428 IEEE TRANSACTIONS ON CONTROL SYSTEMS … Articles/Optimal air-to-fuel... · A linear quadratic...

428 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 22, NO. 2, MARCH 2014

Optimal Air-to-Fuel Ratio Tracking Control WithAdaptive Biofuel Content Estimation for

LNT RegenerationXuefei Chen, Yueyun Wang, Ibrahim Haskara, and Guoming Zhu

Abstract— This paper presents an optimal control method oftracking the desired air-to-fuel ratio (AFR) based upon the adap-tively estimated biofuel content for internal combustion enginesequipped with the lean NOx trap (LNT) aftertreatment system.This biofuel content (or percentage of biofuel) is adaptivelyestimated based upon the exhaust oxygen AFR sensor signalunder both the normal engine operations with lean combustionand the LNT regeneration operations with the closed-loop AFRcontrol. The engine system is approximated by a third-orderlinear system in this paper. A linear quadratic optimal trackingcontroller is used to track the desired engine AFR during theLNT regeneration period. The robust stability of the closed-loop tracking control system with the adaptive biofuel contentestimation is guaranteed over the entire biofuel range and enginespeed between 600 and 5500 rpm by using the robust stabilitycriteria for linear parameter variation systems, where the biofuelgain and engine speed are considered as the variable parameter.Several adaptive control schemes are studied through simulations,and then the selected control strategies are evaluated throughdynamometer tests for a lean burn spark ignition engine. The bestperformance is achieved by the gain-scheduled adaptive scheme.

Index Terms— Adaptive estimation, biofuel content estimation,lean NOx trap (LNT) regeneration control, linear quadratic (LQ)optimal tracking.

I. INTRODUCTION

W ITH the growing concerns of global energy crisis andglobal warming, new technologies have been devel-

oped for lean burn engines with the prime focus on the closed-loop combustion control [1], exhaust emission aftertreatmentand control, alternative fuel technology, and so on.

Biofuel is of interest because of its renewable characteristicsand low emissions [2], [3] such as particulate matter. For dieselengines, biodiesel is commonly blended with petroleum baseddiesel. Comparing with the petroleum diesel, biodiesel hasquite different chemical structure [4]–[6]. Biodiesel moleculesconsist almost entirely of chemicals called fatty acid methyl

Manuscript received April 1, 2012; revised December 21, 2012; acceptedMarch 5, 2013. Manuscript received in final form March 7, 2013. Dateof publication April 12, 2013; date of current version February 14, 2014.This work was supported by General Motors under Contract GB821-NV.Recommended by Associate Editor K. Butts.

X. Chen and G. Zhu are with the Department of Mechanical Engi-neering, Michigan State University, East Lansing, MI 48824 USA (e-mail:[email protected]; [email protected]).

Y. Wang and I. Haskara are with General Motors Company, Global Researchand Development, Warren, MI 48090 USA (e-mail: [email protected];[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCST.2013.2252350

esters, which contain unsaturated olefin components, whereasthe low-sulfur petroleum diesel consists of ∼95% saturatedhydrocarbons and 5% aromatic compounds. Therefore, theblend of biodiesel and petroleum-based diesel has quite dif-ferent combustion characteristics, such as start of combustion,burn rate, and so on. Similarly, for gasoline engines, theethanol is blended with petroleum-based gasoline, leading toquite different combustion characteristics. To optimize thecombustion process for a given biofuel blend, it is necessaryto identify the biofuel content so that the combustion processcan be optimized through fuel injection timing and quantityfor diesel engines and through fuel mass and spark timingfor gasoline engines. It should be considered that biofuelcontains less energy content by volume than that of con-ventional petroleum-based fuel. Therefore, the injected fuelquantity needs to be increased to meet the same engine loadrequirement comparing with the petroleum based fuel.

There are several approaches that can be used to estimatethe fuel content. References [7]–[9] estimate the fuel contentbased upon the oxygen sensor signals [10] proposes to use thein-cylinder pressure signal, the ionization signal is also used toestimate the fuel content in [11], and the ionic polymer-metalcomposite beam sensor is used to estimate the fuel contentthrough identifying the fuel viscosity in [12]. In this paper, theoxygen sensor signal is used to adaptively estimate the biofuelcontent of a flex fuel lean burn engine. A similar techniqueis used for gasoline engines [9], where the air-to-fuel ratio(AFR) of gasoline engines is maintained at the stoichiometriclevel through the closed-loop control. However, neither thediesel engines nor the lean burn spark ignition engines regulateAFR. This introduces an additional degree of difficulty toestimate the fuel content as it has to be completed with thefluctuated AFR. It will be even more challenging with an agingoxygen sensor with slow transient response. However, duringthe regeneration of the lean NOx trap (LNT) aftertreatmentsystem, the engine AFR is controlled in a closed loop forflex fuel lean burn engines, which provides an opportunity toaccurately estimate the fuel content.

The LNT technology is designed to significantly reducethe engine nitric oxide and nitrogen dioxide (NOx) emissionsfor lean burn engines, such as diesel engines [13]–[15]. Toreduce the NOx emissions, a LNT catalyst is utilized to storethe NOx emissions during the lean operation, and when thestored NOx reaches a certain level, the LNT needs to beregenerated through the rich AFR operation. During the short

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CHEN et al.: OPTIMAL AFR TRACKING CONTROL 429

rich operation period, the LNT catalyst releases its stored NOxand regenerates its storage capacity, where the released NOx isconverted into nonpolluting nitrogen because of the rich AFR.

The rich AFR can be achieved either by using postinjec-tion [16] or by extending the main injection [17] to increasefuel injection mass. The quantity of injection needs to be con-trolled in a closed loop to regulate the AFR to the desired levelbased upon the oxygen sensor feedback. The control strategiesfor the closed-loop AFR control were widely studied; see [9]for proportional and integral control, [18] for sliding modecontrol, [19] for adaptive control, and [20] for linear parametervariation (LPV) control. In this paper, an adaptive linearquadratic (LQ) tracking controller is proposed for biofuel leanburn engines to regulate the AFR during the LNT regenerationprocess, the biofuel content is estimated using a gradient-based adaptive law [21]. The advantage of the LQ trackingcontrol is that it constitutes linear feedforward and feedbackcontrols that can be easily computed and implemented withestimated state information subjected to system uncertaintiesand measurement white Gaussian noise [22]. To eliminate thesteady-state error, an integral action is introduced in the LQtracking controller.

The lean burn engine system is approximated in this paperby a third-order linear system with a transport delay betweenthe engine combustion chamber and the exhaust manifold,exhaust manifold filling dynamics and the oxygen sensordynamics. The robust stability of the closed-loop system isalso studied in this paper because of the system uncertaintiesintroduced by the mass-air-flow (MAF) measurement, adaptivefuel content estimation, modeling errors of transport delay,and exhaust manifold filling dynamics. The robust stabilityanalysis of uncertain linear systems has received a lot of atten-tions, particularly in the context of uncertain linear systemswith time-varying parameters [23]–[27]. Most of the existingapproaches use quadratic stability analysis, which is knownas a sufficient condition for the stability of linear systemswith arbitrarily fast time-varying parameters, because it doesnot consider bounds on the time-derivatives of the varyingparameters [23], [24]. This paper investigates the robust sta-bility of the closed-loop systems assuming the estimation erroris LPV inside a polytope with the bounded variation rate[26], [27].

Several adaptive control schemes are studied through sim-ulations with respect to the tracking control and adaptiveestimation performance. The developed tracking control basedon the adaptive biofuel content estimation is validated throughdynamometer experiment validation of a lean burn SI engine.The best performance is reached with the adaptive gain-scheduling scheme. The gain-scheduling adaptive estimationis not only able to track the desired AFR during the fast fuelcontent transition but also able to reduce the estimated fuelcontent fluctuation induced by the oxygen sensor noise.

The main contribution of this paper is the application of theadaptive LQ tracking control to regulate the AFR during theLNT regeneration with guaranteed robust stability with respectto the system uncertainties introduced by the MAF mea-surement, adaptive fuel content estimation, modeling errorsof transport delay, and exhaust manifold filling dynamics.

Fig. 1. Engine system modeling.

The proposed control strategy is demonstrated on the enginedynamometer for a flex fuel lean burn engine.

The rest of this paper is organized as follows. In Section IIthe system model is discussed and Section III presents theproposed adaptive estimation and tracking control algorithms.The robust stability analysis of the closed-loop system isdiscussed in Section IV. Section V provides the simulationstudy results, and the experiment validation is described inSection VI, and Section VII addresses the conclusions andfuture work.

II. ENGINE SYSTEM MODEL

It is well known that the energy content of the biofuel isquite different from that of petroleum fuel. The percentage ofbiofuel content can be estimated based upon the measured theexhaust AFR, charged air, and injected fuel quantity as theachieved AFR for a given injected fuel quantity is related tothe fuel content. A control oriented engine model is developedfor fuel content estimation, where the lean burn engine systemis modeled as a direct fuel injection engine with the exhaustmanifold filling dynamics and oxygen sensor dynamics, seeFig. 1. The physical engine dynamics is shown in the dottedbox called plant. To simplify the control design process, theengine model describes the dynamics from input u to outputx3. It can be observed that the input is the desired AFRprovided by the engine control system, the output is themeasured AFR. In the actual application, the control input willbe converted into the fuel mass mfuel based upon the measuredair charge mass ˙mair.

The input � in the solid box is the equivalence fuel-to-airratio defined by

� = mfuel

mairσDS · α (1)

where mair is the air mass charged into the cylinder, σDS isthe stoichiometric AFR for the petroleum based fuel, and αis the stoichiometric gain between petroleum fuel and biofuelblend defined by

α = σBD

σDS(2)

where σBD is the stoichiometric AFR for the given biofuelblend. The injected fuel mfuel is calculated based upon themeasured charged mass ˙mair and the estimated fuel gain α asfollows:

mfuel =˙mair

ασDSu (3)

where u is the equivalence fuel-to-air ratio calculated by thecontroller, and will be defined in the following section.


Fig. 2. Adaptive LQG tracking control system.

Assuming the transport delay between the cylinder andexhaust manifold can be modeled using the following first-order transfer function:

G1(s) = 1

1 + τ1s(4)

where τ1 is the time constant for the transport delay, whichaccounts for the time between the instant of the fuel injectionand the opening of the exhaust valve. The exhaust manifoldfilling dynamics is also modeled as the first-order dynamicsas follows:

G2(s) = 1

1 + τ2s(5)

where τ2 is the time constant of the charge filling dynamicsand is a function of the effective length of the exhaust manifoldand the exhaust flow rate. In this paper, it is measured fromthe time that the exhaust valve opens to the oxygen sensorsignal changes. The oxygen sensor dynamics is also modeledas the first-order dynamics as follows:

G3(s) = 1

1 + τ3s(6)

where τ3 is the time constant of the sensor dynamics.τ3 increases as the sensor obtains aged.

Therefore, the system transfer function from input equiva-lence ratio U(s) to the output equivalence ratio Y (s) measuredby the oxygen sensor is

Y (s) = X3(s)

= 1

(1 + τ1s)(1 + τ2s)(1 + τ3s)

ασDS

mairMfuel(s) (7)

where Mfuel(s) is the Laplace transformation of mfuel.Equation (7) can also be expressed as

Y (s) = 1

(1 + τ1s)(1 + τ2s)(1 + τ3s)

˙mairα

mairαU(s)

= 1

(1 + τ1s)(1 + τ2s)(1 + τ3s)(1 + δ)U(s) (8)

where U(s) is the Laplace transformation of u, andδ = ( ˙mairα/αmair) − 1 is the system uncertainty because ofestimation error of the fuel content α and measurement errorof the air charge mass ˙mair. In addition, the fuel injectionshot-to-shot variations are modeled as the system noise inputw, and the oxygen sensor measurement noise is represented

by v. This leads to the following nominal state space modelwith δ = 0:

x = Acx + Bcu + Bcwy = Ccx + v (9)

where

Ac =⎡⎢⎣

− 1τ1

0 01τ2

− 1τ2

00 1

τ3− 1

τ3

⎤⎥⎦ , Bc =

⎡⎣

1τ1

00

⎤⎦ , Cc = [ 0 0 1

].

Linear system (9) is then discretized into the followingdiscrete state-space model with a sample period of 25 ms:

x(k + 1) = Ax(k) + Bu(k) + Bw(k)

y(k) = Cx(k) + v(k). (10)

Both the input noise {w(k), k = 0, 1, . . .} and measurementnoise {v(k), k = 0, 1, . . .} are assumed to be zero mean andmutually independent random vectors such that

E{w(k)} = 0, W = E{w(k)w(k)} > 0

E{v(k)} = 0, V = E{v(k)v(k)} > 0 (11)

where W and V are the corresponding covariance matrices.

III. CONTROL STRATEGY DEVELOPMENT

The proposed control algorithm used to regulate the com-bustion AFR in the presence of unknown biofuel content is anadaptive linear quadratic Gaussian (LQG) tracking controller,as shown in Fig. 2, where the adaptive scheme is usedto estimate the fuel gain α (or content); the Kalman stateestimator is used to estimate system state vector x , and theoptimal LQ tracking controller is used to track the desiredequivalence ratio r based upon the estimated states.

A. Adaptive Fuel Gain Estimation

In (7), assuming the injected fuel mass for conventional fuelis known, the air mass can be measured by a mass flow sensorand state x3 is the fuel-to-air ratio measured by the oxygensensor at the exhaust manifold. The only unknown term is thefuel gain α. Reorganize (7) into the following form:

X3(s) = αG(s)1

mairMfuel(s) = αφ(s) (12)

where

G(s) = σDS

(1 + τ1s)(1 + τ2s)(1 + τ3s)

φ(s) = G(s)1

mairMfuel(s).

Discretizing transfer function G(s) defined in (12) yieldsthe following discrete transfer function:

X3(z) = αG(z)1

mairMfuel(z) = αZ(z). (13)

Based upon the gradient method introduced in [21] thatminimizes the instantaneous cost

J (α) =(x3(k) − α(k − 1)z(k)

)22m2

s (k)(14)


where z(k) is the inverse z transformation of Z(z), the adaptivelaw can be expressed as

α(k) ={

α(k − 1) + �ε(k)z(k), for ∀α ∈ [α, α]α(k − 1), otherwise

(15)

where constant α and α are the lower and upper bounds ofthe estimated α(k), respectively; � is the adaptive gain; andε(k) is defined by

ε(k) = x3(k) − α(k − 1)z(k)

m2s (k)

(16)

where m2s (k) = 1 + 0.01zT (k)z(k) is chosen to guarantee the

bounded estimation of α(k).It is well known that the convergence of the estimated α

is guaranteed by the persistent exciting φ(t) assumption [21],where φ(t) is the inverse Laplace transform of φ(s) in (12).Since φ(t) is a scalar function, as long as the fuel flow isgreater than zero, or mfuel > 0, there exist T0 > 0 and ξ > 0such that ∫ t+T0

tφ(τ)φT (τ )dτ ≥ T0ξ (17)

for t ≥ 0. As the above integral is always invertible, thecondition for the persistent excitation is always satisfied, andhence, the estimation convergence is guaranteed.

B. Kalman State Estimation

The Kalman state estimation is a stochastic filter that pro-vides the optimal state estimation for a linear system subjectto Gaussian noise inputs. For a given initial state x(0) and thecurrent measurement y(k), the Kalman state estimator can beexpressed in the following form:

x(k + 1) = Ax(k) + Bu(k) + K f [y(k + 1) − Cx(k)]. (18)

The Kalman filter gain K f can be calculated from thefollowing equation:

K f = H CT[C H CT + V

]−1(19)

where the state error covariance matrix H is solved by thefollowing algebraic Riccati equation:

H = A

[H − H CT

(C H CT + V

)−1C H

]AT + BW BT .

(20)

C. LQ Tracking Control With Integral

Here, a LQ controller is developed to track the desiredequivalence fuel-to-air ratio. To eliminate the steady-stateerror, an integral control is introduced into the LQ controllerby defining the tracking error e(k) as

e(k + 1) = e(k) + y(k) − r(k) = e(k) + Cx(k) − r(k). (21)

Augmenting state vector x(k) =[

x(k)e(k)

]yields the following

state equation:x(k + 1) = Ax(k) + Bu(k) + dr(k)

y(k) = C x(k) (22)

where

A =[

A 03×1C 1

], B =

[B0

]

C = [ C 0 ], d =[

03×1−1

].

The cost function of the LQ controller is defined as

J = EN→∞

{N−1∑k=0

[x(k)T Qx(k) + u(k)T Ru(k)]}

(23)

where the weight matrices Q and R are given so thatQ = QT ≥ 0, and R = RT > 0. Then, the optimal control is

u(k) = −K x(k) + Krr(k) (24)

where

K =[

BT S B + R]−1

BT S A (25)

and S is the solution to the following algebraic Riccatiequation:

S = AT[

S − S(

B(

BT S B + R))−1

BT S

]A + Q. (26)

Kr in (24) is given by

Kr =[

BT S B + R]−1

BT F1 (27)

and

F1 = −[

I − AT + AT SF3 F2

]−1AT SF3 F2d (28)

where F2 = BT R−1 B, F3 = [I + F2 S]−1, and I is an identitymatrix.

Define the dimension of x , y, and u as nx , ny , and nu ,respectively. Partition the state feedback matrix in terms of itsfirst nx columns and its last ny columns

K = [ Kx Ke]. (29)

Then, the optimal control law can be written as follows:

u(k) = − [ Kx Ke] [ x(k)

e(k)

]+ Krr(k). (30)

As not all states are measurable, recall the estimated state x(k)and replace x(k) with x(k) in (30). Then, the LQG control lawcan be expressed as follows:

u(k) = −Kx x(k) − Kee(k) + Krr(k). (31)

IV. SYSTEM ROBUST STABILITY ANALYSIS

The robust stability of the closed-loop system, shown inFig. 3, in the presence of system uncertainty δ is analyzed byusing the approach introduced in [27] for the (LPV) system.For the stability analysis, the system noise input w and theoxygen sensor measurement noise v in (10) are set to zero.Replace the control input with u defined in (31) and (10) canbe expressed as

x(k + 1) = Ax(k)+ B[−Kx x(k) − Kee(k) + Krr

](1 + δ(k))

(32)


where the estimated state x and the tracking error e can beexpressed as

x(k + 1) = Ax(k) + K f[Cx(k + 1) − Cx(k)

]

+B[−Kx x(k) − Kee(k) + Krr

](1 + δ(k)).

(33)

Then, write (32), (33), and (21) into the state-space form

xCL(k + 1) = ACLxCL(k) + BCLr (34)

where

xCL(k) =⎡⎣

x(k)x(k)e(k)

⎤⎦

n×1

BCL(k) =⎡⎣

(1 + δ(k))B Kr

(1 + δ(k))(B + K f C B)Kr

−1

⎤⎦

n×1

and AC L shown in the equation at the bottom of the page, theorder of the closed-loop system is n = 7. Define

A0 =

⎡⎢⎢⎣

A −B Kx −B Ke

K f C AA − K f C

−(B + K f C B)Kx−(B + K f C B)Ke

C 0 1

⎤⎥⎥⎦

(35)

�A =⎡⎣

03×3 −B Kx −B Ke

03×3 −(B + K f C B)Kx −(B + K f C B)Ke

01×3 01×3 0

⎤⎦ (36)

so that the closed-loop system matrix is

ACL = A0 + δ(k)�A. (37)

As the reference input does not affect the system stability, theclosed-loop system (34) with r = 0 is investigated as follows:

xCL(k + 1) = ACL(δ(k))xCL(k). (38)

It is clear that ACL is a linear function of δ(k), and therefore,system (39) is a linear parameter varying system and therobust stability can be analyzed using the approach describedin [27]. This paper focuses on the effect of the fuel contentestimation to stability with the air flow measurement error.The air flow estimation can also be improved using the speed-density approach. From (8), δ can be expressed as follows:

δ(k) =˙mair(k)α(k)

mair(k)α(k)− 1. (39)

Let εair be the percentage error bound for the charged massair measurement. It is easy to obtain that

δ(k)∈[ δmin δmax]=[ (1−εair)

σBDσDS

−1 (1+εair)σDSσBD

−1].

(40)

Define

A1 = A0 + δmin�A (41)

A2 = A0 + δmax�A (42)

so that the time varying matrix (37) can also be expressed inthe following form:

ACL(β(k)) =2∑

i=1

βi (k)Ai (43)

where β(k) ∈ [β1(k) β2(k)]T is the vector of time-varying

parameters in the unit simplex

2 ={

β ∈ R2 :

2∑i=1

βi (k) = 1, βi ≥ 0, i = 1, 2

}. (44)

The rate of variation of the parameters

�βi(k) = βi (k + 1) − βi (k), i = 1, 2 (45)

is assumed to be limited by a priori defined bound b > 0 suchthat

−b ≤ �βi (k) ≤ b, i = 1, 2 (46)

with b ∈ [ 0, 1]. Case b = 0 indicates β(k) is frozen, hence

the system becomes a linear time-invariant system. Althoughb = 1 implies that β(k) is allowed to vary arbitrarily inside 2. Therefore, the bound on the variation rate of δ(k) can beexpressed as

−b(δmax − δmin) ≤ δ(k + 1) − δ(k) ≤ b(δmax − δmin). (47)

Simultaneously, it is also easy to see, from (44) and (45), thatthe following is satisfied:

2∑i=1

�βi (k) = 0. (48)

To model the domain of the bound on time-difference, thevector (β(k),�β(k))T ∈ R

2×2 can be assumed to belong tothe compact set

�b =

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

ξ ∈ R2×2 : ξ ∈ co{g1, . . . , gM }

g j =(

f j

h j

), f j ∈ R

2 h j ∈ R2

∑2i=1 f j

i = 1 with f ji ≥ 0, i = 1, 2,∑2

i=1 h ji = 0, j = 1, . . . , M

⎫⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎭

(49)

where the vectors g j for j = 1, . . . , M can be found to be[g1 · · · gM

]=[

f 1 · · · f M

h1 · · · hM

]

=

⎡⎢⎢⎣

1 1 0 0 b 1 − b0 0 1 1 1 − b b0 −b 0 b −b b0 b 0 −b b −b

⎤⎥⎥⎦ (50)

ACL =

⎡⎢⎢⎢⎣

A −(1 + δ(k))B Kx −(1 + δ(k))B Ke

K f C AA − K f C

−(1 + δ(k))(B + K f C B)Kx−(1 + δ(k))(B + K f C B)Ke

C 0 1

⎤⎥⎥⎥⎦

n×1


TABLE I

ENGINE SYSTEM PARAMETERS

Engine displacement 0.4 LCompression ratio 12.5Engine speed 1500 rpmσDS (gasoline) 14.6σBD (E85) 9.7εair 3%τ1 0.08 sτ2 0.06 sτ3 0.2 s

with M = 6, see [27]. Once the columns of the set �b aredefined, the convex set can be expressed as

(β(k), �β(k))T =M∑

j=1

(f j

h j

)γ j (k) (51)

where γ (k) ∈ M , and M has the similar expression as 2.Choose the Lyapunov matrix P(β(k)) and �(β(k)) to have

the following affine parameter-dependent structure:

P(β(k)) =2∑

i=1

βi (k)Pi =M∑

j=1

γ j (k)Pj (52)

�(β(k)) =2∑

i=1

βi (k)�i =M∑

j=1

γ j (k)� j (53)

where Pj = ∑2i=1 f j

i Pi , and � j = ∑2i=1 f j

i �i . Similarly,ACL(β(k)) also can be converted as

ACL(β(k)) = ACL(γ (k)) =M∑

j=1

γ j (k) A j (54)

with A j = ∑2i=1 f j

i Ai . According to [26] and [27], if thereexist, for j = 1, . . . , M , matrices � j ∈ R

n×n and, for i =1, 2, symmetric positive-definite matrices Pi ∈ R

n×n such that[∑2

i=1

(f ji + h j

i

)Pi A j � j

�Tj AT

j � j + �Tj −∑N

i=1 f ji Pi

]> 0 (55)

for j = 1, . . . , M and[∑2

i=1

(f ji + f l

i + h ji + hl

i

)Pi Al� j + A j�l

�Tj AT

l + �Tl AT

j � j l

]> 0 (56)

with

� j l = � j + �Tj + �l + �T

l −2∑

i=1

(f ji + f l

i

)Pi

for j = 1, . . . , M − 1 and l = j + 1, . . . , M , then (39) isexponentially stable.

V. MODEL CALIBRATION AND SIMULATION VALIDATION

A. Engine Dynamometer Test Setup

The proposed LQG tracking control with adaptive esti-mation is validated on a lean burn SI flex-fuel engine. Thespecifications of the target single cylinder are listed in Table I.

E85 fuel tank

Gasoline fuel tank Fuel

Single cylinder engineHigh pressure Nitrogen bottle

Fig. 3. Engine dynamometer setup.

Fig. 4. Fuel system diagram.

Fig. 3 shows the engine dynamometer test setup used forgenerating engine model calibrations and closed-loop controltests. The engine is equipped with a direct injection fuelsystem. Two fuel tanks, one filled with gasoline and the otherfilled with E85, are connected to a fuel pipe line through afuel switch valve as shown in Fig. 4. Both of fuel tanks areregulated at 5 MPa by two high pressure nitrogen bottles. Theengine is operated at 1500 rpm with 5-bar indicated meaneffective pressure. The engine responses are recorded by theA and D combustion analysis system. Table I lists the calcu-lated engine model parameters obtained from the test data.

The engine is also equipped with variable valve timing(VVT) for both intake and exhaust valves. The exhaust gasrecirculation (EGR) is mainly because of the trapped residualgas. It is true that the residual gas affects the overall AFR.However, as the fuel content estimation is based upon thecharged air mass and the injected fuel quantity, the amountof EGR will not affect estimation accuracy. In addition, theintake of VVT may alter the engine charge air quantity that ismeasured by the MAF sensor. As long as the measurement isaccurate, the fuel content estimation will not be affected. Thatis why the effects of both EGR and VVT are not consideredin this paper.

B. Stability Validation

Table II lists the parameters used for the estimation andcontrol design. The excitation noise covariance matrices Wand V are selected assuming the exciting noise w is muchlarger than the measurement noise v. The LQ control weight-ing matrices Q and R are selected based upon the closed-loopsystem response time and its relative stability.


TABLE II

CONTROL DESIGN PARAMETERS

Q R W V⎡⎢⎢⎢⎣

1 0.012 0.012 0.012

0.012 1 0.012 9.6

0.012 0.012 250 60

0.012 9.6 60 2.6

⎤⎥⎥⎥⎦ 100 1 0.0005

The resulting Kalman state estimation gain is

K f = [4.0543 3.2287 0.6467]T (57)

and the controller is given below

Kx = [0.3426 0.2944 1.1345]Ke = 0.1526

Kr = 2.2992. (58)

The system robust stability analysis is completed by findingthe feasible solutions for (55) and (56) using the MATLAB

linear matrix inequality toolbox. Two positive definite sym-metric matrices P1 and P2 are found with b equal to 1; seeP1 and P2 in Appendix. This indicates that β(k) is allowed tovary arbitrarily fast inside 2 defined in (44) with guaranteedstability, which therefore leads to the conclusion that δ(k)can vary arbitrarily fast for δ(k) ∈ [ δmin δmax

]based upon

(47). Therefore, the closed-loop system robust stability isguaranteed even when the fuel content is changed from onefuel (gasoline) to the other (E85) in one time step. This isalmost impossible in reality.

For the practical applications, the engine transport delay andexhaust manifold filling dynamics are also parameter-varying.More specifically, the transport delay and the exhaust manifoldfilling dynamics can be modeled as a function of engine speedand they can be approximated as follows:

τ1 = τ10 × 3050

Neng, τ10 = τ10 × 1500

3050(59)

τ2 = τ20 × 3050

Neng, τ20 = τ20 × 1500

3050(60)

where Neng is the current engine speed, τ10 and τ20 are the timeconstant values for the engine transport delay and the exhaustmanifold filling dynamics when the engine is operated at1500 rpm. The early linear-parameter-varying modeling workof engine air-to-ratio systems can be found in [20] and [28]. AnLPV controller could be designed to consider such parametervariations in a similar way that was described in [20] and [28].However, this is not the focus of this paper.

To show that the closed-loop system is stable under varyingengine speed, the closed-loop system robust stability undervarying fuel gain estimation error and engine speed is studied.Let

ζeng = Neng − 3050

3050(61)

so that

ζeng ∈ [ ζeng_ min ζeng_ max] = [−0.80 0.80

](62)

_ min maxˆ( , )CL engA ζ δ_ min min

ˆ( , )CL engA ζ δ

_ max minˆ( , )CL engA ζ δ _ max max

ˆ( , )CL engA ζ δδ

engζ

Fig. 5. Closed-loop system matrix ACL varying bound.

which is corresponding to the engine speed varying rangebetween 600 and 5500 rpm. To use the stability analysisapproach described in [27] the closed-loop system matricesmust be an affine function of δ and ζeng. Continuous timesystem matrices Ac and Bc in (9) can be expressed as follows:

Ac = Ac0 + Aτ ζeng, Bc = Bc0(1 + ζeng) (63)

where

Ac0 =⎡⎢⎣

− 1/τ10

0 01/

τ20− 1/

τ200

0 1/τ3

− 1/τ3

⎤⎥⎦

Aτ =⎡⎢⎣

− 1/τ10

0 01/

τ20− 1/

τ200

0 0 0

⎤⎥⎦

Bc0 = [1/τ10 0 0

]T.

As the sample period is fairly small (25 ms), the first-order approximation is used to express the discretized systemmatrices A and B , defined in (10), in the affine form. Theassociated discrete time system matrices are

A = eAc0Ts +eAc0Ts Aτ ζengTs, B = eAc0Ts Bc0(1+ζeng)Ts (64)

where Ts is the sample period. System matrices Acl and Bcl

described below (34) are in terms of (1 + δ)B . To makeAcl and Bcl affine functions of ζeng and δ, a new variableδ = (1 + ζeng)δ is introduced such that

(1 + δ)B = eAc0Ts Bc0

(1 + ζeng + δ

)Ts . (65)

Following the same process described in the beginning of thissection, the closed-loop system can be expressed as the affinefunction of ζeng and δ. Based on the engine speed varyingbetween 600 and 5500 rpm (ζeng ∈ [ ζeng_ min ζeng_ max ]) andδ varying between −0.087 and 0.608 (δ ∈ [ δmin δmax ]),as shown in Fig. 5, using the same stability analysisapproach [27] as the one variable case, four positive definitesymmetric matrices Pi=3,...,6 are found for b equal to one,which indicates that the system is robustly stable when bothtransport delays (τ1 and τ2 because of varying engine speed)and the fuel content estimation error varies in full range


0

1

2

3

4λ

90 110 130 150 170 1900.65

0.75

0.85

0.95

1.05

Time(s)

Fue

l ga

inReference λActual λ

Reference fuel gainEstimated fuel gain

LNT regeneration

Identify fuelwithin 7sFuel switch

Fig. 6. Regular scheme with AFR sensor on the engine (τ3 = 0.2).

within one sample period. Matrices Pi=3,...,6 can be foundin Appendix.

The LQ controller and Kalman state estimator described in(57) and (58) are with fixed control and state estimation gains.However, combined with the adaptive biofuel content adaptiveestimation and compensation, the closed-loop controller isgain-scheduled. As the robust stability is demonstrated forany fuel estimation error and fuel content rate change withingasoline and E85, it indicates that a robust stabilizing con-troller can also be designed. However, the robust controlleris normally conservative and guarantees only the closed-loopstability, whereas the controller presented in this paper notonly guarantees the closed-loop stability but also providesthe desired tracking performance because of the adaptive fuelgain compensation. For an alternative solution, a LPV controlcan be designed to guarantee the stability and performance[27], [29].

Above conclusion is reached based upon the estimation andcontrol gains described in (57) and (58). To demonstrate thatthe robust stability may not be guaranteed with the poorlydesigned state estimation and control gains, we redesignedthe state estimator for (10) by placing the estimation poles at

[0.90 0.89 0.88] (66)

and modified the control gain for (22) by placing the controlpoles at

[0.94 0.86 0.85 0.84]. (67)

There exist no feasible positive definite solutions to P1 andP2 when b is equal or greater than 0.72. This indicatesthat the robust stability of the closed-loop system cannot beguaranteed if the estimation and control gains are not properlydesigned. We recommend selecting proper weighting matricesfor the Kalman filter and LQ control design. Normally, themeasurement noise intensity matrix V shall be far smallerthan the excitation noise intensity W, LQ output weightingmatrix Q shall be used to scale the state variables, and controlweight matrix R can be used for tuning the control gain.

C. Simulation Results

For lean burn engine simulations presented here, the engineAFR is not controlled in a closed loop except during the LNTregeneration, whereas the Kalman state estimation updates theestimated states under all engine operational conditions.

For the purpose of validating the AFR tracking perfor-mance with the fuel content estimation, the LNT regeneration

0

1

2

3

4

λ

Reference λActual λ

90 110 130 150 170 1900.65

0.75

0.85

0.95

1.05

Time(s)

Fue

l ga

in

Reference fuel gainEstimated fuel gain2% estimated fuel

gain deviation

Fig. 7. Regular scheme with an aged oxygen sensor (τ3 = 0.3).

enabling logic is not considered in this paper and a prerecordedlean burn engine AFR signal is used as the reference AFRinput, along with the mass air flow signal. During the open-loop AFR operation, the engine fueling is equal to mass airflow divided by the reference AFR; and during the LNTregeneration, the AFR is controlled by the tracking control.Three adaptive estimation schemes are used in the simulationsas follows.

1) Regular Scheme: the fuel content estimation is updatedwith one adaptive gain all the time.

2) Semiactive Scheme: the fuel content estimation is activeonly during the LNT regeneration process.

3) Dual-Gain Scheme: same as the regular scheme exceptthat two adaptive estimation gains are used, where thesmall gain is used under the open-loop AFR operationand the large gain under the LNT regeneration.

For simplicity, the engine equivalence (fuel-to-air) ratio(� = 1/λ) is converted into the normalized AFR λ in thesimulation plots. To simulate the injector shot-to-shot variationand AFR sensor measurement noise, 3% white noise is addedto the injected fuel quantity and 5% white noise to the AFRsensor output.

Fig. 6 shows the simulation results for the regular scheme(Scheme 1) with the measured AFR sensor time constantτ3 = 0.2. The adaptive gain � is turned to 0.015 to havefast response. The engine is operated under the open-loopAFR operation for most of the time, and the four-s LNTregeneration period occurs every 60 s. During the regeneration,the normalized AFR is controlled in a closed loop and isregulated to be slightly less than one (0.98). Gasoline is usedat the start of the simulation and is switched to E85 at the120th s. As the adaptive estimation is always active, the biofuelcontent estimation converged within 7 s after the fuel switch.However, with an aged AFR sensor that has time constantτ3 > 0.2, the selected adaptive gain (� = 0.015) might be toolarge to have stable biofuel content estimation. Fig. 7 showsthe simulation results with an aged oxygen sensor (τ3 = 0.3),where the fuel content estimation error increases during thetransient AFR operations.

To reduce the adaptive estimation error during the open-loop AFR operation, the second adaptive control scheme(semiactive scheme) estimates the fuel content only duringthe LNT regeneration period using the same adaptive gain asthat in Scheme 1 (regular scheme); see Fig. 8 for simulationresults. It can be observed that the estimated biofuel content


0

1

2

3

4λ

100 120 140 160 180 200 220 2400.65

0.75

0.85

0.95

1.05

Time(s)

Fue

l ga

inReference λActual λ


AFR error

Fuel switchIdentify fuel in the 2ndLNT regeneration periodafter fuel switch

Fig. 8. Semiactive scheme with aged oxygen sensor (τ3 = 0.3).

0

1

2

3

4

λ

90 110 130 150 170 1900.650.750.850.951.05

Time(s)

Fue

l ga

in


Reference fuel gainEstimated fuel gain without MAF errorEstimated fuel gain with 3% MAF error

AFR error gradually decreasing

3% fuel gainestimation error

Fig. 9. Dual-gain scheme with aged oxygen sensor (τ3 = 0.3).

converges in couple of seconds after the start of the LNTregeneration period. The advantage of this scheme is thatit stops the adaptive estimation during the open-loop AFRoperation to eliminate estimation error during the transientAFR operation, however, the disadvantage is that the fuelcontent is not updated until the next LNT regeneration period,which could lead to large engine torque control error. Accurateengine torque control is very important for hybrid powertrains.

The third adaptive control scheme (dual-gain scheme) com-bines the advantages of the previous two schemes. It uses asmall adaptive estimation gain (� = 0.005 for this simulation)during the open-loop AFR operation and a large adaptiveestimation gain (� = 0.015) during the LNT regeneration.Fig. 9 shows the simulation results of the dual-gain scheme.The AFR represented by the dotted line is the fuel gainestimated under the same conditions as shown in Fig. 8. It isobvious that the small adaptive gain used during the open-loopAFR operation is capable of providing an accurate estimationof the fuel content before the next regeneration even thoughit converges slowly. For the practical engine operation, stepfuel content change is not physically possible and it will varyrelatively slowly; see the next section. Therefore, the practicalperformance of the third adaptive control scheme could bebetter.

The AFR trace represented by the dashed line in Fig. 9 isthe estimated fuel content with 3% mass air flow sensor error,leading to 3% fuel content estimation error.

VI. DYNAMOMETER VALIDATION

The fuel content transition process for experimental valida-tion is designed to start operating the engine with one type offuel (for instance, gasoline), and then with the fuel switchedto the other (for instance, E85) in the middle of the test. Afterthe fuel is switched, two types of fuels are mixed in the fuel

0.60.8

11.2

Fue

l G

ain

1.5

2

2.5

Fuel

Pul

se

(m

s)

Fuel Pulse

Fuel Gain

100 200 300 400 500 600 700 8001

1.2

1.4

Time(s)

λ

Reference λMeasured λ

238 240 242 244 246 248

1

1.2

1.4

λ


300 350 400 450 500

1

1.2

1.4

Time(s)

λ Reference λMeasured λ

Misfire or partial burn

Delay

AFR error due to small

adaptation gain

(a)

(b)

Fig. 10. (a) Single adaptive gain for fuel transit from gasoline to E85.(b) Single adaptive gain for fuel transit from gasoline to E85.

line around the fuel switch valve and eventually the fuel line isfilled with the second fuel. Correspondingly, three combustionstages can be clearly observed through the estimated fuel gain:1) combustion with the first fuel; 2) the transition combustionwith the mixed two fuels; and 3) combustion with the secondfuel. Engine throttle is fixed for all tests. In addition, sincethe experimental validation is centered at the AFR controlduring the LNT regeneration, the engine torque balance is notconsidered. As a result, the engine spark timing is also fixedduring the validation tests; otherwise, it would be controlledto keep the engine output torque constant during the LNTregeneration. Similar to the simulations in the previous section,the closed-loop reference AFR is set to 1.0 during the closed-loop LNT regeneration, and the open-loop reference is 1.3when the engine is not in the LNT regeneration mode. To avoidthe interaction between transient AFR control and adaptiveestimation, the fuel content estimation is disabled during AFRtransition for the first 0.6 s. The adaptive estimation gainused in the experiments is retuned such that the fuel contentfluctuation is minimized under the fixed fuel content withthe fastest convergence rate. The retuned adaptive estimationgains are smaller than these used in the simulations becauseof additional MAF sensor noise that is not considered insimulations.

The engine dynamometer test started with one adaptivegain scheme with � = 0.0025. Fig. 10(a) and (b) showsthe test results for the fuel transition from gasoline to E85.The entire transition lasted for 700 s. Fig. 10(a) shows thatthe entire transition consists of three periods (slow-fast-slow),and 40% of the fuel content transition is completed duringthe fast transition period from 300th to 400th s. Because ofthe adaptive estimation error, the AFR control error existsespecially during the open-loop control period. Fig. 10(b)shows the details of the AFR signal from 238th to 248th s


0.60.8

11.2

Fue

l G

ain

100 200 300 400 500 600 700 800

1

1.2

1.4

λ

350 400 450 500

1

1.2

1.4

Time(s)

λFuel Gain



Fig. 11. Dual adaptive gain for fuel transit from gasoline to E85.

TABLE III

SCHEDULED ADAPTIVE GAIN

λ Error 0 0.01 0.02 0.03 0.04 0.05

Adaptive Gain 1e−4 2.5e−4 5e−4 6.2e−3 0.0125 0.0125

0

1

2

3

4

λ

90 110 130 150 170 1900.65

0.75

0.85

0.95

1.05

Time(s)

Fue

l ga

in



Fuel switch

Estimated fuel gaingradually converged

AFR error

Fig. 12. Gain scheduling scheme with aged oxygen sensor (τ3 = 0.3).

and from 350th to 500th s. It is easy to see that the measuredAFR closely followed the reference signal during the LNTregeneration period because of closed-loop control, whereasduring the open-loop AFR operation, some misfire or partialburn occurrs because of the lean limit of the SI enginecombustion caused by the fuel estimation error. The keyobservation from Fig. 10 is that the majority of the fuel contenttransition occurs during the open-loop AFR operation period.Therefore, it is very important to use an appropriate adaptivegain to estimate the fuel content during the open-loop AFRoperation.

Fig. 11 shows the experimental results for the dual-gainscheme. As most of the fuel transition is completed duringthe open-loop AFR operation, the closed-loop adaptive gain iskept at 0.0025, whereas the open-loop gain is set at 0.005. Theexperimental results show certain performance improvement,but the large estimation error exists during the transition.

To improve the fuel content estimation performance duringthe open-loop operation, the gain-scheduling scheme for adap-tive estimation is proposed. Table III lists the tuned adaptivegain as a function of the AFR error. The correspondingsimulation results are shown in Fig. 12. It can be observedthat, with the scheduled adaptive gain, the time for the fuelgain to converge is significantly reduced compared with thedual-gain scheme as shown in Fig. 9. Also, the dynamometertest demonstrates the similar improvement as shown in Fig. 13.

To have a quantitative comparison among three adaptiveschemes used in the test, the mean absolute deviation (MAD)

0.60.8

11.2

Fuel

Gai

n

Fuel Gain

200 300 400 500 600 700 800 9001

1.2

1.4

λ


400 440 480 520 560 600

1

1.2

1.4

Time(s)


Fig. 13. Gain scheduling estimation for fuel transition from gasoline to E85.

TABLE IV

AFR MAD

Single Gain Dual Gain Gain Scheduling

MAD 0.02777 0.02594 0.02476

0.60.8

11.2

Fue

l G

ain

Fuel Gain

200 300 400 500 600 700 800 900

1

1.2

1.4

λ


200 250 300 350

1

1.2

1.4

Time(s)


Misfire

Fig. 14. Gain scheduling for fuel transit from E85 to gasoline.

of the AFR error of each scheme is calculated and listed inTable IV.

Finally, the gain-scheduling adaptive scheme is also testedfor the fuel transition from E85 to gasoline. Fig. 14 shows thetest results with the same scheduled adaptive gain. Comparedwith the fuel transition from gasoline to E85, the transitionfrom E85 to gasoline has a much faster initial transition period.It only took 25 s for the fuel gain to transit from 0.67 to 0.83,whereas it took almost 600 s to complete the rest of the fuelcontent transition. We believe that it is because of the higherviscosity of the E85 than that of gasoline. When the gasolineflow through the fuel line filled with E85, it would take moretime to dilute E85 close to the wall of fuel line with gasolinethan the time to dilute gasoline with E85. As a summary, thedynamometer experiment results show that the proposed LQGtracking control with the adaptive fuel content estimation isfeasible and the gain-scheduling adaptive estimation providesthe best fuel content estimation with accurate AFR trackingduring the LNT regeneration.

VII. CONCLUSION

This paper proposed to use the LQ optimal tracking controlto regulate the AFR of a biofuel lean burn engine duringthe LNT regeneration based upon the adaptively estimatedbiofuel content. The robust stability of the closed-loop systemwith adaptive estimation can be analyzed based upon theframework of the linear parameter varying systems. Sev-eral adaptive control schemes were studied through both


simulations and dynamometer experiments. It showed thatthe proposed LQ tracking control with the gain-schedulingadaptive estimation provided the best fuel estimation per-formance (minimal AFR error) and demonstrated the abilityof regulating the engine AFR during the LNT regenerationfor a flex fuel lean burn engine. It was also found that thefuel content transition from E85 to gasoline was much fasterthan the same process from gasoline to E85 for the sameconfiguration. Future work will include optimizing the engineoperation to maintain the desired torque during the LNTregeneration.

APPENDIX

P1 =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

0.35 −0.05 −0.05 0.24 0.09 −0.06 −0.02−0.05 0.49 −0.07 0.12 0.21 −0.01 −0.09−0.05 −0.07 0.06 −0.01 −0.03 0.05 −0.110.24 0.13 −0.01 1.14 0.41 0.03 −0.110.09 0.21 −0.03 0.41 0.73 0.02 −0.08

−0.06 −0.01 0.05 0.03 0.02 0.06 −0.11−0.02 −0.09 −0.11 −0.11 −0.08 −0.11 1.28

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

P2 =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

0.36 −0.05 −0.06 0.21 0.05 −0.07 −0.02−0.05 0.49 −0.07 0.13 0.21 −0.01 −0.09−0.06 −0.07 0.06 −0.02 −0.03 0.05 −0.110.21 0.13 −0.02 1.14 0.42 0.04 −0.110.05 0.21 −0.03 0.42 0.75 0.03 −0.08

−0.07 −0.01 0.05 0.04 0.03 0.06 −0.11−0.02 −0.09 −0.11 −0.11 −0.08 −0.11 1.28

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

P3 = 10−12

×

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

111.65 −0.72 0.43 0.15 −0.97 0.23 31.06−0.72 0.04 −0.06 0.09 0.08 −0.05 −0.050.43 −0.06 0.34 −0.60 −0.40 0.26 −1.720.15 0.09 −0.60 1.21 0.74 −0.46 3.70

−0.97 0.08 −0.40 0.74 0.60 −0.30 1.590.23 −0.05 0.26 −0.46 −0.30 0.22 −1.42

31.06 −0.05 −1.72 3.70 1.59 −1.42 22.71

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

P4 = 10−12

×

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

114.80 −0.82 0.22 0.47 −0.78 0.03 32.87−0.82 0.04 −0.07 0.10 0.10 −0.05 −0.040.22 −0.07 0.38 −0.69 −0.47 0.30 −2.020.46 0.10 −0.69 1.35 0.86 −0.54 4.30

−0.78 0.10 −0.47 0.86 0.70 −0.36 2.070.03 −0.05 0.30 −0.54 −0.36 0.24 −1.68

32.87 −0.04 −2.02 4.30 2.07 −1.68 24.79

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

P5 = 10−12

×

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

111.80 −0.72 0.40 0.18 −0.95 0.20 31.26−0.72 0.04 −0.06 0.09 0.09 −0.05 −0.040.40 −0.06 0.34 −0.62 −0.41 0.27 −1.760.18 0.09 −0.62 1.25 0.77 −0.47 3.81

−0.95 0.09 −0.41 0.77 0.62 −0.31 1.680.20 −0.05 0.27 −0.47 −0.31 0.22 −1.46

31.26 −0.04 −1.76 3.81 1.68 −1.46 23.05

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

P6 = 10−12

×

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

117.08 −0.82 0.16 0.53 −0.78 −0.03 33.69−0.82 0.04 −0.07 0.10 0.10 −0.05 −0.030.16 −0.07 0.40 −0.71 −0.49 0.32 −2.110.53 0.10 −0.71 1.33 0.84 −0.57 4.38

−0.78 0.10 −0.49 0.84 0.68 −0.38 2.14−0.03 −0.05 0.32 −0.57 −0.38 0.25 −1.7733.69 −0.03 −2.11 4.38 2.14 −1.77 252.81

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

.

ACKNOWLEDGMENT

The authors would like to thank Dr. A. White of mechanicalengineering at Michigan State University, East Lansing, MI,USA, for his contribution in this paper.

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Xuefei Chen received the B.S. degrees in mechan-ical engineering and electrical engineering and theM.Eng. degree in mechanical engineering from Tian-jin University, Tianjin, China, in 2002 and 2005,respectively, and the Ph.D. degree in mechanicalengineering from Michigan State University, EastLansing, MI, USA, in 2012.

He is currently a Systems Development Engineerwith the Advanced Powertrain Group, Chrysler LLC,Auburn Hills, MI. His work focuses on improvingthe overall efficiency and performance of internal

combustion engines with advanced technologies. He is also with Delphi as aCalibration Engineer of the engine management system from 2005 to 2008.His current research interests include modeling and control of automotiveengines and hybrid powertrains, biofuel applications for automotive systems.

Dr. Chen is currently a member of SAE and ASME.

Yueyun Wang received the Ph.D. degree in electri-cal engineering from Shanghai Jiao Tong University,Shanghai, China, in 1987.

He is currently a Staff Researcher leadingadvanced CIDI engine controls development inPropulsion Systems Research Laboratory, GeneralMotors Research and Development, Warren, MI,USA. He was a Technical Advisor with CumminsEngine Company, Columbus, IN, USA, from 1995to 2005, specializing in next generation power traincontrol and diagnostics. Before joining the industry,

he conducted research and taught at several academic institutions, where hewas an Assistant Professor with Shanghai Jiao Tong University, Shanghai,China, an Alexander von Humboldt Research Fellow with Duisburg Univer-sity, Essen, Germany, a Visiting Scholar with Syracuse University, Syracuse,NY, USA, and a Senior Research Associate with Ohio State University,Columbus, OH, USA. He has authored over 100 publications and holds 50U.S. patents and numerous international patents for automotive applications.His current research interests include modeling and simulation, model-basedmultivariable control, robust control, adaptive control, and detection andestimation with application to automotive propulsion systems.

Ibrahim Haskara received the B.S. degrees inelectrical and electronics engineering and in physicsin a double major from Bogazici University, Istanbul,Turkey, in 1995, and the M.S. and Ph.D. degrees inelectrical engineering from Ohio State University,Columbus, OH, USA, in 1996 and 1999, respec-tively.

He has been with General Motors, Warren, MI,USA, since 2005, where he is currently a StaffResearcher, specializing in propulsion control sys-tems with Propulsion Systems Research Lab, GM

Global Research and Development, Warren. From 1999 to 2005, he was aControl Research Scientist with Visteon Corporation, Van Buren TWP, MI. Hehas authored more than 40 peer-reviewed journal and conference papers andholds 26 U.S. patents for various automotive applications. His current researchinterests include control, modeling, estimation, optimization and diagnosticsof automotive systems, particularly in the area of advanced propulsion systemsand engine control management, as well as control of nonlinear systems andcontrol theory in general.

Guoming Zhu received the B.S. and M.S. degreesfrom the Beijing University of Aeronautics andAstronautics, Beijing, China, in 1982 and 1984,respectively, and the Ph.D. degree in aerospace engi-neering from Purdue University, West Lafayette, IN,USA, in 1992.

He is an Associate Professor with the Departmentof Mechanical Engineering (ME) and the Depart-ment of Electrical and Computer Engineering (ECE),Michigan State University, East Lansing, MI, USA.Prior to joining the ME and ECE Departments, he

was a Technical Fellow in advanced powertrain systems of the VisteonCorporation, Van Buren TWP, MI. He was also a Technical Advisor withCummins Engine Co., Columbus, IN, USA. His teaching interests focuson control classes at both undergraduate and graduate levels. His currentresearch interests include closed-loop combustion control of internal com-bustion engines, engine system modeling and identification, hybrid powertraincontrol and optimization, and linear parameter varying control with applicationto automotive systems. He has over 25 years of experience related to controltheory, engine diagnostics and combustion control. He has authored or co-authored over 125 refereed technical papers and holds 40 U.S. patents.

Dr. Zhu was an Associate Editor for the ASME Journal of Dynamic Systems,Measurement, and Control and Editorial Board Member for the InternationalJournal of Powertrain. He is also an ASME Fellow and an SAE Fellow.

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