Enabling Large Load Transitions on Multicylinder Recompression HCCIEngines using Fuel Governors

Shyam Jade, Jacob Larimore, Erik Hellstrom, Li Jiang, Anna G. Stefanopoulou

Abstract— The fuel governor control design methodologypresented in [1] is extended and experimentally validated ona multicylinder recompression homogeneous charge compres-sion ignition (HCCI) engine. This strategy regulates desiredcombustion phasing during load transitions across the HCCIload range. A baseline controller tracks combustion phasingby manipulating valve and fuel injection timings. A referencegovernor is then added on to the compensated system to modifythe fuel injection amount by enforcing actuator constraints.

Experimental results show improved transient responses ofcombustion phasing and load during load transitions, when thepossibility of constraint violations exists. The nonlinear fuelgovernor predicts future model trajectories in real-time, andenables larger load transitions than were possible with thebaseline controller alone. The complexity and computationaloverhead of this strategy are reduced by developing a linearizedfuel governor, which is shown to work well in the entire HCCIload range and for small variations in engine speed.

I. INTRODUCTION

The load range in recompression HCCI engines is boundedfrom below by high cyclic variability, and from above byconstraints on ringing and pressure rise rates [2]. This workaims to design a control strategy that regulates combustionphasing for any load transition in this range.

Auto-ignition timing control in HCCI combustion requirescareful regulation of the temperature, pressure and composi-tion of the cylinder charge. Load transitions in HCCI enginesare achieved through fuel mass changes, which in turn havea significant effect on charge temperature, and consequentlyon combustion phasing. These undesired changes in phasingneed to be rejected. Large load transients can lead to actuatorsaturation, in which case the controller authority is lost. Thisis most pronounced during large load steps down, whenreduced temperatures can result in engine misfires, which areunacceptable for emissions and driveability.

Solutions to this problem using optimal control schemeshave been proposed, see for example [3]–[5]. However,these involve the on-line solving of a nonlinear optimiza-tion problem where the stabilization, tracking and actuatorconstraint requirements have to be satisfied simultaneously.This problem is simplified through the implementation of thefuel governor, which reduces computation time compared tohigher-dimensional optimal control schemes, at the cost ofreduced flexibility in shaping the transient response.

Figure 1 shows an overview of the methodology used in thiswork. Load requirements are converted into desired fuel mass

S. Jade, J. Larimore, E. Hellstrom and A. Stefanopoulou ({sjade,larimore, erikhe, annastef}@umich.edu) are with the Department of Me-chanical Engineering at the University of Michigan, Ann Arbor. L. Jiang(li.jiang@us.bosch.com) is with Robert Bosch LLC, Farmington Hills.

θ50 (k)

θref50 (k)

x(k)

Controller-augmented system

HCCIMulticylinder

Engine

mf (k)

mdesf (k) Fuel Governor

Add-on BlockObserver

uevc(k)

usoi(k)

BaselineController

Fig. 1. System overview: The fuel governor is added on to the controller-augmented system. Estimated states are obtained from the observer.

commands (mdesf ). A baseline controller uses valve timings

and fuel injection timing to track desired combustion phasing(θref

50 ). The fuel governor is then added on to the controller-augmented system to improve transient responses duringlarge load transitions. The governor works by attenuating thedesired fuel amount change when the possibility of futureactuator constraint violations exists.

The fuel governor is based on the reference governorconcept which separates the closed loop design from theconstraint enforcement requirement [6]–[10]. Reference gov-ernors have been applied widely in literature, for example toprevent fuel cell oxygen starvation [11]–[13], in hydroelectricpower generation [14], [15] and in turbocharged diesel enginesupplemental torque control [16].

The paper is structured as follows. The experimentalhardware is introduced in Sec. II. A control-oriented modelfor HCCI combustion is presented, along with validationresults. This model is used in Sec. III to develop a baselinecombustion phasing controller. The fuel governor is developedin Sec. IV, and is shown to improve phasing and load trackingperformance during large load transitions. It enables largerload transitions than were possible with the baseline controlleralone. Finally, in Sec. V, the linearized fuel governor is pre-sented, which reduces computational complexity significantlywith a minor loss in performance. Validation at differentengine speeds demonstrates the efficacy of the approach.

II. HCCI COMBUSTION MODELING

A. Experimental Setup

A four cylinder 2.0 liter GM LNF Ecotec engine runningpremium grade indolene was used in this study. Modificationsto accommodate HCCI combustion include an increasedcompression ratio of 11.25:1, and shorter duration and lowerlift cam profiles to allow for unthrottled operation. In addition

2013 American Control Conference (ACC)Washington, DC, USA, June 17-19, 2013

978-1-4799-0178-4/$31.00 ©2013 AACC 4423

Fig. 2. Typical HCCI in-cylinder pressure trace

to the stock turbo charger an Eaton M24 supercharger wasused. Experiments were run at slightly boosted conditions,approximately 1.1 bar intake manifold pressure. Cylinderpressure measurements were used in the ECU to computecombustion phasing in real-time for feedback control.

The control strategies presented in this paper were im-plemented using a combination of C and Matlab code,and were tested in real-time using an ETAS ES910 rapidprototyping module. The module uses an 800 MHz FreescalePowerQUICC

TMIII MPC8548 processor with double precision

floating point arithmetic and 512 MB of RAM.

B. Control-Oriented Model

The control-oriented model for recompression HCCI com-bustion is based on work done in [1], [17]. The model hastwo discrete states, the temperature (Tbd) and burned gasfraction (bbd) of the blowdown gases1. These states representthermal and composition dynamics of the system respectively.

As seen in Fig. 2, closing the exhaust valve early andopening the intake valve late causes the characteristic negativevalve overlap (NVO) seen in recompression-based HCCIengines [18]. The actuator inputs considered for control,namely the exhaust valve closing timing (uevc), start of fuelinjection (usoi), and mass of fuel injected (mf ), affect chargeproperties in this NVO region. Valve timings are controlledby a hydraulic cam phasing actuator with fixed cam profiles.The intake cam position is fixed. The primary model outputis combustion phasing. This is quantified by θ50 which is theengine crank angle at which 50% of the total heat releaseoccurs. The work output, represented by the indicated meaneffective pressure (IMEP), is a strong function of mf . In thiswork, load transitions are represented by fuel mass changes.

1) Model Equations: For a detailed discussion of modelstructure and equations, please refer to [1], [17]. The keyequation in the model is the Arrhenius integral that computesthe location of the start of combustion (θsoc). It is given by

1 + ksoiusoi =

∫ θsoc

θivc

A

ωpnpc exp

(B

Tc

)dθ (1)

θ50 = α1θsoc + α0 (2)

1The burned gas fraction is the mass fraction of the combustion productsexcluding excess air. Blowdown is defined after the exhaust valve opens.

4 6 8 10 12

4681012

STEADY STATE VALIDATION

θ 50(◦CA

aTDC)

RMSE

=0.66◦CA

Sim

ulation

Data

3.4 3.63.8 4 4.2

3.4

3.6

3.8

4

4.2

IMEP

(bar)

RMSE

=0.06

bar

Sim

ulation

Data

170 180 190

170

180

190

Mass

ofAir(m

g/cycle)

RMSE

=2.53mg

Sim

ulation

Data

0 500 1000 1500 2000 2500

6

8

10

12

TRANSIENT VALIDATION

θ 50(◦CA

aTDC)

0 500 1000 1500 2000 2500320

330

340

350

360

usoi(◦CA

bTDC)

0 500 1000 1500 2000 2500240

245

250

255

260

Cycles

uevc(◦CA

aTDC)

DataSimulation

Fig. 3. Steady-state and transient validation results for the model.

TABLE ILINEARIZATION OPERATION POINT

Quantity (α) Nominal operating point (α) Units

uevc 253 ◦CA aTDCmf 10.7 mg/cycleusoi 330 ◦CA bTDCθ50 7.3 ◦CA aTDCTbd 870 Kbbd 0.85 -

where θivc is the intake valve opening timing, ω is the enginespeed, and pc and Tc are charge pressure and temperatures atangle θ respectively. Here ksoi, A, B, np, αi are parameters.

C. Model Validation Results

The control-oriented model was parameterized using steady-state actuator sweep data recorded at an engine speed of1800 rpm and a boost pressure of 1.1 bar. Figure 3 presentsvalidation results for the model. The plots to the leftdemonstrate that the steady-state simulated and measuredcombustion phasing, load and mass of air agree well.

The plots to the right demonstrate satisfactory closed loopmodel validation. This validation supports the use of themodel for predictive model-based control strategies. In theseplots, a mid-ranging feedback controller, see Sec. III-A, wasimplemented both in simulation and on the rapid prototypinghardware. Identical desired load and θref

50 steps were fed to boththe model and the engine. The predicted θ50, usoi, and uevc

traces match both the magnitude and dynamic behavior of theengine measurements. The uevc drift in Fig. 3 seen after 1500cycles, is attributed to changing environmental conditions,and does not influence the control strategies presented here,where the prediction horizon is of the order of tens of cycles.

D. Model Linearization

The model is linearized about the operating point in Tab. I.Here α is the nominal operating point around which quantity

4424

Hv

Hfusoi (k)

uevc(k)

mf (k)

urefsoi

θ50 (k)

−

+−θref

50 (k)

Baseline controller

uffsoi (k)Feed-

forwardHCCI Engine

Hv → I ControllerHf → PI Controller

Fig. 4. Baseline Controller: uevc and usoi are in a TISO mid-rangingconfiguration, with a model-based feedforward component of usoi.

α is linearized.

x(k + 1) = Ax(k) +Bu(k), y(k) = Cx(k) +Du(k)

B = [Bevc, Bsoi, Bf ] , D = [Devc, Dsoi, Df ]

x =[Tbd − Tbd, bbd − bbd

]T, y(k) = θ50(k)− θ50(k)

u = [uevc − uevc, usoi − usoi,mf −mf ]T (3)

where

A =

[0.31 −112

−1.45× 10−4 0.55

], C =

[−0.096 0

]Bevc =

[−1.50.004

], Bsoi =

[−0.12

0

], Bf =

[33

0.037

]Devc = 0.47, Dsoi = −0.107, Df = 0.7. (4)

This linearized model is used to determine the feedforwardcomponent of the usoi control signal in Sec. III-B, and isused to develop the linearized fuel governor in Sec. V.

III. BASELINE CONTROLLER

The baseline controller in Fig. 1 uses the uevc and usoi

actuators to track θ50. As seen in Fig. 4, it comprises of afeedback loop arranged in a mid-ranging control configuration,and a model-based feedforward usoi component.

A. Mid-ranging based Feedback Loop

Mid-ranging is a two-input single-output (TISO) controltechnique often used in process control [19]. It has also beenused in HCCI engine control applications, see for example[20], [21]. This configuration is useful when one actuatorprovides the required capacity but is slow, while the otheractuator is fast but saturates easily. To provide high resolutionover the entire operating range, the slow actuator returns thefast actuator to its reference set point at steady state.

In the current application, the uevc and usoi actuators actas the slow and the fast actuators respectively. The uevc

actuator has the larger range and greater authority. However,the hydraulic cam phasing actuator is relatively slow, and hasa common value for all cylinders. In contrast, usoi saturateseasily, but can be set independently from cycle-to-cyclefor each cylinder. The θ50 tracking error signal drives a PIcontroller (Hf in Fig. 4) that controls usoi. The slower uevc

moves or mid-ranges usoi back towards its reference set point,using an integral controller (Hv in Fig. 4) driven by the usoi

tracking error for a reference cylinder, here cylinder 1.

Loadstep →

usoi(◦CA

bTDC)

INPUTSStart of Injection Timing

0 50 100300

320

340

360

380

Data

Loadstep →

0 50 100245

250

255

260

265

uevc(◦CA

aTDC)

Exhaust Valve Closing Timing

Cycles

Loadstep →

θ50

(◦CA

aTDC)

OUTPUTSCombustion Phasing

0 50 1000

5

10

15

DataReference

Loadstep →

0 50 1002.5

3

3.5

IMEP

(bar)

Cycles

Torque response

Fig. 5. One cylinder: Baseline controller exhibits reasonable θ50 trackingperformance for small load transitions (mf : 10.5→ 8.8 mg/cycle).

B. Model-based Feedforward

The linearized model in (3) is used to determine thefeedforward component of usoi. In Eq. 5, xss and uss

soi arethe steady state states and injection timing input when thelinearized system is at steady state, with θ50 at θref

50 . Assumingthe current values of uevc and mf to persist at steady state,

xss = Axss +Bsoiusssoi +Bevcuevc +Bfmf

θref50 = Cxss +Dsoiu

sssoi +Devcuevc +Dfmf

∴ usssoi = [0 1]

[(A− I) BsoiC Dsoi

]−1

·[−Bevc −Bf 0−Devc −Df 1

] [uevc mf θref

50

]T. (5)

The feedforward component of usoi is set as usssoi.

C. Experimental Results

The engine response to a small load step (mf : 10.5 →8.8 mg/cycle) for one cylinder and all cylinders are shownin Fig. 5 and 6 respectively. The combustion phasingcontroller maintains θ50 within reasonable bounds, and theload transitions smoothly between the two set-points. Thesudden initial jump in usoi in response to the fuel step iscaused by the feedforward component of usoi computed in(5). The uevc actuator slowly mid-ranges the usoi actuatorback to its reference set point. Note that the uevc actuator iscommon for all cylinders, and so the usoi for each cylindersettles to different reference points.

IV. NONLINEAR FUEL GOVERNOR

Large load transitions result in large changes in the chargetemperature. The baseline controller developed in Sec. III isunable to reject the subsequent large variations in θ50. This isseen in Fig. 7, where the baseline controller exhibits poor θ50

and IMEP tracking performance after a large load step down(mf : 11.4→ 8.8 mg/cycle). The nonlinear fuel governor isdeveloped to improve this poor performance.

4425

Loadstep →

usoi(◦CA

bTDC)

INPUTSStart of Injection Timing

0 50 100300

320

340

360

380

Cylinder 1Cylinder 2Cylinder 3Cylinder 4Reference

Loadstep →

Cycles

uevc(◦CA

aTDC)

Exhaust Valve Closing Timing

0 50 100245

250

255

260

265Common uevc actuator

Loadstep →

0 50 1000

5

10

15

θ50

(◦CA

aTDC)

OUTPUTSCombustion Phasing

Loadstep →

0 50 100

2.6

2.8

3

3.2

3.4

3.6IM

EP

(bar)

Cycles

Torque response

Fig. 6. All cylinders: Baseline controller exhibits reasonable θ50 trackingperformance for small load transitions (mf : 10.5→ 8.8 mg/cycle). Notethe cylinder-to-cylinder variability in θ50 and IMEP.

As seen in Fig. 1, the fuel governor is added on to thecontroller-augmented system, and it modifies the desiredmass of fuel (mdes

f (k)) in response to the observed stateof the system (x(k)). The nonlinear fuel governor uses thenonlinear model of the plant, from Sec. II-B, to calculatefuture trajectories. The fuel governor utilizes the recedinghorizon principle to check for actuator constraint violation,and is discussed in detail in [1]. Similar to [11], a bisectionalsearch is carried out on the desired change in fuel mass untilthe optimal value of a single parameter (β) is found:

mf (k) = mf (k − 1) + β · (mdesf (k)−mf (k − 1)). (6)

Ideally β is set to 1, in which case the fuel governor has noeffect, and the desired fuel step is applied unmodified.

At every time step, the system is initialized at the currentsystem states (x(k)), which are determined from a Luenbergerobserver designed using the model linearization. The closedloop system is simulated over a fixed future time horizon (N)with the fuel level maintained at mf (k) calculated in (6). Theparameter β is reduced if constraint violations are detected,and is increased if all constraints are satisfied. The optimalvalue of β ∈ [0, 1] is obtained subject to a convergencetolerance (ε). This process ensures that the tracking errorbetween the desired and actual fuel levels is reduced.

The actuator constraints considered in this work aresaturation constraints on usoi and uevc and rate constraintson uevc. It was observed that usoi saturation was the onlyactive constraint in experiments, and it was always violatedbefore the uevc constraints. This is a result of the mid-rangingfeedback gains chosen for the baseline controller. Note thatas long as uevc has authority, usoi will be mid-ranged to theset-point where a feasible solution of β ∈ [0, 1] should exist.

A. Experimental Results

For large load transitions, the fuel governor improves thepoor θ50 tracking performance exhibited by the baseline

usoi(◦CA

bTDC)

INPUTS

0 50 100300

350

400

GovernorNo GovernorActuator Limit

0 50 1008

9

10

11

12

Massof

fuel

(mg/cycle)

Loadstep →

Cycles

uevc(◦CA

aTDC)

0 50 100240

245

250

255

260

265Actuator Limit

θ 50(◦CA

aTDC)

OUTPUTSCombustion Phasing

0 50 100−5

0

5

10

15

20Reference

Loadstep →

0 50 1001

1.5

2

2.5

3

3.5

IMEP

(bar)

Cycles

Torque response

Fig. 7. Use of nonlinear fuel governor improves poor θ50 trackingperformance for larger load transitions (mf : 11.4→ 8.8 mg/cycle).

usoi(◦CA

bTDC)

INPUTS

0 50 100300

350

400

Actuator Limit

0 50 1008

9

10

11

12

13

Massof

fuel

(mg/cycle)

Loadstep →

Cycles

uevc(◦CA

aTDC)

0 50 100240

245

250

255

260

265

Actuator Limit

θ 50(◦CA

aTDC)

OUTPUTSCombustion Phasing

0 50 100−5

0

5

10

15

20GovernorReference

Loadstep →

0 50 1001.5

2

2.5

3

3.5

4

IMEP

(bar)

Cycles

Torque response

Fig. 8. Use of nonlinear fuel governor allows load transitions that werehitherto impossible (mf : 12.3→ 8.8 mg/cycle).

controller developed in Sec. III. This is seen in Fig. 7, wherethe baseline controller alone cannot prevent highly oscillatoryθ50 and IMEP variations in response to a large load transition(mf : 11.4 → 8.8 mg/cycle). The fuel governor uses thenonlinear model to predict future constraint violations andslow down the applied fuel mass command. The results ina smaller deviation of usoi from its nominal reference value,and a much smoother transition in θ50 and IMEP.

The fuel governor can also extend the load transition rangeby enabling transitions that would otherwise be impossibleto control. By slowing down the mf command intelligently,an even larger load step down (mf : 12.3 → 8.8 mg/cycle)in Fig. 8 is successfully negotiated. At the specified boostpressure (1.1 bar) and engine speed (1800 rpm), this loadtransition spans the entire load range of recompression HCCI.

As seen in Fig. 7 and 8, the governor typically steps mf

4426

usoi(◦CA

bTDC)

INPUTS

0 50 100300

350

400

Cylinder 2Cylinder 3Actuator Limit

0 50 1008

9

10

11

12

Massof

fuel

(mg/cycle)

Loadstep →

Cycles

uevc(◦CA

aTDC)

0 50 100240

245

250

255

260

265Actuator Limit

θ 50(◦CA

aTDC)

OUTPUTSCombustion Phasing

0 50 100−5

0

5

10

15

20Reference

Loadstep →

0 50 1001

1.5

2

2.5

3

3.5IM

EP

(bar)

Cycles

Torque response

Fig. 9. Potential cylinder-to-cylinder variation after load transition down,caused by cylinder 3 entering a dynamically oscillatory region.

quickly till the usoi constraint is hit. This is followed by aslow relaxation in mf to its desired value, the rate of whichis driven by the uevc response. Note that the usoi constrainthas to be made more conservative than the true value. This isdone to allow for model and observer errors, and to accountfor cylinder-to-cylinder variations.

B. Potential Oscillatory Dynamics after Load Step Down

Figure 9 shows the fuel governor response of differentcylinders for the same load step down studied in Fig. 7. Itillustrates that while the transient response of some cylinderscan be excellent, other cylinders sometimes exhibit highcyclic variability in θ50. The initial IMEP and θ50 responsejust after the load transition is satisfactory for both cylinders,which indicates that the fuel governor improves transitionperformance for all cylinders. However, a few cycles afterthe load transition, the θ50 of cylinder 3 enters an oscillatoryregion, causing noticeable dips in IMEP.

This behavior is attributed to the baseline controllerapplying destabilizing control to cylinder 3. As shown in [22],late phasing HCCI combustion dynamics are oscillatory. Inthese conditions it is important to capture the chemical energycoupling between cycles due to unburned fuel. The onset ofthe oscillatory dynamics varies with load and with cylinder, asseen in Fig. 9. During the load transition, cylinder 3 enteredthis oscillatory region while cylinder 2 did not. As seen in [23],gains designed for stable HCCI dynamics are destabilizingwhen applied in the oscillatory region. Thus the performancegains of the fuel governor will be further improved in futurework with a baseline controller that considers the unburnedfuel dynamics and globally stabilizes combustion phasing.

V. REALTIME IMPLEMENTATION

Implementing real-time predictive control strategies oncommercial vehicle-based embedded hardware is challengingdue to the computational complexity of optimizing nonlinear

TABLE IICOMPARISON OF MAXIMUM RUNTIME FOR DIFFERENT CONTROL

STRATEGIES FOR A STANDARD SERIES OF LOAD TRANSITIONS.

Control Strategy Maximum Normalized MaximumRuntime Runtime

Nonlinear Fuel Governor 8.916 ms 7315%(Arrhenius integral)

Nonlinear Fuel Governor 2.315 ms 1900%(lookup table)

Linear Fuel Governor 0.1271 ms 104%No Fuel Governor 0.1219 ms 100%

models online. Several efforts were made to reduce thecomplexity and computational runtime of the fuel governor:

1) The nonlinear fuel governor optimizes β in (6) fourtimes every engine cycle. Each optimization requiresthe nonlinear combustion model to be simulated severaltimes. The number of model simulations per timestepcan be reduced by shortening the time horizon (N),and increasing the tolerance (ε), as defined in Sec. IV.In this work, N = 12 and ε = 0.05 were used, tobalance performance and computational cost.

2) The Arrhenius integral used to determine the start ofcombustion, see (1), is computationally very expensive.The integral was replaced with a pre-computed lookuptable, based on usoi and Tbd.

3) A linearized fuel governor was developed by replacingthe nonlinear combustion model with the linear modelpresented in Sec. II-D.

Table II shows the typical maximum runtime for differentcontrol strategies for a standard series of load transitions. Allof the above three strategies were run in real-time on the rapidprototyping hardware described in Sec. II-A. Replacing theArrhenius integral with a lookup table results in an appreciableruntime improvement. The linearized fuel governor showsa drastic reduction in maximum runtime. The additionalcomputational overhead of augmenting the baseline controllerof Sec. III with the linearized fuel governor is only 4%.

A. Linearized Fuel Governor at Different Engine Speeds

The linearized fuel governor is promising from a computa-tional cost perspective. To be able to use this strategy acrossthe entire HCCI load-speed operating range, the nonlinearmodel has to be linearized at several operating speeds. Eachof these linearized fuel governors has to be insensitive toa variation in speeds around its nominal operating point.Figure 10 shows that the linearized fuel governor that islinearized at 1800 rpm performs well for a variation inspeeds (±100 rpm). The linear model is unaware of the speedvariation, yet θ50 is maintained within reasonable bounds, andIMEP transitions smoothly from one set-point to the another.

VI. SUMMARY AND FUTURE WORK

The fuel governor controller concept is validated on amulticylinder recompression HCCI engine. The major benefitsvalidated by experiments are improved θ50 and IMEP transient

4427

usoi(◦CA

bTDC)

INPUTS

0 50 100300

350

400

Actuator Limit

Massof

fuel

(mg/cycle)

0 50 1008

9

10

11

12

131900 RPM1800 RPM1700 RPMReference

Loadstep →

Cycles

uevc(◦CA

aTDC)

0 50 100240

245

250

255

260

265

Actuator Limit

0 50 100−5

0

5

10

15

20

θ 50(◦CA

aTDC)

OUTPUTSCombustion Phasing

Loadstep →

0 50 1001.5

2

2.5

3

3.5IM

EP

(bar)

Cycles

Torque response

Fig. 10. The linearized fuel governor performs well for a variation ofspeeds (±100 rpm) around its nominal operating point (1800 rpm).

response during large load transitions (see Fig. 7), and theenabling of larger load transitions than were possible with thebaseline controller alone (see Fig. 8). The entire load rangeat the specified speed and boost pressure can be traversed.

The nonlinear fuel governor is run in real-time on therapid prototyping hardware. Computational load is reducedsignificantly by replacing the nonlinear prediction model witha linear model. This linearized fuel governor is proposed asa viable solution for ECU implementation. It is shown towork well in a range of loads and speeds around its nominallinearization operating point (see Fig. 10).

The HCCI model’s range of validity is extended to differentengine speeds in [24], and will be used in future work todevelop controllers for simultaneous load-speed transitions.The range of validity of the linearized fuel governor can beextended across engine speeds by using multiple linearizations.Characterization of the onset of late phasing cyclic variabilitywill be used to improve the performance of the baselinecontroller in these dynamically oscillatory regions.

ACKNOWLEDGMENTS

The authors would like to thank Jeff Sterniak and JulienVanier of Robert Bosch, LLC for their assistance with trou-bleshooting experimental issues. This material is supportedby the Department of Energy (National Energy TechnologyLaboratory, DE-EE0003533) as a part of the ACCESS projectconsortium with direction from Hakan Yilmaz and OliverMiersch-Wiemers, Robert Bosch, LLC.2.

2Disclaimer: This report was prepared as an account of work sponsored by an agencyof the United States Government. Neither the United States Government nor any agencythereof, nor any of their employees, makes any warranty, express or implied, or assumesany legal liability or responsibility for the accuracy, completeness, or usefulness ofany information, apparatus, product, or process disclosed, or represents that its usewould not infringe privately owned rights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark, manufacturer, or otherwisedoes not necessarily constitute or imply its endorsement, recommendation, or favoringby the United States Government or any agency thereof. The views and opinions ofauthors expressed herein do not necessarily state or reflect those of the United StatesGovernment or any agency thereof.

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