Improved Battery State Estimation Under Parameter Uncertainty Caused by Aging Using Expansion Measurements
Sravan Pannala, Puneet Valecha, Peyman Mohtat, Jason B. Siegel, Anna G. Stefanopoulou
IImproved Battery State Estimation Under Parameter UncertaintyCaused by Aging Using Expansion Measurements
Sravan Pannala, Puneet Valecha, Peyman Mohtat, Jason B. Siegel, and Anna G. Stefanopoulou
Abstract — Accurate tracking of the internal electrochemicalstates of lithium-ion battery during cycling enables advancedbattery management systems to operate the battery safely andmaintain high performance while minimizing battery degrada-tion. To this end, techniques based on voltage measurement haveshown promise for estimating the lithium surface concentrationof active material particles, which is an important state foravoiding aging mechanisms such as lithium plating. However,methods relying on voltage often lead to large estimation errorswhen the model parameters change during aging. In this paper,we utilize the in-situ measurement of the battery expansionto augment the voltage and develop an observer to estimatethe lithium surface concentration distribution in each electrodeparticle. We demonstrate that the addition of the expansionsignal enables us to correct the negative electrode concentrationstates in addition to the positive electrode. As a result, comparedto a voltage only observer, the proposed observer can success-fully recover the surface concentration when the electrodes’stoichiometric window changes, which is a common occurrenceunder aging by loss of lithium inventory. With a 5% shift inthe electrodes’ stoichiometric window, the results indicate areduction in state estimation error for the negative electrodesurface concentration. Under this simulated aged condition, thevoltage based observer had 9.3% error as compared to theproposed voltage and expansion observer which had 0.1% errorin negative electrode surface concentration.
I. I
NTRODUCTION
Lithium-ion batteries are ubiquitous in our portable com-puting devices and are playing a major role in the futureof transportation with the transition to electric vehicles. Tomaintain a balance between power/energy demands and costit is important to have an advanced battery management sys-tem that operates the battery safely, close to its limits, whileminimizing the degradation. Accurate models and state esti-mation techniques are required to achieve this performance.The battery models can be classified as Equivalent circuitmodels (ECMs) and Electrochemical models (EMs). ECMsare widely used in battery management system of electricvehicles because of their computational efficiency and stateestimation using ECMs has been widely investigated [1], [2].Electrochemical models describe the chemical phenomenaoccurring inside the battery and thus capture the internalstates of a battery, making them suitable for advancedbattery control algorithms. Constraints on internal states likenegative solid-surface concentration are required to preventdegradation mechanisms like Lithium plating during high
S. Pannala, P. Mohtat, J.B. Siegel, & A.G. Stefanopoulou are with theDepartment of Mechanical Engineering, University of Michigan, Ann Arbor,MI 48109 { spannala,pmohtat,siegeljb,annastef } @umich.edu P. Valecha is with the Powertrain OBD Calibration, Fiat Chrysler Auto-motive, Chelsea, MI [email protected]
C-rate charging. Full order EMs like Doyle-Fuller-Newmanmodel predict these internal states accurately, but at theexpense of computational effort. Reduced order models, likeSingle Particle Model (SPM), are often used in battery stateestimation and control. The SPM assumes a uniform currentdensity across the electrodes and neglecting the electrolytedynamics, and thus the electrode can be modeled as a singlerepresentative spherical particle. More recently, the SPMwith electrolyte dynamics (SPMe) has been developed whichgives better prediction accuracy compared to SPM.Various observers haven been developed for these reducedorder models [3], [4]. In these observers voltage measure-ment is used to estimate the positive electrode states andthe negative electrode states are indirectly calculated byusing conservation of lithium in the battery [5], since thepositive electrode states are more observable from the voltagemeasurement [6]. Thus, these observers are prone to largeestimation errors when there is model parameter drift dueto aging as the assumption of conservation of lithium nolonger holds and hence a single measurement of voltage isinsufficient to determine both electrode states [7].Lithium intercalation and de-intercalation results in volu-metric changes in both electrodes of a Li-ion battery and de-pends on the concentration distribution across the electrodes.These changes can be measured either by the bulk force [8]or expansion measurements [9] and provide better means toestimate the State of Charge [10] and the State of Health [11]of the battery. There are challenges in utilizing mechanicalmeasurement which include difficulties in instrumenting theforce/expansion sensors in packs and additional sensor cost.This paper develops an observer which uses voltage,expansion and temperature measurements to estimate theindividual electrode particle concentrations. We build on thestate estimators based on voltage error injection to estimatethe concentration in positive electrode particle proposed in[5], and augment the algorithm using the expansion errorinjection to estimate the negative electrode particle concen-tration. With the increase in the number of measurementsignals, improvement of the estimator’s performance undercertain types of model parameter changes was achieved.II. M
ODEL D EVELOPMENT
The battery model presented in this paper is based on theSPM with electrolyte. Additionally a lumped thermal modeland concentration dependent expansion is considered. a r X i v : . [ ee ss . S Y ] S e p . Single Particle Model with Electrolyte The SPMe is a commonly used control-oriented electro-chemical model for the lithium ion battery. It approximatesthe full order Doyle-Fuller-Newman (DFN) model under lowcurrent operation, where the electrode intercalation reactionis uniform across the electrode thickness and decoupledfrom changes in electrolyte concentration. In this case, thevoltage dynamics are dominated by the solid-phase diffusionof lithium. This solid phase diffusion is modeled by usingelectrodes with a single representative spherical particle.Eqs. (1) to (3) show the diffusion equation for a sphericalparticle along with the requisite boundary conditions at thecenter and the surface of the particle. ∂c s ∂t ( r, t ) = 1 r ∂r (cid:20) D s r ∂c s ∂r ( r, t ) (cid:21) (1) ∂c s ∂r (0 , t ) = 0 (2) D s ∂c s ∂r ( R p , t ) = − j ( t ) (3) j = Ia s lA (4)Here j is the intercalation current density which is given byEq. (4), where A is the area, l is thickness of the electrodeand a s = 3 ε s /R p is the surface area to volume ratio of activematerial particles. We then use the Bulter-Volmer equationEq. (5) to solve for the overpotential of the intercalationreaction η , where i is the exchange current density Eq. (6), c ss ( t ) = c s ( R p , t ) is the concentration at the surface of theparticle, the k is the reaction rate constant, and the ( α a , α c )are the charge transfer coefficients. j ( t ) = i ( t ) F (cid:16) e αaFRT η − e − αcFRT η (cid:17) (5) i ( t ) = k ( ¯ c e ( t )) α ( c s,max − c ss ( t )) α ( c ss ( t )) α (6)The electrolyte diffusion equations are derived based onthe assumptions in [5] with boundary conditions: the conti-nuity of c e , and ∇ c e (0 , t ) = ∇ c e ( l t , t ) = 0 . (cid:15) e ∂c e ∂t ( x, t ) = ∇ . ( D effe ∇ c e ( x, t ))+ 1 − t F × I ( t ) l − ≤ x < l − , l − ≤ x ≤ l − + l s , − I ( t ) l + l − + l s < x ≤ l t , (7)where l t = l − + l s + l + . The liquid-phase Ohm’s law isshown in Eq. (8). i e ( x, t ) = − κ eff ∇ Φ e ( x, t ) + 2 κ eff RTF (1 − t ) (cid:18) d ln f ± d ln c e ( x, t ) (cid:19) ∇ ( ln c e )( x, t ) (8)Integrating and applying the boundary condition results in Φ e ( l, t ) = − (cid:18) l − (cid:15) − ) brugg + l s ( (cid:15) s ) brugg + l + (cid:15) + ) brugg (cid:19) I ( t ) κ + 2 RTF (1 − t ) t f ( ln c e ( l t , t ) − ln c e (0 , t )) (9) where the concentration dependence of the κ is neglected forsimplicity, and the term t f = (cid:16) d ln f ± d ln c e ( x, t ) (cid:17) is assumedto be constant.The initial concentrations of the electrodes are given by c + s, = c + s,max ( SOC × ( y − y ) + y ) (10) c − s, = c − s,max ( SOC × ( x − x ) + x ) (11)where SOC is the initial state of charge, c s,max is themaximum particle concentration, y , y are the positiveelectrode stoichiometric windows and x , x are the nega-tive electrode stoichiometric windows defined by the voltagelimits and electrode physical dimensions [12].Finally the terminal voltage of the battery is given byEq. (12) where U is the half-cell open circuit potential, and V R ( x, t ) = R f F j ( x, t ) is the voltage drop due to the filmresistance. V t ( t ) = h v ( c + ss , c − ss , c e , I ( t )) = η + ( t ) + U + ( c + ss ( t ))+ V + R ( t ) − η + ( t ) U − ( c − ss ( t )) − V − R ( t ) + Φ e ( l t , t ) (12) B. Thermal Model
The thermal model used in this paper is a one-state lumpedmodel for battery temperature, C th dT b dt ( t ) = − h ( T b ( t ) − T a ( t ))+ I ( t )( U + ( c + ss ( t )) − U − ( c − ss ( t )) − V t ( t )) (13)where C th is the lumped heat capacity, T a is the ambient airtemperature, h is the heat transfer coefficient, and the onlysource of heat generation inside the battery is joule heating.The effect of Entropic heating can be ignored at the C-ratesof interest. C. Expansion Model
The expansion model used in the paper is based on themodel used in [9].
1) Intercalation induced expansion:
The displacement atthe surface of the particle is obtained by solving stress strainrelationship in the particle with intercalation expansion asdetailed in [9] is given by Eq. (14). u R ( t ) = 1( R p ) (cid:90) R p ρ ∆ V ( c s ( ρ, t )) dρ (14)where ∆ V ( c s ( r )) is the particle expansion function in termsof volumetric strain.
2) Electrode Expansion:
The electrode in a Li-battery ismade of active material, binder and conductive material.In our model we assume that the expansion of electrodecomponents other than the active material to be negligible.We further assume that the electrode only expands in thethrough-plane direction. Using the displacement at the sur-face of particle shown in Eq. (14) and the above assumptions,we obtain the change in electrode thickness: ∆ t = a s lu R ( t ) (15) ) Thermal Expansion: The lumped thermal model inSection II-B, is used to predict the thermal expansion, whichis given by ∆ t th = α th ( T b − T ) . (16)Here α th is the thermal expansion coefficient and T isthe reference temperature, and T b is the battery temperaturegiven by Eq. 13.
4) Total Expansion:
The total electrode expansion is thesum of the expansion of individual electrodes. Pouch cellLi-ion batteries contain multiple layers, So the single layerexpansion is multiplied by the number of layers to find thetotal expansion. Also the cell level expansion is influencedby separator, current collectors and casing. The elasticity ofthese layers are approximated with a linear spring. The totalelectrode expansion is given by Eq. (17), where κ b is tuningparameter. ∆ t e = κ b (∆ t + + ∆ t − ) (17)Now we calculate total battery expansion: ∆ t b = ∆ t e + ∆ t th (18)where the total expansion is calculated by adding the totalelectrode expansion and the thermal expansion.III. O BSERVER D ESIGN
The block diagram of the observer is shown in Fig. 1.Sections III-A to III-C are adopted from [5] and are brieflydescribed below.
A. Positive Electrode Observer
The positive electrode observer uses a copy of model andinjects boundary state error as shown in Eqs. (19) to (21) ∂ ˆ c + s ∂t ( r, t ) = D + s (cid:20) r ∂ ˆ c + s ∂r ( r, t ) + ∂ ˆ c + s ∂r ( r, t ) (cid:21) + p + ( r ) [ˇ c + ss − ˆ c + ss ] (19) ∂ ˆ c + s ∂r (0 , t ) = 0 (20) ∂ ˆ c + s ∂r (cid:0) R + p , t (cid:1) = I ( t ) D − s F a − s l − + p +0 [ˇ c + ss − ˆ c + ss ] (21)where ˇ c + ss is inverted surface concentration calculated usingEq. (28). The observer gains are derived with the backstep-ping approach: p + ( r ) = − λD + s R + p z (cid:20) I ( z ) − λz I ( z ) (cid:21) (22) z = (cid:115) λ (cid:18) r ( R + p ) − (cid:19) (23) p +0 = 12 R + p (3 − λ ) , for λ < (24)where I ( z ) and I ( z ) are first and second order modifiedBessel functions of the first kind, and λ controls the eigen-value locations and determines the convergence rate. Fig. 1. Observer Schematic Diagram. The positive electrode observerdepends on the inverted surface concentration ˇ c + ss from the voltage inversionblock which uses measured battery terminal voltage V t . The voltage inver-sion depends on the open loop Electrolyte concentration estimate ˆ c e . Theestimated positive electrode concentration ˆ c + s is then used in the expansioninversion block in combination with the measured battery temperature T b and expansion ∆ t b to inform the negative electrode observer ˆ c − s usinginverted negative electrode average concentration ˇ c − s,avg . B. Voltage Inversion
In this section we use a nonlinear gradient algorithm whichestimates ˇ c + ss by inverting the nonlinear V t output functiongiven in Eq. (12). V t ( t ) = h v ( c + ss , t ) (25)The dependency of this nonlinear output function on c − ss , Φ e and I ( t ) is suppressed to a single dependence on t . We nowdefine inversion error signal e V ( t ) in Eq. (26) and regressorsignal φ v ( t ) in Eq. (27). e v ( t ) = V t ( t ) − h v (ˇ c + ss , t ) (26) φ v ( t ) = ∂h v ∂c + ss (ˇ c + ss , t ) (27)Gradient update law for ˇ c + ss is given by Eq. (28), where γ v is a tuning parameter. ddt ˇ c + ss = γ v φ v ( t ) e v ( t ) (28) C. Electrolyte Observer
The electrolyte observer used is a open-loop observerwhich has the same form as the model. The equations of theobserver are provided in Eq. (29) with boundary conditions:the continuity of ˆ c e , and ∇ ˆ c e (0 , t ) = ∇ ˆ c e ( l, t ) = 0 . (cid:15) e ∂ ˆ c e ∂t ( x, t ) = ∇ . ( D effe ∇ ˆ c e ( x, t ))+ 1 − t F × I ( t ) l − ≤ x < l − , l − ≤ x ≤ l − + l s , − I ( t ) l + l − + l s < x ≤ l, (29) . Negative Electrode Observer The negative electrode observer uses a copy of model andinjects c − s,avg error as shown in Eqs. (30) to (32) ∂ ˆ c − s ∂t ( r, t ) = D − s (cid:20) r ∂ ˆ c − s ∂r ( r, t ) + ∂ ˆ c − s ∂r ( r, t ) (cid:21) + k − (cid:2) ˇ c − s,avg − ˆ c − s,avg (cid:3) (30) ∂ ˆ c − s ∂r (0 , t ) = 0 (31) ∂ ˆ c − s ∂r (cid:0) R − p , t (cid:1) = − I ( t ) D − s F a − s l − (32)where k − is the feedback gain which determines the sys-tem stability and convergence rate. Note by comparisonof Eqs. (21) and (32), the anode observer does not adjustthe estimate of the concentration gradient, only the averagevalue, and relies on the open loop dynamics for predictionof the concentration gradient. E. Expansion Inversion
We use the expansion measurement ∆ t b and the temper-ature measurement T b to estimate the average negative elec-trode concentration ˇ c − s,avg . The steps followed are describedbelow.
1) Estimating negative electrode particle displacement:
We start by first estimating the thermal expansion by usingthe battery temperature measurement. ∆ˆ t th = α th ( T b − T ) (33)Then we use the positive electrode observer states ˆ c + s ( t ) toestimate positive electrode expansion ∆ t + . ˆ u + R ( t ) = 1( R + p ) (cid:90) R + p ρ ∆ V (cid:0) ˆ c + s ( ρ, t ) (cid:1) dρ (34) ∆ˆ t + = a + s l + ˆ u + R ( t ) (35)Both of these estimates are used to estimate the negativeelectrode expansion as shown in Eq. (37). ∆ˇ t e = κ b (cid:0) ∆ˇ t − + ∆ˆ t + (cid:1) = ∆ t b − ∆ˆ t th (36) ∆ˇ t − = ∆ t b − ∆ˆ t th κ b − ∆ˆ t + (37)Finally the particle displacement at the surface is by ˇ u − R ( t ) = ∆ˇ t − a − s l − . (38)
2) Estimating negative electrode average concentration:
In this section we develop a way to estimate average nega-tive electrode concentration from negative electrode particledisplacement. To start, we first define a new variable ˜ c − s inEq. (39). ˜ c − s ( r, t ) = ˆ c − s ( r, t ) − ˆ c − s,avg (39)where ˆ c − s,avg is the average negative electrode concentrationof the observer states calculated in Section III-D . We now use the ˜ c − s ( r, t ) , ˇ u − R ( t ) from Eq. (38) and Eq. (14) to es-timate the inverted negative electrode average concentration ˇ c − s,avg ( t ) , by solving ˇ u − R ( t ) = h e (˜ c − s ( r, t ) + c − s,avg ( t ))= 1( R − p ) (cid:90) R − p ρ ∆ V (cid:0) ˜ c − s ( ρ, t ) + c − s,avg ( t ) (cid:1) dρ. (40)To solve Eq. (40) we implement a gradient update lawsimilar to voltage inversion in Section III-B. We now defineinversion error signal e e ( t ) in Eq. (41) and regressor signal φ e ( t ) in Eq. (42). Gradient update law for ˇ c − s,avg is given byEq. (43), where γ e is a tuning parameter. e e ( t ) = ˇ u − R ( t ) − h e (˜ c − s ( r, t ) + ˇ c − s,avg ( t )) (41) φ e ( t ) = ∂h e ∂c − s,avg (˜ c − s ( r, t ) + ˇ c − s,avg ( t )) (42) ddt ˇ c − savg = γ e φ e ( t ) e e ( t ) (43)This introduces a dynamic coupling between the concentra-tion state observers for the positive and negative electrodes.IV. R ESULTS AND D ISCUSSION
In this section we present the simulation results of theobserver on the plant model. The diffusion equations in themodel and observer are discretized using Method of Lineswith second-order approximation of the boundary conditions[13]. The following observer parameters are used for allsimulations; γ v = 10 , λ = − , γ e = 10 and k − = 0 . .Additional noise is added to voltage and expansion signalswith a standard deviation of mV for voltage and µm forexpansion. A. Constant Current Charge
First we simulate a constant current charge of 1C. Thesimulated battery is initialized with
SOC = 0 . and theobserver with ˆ SOC = 0 . . We can see from Fig. 2 that ˆ V t , ∆ˆ t b , ˆ c − ss , ˆ c − s,avg , ˆ c + ss and ˆ c + s,avg converge. The terminalvoltage ˆ V t converges faster than ∆ˆ t b as ˆ V t depends on ˆ c ss convergence but ∆ˆ t b depends on ˆ c s,avg convergence whichis slower. This is because ˆ c s,avg is a linear combinationof all ˆ c s ( r ) states and convergence of ˆ c s,avg depends onconvergence of all the states including faster and slowerstates. We compare the performance of the Voltage andExpansion based observer (referred to as V+EXP-obs) whichuses voltage, temperature and expansion measurements forwith the one in [5], which uses only voltage measurement(referred to as V-obs). The root mean square percent error(RMSPE) of ∆ˆ t b , ˆ c − ss , ˆ c − s,avg , ˆ c + ss and ˆ c + s,avg estimates afterfive minutes of simulation are given in Table I. While theRMSPE of positive electrode concentration estimates havesimilar values for both V+EXP-obs and V-obs, the RM-SPE of negative electrode concentration estimates is slightlyhigher for V-obs. ig. 2. Simulation results for 1C Constant Current input with SOC =0 . and ˆ SOC = 0 . . (a) Current (b) Voltage (c) Expansion (d) Voltageand Expansion Errors (e) Surface Concentration of both electrodes c − ss , c + ss (f) Average Concentration of both electrodes c − s,avg , c + s,avg . Voltage andexpansion converge to the measured values within 5 minutes. B. Model Drift due to Aging
As the battery ages a number of parameters in themodel drift from their initial values. Hence, it is importantto evaluate the observer performance with uncertainty inparameters. There are number of aging mechanisms thatcontribute to parameter mismatch during aging, namely lossof lithium inventory (LLI) and loss of active material (LAM).It is known that these aging mechanisms affect the batteryparameters like stoichiometric windows in negative electrode x and in positive electrode y , and active material ratioof negative electrode ε − s , which change as the battery ages[14].
1) Stoichiometric Window Change:
First we simulate acase where both x and y are reduced by 5% in the plantdue to aging, and the parameters in observer are unchanged.The observer and plant are initialized as in Section IV-A. Theresults of the simulations are shown in Fig. 3. We can see thatwhile the ˆ c + ss and ˆ c + s,avg converge for both observers, ˆ c − ss and Fig. 3. Simulation results for Stoichiometric Window Drift for Voltageand Expansion observer and Voltage only observer during Constant Currentcharge at 1C rate with
SOC = 0 . and ˆ SOC = 0 . . (a) SurfaceConcentration of both electrodes c − s,s , c + s,s (b) Average Concentration ofboth electrodes c − s,avg , c + s,avg . ˆ c + s converges for both, but ˆ c − s convergesonly for V+EXP-obs. ˆ c − s,avg converges for the V+EXP-obs but not for V-obs. Thisis because additional feedback in V+EXP-obs compensatesfor the model mismatch in the negative electrode parametersresulting in better estimation of ˆ c − s states, while in V-obsthe ˆ c − s states are calculated by using Lithium conservation.Also, this higher ˆ c − s error in V-obs causes higher error in ˆ c + ss as shown in Table I.
2) Active Material Loss:
Next we simulate a 5% paramet-ric error in the negative electrode volume fraction, ε − s dueto aging. The observer and simulated battery are initializedas in Section IV-A. The results of the simulations are shownin Fig. 4. We can see that while the ˆ c + ss and ˆ c + s,avg convergefor both observers, both ˆ c − ss and ˆ c − s,avg do not convergefor V+EXP-obs or V-obs. Also error of ˆ c − s,avg is higher inV+EXP-obs compared to V-obs as seen from the RMSPEvalues given in Table I. This is because ε − s is used in theoutput function inversion of expansion leading to inaccurateestimation of ˇ c − s,avg , thus resulting in inaccurate estimates of ˆ c − s states in V+EXP-obs. C. Summary of Simulation Results
The outputs concentration state estimation errors for ˆ c − ss , ˆ c − s,avg , ˆ c + ss and ˆ c + s,avg , after the initial convergence period,are given in Table I. These errors are calculated with thevalues after five minutes to simulations to normalize initial-ization errors across the simulations. The negative electrodeconcentrations ˆ c − ss and ˆ c − s,avg of V+EXP-obs have slightlylower errors for Constant Current simulation compared toV-obs. For the 1C charge simulation for the aged cell withchange in Stoichiometric window, the concentration errorsfor ˆ c − ss in V-obs is 9.3% which is much higher than 0.1%for V+EXP-obs. Even ˆ c + ss is higher in V-obs. For the ε − s loss ig. 4. Simulation results for Active Material Ratio Drift for V+EXP-obsand V-obs with SOC = 0 . and ˆ SOC = 0 . . (a) Surface Con-centration of both electrodes c − s,s , c + s,s (b) Average Concentration of bothelectrodes c − s,avg , c + s,avg . The estimates of negative electrode concentrationstates ˆ c − s does not converge for either observer.TABLE ISimulation Error in RMSPE (after 5 minutes) ofConcentration Estimates for V+EXP-obs and V-obsEstimates Simulation Error (%)Fresh Cell Aged CellStoich Change ε − s Loss V+E V V+E V V+E V ˆ c − ss † ˆ c − s,avg § ˆ c + ss † ˆ c + s,avg § Stoichiometric window change Active material loss † Negative/Positive electrode surface concentration § Negative/Positive electrode average concentration case all the concentration errors have high values for boththe observers. While ˆ c − ss of V+EXP-obs has error of 6% andV-obs has a slightly lower error of 4.6%, ˆ c − ss of V+EXP-obshas a lower error of 1.1% against 4.6% of V-obs.V. C ONCLUSION
In this paper we have developed a state observer fora physics based single particle Li-ion battery model byaugmenting the voltage measurement with expansion mea-surement. The observer shows improved convergence ofthe concentration states. The observer performance is alsoevaluated against parametric modeling error representativeof battery aging. This model error causes error in the nega-tive electrode concentration states when using only voltagemeasurement for state estimation. Although the addition ofexpansion measurement doesn’t improve observer perfor-mance in case of negative electrode active material ratio drift, the proposed observer was able to compensate for drift instoichiometric windows. This can be seen in the error ofnegative electrode surface concentration which has a highvalue of 9.3% for voltage only observer, but has a value of0.1% for voltage and expansion observer. Finally, accurateestimation of negative solid-surface concentration can enablemore robust constraints on the state during charging andprevent degradation mechanisms like Lithium plating duringhigh C-rates. A
CKNOWLEDGEMENT
The authors would like to acknowledge the technical andfinancial support of Mercedes-Benz R&D North America.R
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