Design of Model-based Controller with Disturbance Estimation in Steerby-wire

Transcription

1 Desig of Model-based Cotroller with Disturbace Estimatio i Steerby-wire System Saghu Jug 1, Seibum Choi 1,a 1,1a KAIST, Departmet of Mechaical Egieerig, Daejeo, Republic of Korea Abstract. The steer-by-wire system is a ext geeratio steerig cotrol techology that has bee actively studied because it has may advatages such as fast respose, space efficiecy due to removal of redudat mechaical elemets, ad high coectivity with vehicle chassis cotrol, such as active steerig. Steer-by-wire system has disturbace composed of tire frictio torque ad self-aligig torque. These disturbaces vary widely due to the weight or frictio coefficiet chage. Therefore, disturbace compesatio logic is strogly ruired to obtai desired performace. This paper proposes model-based cotroller with disturbace compesatio to achieve the robust cotrol performace. Targeted steer-by-wire system is idetified through the experimet ad system idetificatio method. Moreover, model-based cotroller is desiged usig the idetified plat model. Disturbace of targeted steerby-wire is estimated usig disturbace observer(dob), ad compesate the estimated disturbace ito cotrol iput. Experimet of various scearios are coducted to validate the robust performace of proposed model-based cotroller. 1 Itroductio X-by-wire (XBW) system is beig itroduced i the future automotive as the ext geeratio automotive cotrol system [1]. XBW system is beig developed to provide the driver with the coveiece of drivig, steerig, ad brakig. With this tred, Steer-by-wire (SBW) system is a future-orieted ext-geeratio steerig system with a large attetio i the automotive idustry. I SBW system, mechaical ad hydraulic elemets are removed. Ad electrical sigal ad actuator is used to cotrol the steerig system. Therefore, a driver ad a wheel physically separated completely. There are two mai issues i SBW system cotrol. First issue is applyig reactio torque to the driver to improve the steerig feel. Due to the separatio betwee driver ad wheel, driver caot feel the road iformatio from wheel. Therefore, may studies are udergoig to apply reactio torque to compesate the steerig feel. Secod issue is obtaiig high cotrol performace. Due to the separatio, SBW system must have high trackig cotrol performace. I previous works, developig SBW cotrol system is maily focused o first issue ([], [3], ad [4]). Most of papers use simple PID cotroller as lower level cotroller to obtai the trackig performace. I the paper that proposes a cotroller that respods more strogly to disturbaces, frictio torque ad self-aligig momet are modeled ad added as feedforward term. However, this paper assumes that frictio coefficiet betwee road ad wheel ad vehicle body weight is costat. However, o vehicles with a light weight, such as micro-mobility, weight chages i wide rage depedig o the umber of passegers. I additio, frictio coefficiet betwee road ad wheel varies wide rage with the road coditio [5]. As a result, frictio torque ad self-aligig momet varies i wide rage. Because of this variatio of disturbace torques, costat feedforward term will ot compesate eough for disturbace. This paper proposes the robust lower level cotroller for SBW system. Targeted SBW system is modeled ad idetified through experimet results. Idetified model is used to costruct model-based cotroller. By usig the model-based cotroller, we ca achieve the fast respose i trasiet iput. Also, the frictio torque ad the selfaligig momet varyig i a large rage are treated as system disturbaces. Ad we costruct the disturbace observer (DOB) to estimate the system disturbaces ad compesate it to the cotrol iput. Thus, disturbace is rejected ad we ca achieve the robust cotrol for various sceario. Proposed cotroller is validated through experimet usig SBW system of 3-wheeler micromobility. Experimets are carried out accordig to the three road coditios that idicate frictio torque varies. Results show that frictio torque is well estimated, ad performace of proposed cotroller is guarateed regardless of road coditio. The rest of this paper is orgaied as follows. Sectio presets the system modelig ad idetificatio method. Experimetal setup, idetificatio results are preseted i this sectio. Sectio 3 presets the model-based cotroller with disturbace estimatio desig. Experimetal result of proposed cotroller is presets i sectio 4. Coclusio is provided i sectio 5. a Correspodig author: sbchoi@kaist.ac.kr The Authors, published by EDP Scieces. This is a ope access article distributed uder the terms of the Creative Commos Attributio Licese 4.0 (

2 MATEC Web of Cofereces Steer-by-wire System Modelig & Idetificatio.1 System descriptio I this paper, SBW system of light weigh 3-wheeler micro mobility is targeted. Targeted vehicle operated by frot i-wheel motors, ad 1 rear steerig motor. To aalyse ad validate the proposed cotroller, we costruct the test bech as Figure 1. Overall cotrol algorithm is costructed usig Matlab & Simulik. Costructed cotroller is built i to the MicroAutoBox to geerate the cotrol iput ad receive the measuremet data. () s KG( S) K () s 1 KG( S) I s B s K d Where is commaded steerig agle, is actual d steerig agle, ad K is the feedback gai of closed loop system. To aalye the fruecy respose of the system, we apply 0 to 5 H sie wave as commad iput. Figure show the commad iput ad followig results. Through fruecy respose of the system, we use the empirical trasfer fuctio estimate(etfe) to estimate the trasfer fuctio. Usig the discrete fourier trasform (DFT), we compare the ratio phase betwee commaded iput ad acutal ouput agle. As a results, we ca calculate the bode plot form experimet data ad use it to the system idetificatio. Figure 3 shows the result of ETFE. We apply the commad iput i 0 to 5 H, so we do ot use the iformatio over 5H rage of calculated bode plot. Fially, we ca obtai system parameters I ad B. (5) Figure 1. SBW system hardware ad test bech set up. System modelig & idetificatio Mechaical system of SBW ca modeled as simple d order mass-damper system ([6], [7]). Two BLDC motors drive this system. Torque form motors is trasferred through gearbox ad rotate the steerig wheel. So, we ca summarie the system dyamics uatio as followig uivalet uatio. Figure. Experimet result: Commad ad actual agle for system idetificatio. Where (1) I I NI () s m B B NB (3) s m If we igore the disturbace torque from groud, i.e. T dist = 0, we ca calculate the trasfer fuctio betweet cotrol iput torque T ad steerig wheel agle as follow. () s 1 Gs () T s I s B s () I this research, we costruct the model-based cotroller. Therefore, it is importat to kow the exact model iformatio such as parameters or badwidth. I the uatio (4), system parameters are ukow. Therefore, we use the closed-loop system idetificatio method to estimate the system parameters. The closed loop system trasfer fuctio is calculated as follow. (4) Figure 3. ETFE with idetified bode plot 3 Model-based cotroller desig with disturbace estimatio 3.1 Model-based cotroller desig I previous sectio, targeted SBW system is modeled i d order system ad well idetified. Therefore, we ca costruct the model-based cotroller usig idetified model.

3 Cotrol target of the system is track the real steerig wheel agle to desired commad agle d. Thus, we ca set the error as followig. Ys () T ( SY ) () s T () sds () (10) yr r yd e (6) d Fial cotrol target is to make the error uatio coverge to ero as time passed, error dyamic is costructed as folloig uatio. (7) The order of dyamic uatio of the system is as uatio (1) shows. Geerally, the order of error dyamics follows the system order. But, i this research, targeted system has a feature of wide rage of large frictio. Geerally, frictio i d order system causes the steady-state error. So, we apply the itegral term to the d order error dyamic so that we ca hadle the steadystate error from frictio. Furthermore, we place the pole of gais i sigle poit, we ca tue the gai more coveietly. Combiig system dyamic uatio (1) ad error dyamics (7), we ca orgaie the uatios as follow. (8) The above uatio ca be summaried i terms of u as follow. (9) I above uatio, first part of iput is feed-forward cotrol based o idetified model. Ad T is ukow dist disturbace from groud, ad rest term is formed of PID feedback cotroller. Model-based feed-forward cotroller calculate the cotrol iput from desired commad sigal immediately, it could obtai respose that is much more fast rather tha feedback cotrol oly. If the model is ot accurate, system ca be ustable. However, as show i previous chapter, we assume that system is well modeled ad well idetified. Therefore, we proposed the model-based cotroller. 3. Disturbace estimatio usig disturbace observer I previous sectio, model-based cotroller is costructed. However, the disturbace Tdist is still ukow factor. As metioed before, disturbace of SBW system is domiat factor of cotrol. Thus, disturbace compesatio logic is strogly ruried. I this paper, we use the disturbace observer(dob) to estimate ad compesate the ukow disturbaces. The simple DOB structure of sigle iput sigle output(siso) system is show i Figure 4[8]. The otatio PP, idicate trasfer fuctio of real plat ad omial plat respectively. The fial output y ca represeted as fuctio of referece iput r ad disturbace d as follow. Figure 4. Basic structure ad block diagram of DOB T, T is closed loop trasfer fuctio betweee ry dy r, d ad output y respectively. We ca coclude that if Q-filter Qs ( ) is well desiged, we ca acheive folloig results for low fruecy rage iput uder cutoff fruecy q P() scs () T () s, T () s 0 (11) ry dy 1 P() scs () This result meas that SISO system with disturbace behaves same as omial plat SISO system without disturbace. So disturbace is rejected iterally by disturbace observer. Applyig above result i targeted SBW system, we ca costruct followig euqatios. (1) (13) The estimated disturbacd ˆd is solved by above simultaeous uatios. The result is as follow. (14) Where I ad B represet the differece betwee real ad omial plat. If we assume that system is well idetified so that I B 0, estimated disturbace ˆd coverges to T. Thus, if we combie this result ad dist costructed model-based cotroller i (9), fial form of model-based cotroller is made as follow. (15) Therefore, cotroller composed of model-based feed forward cotroller, disturbace compesatios term, ad feedback cotroller. 4 Experimetal results 3.1 Model-based cotroller desig We coduct the experimet to validate the proposed model-based cotroller with disturbace estimatio. To validate the robust performace of cotroller, we 3

4 MATEC Web of Cofereces costruct the three scearios that represet the various frictio torque-applyig situatio. The disturbaces of SBW system composed of frictio torque ad selfaligig momet as metioed before. However, the experimet oly deals with statioary vehicle scearios, which meas that the disturbace is composed of frictio uiquely. Frictio torque betwee wheel ad road ca be aalyed as follow. T k F (16) fric The otatio k,, ad F represet the costat, frictio coefficiet, ad vehicle vertical load respectively. Equatio (0) implies that frictio torque ca varies by chagig the fircito toruqe coefficiet or vehicle vertical load. Thus, we costruct the three sceario with three differet vehicle vertical loads. Because vertical load is much more easier to measure ad aalye rather tha frictio coefficiet. Table 1 shows the sceario ad situatio that each sceario implies. The case 1 refers to the ormal drivig situatio. The case refers to the system with higher disturbace i the case of high-mu surface or vehicle with heavy load situatio. The case 3 refers to the system with lower disturbace i the case of low-mu surfaces, such as ice or sow road. The case 3 was carried out by liftig the steerig wheel. Figure 5. Experimet results: Sceario 1. Normal drivig situatio. (a) FB oly (b) model-based cotrol with disturbace estimatio. Experimet result for sceario 1 show the effect of model-based cotroller. Oly feedback cotrol, as show i (a), output sigal is lagged ad suppressed due to the frictio. Thus, we ca show that reactio rate is lowered. However, as show i (b), compesatig the model-based feedforward term ad disturbace estimatio results make reactio rate much faster tha (a). Therefore, trackig performace is improved. Table 1. Experimet scearios ad implyig situatio. No. Measured F Case iformatio kgf Normal drivig 145 kgf High-mu surface, loaded vehicle 3 0 kgf Low-mu surface: ice, sow road It ca be said that propsed cotroller has robust cotrol performace if the cotroller performace gurateed through the above scearios with sigle gai ad without additioal gai-schedulig. The experimets are carried out acoordig to the each sceario above applyig the siusoidal wave with 0.3H ad amplitude 30 degree. To cofirm the effect of modelbased feedforward cotrol ad disturbace compesatio logic, we coduct the experimet for each case with two differect cotroller ;(a) oly feedback cotrol, (b) model-based foeedforward cotrol with disturbace estimatio. Cotrol iput of each case is show as follow. (a) (17) (b) (18) Durig the experimet, feedback gais are fixed. The experimet reuslts is show as follows. Figure 6. Experimet results: Sceario. High-mu surface or loaded vehicle. (a) FB oly (b) model-based cotrol with disturbace estimatio. The performace of the proposed cotroller is more promiet i sceario. This sceario implies larger frictio, graph (a) shows the poor trackig performace. Due to the large frictio, system output suppressed a lot ad respose rate becomes low. However, a term that compesates for the disturbace is icluded i the proposed cotroller. Thererfore, cotrol ouput of proposed cotroller shows good perfermace with same feedback gais. 4

5 Miistry of Sciece ad ICT, Korea, uder the Iformatio Techology Research Ceter support program (IITP ) supervised by the Istitute for Iformatio ad commuicatios Techology Promotio, ad the BK1 Plus Program. Refereces Figure 7. Experimet results: Sceario 3. Low-mu surface. (a) FB oly (b) model-based cotrol with disturbace estimatio. Sceario 3 idicates the frictioless system, which meas a system without disturbaces. Frictio torque is the major part of the system as metioed before. Thus, feedback gai is adjusted high-gai. However, if the frictio disappears i that state, the systems becomes ustable as show i (a). As metioed i sectio 3., disturbace observer makes the system to behave as omial plat. Therefore, if the gai is adjusted appropriately so that the omial plat ca operate i stable regio, the proposed cotroller ca obtai good trackig result. The result show i (b). As a results, propsed cotroller ca obtai good trackig performace i various scearios with fixed feedback gai. Therefore, we ca coclude that proposed cotroller has robust cotrol performace i SBW system. Table shows the RMS error for each case of expriemet. Table. RMS error of proposed cotroller No. Measured F RMS error (deg) kgf kgf kgf Y.H.Ki, I.Oh, J.Jeo, J.Chu, H.S.Ah, A ew type of clampig force estimator for electromechaical brake systems, IEEE Trasactios o Mechatroics, Vol.10, December, (005). Yug-Hsiag Judy Hsu, Estimatio ad Cotrol of Lateral Tire Forces Usig Steerig Torque, Ph.D Dissertatio, Staford Uiversity, U.S, (009) 3. Seok-Hwa Jag, Tog-Ji Parkl chag-soo Ha, A cotrol of vehicle usig steer-by-wire system with hardware-i-the-loop-simulatio system, IEEE Trasactios o Mechatroics, Vol.10, December, (005) 4. Hiraku Ogura, Toshiyuki Murakami, Reactio Force Cotrol o Accelerator Pedal ad Steerig Wheel based o Tire-Road Frictio Forces, 35 th Aual Coferece of IEEE idustrial Electroics, (009) 5. Hiraku Ogura, Toshiyuki Murakami, Reactio Force Cotrol o Accelerator Pedal ad Steerig Wheel based o Tire-Road Frictio Forces, 35 th Aual Coferece of IEEE idustrial Electroics, (009) 6. Saket Amberkar, Farhad Bolourcho, A Cotrol System Methodology for Steer by Wire Systems, SAE techical paper series, Steerig ad Suspesio Techology Symposium (004) 7. Paul Yih ad J.Christia Gerdes, Modificatio of vehicle hadlig characteristics via Steer-by-Wire, IEEE Trasactios o Cotrol System Techology, Vol.13, No.6, November, (005) 8. Shihua Li, Ju Yag, We-Hua che, Xisog che, Disturbace Observer-Based Cotrol, Methods ad Applicatios, CRC Press, (014) 5 Coclusio I light weight micro-mobility, disturbace is major part of the SBW system cotrol. Therefore, disturbace compesatio logic was strogly demaded. I this paper, we proposed the model-based cotroller with disturbace estimatio i SBW system. Experimets are coducted to validate the proposed cotroller. Three scearios represetig the various disturbace are selected to validate the robustess of the proposed cotroller. As a result, model-based cotroller with disturbace estimatio obtai robust cotrol performace i various sceario with fixed feedback gai. The results of this research are expected to improve the performace of steerig cotrol of future-micro-mobility vehicle. Ackowledgmet This work was supported i parts by the Natioal Research Foudatio of Korea grat fuded by the Korea govermet (MSIP) (No.017R1AB ), the 5