A MODEL BASED SUPERVISION SYSTEM FOR THE HYDRAULICS OF PASSENGER CAR BRAKING SYSTEMS Harald Straky, Marco Münchhof, Rolf Isermann

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1 Copyrght IFAC 15th Trennal Wod Congress, Barcelona, Span A MODEL BASED SUPEVISIO SYSTEM FO THE HYDAULICS OF PASSEGE CA BAKIG SYSTEMS Harald Straky, Marco Münchhof, olf Isermann Insttute of Automatc Control Laboratory of Control Engneerng and Process Automaton Darmstadt Unversty of Technology Landgraf-Georg-Str. 4, D-6483 Darmstadt, Germany Phone: , FAX: { hstraky, mmuenchhof, rsermann}@at.tu-darmstadt.de Abstract: Ths paper presents the desgn of a model-based supervson and dagnoss system for hydraulc and future electro-hydraulc passenger car brakng systems. A state space model of the brakng system has been derved, whch allows calculaton of the ndvdual wheel brake cylnder pressures as well as the amount of brake ud consumed due to faults n the brakng system. Based on ths model, a real-tme supervson system has been developed, whch allows eay detecton and dagnoss of leakages and ar entrapments n the hydraulc subsystem. Ths supervson system only requres data of sensors whch are already avalable n modern passenger cars. Copyrght IFAC Keywords: brakes, hydraulc, electro-hydraulc, fault detecton, fault dagnoss 1. ITODUCTIO The spatal (hardware-based) and functonal (software-based) ntegraton of control systems sgnfcantly mproved the functonalty of hydraulc brakng systems (Fennel, 1998; Kesewetter et al., 1997; van Zanten et al., 1998). Systems such as antlock brakng (ABS), tracton control (TCS), electronc stablty program (ESP) or the brake assstant (BAS) transform the conventonal hydraulc brakng system nto a complex mechatronc system, whch actvely supports the drver n crtcal stuatons, thus ncreasng actve drvng safety sgnfcantly. The ant-lock system supports the drver by controllng the wheel slp durng brakng maneuvers. A wheel lock up s prevented, ensurng that the car remans maneuverable even durng dffcult brakng maneuvers. The tracton control systems prevents wheel spn, whch would cause a loss of tracton and at the same tme endanger vehcle stablty. The electronc stablty package supports the drver n crtcal lateral dynamc drvng stuatons. A yawng torque s exerted by selectvely brakng ndvdual wheels, thus keepng the vehcle on the desred path. The brake assstant supports the drver n emergency brakng, by automatcally applyng the brakes fully, thus submttng all four wheels to ABS slp control. The hgh level of control authorty mparted to these securty system necesstates permanent montorng of all components. Measures cuently mplemented nclude actve tests upon engne start and valdty checks of sensor and actuator sgnals. Sensor faults and faults of the electroncs such as short crcuts and breaks can be detected relably. Upon detecton of a fault, the control system s shut down, leavng the drver wth the conventonal hydraulc brakng system. Although the hydraulc system serves as a transmsson path for all control commands ssued by the control systems and although the brakng system s the last back-up level, t s the only subsystem that s not montored n cuent desgns. The only securty measure s a redundant desgn whch dvdes the breakng system nto two separate crcuts. If one breakng crcut drops out, the other crcut stll remans functonal provdng 5% of the normal breakng power. Ths causes an elongaton n the breakng dstance and can gve rse to unexpected lateral behavor. esearch caed out at the Unversty of Technology at Darmstadt has shown that nuences of breakng system faults on vehcle dynamcs cannot be compensated by the average drver (Straky et al., 1). Even small faults can have severe consequences: For example, sprayng brake ud can drench the brake dsk, drastcally reducng cton and thus the force that can be generated by the brake.

2 These ssues show that eay detecton of small faults of the hydraulc system s of major mportance. The man causes of brake system falures are leakages, ar and water entrapments. Water nclusons are harmful because of vaporzaton. Most defects are due to wearout (e.g. porous or cut-through hoses), ncoect mantenance (e.g. ar entrapments) or neglected mantenance (e.g. water nclusons). The paper wll descrbe the desgn of a fault detecton and dagnoss system for hydraulc brakng systems. Frst, a model of the hydraulc brakng system s derved. In the followng, ths model wll be used to generate reference values for the amount of brake ud consumed by the brakng system. The model wll be fed by pressure sensors mounted at the master brake cylnder. The effectve amount of ud consumed s determned om the vacuum brake booster daphragm dsplacement. Thus, one can obtan two dfferent values for the volume consumed by the brakng system. The dfference between these two volumes ndcates the presence and the severty of a fault. In addton to ths nformaton, the system s also able to dstngush between ar nclusons and leakages. A coelaton analyss based technque s used for the fault classfcaton. umercal examples prove the feasblty of the chosen approach, the fdelty of the brake system model and the accuracy of the fault detecton and classfcaton methods.. THEOETICAL MODEL In ths secton, a model of the brakng system wll be derved. The nternal dynamcs of the ABS/ESP system are not taken nto account. For the hydraulc unt, only those control valves are modeled, whch are open durng normal drvng operaton. ormal operaton wll refer to the ABS havng no control authorty over the pressure buldup. A schematc vew of the smplfed hydraulc crcut s presented n Fg. 1. The mechancal desgn already offers a certan degree of fault tolerance, because the hydraulc system has been dvded nto two brake crcuts, each actng on two of the four wheel brakes. Two dagonally opposng brake cylnders are nterconnected nsde the hydraulc unt, thus formng one brake crcut. Each crcut s suppled wth ud om one chamber of the master brake cylnder. The ntermedate pston, located nsde the master brake cylnder, seals the two crcuts. If a pressure loss occurs n brake crcut I, the left return sprng s compressed fully and the ntermedate pston abuts the housng, thereby enablng a pressure buldup n crcut II. On the contrary, f a pressure loss dsables brake crcut II, the push-rod pston wll come nto contact wth the ntermedate pston as the rght return sprng gves way. Ths allows pressurzaton of crcut I. In both cases, the avalable brakng force s halved by the loss of one crcut, whereas the operatng force that the drver must apply remans unchanged. Intermedate Pston Crcut I eservor Push-rod Pston Front Left ear ght Front ght ear Left Check Valve Crcut II Vacuum Brake Booster Master Brake Cylnder Valves n the Hydraulc Unt Hydraulc Lnes Wheel Brake and CheckValve Fg. 1: Schematc Vew of the Hydraulc System Central valves are bult nto the master brake cylnder allowng equalzaton of the ud level due to changes n the temperature or due to worn brake pads. If the brakes are released, the two central valves open and brake ud can be exchanged wth the ud reservor va the snffer holes. Hydraulc lnes conjon the master brake cylnder and the hydraulc unt. Valves n the hydraulc unt can drect the hydraulc ow n dfferent ways. As was already mentoned, the hydraulc unt wll be modeled as beng nactve. In ths mode, the nlet valves are open. In parallel to each nlet valve, there s a check valve, whose task s to expedte releasng the brakes. Four brake lnes transport the brake ud to the wheel brake cylnders. Ths s where the pston presses the cton pads aganst the brake dsks. In conjuncton wth the oatng calper, the pressure dependent clampng forces are generated. More detaled descrptons of hydraulc and electrohydraulc brake systems for passenger cars can be found n (Burckhardt, 1991) and (ITT Automotve, 1995). The hydraulc system wll be modeled as a process wth lumped parameters. Employng the analogy between electrc and hydraulc crcuts (Isermann, 1999; Backe, 199), the brake system can be descrbed by four four-termnal electrc networks (one per wheel brake). In ths model, both brake crcuts are decoupled, as can be seen n Fg.. The pedal force exerted by the drver pressurzes the chambers of the master brake cylnder. Pressure coesponds to voltage n the electrc equvalent crcut dagram. Thus, the pressure sgnals om the sensors are modeled as deal voltage sources. A capactance s connected n parallel to each voltage source capturng the compressblty of the ud enclosed n the master brake cylnder. Upon pressurzaton of the master brake cylnder chambers, brake ud wll be forced nto the wheel

3 brake cylnders. The ow to the ndvdual wheels s denoted as,,, and. p p C Wheel Brake Cylnder C Hydraulc Lnes Front ght Brakng Subsystem L L L, L, Ta, Tr, Check Valve Ta, Tr, Front Left Brakng Subsystem I C II Master Brake Cylnder Chambers C I ear Left Brakng Subsystem Ta, Tr, Check Valve Ta, Tr, L, L, L Hydraulc Lnes L ear ght Brakng Susbsystem C Wheel Brake Cylnder Fg. : Equvalent Crcut Dagram of the Hydraulc Brakng System The nlet valves located nsde the hydraulc unt drastcally reduce the stream area n comparson to the conduts. Therefore, these constrctons represent large hydraulc resstances. Usng Bernoull s equaton, the valves n the hydraulc unt have been modeled as orfces assumng turbulent ow through the valve mouth. The loss coeffcent depends on the drecton of the ow due to the aforementoned check valves. In the equvalent crcut dagram, the dependency on ow drecton has been taken nto account by the ncluson of two dodes and two resstors, Ta, and Tr,, {,,, }, per valve combnaton. The nerta of mass of the ud contaned n the conduts antagonzes any change of velocty. Ths effect s captured by four nductances L. The subsystems, whch embody the transmsson lne characterstcs, also contan lnear resstors, whch replcate the lamnar ow losses n the tubes. The four wheel brake cylnders have been modeled as non-lnear capactances C( V ), whch capture the non-lnear p V characterstcs of the ndvdual brakes. These curves are llustrated n Fg. 3. The runnng of these curves s nuenced by the compressblty of the ud contaned n the brake lnes, the pressure-nduced hose wdenng, the broadenng of the calper and the ar gap between the cton pads and the brake dsk, whch must be traversed by the cton pads f the brakes are engaged. The condensed state space representaton of the entre brakng system s gven as x = a( x) + B u (1) T T y = c x+ d u wth the state vector x = V V V V () ( ) T C p p Pressure n Wheel Brake Cylnder Front ght p / bar Brake Flud Consumed V / cm³ Pressure n Wheel Brake Cylnder rear left p / bar Brake Flud Consumed V / cm³ Fg. 3: onlnear elaton between Pressure Appled at and Volume ngested by the Wheel Brake Cylnder. Left: Front ght Wheel Brake Cylnder ght: ear Left Wheel Brake Cylnder and the state space matrx T, L, 1 L L L C ( V ) T, L, 1. L L L C ( ) ( V a x = ) T, L, 1 L L L C ( V ) T, L, 1 V L L L C ( V ) (3) The nput dstrbuton matrx 1 1 L L B (4) = 1 1 L L s allocatng the nput vector I u =. (5) These two master brake cylnder chamber pressures are recorded by pressure sensors n cuent producton passenger cars. The model output,.e. the amount of brake ud consumed, s determned by the output dstrbuton vector T c = ( ) (6) and the drect transmsson vector T d = C C. (7) ( ) II The turbulent resstance s pecewse constant, assumng the values Ta, for T, =. (8) Tr, for < The ntegrals n the a matrx evaluate to dt = p V,,,, C V ( ) I ( ) { } T (9)

4 All system parameters have been dentfed by analyss of expermental data. These data have been obtaned om measurements at a test-bed as descrbed n (Straky et al., 1) 3. MODEL VALIDATIO Dsplacement Sensor eacton Washer (ubber) Daphragm Magnet elease Swtch Workng Chamber Vacuum Chamber Amount of Flud Dsplaced / cm³ Daphragm Poston / cm Although the amount of lqud consumed by the brakng system cannot be measured, t s stll possble to valdate the model. Valdaton can be caed out by comparng the wheel brake pressure sensor sgnals wth the reconstructed wheel brake pressure, explotng equaton (9). Fgure 4 shows a comparson between smulaton and expermental data for the ont left and rear left wheel. These dagrams not only prove the hgh fdelty of the model, they also llustrate the dfference n dynamcs. Input of the Model: Measured Brake Pressure n the Master Cylnder, Prmary Crcut Chamber, I Output of the Model: Smulated Pressure n the Wheel Brake Cylnder ear Left p Measured Pressure n the Wheel Brake Cylnder Input of the Model: Measured Brake Pressure n the Master Cylnder, Prmary Crcut Chamber, Output of the Model: Smulated Pressure n the Wheel Brake Cylnder Front Left p Measured Pressure n the Wheel Brake Cylnder Fg. 5: Inuence of the eacton Washer on the Calculaton of the Volume Consumed by the Brakng System Once the effectve volume has been obtaned, one can look at the dfference between the reference volume Vef and the actual volume V Act consumed by the brake system. The dfference of these two volumes yelds V Fault,.e. the change n the consumed volume due to faults. A value close to zero sgnals fault-ee operaton, meanng that there are no ar entrapments, no leakages and no unusual hose wdenngs. ear Left, p,meas Front Left, p,meas Eor Eor 5. FAULT MODELIG AD DIAGOSIS Brake Pressure / bar Tme / sec Brake Pressure / bar Tme / sec Fg 4: Comparson of Smulaton and Measurements Left: ear Left Wheel Brake Cylnder ght: Front Left Wheel Brake Cylnder 4. MODEL BASED FAULT DETECTIO The state space system descrbed n the precedng secton allows the calculaton of the amount of hydraulc ud consumed by a fault-ee brakng system. Ths nformaton does not suffce to mplement fault-detecton methods snce no drect measurement of the effectve amount of consumed brake ud s avalable. Ths nformaton must thus be reconstructed. The dsplacement of the push-rod pston coelates to the amount of ud pumped nto the brakng system. Unfortunately, sensory nformaton about the actual locaton of the push-rod pston s not avalable. However, lookng at the cut-away drawng of the vacuum brake booster n Fg. 5, one can see that the reacton washer couples the push-rod pston and the daphragm. The daphragm poston s already sensed n modern passenger cars. Ths nformaton can be transformed usng the daphragm dsplacement-volume consumed relaton shown n Fg. 5. The nonlnearty s ntroduced by the compressblty of the reacton washer whch s made out of rubber. The aforementoned calculaton of V Fault provdes drect nformaton about the severty of a fault. The type of fault,. e. leakage, ar ncluson and so forth, can be determned by employng a coelaton analyss approach. The coelaton coeffcent provdes a measure for the degree of lnear dependency between two sgnals y t. The magntude of the coelaton x() t and () coeffcent s constraned by 1, where a value close to ether -1 or +1 sgnals a lnear relaton between the two sgnals. The coelaton coeffcent for two dscrete sgnals (Papouls, 1991) s gven by ηxy ηx ηy xy =, (1) σxσ y where the mean values are gven as 1 ηxy = x() y() (11) = 1 ηx = x() (1) = 1 ηy = y() (13) = and the standard devatons are and 1 1 σ x = x () x() (14) = = 1 1 σ y = y () y() (15) = = by defnton. denotes the number of samples. Snce the algorthm wll be employed for on-lne

5 fault detecton and dagnoss, a slghtly dfferent calculaton scheme has been mplemented. The sgnfcance of the coelaton coeffcent ncreases wth the number of data ponts. The man advantage of the coelaton analyss over other methods s the fast and easy calculaton, whch s essental for the performance of a real-tme capable fault-detecton and dagnoss system. In order to classfy the fault occued, the procedure needs nformaton about the behavor of VFault n the presence of dfferent types of system eors. Therefore, models of typcal brake system faults wll now be derved. ages can be modeled as orfces. The volume owng through such openngs s gven by VFault = k p p dt (16) k where s the unknown leakage coeffcent and p s the ud pressure at the damaged spot. Ths pressure tself s not known but can be approxmated by the master brake cylnder pressure, thus VFault p p dt. (17) p t p t dt p I () () denotes the atmospherc pressure. Thus, f the loss volume V coelates wth the ntegral of the Fault square root of the excess pressure n one of the man brake chambers, ths would allude to the presence of a leakage. If ar s entrapped n the brakng system, ths ar wll be compressed upon pressurzaton of the brakng system. Isothermal compresson and expanson have been assumed. The equaton of states for deal gasses yelds V t p t = V p, (18) VAr () (), Ar Ar Ar where denotes the volume of the ar entrapment subject to the pressure p Ar. V Ar, denotes the ntal volume at atmospherc pressure p. Upon pressurzaton, the ar nclusons gve way, resultng n more ud beng draned om the master brake cylnder. Ths addtonal volume s gven as VFault = VAr, VAr. (19) par p = VAr, par The actual pressure n the ar entrapments s unknown and also approxmated by the pressure n the master brake cylnder, leadng to p VFault. () p t Based on ths dervaton, the fault dagnoss system wll analyze the coelaton coeffcents I () p VFault, V, p p The st coelaton coeffcent, nclusons, whereas the latter, Ar Fault I (1) Ar, sgnals ar, reacts on leakages. Fgure 6 shows the structure of the model based fault detecton and dagnoss system, whch has been developed n ths paper. Drver FAULT DETECTIO FAULT DIAGOSIS Brake Actuaton onlnear Statc Model of the eacton Washer V = f ( x ) act 1 Severance Type x m d V act V ref esdue: r = V Fault Loss Volume V Fault I x d Sensor Data Avalable x d I I Θ as Analytcal Symptom onlnear Dynamc Hydraulc Brake System (Eghth Order State Space Form) I x = a( x) + B T T I Vref = c x + d p I Fault Dagnoss Usng Coelaton Analyss p () () I t p = () Ar VFault t, t = VFault, p dt amb ( ) Poston of Daphragm n Vacuum Brake Booster Pressure n Master Brake Cylnder Chamber, Brake Crcut II Pressure n Master Brake Cylnder Chamber, Brake Crcut I I V Fault I p Fg. 6: Structure of the Model Based Fault Detecton and Dagnoss System 6. ESULTS In ths secton, the performance of the fault detecton and dagnoss algorthm s evaluated. Fgure 7 shows a seres of brake actuatons. The st segment depcts the fault-ee case, whereas the other three segments llustrate the behavor n the presence of faults. The expermental setup has allowed the ncluson of two knds of faults, namely ar entrapments and leakages. To summarze the fndngs, faulty behavor has always been detected very eay and relably. Upon detecton of a fault, on-lne calculaton of the coelaton coeffcents wll be ntated. Fgure 7 dsplays the development of both coelaton coeffcents and the volume V over tme. Fault As was already stated, the st case llustrates the fault ee case. For the second brake actuaton, the coelaton coeffcent Ar s larger than. The dagnoss system wll thus conclude that there s ar entrapped n the system. The next segment llustrates the effects of ncludng a leakage. ow, the coelaton coeffcent s much larger than Ar, whch dmnshes over tme. The fault dagnoss system would consequentally report a leakage to the drver.

6 For the fourth and last brake operaton, the coelaton coeffcent runs back to zero after ts ntal jump to +1. The other coelaton coeffcent goes to 1 and remans there. ecallng that values of both +1 and 1 ndcate coelaton, the fault would coectly be classfed as an ar entrapment. Mode of Operaton: Force Force Force Dsplacement Bult-In Fault: one 1,55 cm³ Ar Front Left 1,5 cm³ age Front ght 1,6 cm³ Ar Fault Dagnosed: one 1,45 cm³ Ar 1,15 cm³ age 1,55 cm³ Ar Sgnals Suppled to the Dagnoss System Model Based Fault Detecton Analyzng Analyatcal Symptoms Fault Dagnoss Measured Daphragm Dsplacement / mm Measured Brake Pressure / bar Calculated Loss Volume / cm³ Coelaton Coeffcent Actuaton 1 Actuaton Actuaton 3 Actuaton 4 Ar Fault Detected Fault Detected Fault Detected Tme / sec Fg. 7: On-lne Fault Detecton and Dagnoss effectve amount of ud consumed s calculated om the dsplacement of the vacuum brake booster daphragm. Two common types of faults are classfed, ar nclusons and leakages. Classfcaton s accomplshed by employng a coelaton analyss scheme. The man advantage of ths method s the small computatonal expense resultng n real-tme capablty of the algorthm. The supervson system only requres data of sensors whch are already avalable n modern passenger cars. Due to the lkeness of hydraulc and electrohydraulc brakng systems, t s easly possble to use the presented methods to cover electro-hydraulc brakng systems as well. Here, one can use more afuent sensor sgnals, snce all four wheel brake pressures and the pressure and volume stored n the accumulator are sensed. These addtonal nformaton allow wheel-ndvdual fault detecton and dagnoss. Upon detecton, dagnoss and localzaton of faults, the system can ntate countermeasures such as for example nform the drver about necessary mantenance or repar work. Ths paper contrbutes enormously to an ncrease n drvng safety of passenger cars. 7. COCLUSIOS Ths paper dscussed the desgn of a model-based fault detecton and dagnoss system. It was llustrated how the functonal ntegraton of analytcal process knowledge can expand the functonalty of a mechatronc system by provdng the drver wth nformaton about the state of the brakng system and by warnng hm of arsng eors, whch mght eventually lead to accdents. Frst, a model of the hydraulc brakng system was derved. Ths development was based on the analogy between hydraulc and electrc crcuts and resulted n an eghth order non-lnear system. All parameters have been dentfed om measurements at a brakng system test-bed. Comparsons of smulatons and expermental data have proven the hgh fdelty of the model. Based on ths model, a fault detecton and dagnoss system has been mplemented, whch allows eay detecton, dagnoss and localzaton of small, drftng faults such as leakages or ar entrapments n the hydraulc system. Ths fault detecton and dagnoss procedure supervses the amount of brake ud consumed by the brake system. The reference value s generated by utlzng the aforementoned brake system model, whch s fed by pressure sensors mounted at the master brake cylnder chambers. The EFEECES Backé, W. (199): Grundlagen der Ölhydraulk, Voesungsumdruck der WTH - Aachen Burckhardt, M. (1991): Bremsdynamk und Pkw- Bremsanlagen, ehe Fahrwerktechnk, Vogel Fachbuch. Fennel, H. (1998): En Konzept zur Beheschung der Fahrdynamk, Automobltechnsche Zetschrft ATZ 1, 3 ff. Isermann,. (1999): Mechatronsche Systeme, Sprnger Veag. ITT-Automotve (1995): Bremsen Handbuch - Elektronsche Bremssysteme, Autohaus-Veag. Kesewetter W., Klnkner W., echelt W., Stener M. (1997): Der neue Brake-Assst von Mercedes- Benz, Automobltechnsche Zetschrft ATZ 99, S. 33 ff. Papouls, A. (1991): Probablty, andom Varables and Stochastc Processes 3rd Edton, Boston WCB/McGraw-Hll. Straky, H., Kochem, M., Schmtt, J., Hld,., Isermann,. (1). Inuences of Brakng System Faults on the Vehcle Dynamcs. 3 rd IFAC Workshop Advances n Automotve Control, 8 th - 3 th March 1, Kasruhe, Germany. van Zanten A., Erhardt., Landesfend K., Pfaff G. (1998): VDC System Development, Internatonal Congress & Exposton SAE, 3-6 February, Detrot.