A Control Design and Calibration Reduction Methodology

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A control design and calibration reduction methodologyfor AFR control in gasoline engines

Sai S.V. Rajagopalan a ,n , Shawn Midlam-Mohler b , Stephen Yurkovich c , Kenneth P. Dudek d ,Yann G. Guezennec b , Jason Meyer ba General Motors Research and Development Center, 30500 Mound Rd., Warren, MI 48090, United Statesb Center for Automotive Research, The Ohio State University, Columbus, OH 43212, United Statesc Department of Systems Engineering, University of Texas at Dallas, Richardson, TX 75080, United Statesd CAR Technologies LLC, Columbus, OH 43212, United States

a r t i c l e i n f o

Article history:Received 9 May 2013Accepted 26 February 2014Available online 25 March 2014

Keywords:AFR controlServo-mechanismCoordinated controlCalibration reductionLinear parameter varying systemsOf ine calibration

a b s t r a c t

A control architecture for air to fuel ratio (AFR) control of gasoline engines designed to work with switchingand/or wide range oxygen sensors, with the goal of minimizing calibration effort while meeting performancerequirements, is described. A high bandwidth, dithered inner-loop reference tracking controller with pre-catalyst oxygen sensor feedback coupled with a low bandwidth setpoint tracking outer-loop with postcatalyst oxygen sensor feedback, is used to control engine exhaust and O 2 storage in the three-way catalyst(TWC), respectively. A total synthesis inspired design ensures that signi cant non-linearity in the system ishandled through a coordinated and corrective action and expected response blocks in the open-loop,without burdening the closed loop controller. Calibration is achieved of ine, through closed loopoptimization using genetic algorithms, while simultaneously meeting performance and stability criteriawith signi cantly reduced need for in-vehicle tuning. Experimental results show comparable emissionsperformance with the stock OEM AFR controller under warmed up conditions over a standard drive cycle.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Gain scheduled, engine crank angle synchronous controllersare typically used in the automotive industry for robust emissionscontrol of internal combustion engines, because of the non-linearityand critical dependence of engine and TWC behavior on parameterssuch as load, speed, system pressures and temperatures. Gainscheduling provides a means of dealing with nonlinearity throughlocalized linearization, and smooth transition between localizedcontrollers during transients. Model hysteresis is typically employedfor smooth transition across zones, and closed loop gains for

emissions control are tuned in-vehicle to achieve best emissionsperformance while meeting on-board diagnostics and drivabilityrequirements. Any desired feature or behavior in the output signalsfor control or diagnostic purposes is typically induced throughheuristic algorithms with conditional branching. While having thislevel of exibility in the software is an advantage, the calibra-tion effort associated with such an implementation can result insigni cant overhead. The main motivation of this work is thus to

reduce the calibration effort involved in the air to fuel ratio controlloop that uses available model based control design techniques thatare uniquely suited to address real world issues.

In an AFR control system, two plants , i.e., the engine and theTWC, are to be controlled to achieve optimal tailpipe emissionsperformance while maintaining drivability and on-board diagnos-tics capability. The engine needs to be controlled through fuelinjection, spark timing and air management for stoichiometricoperation and torque delivery and the oxygen (O 2 ) storage inthe three-way catalytic converter (TWC) is controlled to preventbreakthroughs of carbon monoxide (CO), oxides of nitrogen (NO x)

and total hydro-carbons (THC). The two

plants

operate at differenttime scales; the engine operation has a much higher bandwidththan a TWC (unless the TWC is signi cantly aged). Feedbackmeasurement on AFR is obtained through two O 2 sensors mountedbefore and after the TWC. The O 2 sensors can be of switching orwide range type. It is important to note that two sensors arerequired for AFR control because a functioning TWC acts as a heavy

lter and modulator of the engine exhaust, and renders the systemunobservable until breakthrough occurs at the tail pipe, at whichpoint the control system has already failed emissions. Thus usingtwo sensors is the current industry standard. A schematic of thecomplete plant is shown in Fig. 1.

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Control Engineering Practice

http://dx.doi.org/10.1016/j.conengprac.2014.02.0200967-0661/ & 2014 Elsevier Ltd. All rights reserved.

n Corresponding author.E-mail address: [email protected] (S.S.V. Rajagopalan).

Control Engineering Practice 27 (2014) 42 53


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The critical dynamic effects that govern the behavior of thesystem and hence need to be modeled with good accuracyor compensated for through a robust control architecture are asfollows:

1. Air dynamics : Air dynamics are governed by the position of thethrottle, manifold pressure ( P Man ), intake and exhaust valvetiming, intake system temperature, and engine speed ( N ).Volumetric ef ciency (VE) is a metric used to quantify thelumped effects of an intake ow phenomenon in a mean valuesense. VE tables in combination with residual gas fractionestimates are typically used to calculate the air charge trappedin the cylinder, which in turn is used to calculate and predictthe appropriate fuel quantity to be delivered. The use of massair ow sensors (hot wire or hot lm types) is typical and theyare placed at a suitable location in the intake, to ensure smooth

ow through them. However production sensors suffer fromslow response (during transient conditions) and measurementerrors during certain conditions such as ow reversion.

2. Fuel dynamics : Fuel dynamics are characterized by the behavior of the fuel droplets after injection. For port fuel injected vehicles, thefuel dynamics are strongly dependent on temperature and air owrate. At low temperatures, the fuel does not atomize suf ciently,resulting in fuel puddling in the intake runner. These puddles actas a dynamic system between the actuator and the cylinder fuelmass. For direct injection engines, fuel dynamics are typically not amajor problem because of suf cient atomization and mixing within-cylinder air. Fuel dynamics is particularly important because theclosed loop air-fuel ratio control mechanism relies on using fuelingas the sole control input.

3. Plant delay : Plant delay is characterized by the number of engine events or engine cycles (or time) it takes for the injectedmass of fuel to reach the pre-catalyst oxygen sensor, placedupstream of the three-way catalyst, typically at the con uenceof the exhaust runners. This includes the engine delay fromintake valve closing to exhaust valve opening, and the transportdelay of the exhaust gases from the exhaust runner tothe con uence point where the pre-catalyst oxygen sensor islocated. It is typical for engine control systems to run in anengine crank angle synchronous domain (also called eventsampled domain). Although the engine delay is xed (in the

event domain) and related to the number of cylinders in the

event/crank angle domain, the transport delay depends onthe mass ow rate, and is a variable when sampled in the timedomain or event domain.

4. Catalyst oxygen storage : Three-way catalyst O 2 storage is a verycomplex nonlinear phenomenon. The catalyst contains O 2storage sites which can store or release O 2 , based on owconditions. When the catalyst is saturated with O 2 , it is veryeffective in oxidizing CO and THC, but is very poor in reducingNO x. When it is completely depleted of oxygen, the NO xreduction is maximized, but CO and THC oxidation is degraded.Maximum conversion ef ciency is achieved only in a smallregion around a stoichiometric fuel to air ratio. The conversionef ciency for NO x rapidly falls off when leaner than thestoichiometric air fuel ratio, while conversion of CO and THCis still high in the region richer than the stoichiometric air fuelratio. It has been shown that dithering (high frequency rich tolean toggle of the inlet feedgas around stoichiometry) the inletfeed-gas to the TWC has the following bene ts: (i) it improvesthe THC conversion ef ciency of the catalyst, thus allowingmuch larger AFR deviations, and reduces the productionof ammonia ( Defoort, Olsen, & Willson, 2004 ); (ii) provides ameans of evaluating the measured pre-catalyst O 2 sensorvoltage in a switching sensor platform to keep track of theEQR indirectly; and (iii) creates an opportunity for mandatedon-board diagnostics of the O 2 sensors and TWC through signalperturbation. Thus it is typical for most production controlalgorithms to incorporate a dither implicitly through the feed-back control strategy. It is also important to understand thedynamics of hydrogen gas production in the catalyst due towater-gas shift reactions. During lean to rich transitions, thecatalyst produces signi cant amounts of H 2 gas, which affectsthe behavior of the post-catalyst O 2 sensor as described below.

5. Sensor dynamics and deception : Besides the time it takes for theconstituents of the exhaust gases to diffuse through theprotective layer on the sensor to reach the Nernst cell whichis typically modeled using rst order sensor dynamics, anothercritical non-linear phenomenon to be considered is the varyingdiffusion rate of different gas species in engine exhaust,through the sensor ( Buglass, Morgan, & Graupner, 1998 ). Thevarying diffusion rates of different species deceive the sensorinto measuring an AFR value that is different from the true

chemical AFR of the engine exhaust gas. Hydrogen gas and

Fig. 1. Schematic of the engine, TWC, sensors and actuators.

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controlled system. For tracking control systems, the norm is tode ne the tracking performance based on the reference trajectory.But in the case of the AFR control system, because the objective isto meet emissions standards, the performance is de ned based onthe ability to minimize harmful emissions measured at thetailpipe. This is quanti ed through mandated emissions testprocedures based on speci c driving cycles. Therefore, the controlproblem can be de ned as a setpoint tracking problem for thecatalyst O 2 storage, and a reference tracking problem for engineout emissions, with fuel as the control input. This can be illustratedas shown in Fig. 4. The objective amounts to designing controlinput u (which represents the commanded fuel) based on mea-surements y1 and y2 (which are the pre- and post-catalyst O 2sensor measurements), so that the state x2 (O2 storage) is at adesired setpoint r 2 , and the state x1 (engine out chemical EQR)follows a desired trajectory r 1 . The state x1 is controllable andobservable, while the state x2 is controllable, but is unobservableas long as there is suf cient O 2 storage. This is because, duringnormal operation the catalyst is able to aid in redox reactions andhence the post-catalyst O 2 sensor measurement is always atstoichiometry. Because the dynamics of the catalyst are muchslower than those of the engine, and because using the state x1 isthe only way to control x2 , the tracking problem for state x1 plays acrucial role in achieving the desired performance targets. In thiswork, a novel solution to designing and calibrating the trackingcontroller action u 1 (of the inner-loop) is proposed. It will be seenthat the control action u 2 (from the outer-loop) acts as a modi erto the reference input r 1 , having no effect on the inner-loopcompensator feedback, thereby decoupling the feedback controlactions of the two compensators. The functions , and arestrongly nonlinear and are modeled using linear parameter vary-ing (LPV) techniques to best approximate the non-linearities.Hence the compensator designed is also linear parameter varyingin nature. The control problem has the following features thatinduce strong nonlinearities and stability issues: (i) variable plantdelay, (ii) operating condition dependent behavior and (iii) satura-tion nonlinearity in the measurement signal for binary sensorfeedback, which is further corrupted by varying gas diffusion ratesthrough the sensor. The salient features of the chosen architectureto tackle these problems include: (i) coordinated open and closedloop control action, (ii) modular control design to accommodatemultiple control objectives and new changes easily with minimalimpact on the closed loop, (iii) shifting the bulk of the calibration

burden from the closed loop parameters (tuned through multiple

emission tests) to the open loop parameters (calibrated using set-point engine mapping), through the ability of regulating thepre-catalyst O 2 sensor readings to non-stoichiometric values tocompensate for sensor deception and other effects, therebyachieving asymmetric operation, and managing the dithering of the engine out AFR through proper choice of a dithering signalfrequency, amplitude and bias depending on operating conditions.

Fig. 5 illustrates the control architecture design. A servome-chanism that uses a feedforward feedback control structure formsthe back-bone of the inner-loop. In addition, the feedforwardcommands are coordinated with an expected response to thecommanded open loop control action, using the features of thetotal synthesis design process ( Gejji, 1980 ). In the inner-loop,the expected response from the plant due to the control input(i.e., injected fuel), is compared to the measured response from thepre-catalyst O 2 sensor, and the error is used to drive the inner-loopcompensator. Various scaling blocks are used so that the controlaction is directly proportional to the change in pre-catalystnormalized fuel to air equivalence ratio (EQR) desired.

The slower outer-loop is used to maintain the O 2 storage at adesired level. The two closed loops work hand-in-hand to providedisturbance attenuation and robustness to modeling errors, bestexplained in terms of ideal behavior. Because of the coordinatedactions between the M (open-loop control action) and correspond-ing T (expected response to control action) blocks, no feedbackcontrol action will be necessary if (in the ideal case) the plantbehaves exactly as expected, in which case the desired controlaction is achieved open loop. Hence, the desired asymmetricresponse can be accommodated through control oriented model-ing (for expected response) and open loop control action, therebycompletely eliminating experiment based calibration effort fromthe feedback loop. The control oriented models used in theexpected response block capture the most signi cant dynamicsof the plant and run in real time. The architecture consists of twosumming junctions, namely the error junction and the fuelsumming junction. All the T block outputs act at the error junction,while the M block outputs act at the fuel summing junction. Forswitching O 2 sensors, additional signal processing is needed at theerror junction. For example, saturation nonlinearities for the sumof all the T junction contributions is required to account for thesaturation behavior of the sensor. It is to be noted that this blockdiagram is a generalized representation of the architecture toillustrate signal ow, and a speci c implementation is described in

the following section.

Fig. 4. Control problem description: nonlinear maps represent the behavior of the engine and the oxygen sensor.



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2.1. Open-loop command generators

There are four open loop command generator pairs depicted inthe architecture, with subscripts A, B, C and D. The rst commandgenerator corresponds to open loop corrections performed basedon engine operating conditions (such as correction for sensordeception). It drives the system through blocks M A and T A , whereM A produces the desired fuel contribution that achieves thedesired asymmetry, and T A produces the corresponding expectedresponse at the pre-catalyst O 2 sensor due to this fuel contribution.The second generator corresponds to the setpoint generator forthe outer-loop. This block generates the appropriate open loopcontrol action required to rapidly bring the O 2 storage in thecatalyst to a desired level based on operating conditions. Anexample of such an action is during fuel cutoff, where the catalystis completely saturated with O 2 . This could potentially lead to NO xbreakthroughs during acceleration. Hence under such cases theseblocks command enough fuel to deplete the catalyst of stored O 2 ,and bring the stored O 2 to acceptable levels. This open loop controlaction is coordinated through the blocks M B and T B . The third pair,M C and T C , maintains the O 2 storage at a desired setpoint. Thisis achieved in conjunction with the outer-loop compensator. The

nal pair, M D and T D , accounts for forecastable disruptions suchas certain air estimation errors (an example being ow reversionat the MAF sensor) and fuel purge.

2.2. Inner-loop

The inner-loop is a reference tracking controller that providesrobustness and disturbance rejection. Fig. 6 illustrates the inner-loop in its simplest form ( Rajagopalan et al., 2009 ), so that the

functions of the various components can be discussed separately.

There are two junctions in the loop: the rst is an error junction,wherein the error signal that drives the inner-loop compensatoris calculated based on the sum of all the reference signals fromthe T blocks producing the expected response and the actualmeasured response, while the second is a multiplicative controlaction junction, where the inner-loop contribution multiples thecontributions from the M blocks in a multiplicative fashion.Because the architecture is valid for both switching sensors andwide range sensors, the error can be either a voltage error or anEQR error. In the gure, GPP refers to the predicted cylinder aircharge mass, which is a one step ahead prediction for four cylinderengines, and a two step ahead prediction for six or eight cylinderengines. Engine operating conditions may refer to the schedulingvariables: manifold pressure ( P Man ), engine speed ( N ) and coolanttemperature ( T Cool ). In this study, the engine was completelywarmed up during testing and hence only manifold pressureand engine speed were considered for scheduling, while coolanttemperature was xed at 363 K. A discussion of the elements of the inner-loop is now presented.

2.2.1. Reference dither generator The reference dither generator produces a sinusoidal or trian-

gular reference signal, whose frequency and amplitude are func-tions of the operating condition. The mean of the dither signalgenerated is zero, while its amplitude has a magnitude of unity.A sinusoid or triangular wave is chosen over a square wave tofacilitate an easy way for the outer-loop to correct the reference bymerely changing the mean value of the dither signal, therebychanging the average AFR of the perturbation induced. This shiftin the mean value of the dither manifests itself as a change in

the duty cycle of a binary O 2 sensor. Fig. 7 shows the details of the

Fig. 5. Proposed control architecture.

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dither generator. At low engine load conditions, the frequency of the dither signal commanded is small because gas transport isslow and hence the plant lters out the fast dynamics. On theother hand, one can use a higher frequency at high load conditionsfor the same reasons. The amplitude of the sine wave is alsomodi ed based on engine operating conditions also. Moreover, theamplitude of the sine wave plays an important role in drivabilityand NVH, and hence at low load conditions, a smaller amplitudeis desired, while at high loads a large amplitude is requiredto discern the switching effects of the pre-catalyst O 2 sensorby improving the signal to noise ratio. Cylinder imbalance, forexample, is a source of noise that can cause random switchingbehavior when switching around stoichiometry.

The outer-loop acts through the dither generator to modify thebehavior of the inner-loop. This is achieved by changing the meanvalue of the sine wave based on the desired change in the catalystO2 storage. For example, if one wishes to deplete storage, then theaverage value of the sinusoid is 4 1. This desired EQR from thedither generator is converted into a fuel input in the open loop

fueling block which acts as the M part. The offset correction block

is used to correct for errors such as sensor deception. Thiscorrected desired EQR is then used by the expected responseblock to generate the appropriate response.

2.2.2. Open loop fueling The open loop fueling block converts the desired EQRs ( EQROL;

EQRdith ) from the dither generator to an equivalent fuel command.This is achieved using the air prediction model. The equations thatyield the desired open loop fuel and dithered fuel commands( fuelOL; fueldith ) are given by

fuelOL GPP 14 :7

EQR

fueldith GPP 14 :7

EQRdith ; 1

where GPP is the one step or two step ahead predicted air mass

ingested into the cylinders.

Fig. 7. Dither generator.

Fig. 6. Inner-loop block diagram.



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2.2.3. Expected plant responseThe expected response block determines an ideal desired

expected response ( EQRdes or V des ) of the plant based on thefueling command and the operating conditions. Fig. 8 illustratesthis block. An idealized plant model is necessary to calculate anexpected response to an open loop fueling command. For thispurpose, the plant model which is modeled using techniquesdescribed in Rajagopalan (2008) consists only of the plant delay,

mixing and sensor dynamics, and any nonlinear effects due to theswitching sensor. A fuel dynamics model is not included in theexpected response because the commanded open loop base fuel isprocessed through a fuel dynamics compensation block which willbe described shortly, and it is assumed that the fuel dynamicseffects are completely compensated.

The delay model and the sensor model and switching curve (forswitching O 2 sensors) described in Rajagopalan (2008, p. 33) areused to calculate the expected response. The switching sensormeasurement is ltered to improve tracking in the linear region.This helps minimize steady state errors by slowing down theswitching response. A saturation is imposed so that only theinformation in the linear region is taken into account. This isbecause the nonlinear region of the sensor curve does not havea xed behavior for all operating conditions. It is affected bythe temperature of the sensor and also its age. This phenomenon isdescribed by Riegel, Neumann, and Wiedenmann (2002) . Also,because the saturation bounds are smaller than the physicalsaturation values of the switching sensor, stability of the closedloop system is improved. EQRdes refers to the desired pre-catalystEQR, while V des refers to the desired pre-catalyst EGO voltage froma switching sensor after signal processing. V PreCat refers to thedesired pre-catalyst EGO voltage before signal processing.

2.2.4. Inner-loop compensator The inner-loop compensator is the most critical element for

performance and stability of the AFR control system. For thiscompensator, a proportional integrator controller along with lead lag action is adopted. Fig. 9 depicts the details of the tracking

compensator (represented in Fig. 6) in detail, along with the fueldynamics compensation block.

The error signal between expected and measured responsefunctions as the input to the control system, and can either bean EQR error or a voltage error depending on whether the pre-catalyst sensor is of wide range or switching type, respectively.The integral and proportional gains are scheduled as functions of P Man , N and T Cool using linear spline techniques ( Dudek, 2006 ).

A backward looking integrator is adopted for the discrete inte-grator, and for input uInt and output yInt with event index k thedifference equation can be described as

yInt k yInt k 1 u Int k: 2

The transient compensator functions as a lead lag compensatorto attenuate undesirable frequency response in the system. Thedifference equation with input uLL and output yLL can be expressed as

yLLk 1 yLLk 1 2 yLLk 2 0 uLLk 1 uLLk 1 2 uLLk 2; 3

where 1;2 ; 0;1;2 are scheduled on parameters such as P Man , N and coolant temperature using linear splines. The inputs to theintegrator u Int and the transient compensator uLL are given by

u Int k K Int r k ym kuLLk K LLr k ym k 4

where K Int is the integrator gain, K LL is the proportional gain, r k isthe reference trajectory which could be an EQR or voltage signal, and ym is the measured pre-catalyst EQR or voltage. The outputsof the integrator and transient compensator are then summed toobtain the total feedback control compensation. Since the feedbackcontroller modi es the open loop control action in a multiplicativesense, the output of the feedback compensator is multiplied with theopen loop control action. Hence if the error signal to the feedbackcompensator is zero, then the open loop compensation is multipliedwith the dither signal perturbed open loop fuel, performing noclosed loop action. With fuel as the control input and O 2 /AFR measurement as feedback, this multiplicative control action isadvantageous because the commanded fuel to the injector is scaledin terms of the desired change in EQR based on feedback from thepre-catalyst O 2 sensor, thus reducing the need for gain scheduling.The total nominal control action ( FuelNom) comprised of the feedfor-ward ( FuelOL ) and feedback compensation ( FuelCL) can be written as

FuelNom FuelOLFueldith FuelCL: 5

This nominal fuel is then used to calculate a fuel dynamics compen-sated nal fuel command FuelComp (Dudek, 2006 ) through the inver-sion of the fuel dynamics model.

2.3. Calibration of inner-loop control gains

Using experimental, data-driven plant modeling, a numericaloptimization method is adopted for calibration of the closed loopFig. 8. Expected response block.

Fig. 9. Inner-loop compensator and fuel dynamics compensation block.



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controller gains ( Liu et al., 2011 ). Genetic algorithm optimizationalgorithms which are extensive direct search methods with builtin randomization are well suited for this problem because thereare minimal chances of ending up in a local maxima/minima dueto an exhaustive search over the de ned space. Being a directsearch algorithm, genetic optimization requires suf cient compu-tational power to achieve results in a reasonable time. To this end,a Microsoft Windows XP based parallel computing cluster built

at Center for Automotive Research of The Ohio State Universitywas utilized to solve the problem. MPI and OpenMP were used toparallelize the code written in FORTRAN. The cluster utilizedconsists of 12 dual core CPUs and 4 quad core CPUs that wereconnected together using a gigabit ethernet network. DeinoMPI,an implementation of MPI-2 for Windows, was used as the systemlevel middle ware and remote process manager. The optimizationsetup is shown in Fig. 10 . The cost function ( J ) to be minimized isde ned as

J Stability Penalty ndata

k 1EQRdes EQRmeas 2 ; 6

where ndata is the number of data points in the simulation, andEQRmeas is the measured pre-catalyst EQR response from the plant.The same EQR dependent cost function is used for both a switch-ing sensor and a wide range sensor because the magnitude of thevoltage information from a switching sensor does not give anyindication of pre-catalyst EQR or emissions, due to sensor satura-tion. Hence using EQR provides a better performance. The stabi-lity penalty term will be discussed later.

A high delity plant model is used to approximate the behaviorof the real plant, and is different from the control oriented modelsused to represent critical system dynamics in the expected responseblock ( T blocks). The high delity model includes a charge model(Dudek, Guezennec, Meyer, & Wiggins, 2008 ) derived from a wellcalibrated GT-Power model ( Meyer, 2007 ), coupled with an exhaust

geometry based plant delay model ( Rajagopalan et al., 2012 ). Thecontrol oriented models, which were used in the expected responseblock on the other hand, consist of a fuel dynamics compensationmodel ( Dudek, Davis, Wiggins, & Walker, 2007 ) for fueling, and asimpli ed plant delay prediction model ( Dudek, Guezennec, Meyer,Midlam-Mohler, & Yurkovich, 2012 ) for the expected responseblock. For both the high delity model and the simpli ed controloriented models, switching sensors and wide range sensors are

implemented using a table look-up between the actual air

fuel ratio(or voltage) and the perceived air fuel ratio (or voltage) lteredthrough a rst order sensor dynamics model with a time constant of 0.2 s for the wide range sensor and 0.15 s for the switching sensor.To maximize performance and robustness, plant disturbance pro-

les based on real world data were used for fueling and otherparameters ( P Man , N ) in the plant model. Errors in manifold pressureand engine speed simulate in-cylinder air estimation errors in theengine event domain. An additional disturbance was introducedfor delay estimation. These disturbance pro les induce a differencebetween expected response and the measured plant response.A fueling disturbance is used to emulate errors in wall wetting,injector errors, etc., and is injected into the fuel summing junction.For delay errors and fuel injection errors, the arrival of thedisturbance was determined through a Poisson distribution, whilethe magnitude of the disturbance is based on a uniform distribution.The arrival rate and the distribution functions for the distributionsare chosen based on input from plant experts based and real worldexperience. Sensor deception was simulated using an operatingcondition (engine speed vs manifold pressure) based table look-upfor the AFR shift from experimental data collected in an enginedynamometer. The testing process involved running the vehicle in open loop where all closed loop fueling control is disabled, andcollecting data such as system pressures, temperatures, enginespeed, air- ow, outputs of switching and wide range sensors overthe US FTP and US06 cycles, along with other custom drive cycles

Fig. 10. Block diagram for calibration of inner-loop control gains.



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designed to maximize system excitation over the widest operatingconditions.

Stability analysis for platforms with wide range sensor feed-back is discussed next; for switching sensor based feedback, theanalysis is more complicated and is omitted here. For the widerange sensor case, two levels of stability checks were used. Anonline steady state frozen parameter eigenvalue check was usedduring optimization, and a linear matrix inequality (LMI) check to

analyze global stability of the closed loop system was used a posteriori . Pole checking of the frozen parameter system does notguarantee stability of the closed loop system, and is only used asa standby during closed loop optimization. For the online stabilitycheck, the cost function was penalized based on the location of the maximum eigenvalue of the closed loop system at differentoperating conditions. The following assumptions are made toanalyze the location of the eigenvalues of the closed loop system:(i) the plant delay is assumed to be at its maximum value at whichthe potential for instability is maximum, (ii) the open loop fuelingis considered as a third scheduling variable affecting the system,thus acting as an af ne gain multiplier, and (iii) the fuel dynamicscompensation cancels the fuel dynamics in the plant model.

The scheduling parameters of the system are hence P Man , N andopen-loop fueling, which is a direct function of engine air- ow.Because the air- ow is a strong function of P Man and N , andbecause the stability analysis is done at steady state, one can writethe air- ow in terms of P Man and N using the volumetric ef ciency,thereby reducing the three parameter system to a two parametersystem. The two-dimensional operating space is then gridded, andthe closed loop eigenvalue checks are performed at the grid points.As an example, the P Man grid points could be between 15 10 3 and105 10 3 Pa, while the N grid points could be between 84 and524 rad/s. The LMI check used is based on the zone boundarybased parameter dependent Lyapunov matrix, as described in Tan,Grigoriadis, and Wu (2000) . The method guarantees stability of aparameter dependent system matrix, whose maximum deviationsin each scheduling parameter at each grid point are known.For the LMI check, the maximum rates of change of the schedulingparameters assumed are P Man A 40 10 3 ; 40 10 3 Pa and N A 10 ; 10 rad =s. The bounds on these maximum rates of change of parameters are engine speci c and are obtained fromthe chassis dynamometer based open loop testing of the engine,sensor and actuator set to be used, as well as feedback from plantexperts for extreme environmental conditions. The penalty forstability in Eq. (6) can now be de ned as

Stability Penalty 0 if max r threshe max thresh 1 otherwise( 7

where max is the maximum eigenvalue for the closed loop systemmatrix, and thresh is the maximum allowable threshold eigenvalue.Calibration of the inner-loop compensator based on ndata

300 000, consisting of scheduling parameters (manifold pressure,engine speed, etc.), inputs (fuel command, throttle position andother measurements required for plant modeling) and measuredoutputs (pre and post catalyst AFR from switching and wide rangesensors, and other outputs required for the modeling effort) tookabout 4 h on the computing cluster, subject to terminationcriterion de ned as 5000 generations. Further execution of thegenetic algorithm yielded little bene t.

2.4. Outer-loop

The outer-loop is used to bias the inner-loop compensator, totrack a pre-de ned reference chemical AFR. Correcting the inner-loop to control towards true stoichiometry prevents O 2 storage

drift and emissions breakthrough. The outer-loop acts as a reference

modi er to the inner-loop through the T blocks when a correspond-ing M block control action is performed. Under most conditions, theloop action is decoupled from the inner-loop feedback throughreference modi cation and slower loop time, thus preventingunwanted interaction between the inner- and outer-loop control-lers, and also proving advantageous for stability analysis of theinner-loop tracking compensator. Asymmetry in the inner-loopbehavior is achieved by varying the average value of the AFR,imposed by the dither signal. This bias is provided by the outer-loop compensator based on the error between the expected andmeasured post-catalyst voltage. In this study, a binary O 2 sensor wasused for post-catalyst O 2 because, as long as the O 2 storage in thecatalyst is balanced, the variation in the O 2 sensor will be slow, andmostly within the linear range of the sensor. The architecture can beeasily adapted for a wide range sensor, in which case AFR would beused instead of sensor voltage for feedback and calibration. Fig. 11shows the blocks of the outer-loop controller. The break throughcorrection term is used for emergency corrections when the O 2storage prediction is inaccurate and emissions break-through isobserved through the post-catalyst O 2 sensor. Control of O 2 storageis achieved through the forecastable disruption compensationblocks in scenarios such as fuel cutoff, where rapid control actionis required to achieve optimal storage.

2.5. Calibration of the outer-loop compensator

The calibration of the outer-loop compensator is performedonce calibration of the inner-loop compensator is achieved. Thus adecoupled calibration scheme for the two loops is proposed. Oneof the main considerations for calibration of the outer-loop is theneed to accommodate and compensate for the post-catalyst O 2sensor deception due to H 2 gas generated by the TWC. For thispurpose, a calibration algorithm is developed ( Midlam-Mohler,Rajagopalan, Dudek, Yurkovich, & Guezennec, 2011 ) where theconverter O 2 storage model ( Rajagopalan, 2008 , p. 20) is usedto keep track of the O 2 stored, based on pre- and post-catalystO2 measurement. The output of this model is compared withthe actual O 2 measurement from the post-catalyst O 2 sensor, togenerate representative statistics for sensor deception. This statis-tical model is then used as a source of disturbance to generateoptimal calibrations for the controller through closed loop simula-tion of the complete system. Fig. 12 illustrates the calibrationprocess for the outer-loop. The set-point voltage for the outer-loopsensor is determined based on knowledge from plant experts,lending to further in-vehicle calibration if necessary. Using thecluster described above, calibration of the outer loop took 1.2 h

over ndata 300 000.

Fig. 11. Outer-loop compensator.



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3. Experimental results

The architecture described in the previous sections was imple-mented and compared to the stock AFR controller in-vehicle ona chassis dynamometer. The vehicle was equipped with a 2 :410 3 m 3 four cylinder, port fuel injected gasoline engine withvariable valve timing. A dual channel Horiba gas analyzer was usedfor simultaneous measurement of pre- and post-catalyst O 2 , CO,NO x and THC in ppm, while a fast H 2 analyzer was used formeasurement of H 2 gas. ETAS-INCA and NI-LABVIEW data acquisi-tion and calibration environments were used for data loggingwhile a dSPACE microautobox was used for rapid-prototyping of the control algorithm. The chassis dynamometer is equipped witha driver aid, which displays the vehicle speed target as a functionof time thus facilitating the driving of standard test cycles. Datafrom the stock-control in open-loop fueling mode was used todevelop mathematical models of the engine, catalyst etc., andthe models thus obtained were used to design and calibrate theAFR controllers through of ine computation. The control algo-rithm was developed in the MATLAB/Simulink environment andthen downloaded into a dSPACE micro-autobox system. The newcontrol algorithm was implemented through a by-pass mechan-ism, where only the desired parameters were overwritten in theengine control module. This facilitated re nement of only the fueland air control, while leaving actuation of other variables such asspark and cam position, to the base engine control algorithm. Theby-pass mechanism was realized through the use of the dSPACENEXUS pod, coupled with a development engine control module.Validation of the developed control algorithm was performedon the chassis dynamometer by comparing the performance of the new controller with the stock vehicle control algorithm on thesame test cycles (e.g. FTP-UDDS, DieselNet ). The vehicle waswarmed up to remove any effects of cold catalyst conditions,which are typically addressed through other control algorithms.Fig. 13 a and b compares the relative performance of the inner-loopAFR regulation through histograms of the measured pre-catalyst

EQR through a UEGO sensor for a hot start FTP-UDDS cycle. The

EQR histogram helps visualize the deviation of engine-out andtailpipe emissions by binning the data from a drive cycle test as apercentage of the total data-points in the dataset. The center valueon the x-axis of the histogram represents the mean, while thespread around the mean indicates the standard deviation orvariance of the data over the drive cycle test. It is observed thatthe performance of the controller based on the new architecture isequal to or better than the stock controller in terms of thestandard deviation of the AFR (3.81% for the stock and 2.61% forthe new controller). A better understanding of the performance isobserved in Fig. 14a and b, which depict the histograms of thepost-catalyst AFR. The stock controller has a standard deviation of 2.09%, while the new controller has a standard deviation of 1.25%.Although such histograms provide an idea about performance,there is no substitute to directly comparing the measured tail-pipeemissions. Fig. 15a and b compares the tailpipe results betweenthe stock controller and the new controller using a Horibagas analyzer for two different drivers (the latter being a moreaggressive driver), for a hot FTP-UDDS run on the chassis dynam-ometer. It can be seen that the new controller has better emissionsperformance. For the normal driving case, using the new controller(shown in red), reduced CO emissions were reduced by 25%compared to stock (represented in blue), THC was reduced by45%, and NO x was reduced by 15%. For the aggressive driving case,the CO emissions were the same, THC was reduced by 35% and NO xby 20%. It is to be noted that this is a lumped emissions estimatefor the whole driving cycle, and not a bagged emissions test, whichis typically the norm for emissions quanti cation in the industry.Most importantly, the calibration effort to tune AFR control gainswas signi cantly reduced by performing all calibrations throughof ine computation. In fact, once vehicle data was collected inopen-loop operation for modeling and closed-loop optimizationpurposes, the controller gains utilized were directly obtained fromof ine computation, without need for further in-vehicle tuning.Thus the existing practice requiring the tuning of feedbackcontrol gains through multiple iterative tests has been replaced by

of ine calibration and automatic tuning without the need for any

Fig. 12. Outer-loop calibration process.



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in-vehicle modi cation, thus saving a multitude of man-hours andcalibration cost. Also, the modular nature of the control architec-ture where the most calibration intensive tasks have been movedto the open loop, allows for easier inclusion of future enginetechnology and hardware, without increasing calibration complex-ity. This has the potential to save computation and memoryrequirements for future controllers, because of code reuse. Onenotable requirement for the approach described in this paper isthe need for a computational cluster. Although the authors did notperform a cost vs bene t and sizing study for the computingcluster, the cost of a cluster described in this paper is at least anorder of magnitude cheaper than infrastructure costs associated

with repeated vehicle testing, and loss in time to market.

4. Conclusion

This paper describes a novel control architecture for air tofuel ratio control of gasoline engines, along with a rapid of inecalibration method that signi cantly reduces in-vehicle calibrationeffort. Experimental data is used to model the system usingLPV techniques which is then used in a servo-mechanism basedarchitecture for the design of a parameter dependent feedbackcontrol. LPV based gain scheduling control accommodates thenonlinear behavior of the plant, while a total synthesis inspiredcontrol architecture helps in transitioning calibration burdenfrom the closed loop to the open loop. Cluster computing is

utilized to calibrate the controller gains in the closed loop through

Fig. 13. Histogram of pre-catalyst AFR measurement for hot FTP-UDDS cycle. (a) Stock controller. (b) New controller.

Fig. 14. Histogram of post-catalyst AFR measurement for hot FTP-UDDS cycle. (a) Stock controller. (b) New controller.

Fig.15. Tail-pipe emissions for hot FTP-UDDS cycle. (a) Normal driving. (b) Aggressive driving. (For interpretation of the references to color in this gure caption, the readeris referred to the web version of this paper.)



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minimization of a cost function that is designed to achieve desiredemission performance metrics. A weak stability constraint (thatdoes not guarantee global stability) is imposed during optimiza-tion through a frozen pole check of the closed loop system, while arigorous analysis to guarantee asymptotic stability of the closedloop system is conducted after the control design is xed, throughan LMI based analysis of the closed loop system using a parameterdependent Lyapunov technique. With the cost of computing

decreasing drastically, this method reduces the need for prototypevehicles, testing facilities and man-hours, especially consideringthat automotive OEMs have to deal with a multitude of enginetypes, vehicle platforms and variations in hardware. Comparisonwith the stock controller over the warmed up FTP-UDDS drivingcycle reveals good performance with a signi cantly minimizedcalibration requirement because of of ine tuning of calibrationgains and parameters for the closed loop controller. The mainreason for the simpli cation of the calibration process is thedesign of an architecture that facilitates moving most of thecalibration effort into open loop modeling and controller referencegeneration, rather than iterative feedback tuning of closed loopcontrol gains and parameters, to compensate for the variousnonlinearities and measurement errors. In particular, this freesthe closed loop system from the responsibility of achieving thedesired dithering response as well as asymmetry in the controlaction in the face of varying plant delays and measurementuncertainty.

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