the ight ide of the bu to the left, deignated a follow: ight-ight, ight, cente-ight, cente, cente-left, left and left-left. Each table i obtained with two et of calibation data, one at a lowe eno height (at aound 7 inche fom the magnetomete to the magnet) and the othe at a highe eno height (at inche fom the magnetomete to the magnet). Each half-cicle in the table conit of vetical and hoizontal field of the make that ae collected at -cm inteval of lateal diplacement. The magnetic table clealy depict the nonymmetical natual fo the magnetic field due the adjacent feou mateial. Figue.3. 4 Bu Font Magnetomete Calibation Table

13 .3.4 Signal Poceing Figue.3. 4 Bu Rea Magnetomete Calibation Table The magnetomete ignal poceing fo the peak-mapping method involve thee pocedue: peak detection, eath field emoval and lateal diplacement table look-up (ee Figue.3.3 fo block diagam of ignal poceing algoithm). Although it i taightfowad in pinciple, it become complicated when the eliability of the poce i the majo concen. Many paamete in the lateal ening ignal poceing oftwae need to be tuned in ode to povide conitent lateal diplacement infomation egadle of vehicle peed, oientation, opeating lateal offet and vehicle body motion. Debugging can become vey time conuming when failue condition cannot be eceated. To impove the eliability of the lateal ening ytem with the magnetic oad make, PATH ha developed a econtuctive oftwae ytem fo the lateal ening ignal poceing. When pecified a a econtuctive un, the eal-time oftwae in the vehicle, beide poceing data a uual, toe all eno data in memoy and late dump the data into a file. Signal poceing oftwae identical to the one un in the ealtime envionment can late on be geneated in a dektop compute uing the data toed duing vehicle teting a input with the ame QNX opeating ytem. In uch a etup, any eoneou ituation can be eceated in a lab envionment and debugged with eae.

14 Logic baed on Vaiance Vaiance Calculation y Bv Low Pa Filte z - z - z - z - z - Peak Finde Syncho latet peak Bv Eath latch Bv Peak latch - + Bv y y y 3 Bh Peak latch Bh Eath latch - + Mapping y 4 Bh Bh Low Pa Filte z - z - z - z - z - Figue.3.3 Peak-Mapping Magnetomete Signal Poceing Block Diagam.4 Steeing Actuato Deign.4. Bu Steeing Actuato Requiement The Top level (cloed-loop) teeing actuato ytem equiement ae lited a follow: Functionality: Tun on/off by oftwae Vaiable dive eitance capability High pefomance tee poition evo Emegency hut-off Ability to impoe mall foce ocillation on hand wheel Pefomance: Cloed loop evo bandwidth: at leat 4 Hz fo mall amplitude Maximum lew ate: at leat 3 degee/ec at the tie (5-6 degee/ec at hand wheel) No ocillation/vibation on hand wheel Poition evo accuacy: bette than degee at hand wheel Zeo poition accuacy: bette than degee at hand wheel Contol Reolution: bette than. degee at hand wheel Safety Fail to no toque Self diagnoi ability Max toque/ate/powe potection

15 Kill witch Intallation Column intallation above ait component Low noie level Input/output Input: teeing command (poition o toque), on/off command Output: teeing poition(), actuato tatu and/o fault flag The Component level teeing actuato (open loop) pecification deived fom the toplevel equiement ae lited a follow: Maximum toque: 8- N-m Maximum lew ate: fate than 5-3 degee/ec at tie (5-6 degee/ec at hand wheel) Range: full ange of the teeing angle Poition eno eolution: bette than. degee at hand wheel Zeo poition accuacy: bette than - degee at hand wheel Command ate: fate than Hz (if digital), o analog connection between moto cicuit and Hot compute. Time contant fo the cuent/toque command epone: fate than 5 m. Fault flag fo the open-loop ytem. The moto hould be able to be Back diven by the dive..4. Steeing Actuato Sytem Configuation Figue.4. how the block diagam of PATH teeing actuato. The moto aembly i manufactued by NSK. A hown in Figue.4. and Figue.4.3, teeing actuato moto aembly conit of a teeing column, DC moto actuating teeing column, an electomagnetic clutch and angle eno meauing teeing wheel poition. The DC moto connect to the teeing column though clutch and eduction gea. An incemental encode i mounted on the moto haft to meaue the elative poition of teeing wheel. A multi-tun potentiomete i connected with column haft via pulley gea and belt to meaue the abolute poition of teeing wheel. Moto cuent and clutch ON/OFF i contolled by ECU. Uppe level compute can alo contol the clutch by iuing clutch command to ECU. A cuent loop contol i built in ECU a hown in Figue.4.4. ECU eceive toque command fom uppe level compute and iue coeponding cuent command o that DC moto will geneate equied toque. Stict tat and hut down equence ae defined to pevent eoneou opeation. ECU ha ome built-in elfdiagnotic featue. Failue will be declaed when toque command i ove allowed limit, powe upply to the moto i out of ange and moto i oveheated. The health condition of moto i feedback to uppe level compute though moto condition ignal.

16 Moto Aembly Toque command Clutch Moto condition Powe on/off Encode Potentiomete Steeing Actuato Contolle Calibation Poition evo Tanition Fault detection Steeing angle command Manual/Auto Ready Failue code Calibated teeing angle Figue.4. Block diagam of teeing actuato Figue.4. Steeing actuato intallation

17 Figue.4.3 Schematic of teeing actuato moto aembly Steeing actuato contolle i a oftwae package deigned by PATH eeache which ha following function:. Calibation. The function of calibation i to find zeo teeing angle of the bu.. Poition evo. Poition evo i a cloed loop contol. It eceive teeing angle command and iue toque command to teeing actuato hadwae o that the teeing wheel will tun to the deied teeing wheel angle poition. 3. Smooth tanition between manual and automatic contol. 4. Fault detection fo eno and moto. Figue.4.4 Cuent dive loop in ECU

18 .4.3 Poition Sevo Deign Poition evo i the key function of teeing actuato. Succeful lateal contolle deign equie at leat 4-5 Hz cloed evo loop bandwidth with -degee accuacy on teeing wheel. Befoe the evo deign can be caied out, extenive expeiment ae conducted to tudy open loop chaacteitic of teeing actuato. The expeimental eult eveal a quite challenging evo deign poblem. Deign of a 4-foote bu teeing actuato will be ued a an example fo illutation pupoe. A. Open loop model identification Fit, weep ine technique i ued to identify open loop fequency epone fom toque command (V) to teeing wheel angle (degee) with diffeent input amplitude. A hown in Figue.4.5, the open loop bandwidth of 4 foote bu teeing actuato i le than Hz. Second, a low amp input i ent to tudy the effect of fiction on the oad. A hown in Figue.4.6, the fiction effect i o dominant that the teeing wheel tat moving only when toque command almot eache it half of full capacity (V). Thi mean the actuating moto i unde poweed. Although thi may facilitate dive taking ove unde emegency ituation, the unde poweed moto will poe ignificant difficulty fo evo loop deign. Thi i epecially tue fo low peed application uch a peciion docking. Thid, the teeing mechanim of oiginal bu ha about degee (teeing wheel) of backlah. Such had nonlineaity, if not popely teated, may lowe tacking accuacy, intoduce limit cycle o even detabilize whole loop. Magnitude(db) Open loop fequency epone fo 4 foot bu teeing actuato Model amp=.5 amp= Fequency (Hz) -4-6 Phae(degee) Fequency (Hz) Figue foote bu teeing actuato open loop fequency epone

19 Toque command (V) Steeing wheel angle (degee) Time(ec) Time(ec) B. Cloed loop evo deign Figue.4.6 Fiction effect Figue.4.7 how the cloed loop diagam of teeing actuato poition evo. To adde deign difficultie mentioned above, diffeent tategie ae adopted. Fit, loop haping i ued to inceae cloed loop bandwidth a much a poible. In ode to ovecome fiction effect and achieve about degee tacking accuacy up to 4o5 Hz, the gain of evo contolle ha to be ufficient high. Howeve, high gain aco all fequency may excite high fequency uncetain dynamic. A hown in Figue.4.8, a PD contolle i teted fit. Although the gain i not high enough to meet degee accuacy equiement, the epone aleady how a high fequency chatteing. Theefoe, the fequency epone of evo contolle need to be caefully haped to meet tingent pefomance equiement and avoid exciting high fequency uncetain dynamic imultaneouly. Figue.4.7 Cloed loop diagam of teeing actuato poition evo

20 5 Steeing command Steeing angle Angle(degee) Time(ec) Figue.4.8 Step input of a PD contolle Afte loop haping deign, a baeline high gain linea evo contolle that atifie diffeent pefomance equiement unde mot cenaio i obtained. The next tep i to take cae of diffeent nonlinea phenomena which may have ome impact on ytem pefomance unde cetain condition. The fiction effect will be tudied fit. Although the gain i high enough to ovecome fiction and bing tacking eo within equied degee ange a hown in Figue.4.9, the fiction can till low ytem epone when command input amplitude i mall. Fiction compenation i added to peed epone a hown in Figue.4.. An adaptive featue i alo ued to accommodate fiction change due to diffeent oad condition.

21 8 Steeing wheel angle (degee) Steeing Angle Steeing Angle Command Time(ec) Figue.4.9 Fiction effect fo mall amplitude command 8 Steeing wheel angle (degee) Steeing Angle Steeing Angle Command Time(ec) Figue.4. Step input with fiction compenation In ou actuato deign, the moto toque command i alway atuated due to it unde poweed natue. Such atuation may caue lage ovehoot a hown in Figue.4. when command i lage. A tajectoy ehaping technique and low-and-high gain deign ae ued to adde uch windup poblem. Figue.4. how the tep input eult with anti-windup deign. Unde thi deign, the ovehoot diappea.

22 7 6 Angle(degee) Steeing command Steeing angle Time(ec) Figue.4. Ovehoot when command input i lage 5 4 Angle(degee) 3 Steeing command Steeing angle Time(ec) Figue.4. Step input with anti-windup A we mentioned befoe, -degee backlah exit in the bu teeing mechanim. Limit cycle in fom of mall ocillation aound equilibium point i geneated due to the backlah (Figue.4.3). Such ocillation geneate high fequency ound and may hoten the life of teeing actuato. A nonlinea compenation i ued to eliminate uch limit cycle and eult i hown in Figue.4.4.

23 Angle(degee) Angle(degee) 3 Steeing Angle Command Steeing Angle Time(ec) Enlagement fo 5-8 ec Time(ec) Figue.4.3 Limit cycle due to backlah in the teeing mechanim Angle(degee) Angle(degee) 3 Steeing Angle Command Steeing Angle Time(ec) Enlagement fo 5-8 ec Time(ec) Figue.4.4 Limit cycle eliminated The final cloed loop fequency epone i hown in Figue.4.5 with 6-7 Hz bandwidth.

24 Figue.4.5 Cloed loop epone.5 Peciion Docking Lateal Contolle Deign.5. Pactical Iue In Deigning Steeing Contol Safety i the fit conideation of any tanpotation ytem deign. Exteme eliability and obutne i the fundamental equiement fo any automatic vehicle contol ytem. In geneal, an ideal automatic vehicle contol ytem hould be extemely eliable, with good ide quality, long life cycle, and elatively low cot. In addition, the fact that almot eveyone ha eithe idden in o diven a ca ceate an unuual obtacle in deigning an automated vehicle. Since mot people can diffeentiate between good dive fom bad one, they will natually demand a good ide quality fo any automatic vehicle. By human natue, fo example, bad pefomance, even duing a -econd duation, can ceate a tonge impeion than a -hou good ide could. In that ene, the automatic vehicle contolle ha to pefom unde all the uncommon cenaio, and impove any wot pefomance a much a poible. To deign any optimal ytem, the development pocedue i often adopted to the pecific poblem. Contol ynthei i elected accoding to it appopiatene to the ening ytem, the plant dynamic and the pefomance equiement. In the deign of the cuent PATH docking contol algoithm, a lateal efeencing ytem baed on oadway magnet make i choen a the default ening ytem. Such ening ytem ae geneally of imple natue and ae moe eliable becaue of the hot ditance between the eno and the make. Howeve, it doe impoe tingent deign equiement fo the contolle ince look-down ytem typically do not povide enough phae lead fo adequate high-peed teeing contol. Dicete make may alo adveely affect low-

25 peed accuacy and moothne. Futhemoe, vehicle dynamic vay geatly aco diffeent opeational velocitie, and thi iue mut be addeed by any contolle deign. Thi Section focue on the deign of a obut teeing contolle baed on oadway make. In paticula, it how that a ingle contolle i adequately to the geneal teeing contol poblem unde vaiou opeating condition without witching between diffeent contolle. Such witching in pactice can be vey poblematic. And uch contolle, if achievable, would be a bette ytem choice becaue it imultaneou uitability with multiple teeing contol cenaio..5. Contol Poblem Fomulation A. Pefomance Requiement A bu peciion docking contol ytem i a ubet of an automated teeing contol ytem fo a Bu Rapid Tanit application. An automated teeing contol ytem tageted towad a Bu Rapid Tanit application i equied to pefom all nomal teeing function fom leaving a bu tation to aiving at a bu tation with extemely high eliability. It hould be obut againt diffeent oadway geometie, unknown vehicle loading, vaiou peed, and changing oadway uface condition. An ideal element of uch automated teeing contol ytem i a high-gain obut vehicle lateal evo that tee the vehicle to follow any deied tajectoy a long a uch tajectoy i defined within the limitation of the vehicle capabilitie. The cloed-loop pefomance equiement fo a geneal Bu automated teeing contol algoithm ae defined a follow:.. mete maximum tacking eo fo highway diving without any pio knowledge of the oadway..5 mete maximum tacking eo fo.3-g automated teeing maneuve without any pio knowledge of the oadway 3.. mete maximum tacking eo fo vehicle peed le than 5 m/ on taight ection of the oadway fo docking accuacy 4. No noticeable ocillation at fequencie above.3 Hz fo paenge comfot, and.4 minimum damping coefficient fo any mode at lowe fequencie 5. m/ maximum lateal acceleation deviation between the lateal acceleation ceated by the vehicle and that fom the oad 6. Conitent pefomance unde vaiou vehicle-opeating condition Requiement, and 6 adde cenaio othe than peciion docking. They ae included imply becaue that a peciion docking eady contolle hould alo be Bu Rapid Tanit eady. They ue vitually the ame vehicle and infatuctue component.

26 In addition to the above pefomance equiement, a deign pefeence wa impoed fo the contolle tuctue: a unifom contol tuctue i pefeable ince it will not equie tanition between diffeent contolle. The tanition between diffeent contolle uually inceae the complexity of the contolle deign, and often educe the obutne of the oveall ytem. Thi deign pefeence puhe fo a ingle contolle that wok fo all nomal bu opeating cenaio without any tanitioning between diffeent contol configuation. B. Vehicle Mode Many eeache ue bicycle model fo vehicle teeing contol. Howeve, mot bue have a elatively oft upenion. The oft upenion ignificant althe the fequency chaacteitic of the lateaal vehicle dynamic fom that pedicted by the bicycle model. In ode to tudy the influence of the upenion oll dynamic on the teeing contol deign, a 3 DOF vehicle model that include lateal, yaw and oll dynamic i ued fo the contolle deign. The chematic diagam of the 3 DOF vehicle model i hown in Figue.5.. The pung ma (m ) inteact with the font and ea unpung mae via the font and the ea upenion, whee K f, D f and K, D ae the otational ping and dampe coefficient fo font and ea upenion, epectively. The oll axi i defined a the line connecting the oll cente of the font and ea upenion a hown in Figue.5.. It can be found that the vehicle geometic paamete that affect the coupling between lateal and oll dynamic the mot i, the ditance between the pung ma CG and the oll axi. Additional vehicle paamete ae defined a follow: β i the ide lip angle between vehicle longitudinal axi, velocity vecto v at CG, and ψ & the vehicle yaw ate. Othe paamete: δ f the font teeing angle, I ψ the yaw moment of inetia, M the ma of the vehicle, l=l f +l the wheel bae, c f and c the linea coneing tiffne of the font and ea tie, epectively. h m

27 Figue.5. Schematic diagam of 3 DOF vehicle model Unde contant peed condition, the dynamic equation of motion ae deived uing the Newtonian method. Auming mall angle and uing the linea tie model, the linea dynamic equation of the vehicle model with epect to the oad efeence fame ae deived and hown in Eq. (.). The tate-pace epeentation take the fom of x & = Ax + Bδ + d. The tate vaiable ae: y, y&, the lateal diplacement at CG w..t. oad efeence fame and it deivative; ψ, ψ&, the yaw angle w..t. the oad efeence fame and it deivative; a well a φ, & φ, the oll angle and it deivative. The oad efeence fame i attached to the oad cente at a point adjacent to the vehicle CG with X axi tangent to the oad tajectoy and move along the oad with the ame peed a the vehicle. The input i the font teeing angle (δ). The ditubance ae: ρ, the oad cuvatue; ψ& d, the deied yaw ate fom the oad; F wy, the ditubance foce at CG along the y diection; and F x, the font tie foce along the tie oientation. Since no bu paamete wee not available duing the deign poce, paemete gatheed fom vaiou ouce wee ued fo the contol deign pupoe. It tuned out that the final contolle paamete wee cloe enough to thoe eulted fom the geneal vehicle paamete due to the obut deign method. Only a couple tuning tep within two day came the final deign paamete.

28 + Λ Λ + Λ Λ Λ Λ Λ Λ = d d d B B B y y R R v A A v A R v A A v A R R v A A v A y y dt d δ φ φ ψ ψ φ φ ψ ψ & & & & & & (.) whee the coefficient ae defined a follow: M c c A f ) ( + =, M c l c l A f f ) ( + =, I ψ c l c l A f f ) ( 3 + =, I ψ c l c l A f f ) ( 4 + =, m x x h m MI MI = Λ, m x m h m MI Mm h = Λ, ) ( ) ( m x f m m x f h m MI K K gh m m h I R + + = γ γ, ) ( m x f m h m MI D D m h R + =, ψ γ γ I l l R f f ) ( 3 =, 4 ) ( ) ( m x f m f m h m MI K K gh m M m h R + + = γ γ, 5 ) ( m x f h m MI D D M R + =, M F c B x f ) ( + =, I ψ F c l B x f f ) ( + =, ρ ψ v v A F M d d wy Λ + Λ = &, d f f v I c l c l d ψ ψ & ) ( + =, ρ ψ 3 v v A F M d d wy Λ Λ + Λ = & (.) C. Contol Poblem Fomulation Since mot vehicle lateal ening ytem povide lateal meauement at a cetain eno location, the contol fomulation tat with uing a typical uch lateal meauement fo teeing contol. Auming thi meauement i taken at a location d mete in font of CG, the lateal diplacement at the eno location can be witten a ψ φ S h d y y + + =, (.3) whee h i the ditance fom the eno to the oll axi. Diffeentiating Eq. (.3) twice and auming v i contant, the vehicle lateal acceleation tanfe function at the eno location S, V S (), i deived by uing Eq. (.) a [ ] ( ) ) ( ) ( ) ( ) ( ) ( B A I h d V y f f S S δ δ = =. (.4) Altenatively, V S () can be defined a ) ( ) ( ) ( ) (,,, G h G d G V y S δ φ δ ψ δ & & & + + = (.5)

29 whee ( ), ( and ( ae tanfe function fom teeing angle to y&, ψ& G y&, δ G ψ&, δ ) G & φ ), δ and φ &, epectively. Figue.5. depict a geneic block diagam of a teeing feedback ytem baed on lateal diplacement meauement. The vehicle lateal model conit of five ubytem: actuato dynamic (A()), oad efeence (deied lateal acceleation at the eno location: & y ef = v ρ ), vehicle dynamic at eno (VS()), vehicle kinematic (/ ) and contol law (C()). The goal of teeing contol ynthei i to detemine a contol law C() that i capable of tabilizing the vehicle lateal dynamic with ufficiently high gain to atify the pefomance equiement. One majo challenge in chooing the contolle C() i to maintain enough tability magin unde the delay and uncetaintie fom V S () and A(). ρ v y& ef A() V S () + - y S δ f y& S -C() Figue.5. Vehicle teeing contol block diagam.5.3 Baic Steeing Contolle Deign A. Contolle Requiement The tability and pefomance equiement ae examined fo the implified teeing cloed-loop ytem decibed in Figue.5. a y ( ) = v ρ( ). (.6) + A( ) V ( ) C( ) S In ode to pevent exceive teeing ocillation, ufficient phae magin (pm) and gain magin (gm) ae equied fo the above ytem: A( jω p ) V a well a ( jω p ) C( jω p ) A( jω p ) VS ( ω p ) C( jω p ) > ( π pm), at = ; (.7) ω ω S A( jω ) V ( ω ) C( jω ) p g S g g < ω g A( jω g ) VS ( jω g ) C( jω g ), at = π. (.8) gm ω g p

30 In ode to maintain a tight lane-keeping ability, the following lane-tacking equiement i impoed: y ( t) K max( v ρ ). (.9) a The equiement in Eq. (.9) guaantee that the lateal diplacement deviation ( y ) hall not exceed K a mete fom a m/ tep input of the efeence oad acceleation (v ρ). By uing the inequality v ρ y ( t) L up max( v ρ) A( ) VS ( ) C( ) jw A( ) VS ( ) C( ) = (.) + = + whee L - denote the invee Laplace tanfom, Eq. (.) can be ewitten a Ka. (.) A( ) V ( ) C( ) + S = jw Eq. (.7), (.8) and (.) ae the baic deign equiement fo the contolle C(). C() need to upply the neceay phae lead (minimum phae magin plu ytem delay) at gain-coove fequency baed on Eq. (.7); and Eq. (.) indicate that thi coove fequency inceae a K a deceae. Figue.5.3 plot the equied phae lead at the gain coove fequency fo C() with epect to diffeent vehicle peed uing a typical 3 DOF vehicle model. Accoding to Figue.5.3, a the vehicle peed goe above 3 m/ and d = m, C() i equied to delive at leat degee phae lead when ω i choen aound Hz, a citical ange fo high peed opeation. Thi obevation ugget that a lateal ening ytem that poduce only lateal meauement nea the vehicle CG ceate a tingent deign poblem fo a obut teeing contolle at high peed. On the othe hand, thi containt i geatly educed when the lateal deviation i meaued at ome ditance in font of the vehicle. Figue.5.3 alo how the coeponding equied phae lead fo C() when the meauement i taken 5 mete in font of CG. In uch cae, only -degee phae lead at ω = Hz i equied. A imple lead-lag compenato fo p the output y uffice to tabilize the cloed-loop teeing contol ytem at high peed. p Contolle Phae Requiement (6 deg magin) with Poition Feedback at CG (LeSabe 3 D Model) Contolle Phae Requiement (6 deg magin) with Poition Feedback at Seno (5m in font of CG) (LeSabe 3 D Model) Requied Phae Coove (deg) Requied Phae Coove (deg) Velocity (m/) Gain Coove Feq. ( x Hz) Velocity (m/) Gain Coove Feq. ( x Hz) Figue.5.3 Contolle phae equiement (6 degee phae magin) at gain coove fequency: (a) Left: d = m; (b) Right: d = 5 m. B. Look-ahead Steeing Contolle

31 The analyi the ection above ugget that the geneic vehicle teeing contolle depicted by Figue.5. i a good candidate fo teeing contolle deign. Accoding to Eq. (.5), the look-ahead ditance d can be egaded a an additional contol paamete along with the paamete of C(). To invetigate the effect of thi exta degee of feedom with epect to the teeing contolle deign, the imple cloed-loop tuctue with two contant contol gain (d and C() = k c ) i choen at any given vehicle velocity in thi ection a in Eq. (.3): y ( ) = v ρ( ). (.3) + A( ) V (, d ) k S c The following optimization technique i then deived to obtain the optimal contol gain that attain the cloed loop equiement (.7), (.8) and (.): Fo evey vehicle peed v and fo any given d, the maximum attainable phae magin, β (, v), i obtained a max β d max ( d, v) = max A( jwg ) VS ( jωg, d, v) ω p ω R, A( jw ) V ( jω, d, v) ω p S p g gm ( ( A( jω) V ( jω, d, v) )) S, (.4) whee the fequencie ω p and ω g ae detemined by A( jω ) V ( jω, d, v) =, (.5) β ( g S g ) ( d, v) ( A( jω ) V ( jω, d, v) ) max =. (6) p S p The local optimal choice of k c that eult in the maximum attainable phae magin, β (, v), fo a given d i defined by max d ω p k c ( d, v) =. (.7) A( jw ) V ( jω, d, v) p S p The optimal choice of the contol gain pai ( k c (v), d (v) ) that atifie the tability equiement (.7) and (.8) fo any given vehicle peed v i calculated a k ( v) = max k ( d, v = k ( d ( v), v. (.8) c d R, βmax ( d ) > pm ( ) ) c c Finally, the lane-tacking pefomance i examined by uing Eq. (.) and (.8) a K ( ) a v. (.9) A( ) V (, d ( v), v) k ( v) + S c = jw Since Eq. (.9) uually povide a athe conevative etimate, an altenative method fo a moe pecie eo bound i to diectly compute the maximum tanient eo with epect to a m/ tep oad acceleation input though invee Laplace tanfomation. Figue.5.4 how the maximum attainable phae magin ( β ) baed on Eq. (.4) and the local optimal contol gain ( k c ) a in Eq. (.8) uing a the minimum gain magin max

32 (gm). The plot of β max confim that inceaing the look-ahead ditance doe impove the attainable maximum phae magin to within the equiement; the plot of k c ugget that highe gain i poible at low peed. Figue.5.5 diplay the optimal contol gain pai ( k c (v), d (v) ) computed by Eq. (.8), Figue.5.6 how the eultant maximum tanient eo and eo bound (K a by Eq. (.9)). Thee optimal gain pai guaantee at leat 5-degee phae magin (pm i et fo 5 degee in the above computation) and gain magin of 6 db fo each vehicle peed. Initial obevation of Figue.5.5 eveal two phenomena that follow engineeing intuition: () the optimal look-ahead ditance inceae a the peed inceae; () the lage the look-ahead ditance, the malle the feedback gain; (3) lage feedback gain i equied at vey low vehicle peed. It i inteeting to notice fom Figue.5.5 that a look-ahead ditance of about to ca-length i geneally adequate fo teeing contol. It i taightfowad to how that the mooth optimal gain cuve aue the obutne of the gain-cheduling algoithm with epect to peed vaiation. Figue.5.6 illutate the lane-tacking ability of the optimal gain pai. The gain pai eult in 8 cm maximum tacking eo (including tanient) fo evey.g lateal oad ditubance without any pio knowledge of oad cuvatue. It demontate the poibility of uing contant feedback gain with contant look-ahead ditance to achieve all lane-tacking equiement pecified in Section 3. at any peed. Figue.5.4 futhe indicate that the attainable phae magin between 3 and 4 m/ ae lage than thoe between and m/. Thi chaacteitic i omewhat counte intuitive. Unde contant look-ahead ditance, the coupling among lateal, yaw and oll of the tet vehicle equie the contolle to povide moe phae lead aound Hz when the vehicle peed i between and m/ (a een in figue.5.3). The need fo lage phae lead eult in lage k c (v) and malle d (v) at vehicle peed between and m/, a well a lage tanient eo aound m/. A fequency haped look-ahead ditance (G d ()) can elax uch limitation and will be dicued in the peviou ection. Maximum Phae Magin Baed on LeSabe 3 D Model (gain magin>) Optimum Feedback Gain fo Maximum Phae Magin Baed on LeSabe 3 D Model (gain magin>) 8 7 Maximum Phae Magin (deg) Optimum Feedback Gain, k c Vehicle Speed, v (m/) Look ahead Ditance, d (m) Vehicle Speed, v (m/) Look ahead Ditance, d (m) 5 Figue.5.4 Maximum attainable phae magin and optimal gain baed on 3 DOF model with contant contol paamete (k c, d ), (gm=): (a) Left: β ; (b) Right: k. max c

33 Optimum Contol Paamete Baed on LeSabe 3 D Model Optimum Feedback Gain (k c ) (phae magin>5 deg; gain magin>) Optimum Look ahead Ditance (d ) Vehicle Speed (m/) Figue.5.5 Optimal contol gain pai ( k c, d ) baed on 3 DOF model with contant contol paamete (pm=5 deg, gm=) Maximum Eo pe m/ Step Road Accel. Input uing Optimal Gain (LeSabe 3 D Model: PM>5deg, GM>).35.3 C()=k c *[.578]/[.683] Tacking Eo (m).5..5 Maximum Tanient Eo Ka= /( +A()V()C()) Vehicle Speed (m/) Figue.5.6 Reultant maximum tanient eo fom the optimal contol gain (in Figue.5.5) baed on 3 DOF model with contant contol paamete (pm=5 deg, gm=) C. Optimal Fequency-Shaped Look-ahead Steeing Contolle The eult in the peviou ection imply that a imple contolle combining contant feedback gain and contant look-ahead ditance may achieve all pefomance equiement decibed in Section 5.3. fo both peciion docking and othe BRT opeation. Howeve eveal pactical containt limit the feaibility of uch imple implementation. The amplification of the meauement noie limit the length of the look-ahead ditance to a couple of ca length; high feedback gain with lage look-ahead ditance can eaily excite the non-lineaity o unmodeled dynamic in the teeing

34 actuato o mechanim; lage look-ahead ditance ceate noticeable teady tate tacking eo duing cuve. In ode to adde both the pactical limitation and the pecific phae lead equiement aociated with the contant look-ahead ditance depicted in Section 5..3.C, a fequency haped look-ahead contolle law i popoed a V ) = G ( ) + d ( v) G ( ) G ( ) h G ( ), (.) S ( y&, d, δ ψ& δ + & φ, δ along with a feedback compenato C( ) = k ( v) G ( ). (.) c c Following the deign philoophy of minimum contolle tanition, two peedindependent filte, G d () and G c (), ae choen fo invetigation in thi ection. In ode to educe both the effect of the teady tate tacking bia and the unwanted excitation of the high fequency unmodeled dynamic, G c () conit of a low-fequency integato and high-fequency oll-off. Similaly, G d () i made of a high fequency olloff potion and a mid-fequency lead-lag filte to limit the look-ahead amplification and to povide exta look-ahead between.5 and Hz. In thi ection, thee two additional contol filte ae choen a 5π ( +.5π ) G c ( ) = (.) ( +.π )( + 5π ) π ( +.4π ) G d ( ) = (.3) ( +.8π )( + π ) Ineting G d () into V() a in Eq. (.) and appending G c () to all open loop tanfe function immediately afte V() fo Eq. (.4) to (.7), the coeponding optimal contol gain pai ( k c (v), d (v) ) that atifie the tability equiement (.7) and (.8) fo any given vehicle peed v i calculated a in Eq. (.8). The optimal contol gain pai ( k c (v), d (v) ) coeponding to the contol filte ( G c (), G d () ), a well a the eultant maximum tanient eo and eo bound (Ka) ae plotted in Figue.5.7 and.5.8. Similaly, the optimal gain pai guaantee at leat 5 degee phae magin and 6 db gain magin fo any vehicle peed. A the eult of the additional phae lead ceated by the lage look-ahead ditance between.5 and 3 Hz, the fequency-haped look-ahead cheme ende a moe deiable optimal gain pai chaacteitic. Geneally peaking, the look-ahead ditance inceae and the feedback gain deceae a the vehicle peed inceae. Moe pecifically, ( k c (v), d (v) ) emain almot contant fo vehicle peed between 5 and 3 m/. Thi indicate that a contant contolle can wok almot optimally fom medium to highway peed. Geneally peaking, the elatively flat gain with epect to velocity imply that the contolle i moe toleant to velocity eo.

35 Figue.5.8 how that the eultant maximum tacking eo (including tanient) i le than 5 cm fo evey.g lateal oad ditubance without any pio knowledge of oad cuvatue. It atifie all lane-tacking equiement pecified in Section.5. at any peed. Optimum Contol Paamete Baed on LeSabe 3 D Model Optimum Feedback Gain (k c ) (phae magin>5 deg; gain magin>) Optimum Look ahead Ditance (d ) G d ()=d *[ ]/[ ] Vehicle Speed (m/) Figue.5.7. Optimal contol gain pai ( k c, d ) baed on 3 DOF model with fequency haped look-ahead contol (pm=5 deg, gm=) Maximum Eo pe m/ Step Road Accel. Input uing Optimal Gain (LeSabe 3 D Model: PM>5deg, GM>).5 G d ()=d *[ ]/[ ] C()=k c *[.578]/[.683] Tacking Eo (m).4.3. Maximum Tanient Eo Ka= /( +A()V()C()) Vehicle Speed (m/) Figue.5.8. The eultant maximum tanient eo and K a baed on 3 DOF model with fequency haped look-ahead contol (pm=5 deg, gm=) D. Final Contolle Implementation

36 The above ection povide tong agument fo implementing the fequency-haped look-ahead teeing contolle in pactice: imple, obut and atifying pefomance equiement. Eq. (.) can be diectly adopted fo contolle deign when the yaw angle meauement i available. On the othe hand, when the vehicle ue a look-down lateal ening ytem fo lateal contol, the yaw angle can be etimated by a econd lookdown meauement. Unde the aumption that the ditance fom all eno to oll axi ae about the ame, the lateal diplacement at a vitual look-ahead ditance, d, in font of the CG can be eaily appoximated accoding to Eq. (.3) a y f yb y y f + ( d l f ) (.4) L whee y f and y b ae the lateal meauement in font and back of the vehicle, epectively, and L i the ditance between thee two eno. The final teeing contol algoithm implemented in the tet vehicle need to atify both tacking accuacy and ide comfot equiement fo all opeational cenaio dicued in Section.5. at vaiou vehicle peed egadle of the following uncetaintie: oad adheion vaiation, incoect oad cuvatue infomation, eno noie, actuato bandwidth, vehicle dynamic change, oft upenion mode, and vehicle paamete. Uing the analyi eult fom thi pape with ome tuning in the vehicle, the following final fequency haped vitual look-ahead lane-keeping contol algoithm wa developed and implemented: δ = k G ( ) ( k ( ) + k G ( )) y k G ( ) y (.5) c c c ( ) int e d f e d whee δ c i the teeing command, k int the integato at font eno location, G d the vitual eno look-ahead filte, G c the compenato at the vitual eno location, k e and k c ae the gain-cheduled contant. Notice that k = ( d d ) L. Thee two gain-cheduled b e f / coefficient follow the velocity dependent elationhip fom Figue.5.7. Thi final algoithm conit of thee linea filte imila to thoe hown in Figue.5.9. Thee filte ae baically light vaiation of G c and G d a decibed in the lat ection. Some mall modification wee made though limited vehicle tuning to adde ubjective tadeoff a well a cetain identifiable unmodeled dynamic. Thee thee filte and thei pimay function ae decibed a follow: An integal contol, k int (), that keep the teady tate tacking eo at the font eno to zeo. A fequency haped look-ahead ditance, G d (), that povide moe look-ahead ditance aound the vehicle lateal mode and oll-off of the look-ahead ditance at highe fequencie. A evo contolle, G c (), that ue the fequency haped vitual diplacement a input and compenate it fo the actuato and noie.

37 5 Steeing Contolle Tanfe Function: Kint Steeing Contolle Tanfe Function: Kext Steeing Contolle Tanfe Function: Gc Gain(db) 5 Gain(db) 5 Gain(db) tee = kc*gc * ( (Kint + ke*kext) * yf ke*kext * y ) 5 tee = kc*gc * ( (Kint + ke*kext) * yf ke*kext * y ) tee = kc*gc * ( (Kint + ke*kext) * yf ke*kext * y ) 4 4 Phae(deg) Phae(deg) 4 Phae(deg) 6 Fequency (Hz) 6 Fequency (Hz) Figue.5.9. Final contolle fequency epone (Left: k int (), Cente: G d (), Right: G c ()). 4 Fequency (Hz).6 Detailed Bu Peciion Docking Softwae Stuctue The ection decibed the detailed Bu Peciion Docking Softwae tuctue. The geneal tuctue i hown in figue.6.. coodination contol if docking longitudinal contol enable lateal contol heatbeat DVI vehicle IO teeing actuato inne loop Figue.6. Bu peciion docking oftwae tuctue The lateal contol oftwae get a tigge fom the magnetomete evey mec, and ead the following 8 tuctue fom the databae: o magnetomete (DB_LAT_INPUT_MAG) - lateal and vetical axi of font 7 eno - lateal and vetical axi of ea 7 eno - oveall magnetomete health fom the 4 eno o teeing actuato input (DB_LAT_CONTROL_INPUT) - teeing angle at the tie (deg) - actuato eady (=not eady, =eady) - actuato tatu (=manual, =automatic)

38 - actuato fault mode (=none, to 7=fault) o othe lateal eno (DB_LAT_INPUT_SENSORS) - lateal acceleation - teeing actuato witch (on o off) - tanition toggle witch (manual, none o automatic) - tanition enable witch (on o off) - longitudinal enable witch (on o off) o vehicle peed (m/) fom the J939 bu (DB_J939_CCVS) o cuent vehicle gea fom J939 bu (DB_J939_ETC) o yaw ate (ad/ec) fom the gyo (DB_GYRO) o DVI lateal mode fom the button (DB_DVI_MONITOR) In the docking longitudinal contol enable, it alo ead: o longitudinal coodination input (DB_LONG_COORD_OUTPUT) - longitudinal contolle tatu (=manual, =automatic) - longitudinal contolle fault mode (=none, =paking bake) - bake oveide (tue o fale) - bake witch (on o off) - thottle witch (on o off) The lateal contol oftwae wite the 6 following tuctue to the databae. Evey mec, it wite: o lateal output fo the teeing actuato (DB_LAT_CONTROL_OUTPUT) - teeing actuato mode (=manual, =automatic) - deied teeing angle (deg) o lateal coodination output fo longitudinal contol (DB_LAT_COORD_OUTPUT) - command fo the longitudinal contolle (=manual, =automatic) - command to eume longitudinal contolle afte topping (tue o fale) - etimated longitudinal poition of the bu fom the magnet (m) - top make numbe fo the next bu top And evey 5 mec, it wite: o compute heatbeat (DB_LAT_HEARTBEAT_OUTPUT) o DVI led and ound (DB_DVI_LEDS) - geen led (on when tanition to automatic i eady) - blue led (flahing when tanitioning to automatic, on when in automatic contol) - ed led (on if lateal fault, flahing if emegency fault, off if no fault) - ambe led (flahing if longitudinal fault, off if longitudinal contol on) blue geen ed ambe

39 - eady ound (on if lateal contol i eady to engage) - confimation ound (on if dive puhe the tanition witch) - take ove ound (on if end of magnet) - emegency ound (on if emegency lateal fault) o DVI output to the monito (DB_LAT_DVI_OUTPUT) - oveall mode of the lateal poce fo the docking cenaio: DOCK_SELECT: elect docking cenaio DOCK_START_WARNING: automatic tanition i engaging DOCK_ACTIVE: automatic contol on DOCK_FINISHED: docked, waiting at the bu top DOCK_FROM_PARKED: leaving bu top DOCK_NOT_IN_DRIVE: docked, paking bake o not in gea fault DOCK_BRAKE_ON_ERR: dive hit the bake => longitudinal contol i diabled and lateal contol i till engaged DOCK_FAULT: fault code, lateal contol i diabled - magnet ead (tue o fale) - lateal ytem eady to tanition (tue o fale) - automatic tanition enable fo docking (tue o fale) - tation numbe fo docking (=none, =fit tation o =econd tation) - main lateal fault (=none, &= fault, - to 6=emegency fault) - additional fault fo actuato and magnetomete (unued in the demo) - tavel diection (=unknown, =nothbound o =outhbound) - lane ID (=unknown, =ight o =left) - lane change diection (=none, =ight o =left) - lateal offet (cm) - etimated lateal meauement duing lane change (cm) - emaining ditance to the end of the magnet (m) - vehicle peed (4*m/) 3. Fault/failue analyi, diagnoi and afety deign conideation Safety i the mot impotant conideation fo any automated vehicle deign. Safety iue include fault and failue analyi, diagnoi and afety deign. Thi ection dicue the implemented fault detection ytem in the tet vehicle, the bench afety analyi fo the teeing actuato, a well a othe fault and failue analyi. 3. Implemented Fault Detection Sytem The fault detection and failue management ytem ae the cucial component in any automated vehicle ytem. In the peciion docking ytem deigned unde thi poject, we tied to include mot of the cucial component failue detection in the implementation. Howeve, the complexity of uch deign inceae a the complexity of the failue cenaio inceae. Due to the limited time and eouce available fo the poject, the detection deign may not be a compehenive a it would equied fo field-

40 tet eady automated bue. Futhemoe, edundancy i not implemented fo thi tet ytem fo the ame eouce limitation. Again, we ae awae of the fact that any poible ingle point failue hould have edundancy to potect the ytem afety and integity. Two level of fault detection ae implemented fo the tet bue: component level fault detection and highe-level lateal contol fault detection. Two component-level fault detection ae implemented. The magnetomete manufactue deigned hadwae fault detection fo each magnetomete, and PATH deign oftwae fault detection fo the mat teeing actuato. Each magnetomete povide a digital health ignal output to ignify any detected failue in the magnetomete electonic. The teeing actuato moto povide alo a digital failue output that indicate a hadwae/electonic moto failue by the manufactue. The mat teeing actuato oftwae deigned by PATH include local fault detection that addee the following poible failue ituation: moto failue detected by the moto electonic (moto failue), no powe (powe off), conflicting command indicating hot compute poblem (command failue), teeing actuato lowe-level dive failue (dive failue), encode inconitency (encode failue), teeing pot inconitency (teeing pot failue), and initialization poblem (tat up failue). The following lit the coeponding fault code numbe: = none = moto failue = powe off 3 = command failue 4 = dive failue 5 = encode failue 6 = teeing pot failue 7 = tat up failue The implemented main lateal contol fault can be omewhat elf-explained by the following deigned main lateal contol fault code: = no fault = yaw ate = actuato pot eno - = miing magnet - = peed -3 = magnetomete health -4 = teeing actuato -5 = timing -6 = multiple fault

41 The fault code mean no fault. Poitive fault ae geneally not fatal. The moe negative the fault numbe i, the moe eiou the implication of the fault would be. The fault detection ae deigned to incopoate the input fom the lowe-level component fault detection a well a highe-level logic to povide an moe clea oveall aement fo the ytem health. The fault code i ued in vaiou DVI contol and lateal contol tate machine. 3. Bench Analyi: Fault Detection of Steeing Actuato Due to the time limitation and afety implication fo expeimenting failue analyi unde an automated bu, a hadwae in the loop (HIL) envionment wa ceated to tudy one of the majo afe-citical component in the peciion docking automated ytem: the teeing actuato. The fault detection in a HIL imulation contain two majo potion: the HIL imulation and the fault detection tudy. The hadwae etup and algoithm implementation of the HIL imulation will be peented in ection 3... The imulation hadwae include pat of the eal teeing ytem, a eal-time compute, a et of eno, a teeing actuato, and a eaction moto, all in a bench. The fault detection, decibed in Section 3.., i model-baed fault detection cheme that utilize a minimum et of electic component and imple algoithm to detemine faulty teeing actuato befoe automation. 3.. Baic Hadwae Setup Figue 3..(a) and 3..(b) how an HIL imulation etup. The eential hadwae of the HIL imulation contain fou pat: () eal mechanical mechanim, () actuato, (3) eno, and (4) contol and data tanfe unit. The teeing wheel, teeing actuato, haft, toion ba, and ack & pinion ae in the ame cale of typical paenge auto pat. The eaction moto i employed to mimic the oiginal ytem fom two majo apect: () the dynamic of the teeing ytem and () extenal foce and ditubance fom the tie. Fo example, the load and ditubance include the inetia foce of the tie and the aligning toque eulted fom tie duing coneing. The ait toque i to imulate that geneated by powe teeing in a vehicle. Toque eno and poition encode ae utilized fo meauement and fo imulation. Fo intance, encode B detemine the teeing angle on tie. Incopoated with vehicle lateal dynamic, the angle can be ued to geneate the aligning toque duing coneing. Deflection between the uppe and the lowe column can be employed to poduce ait toque, i.e. τ ait = f ( θa θb ). ECU i ued to upply and contol the cuent into the DC moto. The I/O boad, AT-MIO-64E-3 and AT-AO-6, ae ued to ead the meauement, to output the toque command, and to communicate with the compute.

42 Steeing Actuato Encode A Toion Ba Toque Seno Encode B Reaction Moto Rack and Pinion Figue 3..(a) Oveview of teeing wokbench Figue 3..(b) Steeing wokbench 3.. Actuato Thee ae two moto acted a actuato ued in the wokbench: teeing actuato and eaction actuato. The teeing actuato i imila to thoe ued in automated vehicle. The eaction actuato i added to imulate the actual eaction fom the vehicle and the oad a well a the chaacteitic of the teeing ytem. Geneally, the chaacteitic and eaction include the powe ait teeing, tie foce, load, fiction, damping, etc. Thee will be detailed in the following ubection. Table 3. how the pecification of the two actuato. Note that the toque of the eaction moto i much lage than that of the teeing actuato becaue, fo example, the eaction moto may need to imulate the

43 lage ditubance fom the oad in a udden. Thi will equie a lage foce at that time intant. Steeing Column Actuato Retoing Foce Actuato Gea type Wom and wom gea Wom and wom gea Gea atio 6.5 : 7 : Moto type DC buh moto with clutch DC buh moto Rated voltage DC V DC V Rated cuent 5 A 3 A Rated moto peed 5 pm 5 pm Rated toque.5 Nm.6 Nm Rated output 35 W 7W Toque contant.4 Nm/A.54Nm/A Moto inetia.6 g-m.4 g-m Table 3. Compaion between teeing and eaction moto 3..3 Model Conideation Powe Ait Steeing Figue 3.. how a typical chaacteitic cuve of the ait toque veu deflection on the toion ba. The lope of thi cuve ie up a the deflection inceae. The moe the dive effot i, the lage the deflection on the toion ba will be. The atio between the applied toque of the dive and the ait toque will then become malle. The ait toque will geneally compenate the extenal load and ditubance at lage deflection while human dive hand will compenate uch foce at mall deflection. Figue 3.. Ait toque veu deflection of toion ba plot

44 Self-aligning Toque Aligning toque decibe a tie tendency to tee about a vetical axi though the cente of the pint (the oigin of the tie axi ytem). Uually the tie tend to align it heading with it path. The aligning toque come fom the hape of the ditotion in the footpint. The elatic ditotion inceae fom font to back and thi give an uneven ditibution of lateal foce along the length of the pint. Figue 3..3 how the deflection of the tie contact patch in a implified tie model. Given foundation tiffne, c, and mall defomation, the concentated foce i appoximately cl α while 3 the moment along the vetical diection i cl α, wheeα i the lip angle. In elatic egion, the moment will be inceaing popotionally withα ince the moment i independent of c and l. Aligning toque Tie deflection Concentated foce α l x Figue 3..3 Tie tead deflection in elatic egion A the ea of the tead in the footpint lide, the local defomation in the liding egion eache the limit, hown in figue Fit, the total lateal foce till inceae but it i not a much a that geneated by uing linea tie model at the ame lip angle. Secondly, the concentated foce will move fowad, cloe to the tie cente. Due to the above two effect, the moment may each the peak value in the tanitional egion, a hown in figue 3..5.

45 Aligning toque Tie deflection Concentated foce α l l x Figue 3..4 Tie tead deflection in tanitional egion Elatic Region Fictional Region Tanitional Region Figue 3..5 Aligning toque veu lip angle plot Once the total lateal foce eache the maximum value, it i often efeed to a the fictional egion. In thi egion, a the lip angle goe up, the eultant lateal foce will be focued much cloe to the cente of the tie and the moment will continue falling off. At thi tage, the aligning toque i dicued baed on the viewpoint of the tie itelf. Fom the apect of the whole ytem, thi toque i not equivalent to that applied to the teeing mechanim. The aligning toque will be amplified o educed becaue of intoducing teeing geomety, uch a cato, cambe, and inclination angle. In many deign of automotive teeing ytem, thee angle ae ued fo bette vehicle lateal chaacteitic. The teeing geomety ha to be taken into conideation when implementing HIL imulation. Fo example, Figue 3..6 how kingpin offet due to the

46 effect of cato angle. The mechanical tail epeent fo the kingpin offet while the pneumatic tail eult fom the uneven ditibution of the lateal foce. The tee toque i given by the um of mechanical tail plu pneumatic tail time the lateal foce. Thi will ait human dive in fate teeing wheel aligning, epecially at low peed. Vitual Kinpin Total Lateal Foce Pneumatic Tail Mechanical Tail Figue 3..6 Cato angle effect on aligning toque The aligning toque depend on the teeing geomety and the lip angle of the font tie. Slip angle ae detemined baed on the inteaction among the gound, the vehicle, and the tie. In the HIL imulation, the inteaction have to be imulated by uing compute pogam. In thi tudy, a bicycle model with nonlinea tie chaacteitic ha been utilized to calculate the lip angle at each time intant. The equation of motion of a bicycle model ae hown a follow. my& = F ( α ) + F ( α ) (3.) whee u f f I & ε = F ( α ) l F ( α ) l (3.) zz f f m : vehicle ma I zz : moment inetia of yaw motion α : lip angle l, : ditance between C.G. and font/ea axle F : lateal foce at font/ea axle. i Fiction, Damping, and Inetia Foce In the eal teeing ytem, thee ae lage fiction and damping foce fom the tiegound inteface, ack & pinion, joint, tie intinic popetie, etc. The eal ytem ha lage load, uch a the wheel inetia. Howeve, in the wokbench etup the imulated ytem only contain pat of the eal hadwae. To mimic the actual ytem, thee foce have to be included duing the imulation Implementation of HIL Simulation

47 The effect mentioned in ection 3..3 hould be included to imulate the majo chaacteitic of the vehicle teeing ytem. Mot of the above effect ae imulated uing the eaction moto. Ideally, the wokbench can pefectly mimic the eal ytem if the moto doe not have it own dynamic. Howeve, it i not tue in the eal wold. The moto dynamic may eult in ome poblem that the eal teeing ytem doe not have. In fact, thee i a tability poblem in implementing the ait toque. The tability poblem aie afte adding the lage ait gain into the imulation. Fom the pepective of the eaction moto, it ECU eceive the command of the aligning toque and the ait toque to dive the ytem fom the lowe column. The magnitude of the ait toque depend on the deflection between the uppe and the lowe column. Figue 3..7 how the block diagam of the implified wokbench model. In thi diagam, the input i the toque command and the output i the deflection of the toion ba. Self-aligning toque command + G 3 + Applied toque on hand wheel + G G + θ θ k Ait toque command K k Figue 3..7 Block diagam of implified teeing ytem wheeg and Gae the tanfe function ( fom τ i to θ i) of uppe/lowe teeing column G i the tanfe function of ECU with eaction moto dynamic 3 θ and θepeent the angula diplacement of uppe/lowe teeing column k i the ping contant of the toion ba and k i the gain of the ait toque. If the moto dynamic i ignoed, ay G 3 equal to unity, the oveall cloed loop tanfe G function fom the moto command to θ θi, wheeg andg ae + k( G+ G) + kg nd table ode ytem with elative degee. The Nyquit plot of k ( G + G ) + k G will neve encloe fo any poitive ait gain,, ince the phae of G and G can only vay fom to 8 degee. Afte the moto dynamic, G 3, i intoduced into the ytem, the cloed-loop tanfe function will k

48 GG 3 become + k ( G + G ) + k G G 3. Becaue the dual-ma ping ytem i lightly damped, k( G+ G) can be vey cloe to with little phae magin. Aume that G 3 ha elative degee of and i a table, minimum-phae tanfe function. If the bandwidth ofg3 i not much highe than that of kg, the eultant vecto, k( G+ G) + kgg3, can be on the left hand ide of at ome fequency, a hown in figue Thi implie that the Nyquit plot will encloe and will lead to an untable ytem. Im kgg 3 k ( G + G ) + k G G 3 k ( G + G ) Re Figue 3..8 Nyquit plot of k( G+ G) + kgg3 Figue 3..9 Bode plot fom moto command toθ θ The bandwidth of the actuato LR cicuit i ove Hz. The dynamic i ignoed in the dicuion.

49 By uing the fequency weeping technique, the identified Bode plot i hown in figue In the diagam, it how that the natual fequency of the ma-ping ytem i aound Hz and the phae i appoaching 7 degee at high fequency. The open-loop GG 3 tanfe function fom toque command toθ θ i. Baed on the + k( G+ G) aumption made in the peviou paagaph, thi implie that the elative degee of the open-loop tanfe function i 3, which follow the identified eult. Theefoe a pecompenato ha been pecifically deigned to tabilized the inne loop fo the high ait gain. Thi peent anothe diffeence between the eal hydaulic ait behavio and the one in the HIL imulation. Howeve the diffeence, hopefully, only how up in the highe fequency dynamic, which i not a concen fo thi tudy Model-baed Fault Detection The HIL imulation i eventually employed to tudy the fault detection of the teeing actuato. Thi tudy focue on model-baed fault detection and identification. Fault identification i conducted by compaing the identified faulty ytem with a model of the fault fee ytem. In thi ection, the actuato fault detection include the two pat: () the baic knowledge of the moto dynamic and it contol unit; () the fault detection algoithm, a peented in ection and 3..5., epectively Baic Knowledge of Moto Dynamic and ECU Figue 3.. how the DC moto dynamic. Thee i a fit-ode dynamic between the cuent and the effective voltage applied to the moto cicuit. The toque geneated i popotional to the cuent by the toque contant, K t. The induced voltage will deceae the effective voltage applied to the moto cicuit. An intuitive idea to follow the cuent command i that ECU can inceae it output voltage to compenate fo the back emf and educe the phae lag eulted fom the moto dynamic by utilizing the infomation fom the built-in voltage and cuent eno. Cuent Command ECU v + L + R i K t J ω v b K b Figue 3..: Block diagam of moto dynamic K : toque contant; K : back emf contant; J : moment of inetia t b

50 In ummay, thee ae two voltage ouce: () the applied voltage fom the ECU; () the induced back electomotive foce (back emf) fom the moto. Uually the voltage applied to the moto i in pule width modulation (PWM). Thi PWM ignal can each up to 5 khz in ome application. Feeding into the cicuit, the moto peent an inductive load and it inductance filte much of the high-fequency enegy. The cuent will ie up a PWM ignal i on and fall off a the PWM i off. The eult i that the cuent look like a DC ignal with ome ipple on it, a hown in figue 3... So the low fequency ignal in the PWM can be meaued by uing the low pa cicuity with lage impedance. Fom Faaday law, the back emf will be induced againt the amatue voltage a the oto winding pinning in the magnetic field. Ideally, if the two voltage ae examined individually, the fault in the moto o in the ECU can be identified. Figue 3.. Cuent in PWM moto eemble DC with ipple (a moto' inductance filte high-fequency enegy fom the PWM dive voltage) Since the ECU i often ued to pefom the cuent contol, it will have incoect epone if the fault exit in eithe the moto o the ECU itelf. Eithe fault will lead to the failue of the automated teeing ytem. Fo example, if the teeing wheel i tuned by human dive, thee will be emf poduced fom the moto accodingly. To keep zeo cuent though the moto cicuit, the ECU ha to take ome eaction. Failed o incoect epone implie the malfunctioned moto/ecu. Figue 3.. illutate thi idea. PWM Signal Lowpa Cicuit Meaued Output Fault Detection Algoithm Faulty o nomal Deied Output / Contol Goal Fault Detection Algoithm Figue 3.. Schematic of fault detection Figue 3..3 how the compaion between the meaued epone fom the teeing actuato ECU and the angula peed of the moto time the nominal back emf contant. Thi wa pefomed unde the lage toque inuoidal input at 9 Hz by utilizing the

51 eaction moto. A can be een, the voltage geneated fom the ECU follow the deied ignal well. Thi implie the etimated back emf contant, K, i appoximately equal to the nominal value, K. b ˆ b Figue 3..3 Voltage and Time (the olid line epeent fo the deied voltage baed on the model and the dah line tand fo the actual output fom ECU) Howeve, in mot ituation on highway the angula peed of the teeing wheel i mall. A the ignal i mall, the noie, the ditubance, and the unmodeled dynamic may contaminate the meaued ignal ignificantly. Figue 3..4 ketche the deied and the meaued ignal unde the mall-input ituation. It i difficult to etimate the back emf contant, K, due to the low ignal-to-noie atio. ˆ b

52 Figue 3..4 Voltage and Time (the olid line epeent fo the deied voltage baed on the model; the dah line tand fo the meaued output fom ECU) In thi tudy, a leat quae algoithm i employed to pefom the fault identification tak. The leat quae algoithm i a imple and obut appoach. Thee ae two eaon fo the populaity of the leat quae etimation theoy. The fit eaon i the eae of computation. The econd i the deiable theoetical popety of being the bet linea unbiaed etimation. Conide the following tatitical model: m d v = θv + (3.3) i i e i d m whee v i and vi ae the deied and meaued voltage, epectively, ei i the noie, and θ i defined to be unity if the ytem i nomal. By minimizing the cot m d function, J( θ) = v θv, the etimation of θ i hown in the following manne: ˆ θls = ( v v ) v v = d* d d* m i i vv d i m i d ( v ) i K b tue b (3.4) ˆ b The etimated back emf contant, K, i detemined given the data in the pat. A hown in figue 3..3 and 3..4, the lage input ha good S/N atio and, conveely, the mall input ha poo S/N atio. Intuitively, it can be infeed that the lage the input ignal i, the fewe the data point ae needed fo the deied accuacy of the etimato. Thi idea can be futhe elaboated a follow. Eq. 3.3 can be ewitten in matix notation: tue vm = vdθ +e % % %, whee e % ~ N(, I ). (3.5)

53 T tue ˆ tue vd ( vdθ + e) tue E[ θls θ ] = E[ % % θ ] T % =. (3.6) vd vd %% v ( v θ + e) v ee v E E E T tue T T ˆ tue d d tue d d [( θls θ ) ] = [( % % ) ] [ ] T % θ = % T%%% = T vd vd ( vd vd) vd vd %% %% %%. (3.7) Eq. 3.6 how that the leat quae etimate i unbiaed and Eq. 3.7 indicate that the algoithm i conitent. By definition, conitent mean that the vaiance will appoach zeo a the length of the data goe to infinity. It implie that the leat quae etimate will convege to the tue value with pobability if the length of the equence i lage enough. The etimation accuacy with a cetain confidence can be achieved by etting the coeponding vaiance. Small ignal need moe ample than lage ignal to each the ame vaiance, i.e. accuacy. Hence, a vaiable time window can be employed to conduct the tak. A fo making deciion, it i often difficult to et a ingle thehold to identify the ytem tatu a faulty o healthy. Single thehold will eaily lead to the poblem of fale alam o mied detection. Let uppoe that figue 3..5 how the pobability denity function of the etimated ytem paamete of the nomal and faulty moto. Given the two pecial cae that the mean value of the actual ytem paamete ae 5 % K tue b and % K tue b, epectively, it i eay to ditinguih the moto tatu by etting a ingle thehold ince the denity function do not ovelap. What if a faulty moto with a mean of the ytem paamete, 8 % K tue b, i alo included in the model et? The ingle thehold will fail in mot cae. Thi example how that the difficultie lie on thee thing: () the etimated paamete epeent the noiy veion of the tue value; () uing ingle thehold will eaily caue fale alam and mied detection; (3) the faulty condition of the moto/ecu ha to be clealy defined. Paticulaly, how can the two moto, with the tue paamete, 99.5 % K and % K tue, be ditinguihed? It implie that thee will be ome gey aea unde which it i not eay to detemine the fault. tue b b

54 Faulty Nomal Pobability Abomal Moto Faulty? Nomal Moto 5% Single Thehold % Etimated back emf contant ( % K ) tue b Figue 3..5 pobability ditibution of nomal and faulty moto ytem paamete Intoducing ome intemediate tate and baic ule can help detemine the ytem fault. Fo example, the fault diagnoi can be conducted by uing the citeia in figue fault _ flag = (Healthy) if m3 > m4 fault _ flag = (Not yet detemined) if m4 > m5 o m > m3 fault _ flag = (Pobably Faulty) if m5 > m6 o m > m fault _ flag = 3 (Faulty) if < m6 o > m m > m > m > > m > m > m > m, m, m3, m4, m5, m6 R,whee i the atio between Kˆ b and K. b m 6 m 5 m 4 m 3 m m Figue 3..6 citeion of the ytem diagnoi Figue 3..7 how the expeimental eult of a nomal moto/ecu combination. Befoe the fit etimation eult come out, the etimate i et to one. The teeing input tat at 6 ec and the fit identified eult how up at.5 ec. The fit eult i delayed by 5.5 ec becaue the magnitude of the input i vey mall,.5 Volt peak to peak, and a wide time window ha to be ued to collect data. Between.5 and ec, the fault flag how not-yet-detemined ince the magnitude of the meaued voltage, dotted line, fa exceed the deied voltage, olid line, fom 8 to.5 ec.

55 Figue 3..7 Moto/ECU in healthy condition Figue 3..8 how the identified eult in a fault cenaio. In thi HIL imulation, the tue back emf contant i et to be 4% of nominal value. The etimated paamete ange fom. to.7. By uing the citeion hown in Figue 3..6, the fault flag doe not how faulty all the time. It alo tay in pobably faulty and not yet detemined ometime. In fact, at thi tage the deciion-making only incopoate the citeion in Figue If ome ule can be intoduced in the deciion-making, the pobability of fale alam and mi detection will geatly deceae. The baic ule ae concluded a follow: I. Vehicle automation i allowed if the ytem tatu emain nomal within a cetain time peiod. II. If the ytem tay in the pobably-faulty tatu fo a long time and the powe of the deied ignal exceed ome value, the condition will tun out to be faulty. III. If the tatu i not-yet-detemined fo ome time and if the ignal powe in the time window i lage than a cetain quantity, it will be et to pobablyfaulty. IV. If the ytem tatu fall into faulty, the ytem will be identified a faulty and a waning ignal mut be given.

56 Figue 3..8 Moto/ECU in faulty condition 3..6 Concluion A hadwae-in-the-loop imulation ha been developed fo tudying the fault detection of the teeing actuato. The imulation mimic mot oad-vehicle inteaction and ytem eaction though the teeing mechanim. The detection i model-baed, utilizing onboad eno to collect input and output datum. The leat quae algoithm i utilized to pefom the ytem identification tak. The multiple-thehold method incopoated with the baic ule can be ued to detemine the fault with the leat poibility of fale alam. 4. Demontation of peciion docking ytem Two demontation have been pefomed with the 4 ft bu: the fit one at Wahington DC on June, the econd one i at San Diego on Augut. 4. Peciion Docking cenaio in Wahington DC Peciion docking demo cenaio in Wahington DC i hown in Fig. 4.. Bu tat at the beginning of the docking cuve diven manually. Duing the taight-line egment,