Adaptive Observer for Joint Estimation of Oxygen ... - IEEE Xplore

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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 23, NO. 1, JANUARY 2015

Adaptive Observer for Joint Estimation of Oxygen Fractions and Blend Level in Biodiesel Fueled Engines Junfeng Zhao, Student Member, IEEE, and Junmin Wang, Member, IEEE Abstract— In this paper, a dynamic oxygen fraction model for a biodiesel-compatible engine with a dual-loop exhaust gas recirculation (EGR) system is developed. When oxygenated fuel is applied in an engine, the intake manifold oxygen fraction, which is an important factor for both combustion and emissions, can be chosen as a new reference for evaluating the equivalent EGR level instead of EGR ratio. Based on this model, an adaptive observer is designed, and it is able to simultaneously estimate the oxygen fraction states and unknown fuel blend level. The adaptive observer introduced here is advantageous for its simple convergence condition and its efficient implementation. The analysis of the observer’s convergence and robustness is detailed. The performance of the observer is validated by the simulation and experimental results. The difference of intake oxygen fractions between pure diesel (B0) and pure soybean biodiesel (B100) are studied. The adaptive observer is expected to be valuable for adaptive control of the combustion and emissions of biodiesel-compatible engines. Index Terms— Adaptive observer, biodiesel, blend-level estimation, diesel engine, dual-loop exhaust gas recirculation (EGR).

N OMENCLATURE Variables Av BL Fi θ Ne Pi R Ti W MW Subscripts λ ψ ηv air c e

Effective area of the valve. Blend level. Oxygen fraction at point i . Oxygen consumption factor. Engine speed (r/min). Pressure at point i (bar). Universal gas constant. Temperature at point i (K). Mass flow rate. Molar weight. Air–fuel equivalence ratio. Molar N2 /O2 ratio in fresh air. Volumetric efficiency. Fresh air. Compressor. Engine.

Manuscript received July 6, 2013; revised December 22, 2013; accepted March 15, 2014. Date of publication April 8, 2014; date of current version December 15, 2014. Manuscript received in final form March 19, 2014. This work was supported by the Department of Energy under Award DE-PI0000012. Recommended by Associate Editor K. Butts. The authors are with the Department of Mechanical and Aerospace Engineering, Ohio State University, Columbus, OH 43210 USA (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCST.2014.2313003

eo est maf mes t

Engine out. Estimated. Mass airflow. Measured. Turbocharger.

Abbreviations AFR Air–fuel ratio. DOC Diesel oxidation catalyst. DPF Diesel particulate filter. EGR Exhaust gas recirculation. ECU Engine control unit. HEGR High-pressure loop EGR. LEGR Low-pressure loop EGR. LHV Lower heating value. LTI Linear time invariant. LTV Linear time variant. LPV Linear parameter varying. MAF Mass airflow. MAP Manifold absolute pressure. MIMO Multiple-input multiple-output. SCR Selective catalytic reduction. UEGO Universal exhaust gas oxygen. VGT Variable geometry turbocharger. I. I NTRODUCTION

B

IODIESEL is a renewable fuel, which can be used as a potential alternative of the depleting fossil fuels. A conventional diesel engine can be made biodieselcompatible without much physical modifications. However, the ECUs in conventional engines are designed with careful and laborious calibrations for regular diesel fuel. Naturally, if biodiesel blend is added to the tank while the ECU is not aware of, the engine performance may degrade or even deteriorate [1], [2]. To achieve optimal combustion and minimum emissions, the future biodiesel vehicles should equip with an online fuel property identification system, which is able to identify fuel types, so that the engine control strategies can be adjusted accordingly. Several published studies have tried to directly detect biodiesel blend level through specialized sensors, such as electrochemical sensor [3], near-infrared spectroscopy, or nuclear magnetic resonance sensor [4]. However, those are expensive lab-grade sensors, whose reliability and cost are major concerns for production applications. In practice, estimation systems based on mass produced sensors or sensors those have already been available on vehicles are more

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ZHAO AND WANG: ADAPTIVE OBSERVER FOR JOINT ESTIMATION OF OXYGEN FRACTIONS AND BLEND LEVEL

desirable. An approach based on the common-rail pressure signal for identifying the fuel types was developed in [5]. Snyder et al. [6] pointed out that biodiesel is an oxygenated fuel, which differs from the conventional diesel. In addition, the difference can be detected by a wideband oxygen or UEGO sensor at the exhaust manifold. If mass airflow rate and fuel mass flow rate are measured too, oxygen content in the fuel, or equivalently the blend level, can be determined. This approach was proven to be effective through simulations and experimental validations. The influence of EGR on this oxygen-based estimation approach was investigated in [7], and it was demonstrated that higher EGR levels are beneficial to improving the accuracy of the blend-level estimation. EGR is now widely used in modern engines for various purposes, such as lowering the combustion temperature and reducing the engine-out NOx emissions. The principal mechanism of EGR being able to reduce NOx is that it lowers the oxygen concentration for combustion [8]. In biodiesel’s combustion, EGR is no longer as effective as it was in diesel’s combustion, primarily due to the presence of oxygen in the fuel and the additional oxygen in the exhaust gas being recirculated back to the intake manifold. Thus, intake oxygen fraction is a more proper indictor of true EGRs dilution effect when biodiesel blends are fueled in the engines. Production engines estimate the EGR ratios by relying on calibrations with respect to the EGR valve opening angles, and they are short of direct measurement for intake oxygen fraction [9]. Thus, it is necessary to design a real-time oxygen fraction observer based on other easily obtained measurements [10]. In [11] and [12], an observer based on input estimation technique and a Luenberger style observer are designed to estimate EGR flow rate in engines equipped with singleloop EGR systems, respectively. In [13], a static model for intake oxygen fraction in a single-loop EGR diesel engine, which is fueled with biodiesel blends, is proposed. Wang [14] and Chen and Wang [15] have designed Luenberger-like intake air-fraction observers for diesel engines equipped with dual-loop EGR systems. The dual-loop EGR system, which consists of both HEGR and LEGR, is a novel approach employed to reduce engine-out emissions and enable advanced combustion modes. It offers the flexibility of controlling the intake gas temperature and oxygen fraction separately [16]. Meanwhile, this configuration increases the complexity of intake oxygen fraction estimation. The observers have been validated by the engine experimental results. However, the observers become invalid when the engine is fueled with biodiesel blends other than pure diesel fuel, as the model used for the system does not take the fuel property variation, especially variation of the stoichiometric AFR for different fuels, into consideration. In this paper, an adaptive observer is developed, which is not only able to conduct the oxygen fraction estimation for engines running biodiesel blends, but also to perform the estimation of blend-level simultaneously. Joint estimation of states and parameters in state-space systems is of practical importance for adaptive control. Recursive algorithms designed for this purpose are usually known as adaptive observers, and some approaches have been developed in [17]–[20]. However, most

81

Fig. 1. Schematic diagram of diesel engine equipped with dual-loop EGR system.

of them only apply to LTI systems. In [21] and [22], an adaptive observer, which is applicable for LTV MIMO systems, is presented. In this paper, a similar adaptive observer is developed for a dual-loop EGR engine system running biodiesel fuels. The first contribution of this paper is to extend the application of previous work in [14] to the engine systems, which are fueled with biodiesel blends. Unlike the previous work, the proof of the observer’s stability and convergence does not require the complementary support from examining the entire engine operating range. In addition, the adaptive observer designed in this paper is able to conduct the biodiesel–diesel blend-level estimation simultaneously. The capability of joint estimation of oxygen fractions and blend level makes the observer quite valuable for the adaptive control of biodieselcompatible engines. This paper is organized as follows. In Section II, the oxygen fraction dynamic model is developed for a biodieselcompatible engine with a dual-loop EGR system. An adaptive observer, which considers the fuel property variation, is designed in Section III. Following that, the simulation and experimental results are given in Sections IV and V, respectively, which lead to some conclusive remarks in the end. II. S YSTEM M ODELING A schematic diagram of a diesel engine is shown in Fig. 1. The engine is equipped with an HEGR, an LEGR, a VGT, and aftertreatment systems including a DOC, a DPF, and an SCR system. The air-path loop of the system is divided into different sections, which are numbered as in Fig. 1. The control volume Vi for each section is fixed. The charge pressure Pi and the temperature Ti in each section are monitored by pressure sensors and thermocouples, respectively. Through the low-pressure EGR valve, the low-pressure EGR gas, which has been filtered by the DOC and DPF, and cooled by the LEGR cooler, is mixed into the intake fresh

82


TABLE I F UEL P ROPERTY D IFFERENCE

air in Section I. The hot and unfiltered high-pressure EGR gas joins the charge after the compressor and intercooler. The flow rates of both HEGR and LEGR are controlled by two EGR valves separately. An UEGO sensor, as the ones now commonly used in diesel engines, is mounted at the exhaust manifold to monitor the exhaust oxygen fraction and provide the information to the ECU in the form of air–fuel equivalence ratio, denoted by λm . However, when the engine is fueled with biodiesel or biodiesel blends, λm = AFRm /AFR s is no longer a correct indicator of air–fuel equivalence ratio, since the stoichiometric air–fuel ratio AFRs for biodiesel is different from that of diesel, which is shown in Table I. The pure biodiesel can be labeled as B100, and B0 represents the pure petroleum diesel. The mixture ratio is called blend level, e.g., B20 represents a mixture of 20% (by volume) biodiesel fuel and 80% diesel. The blend level can serve as a marker of the fuel property of the mixture. The measurement mechanism of the UEGO sensor is that the sensor compares the oxygen content of the exhaust gas to that in the fresh air. Due to the oxygen concentration difference, a pump current can be induced and it directly indicates the oxygen concentration in the exhaust gas. Although the output of an UEGO sensor is given in the form of λm , its measurement is actually the oxygen concentration. Thus, it is reasonable to convert the output λm back to the measured oxygen concentration to make it applicable when fuel property variation exists. In addition, the interpretation for lean-burn condition can be done by the following equation: F3,mes =

(λm − 1) · Fair λm + 1/AFRs,B0

(1)

where Fair is the oxygen fraction in fresh air, F3,mes is the measured exhaust oxygen fraction, and AFRs,B0 represents the stoichiometric air–fuel ratio of diesel fuel. In (1), Fair and AFRs,B0 are constants. Thus, the exhaust oxygen fraction is only a function of the measured λm given by an UEGO sensor despite of fuel property variation. However, the stoichiometric air–fuel ratio AFRs is fuel dependent and determined by the average fuel molecule form, which can be generally written as Cx H y Oz [23]. Then, the combustion

Fig. 2.

Blend level and its corresponding oxygen consumption factor.

chemical equation can be generalized as shown in (2) at the bottom of the page, where ψ is the molar N2 /O2 ratio, n p is total moles of exhaust gas, and x j is the mole fraction of species j in the exhaust gas. Under the assumption of complete combustion, the mass ratio of consumed fuel and oxygen, which is also named oxygen consumption factor in this paper, can be written as z y MW(O2 ) x+ − 4 2 (3) θ= MW(Cx H y Oz ) where MW is the molar weight. According to the results from [24], the relationship between blend level (BL) and oxygen consumption factor can be described as a linear correlation θ (BL) = g1 ·

BL + g2 100

(4)

where g1 = −0.45, g2 = 3.34. The correlation is also shown in Fig. 2. Therefore, the oxygen fraction dynamics in the exhaust manifold can be formulated as RT3 (F2 We − W f · θ (BL) − F3 Weo ) F˙3 = P3 V3

(5)

where Weo is the engine-out mass flow rate, W f is the fuel injection rate, whose information can be provided by the ECU, and We is the gas charge into the cylinders, which can be estimated by the speed-density equation We =

ηv p2 Ne Vd RT2 120

(6)

z y (O2 + ψN2 ) → n p (x Ca Hb Ca Hb C x H y Oz + λ x + − 4 2 +x CO CO + x CO2 CO2 + x O2 O2 + x N2 N2 +x NO NO + x NO2 NO2 + x H2 O H2 O + x H2 H2 )

(2)


where ηv is the volumetric efficiency, Ne is the engine speed, Vd is the displacement of the engine cylinders, and R is the universal gas constant. The oxygen-fraction dynamics before the compressor can be described by (7)

where WMAF is the intake fresh airflow rate and Wc is the mass flow rate through the compressor. Here, the oxygenfraction dynamics in the LEGR is ignored, and it is assumed that F3 ≈ F5 . This simplification is reasonable since the variation of oxygen fraction through the after treatment system is small during normal operations without active DPF regenerations [25]. The oxygen-fraction dynamics at the intake manifold can be described by RT2 [Wc (F1 − F2 ) + WHEGR (F3 − F2 )] F˙2 = P2 V2

(8)

where WLEGR and WHEGR are the mass flow rates through the LEGR and HEGR valves, respectively. They can be approximated by the following valve flow equation: ⎡ ⎤ ⎧ γ +1 γ +1

⎪ 2(γ −1) 2(γ −1) ⎪ 1 A 2 (u ) p 2 pd v v u ⎪ √ ⎣ ⎦ 2 ⎪ ≤ γ , ⎪ ⎪ γ +1 pu γ +1 ⎪ RTu ⎪ ⎪ ⎪ ⎨

pd γ2 2γ pd γ γ+1 Wv = Av (u v ) pu ⎪ , + √ ⎪ ⎪ γ −1 pu pu RTu ⎪ ⎪ ⎪

γ +1 ⎪ ⎪ 2(γ −1) pd 2 ⎪ ⎪ ⎩ > pu γ +1 (9) where pu ( pd ) and Tu (Td ) are upstream (downstream) pressure and temperature, Av is the effective area of the valve, and u v is the valve open percentage, which can be obtained through calibration in practice. To sum up, the air-path loop dynamics can be written in the following state-space form: ⎞⎛ ⎞ ⎛ ⎞ ⎛ F˙1 0 k1 WLEGR −k1 Wc F1 ⎝ F˙2 ⎠ = ⎝ k2 Wc −k2 (Wc +WHEGR ) k2 WHEGR ⎠ ⎝ F2 ⎠ 0 k3 We −k3 Weo F3 F˙3 F˙

⎛

⎞

A(t )

F

k1 WMAF Fair ⎠ 0 −k3 W f θ

+⎝

A(t )

⎞

⎛

k1 Fair 0 0 ⎠ WMAF + ⎝ 0 ⎠ θ 0 −k3 W f

+⎝

B(t )

F

(12)

(t )

or F˙ = A(t)F + B(t)u + (t)θ

(13)

where the mass airflow rate WMAF can be treated as input u, while the fuel blend level θ is a parameter needs to be identified. III. A DAPTIVE O BSERVER D ESIGN In Section II, the model of the air-path loop is developed and written in a form of classical state-affine system with the undetermined parameter separated. It can be observed from (12) that the model is also an LPV system. The parameter vector of the system can be denoted by δ = ( k1 k2 k3 Wc Weo WLEGR WHEGR W f We ). (14) To reduce the computational effort required by a gainscheduled LPV observer, the observer will be designed with the parameter vector δ obtained in real time and treated as constant at every time step. θ , which is determined by the fuel composition, will be first assumed to be a known parameter. Based on this assumption, a classic state observer will be designed. Then, an adaptive observer for joint estimation of parameter and states will be designed based on this classic state observer. For the above system described by (10) and (11) under any fixed operating condition with constant parameter vector δ, a Luenberger-like observer can be designed in the following form: ˙ ˆ Fˆ = A(t) Fˆ + B(t)u + (t)θ + L(t)(y − C F) (15) where Fˆ is the estimated oxygen-fraction vector, and L(t) = (L 1 L 2 L 3 )T is the observer gain vector, which needs to be determined based on the analysis of convergence. The estimation errors of the states can be expressed as ˆ F˜ = F − F.

(16)

Then, the dynamics of the estimation error vector can be described by

where ki = RTi /Pi Vi > 0. The output of the system is the oxygen fraction in the exhaust manifold, which can be measured by an UEGO sensor as mentioned earlier. The system output can be expressed as

C

⎞

⎛

(10)

D(t )

y = F3 = ( 0 0 1 )( F1

The system can also be written in another form ⎞ ⎛ ⎞⎛ ⎞ F˙1 F1 −k1 Wc 0 k1 WLEGR ⎝ F˙2 ⎠ = ⎝ k2 Wc −k2 (Wc +WHEGR ) k2 WHEGR ⎠ ⎝ F2 ⎠ 0 k3 We −k3 Weo F3 F˙3 ⎛

F˙

RT1 (WLEGR · F3 + WMAF · Fair − Wc · F1 ) F˙1 = P1 V1

83

F2

F3 )T.

˙ F˙˜ = F˙ − Fˆ ˆ − L(t)(z − zˆ ) = A(t)(F − F) ˜ = A(t) F˜ − L(t)C F.

(17)

A Lyapunov function candidate is selected as (11)

V =

1 ˜2 1 ˜2 1 ˜2 F + F2 + F3 > 0. 2 1 2 2

(18)

84


Clearly, it is radially unbounded and its derivative can be expressed as

In addition, ϒ(t) will be specified. The dynamics of the combined estimation error z˜ can be computed as [21]

V˙ = F˜1 F˙˜1 + F˜2 F˙˜2 + F˜3 F˙˜3 = − k1 Wc F˜12 + k1 WLEGR F˜3 F˜1 − L 1 F˜3 F˜1 + k2 Wc F˜1 F˜2 − k2 (Wc + WHEGR ) F˜22 + K 2 WHEGR F˜2 F˜3

˙ θ˜ − ϒ θ˙˜ − σ. (25) z˙˜ = (A − LC)˜z + ((A − LC)ϒ + − ϒ)

− L 2 F˜2 F˜3 + k3 We F˜2 F˜3 − k3 Weo F˜32 − L 3 F˜32 .

V˙ = F˜1 F˙˜1 + F˜2 F˙˜2 + F˜3 F˙˜3 = −k1 Wc F˜12 + k2 Wc F˜1 F˜2

Since V2 > V1 , P2 > P1 , (P2 is the boost pressure and P1 is very close to the ambient pressure), and usually T2 is only slightly higher than T1 due to the function of intercooler after compressor, the following inequality holds: (21)

Then, V˙ < 0 can be guaranteed. This proof does not require any experimental support for examining the entire operating range as [11] did, but only gains assistance from the physical insight, which is not only guaranteed in the entire operating range, but also generally true for various engine setups. Now, the blend level θ needs to be treated as an unknown parameter. In practice, the blend level only changes when the tank is refueled; thus, θ can be regarded as a constant parameter, which needs to be determined through online estimation. Then, in the former state estimation (15), the unknown θ needs to be replaced by its estimation θˆ . Therefore, the state estimation equation can be rewritten as ˆ + σ (t) (22) F˙ˆ = A(t) Fˆ + B(t)u + (t)θˆ + L(t)(y − C F) where σ (t) is added to compensate for the difference between θ and θˆ [21]. Later, the reason for adding this term will be explained in detail. Similar to (16), the estimation error of the input can be ˆ Since the input θ is constant, its denoted as θ˜ = θ − θ. ˙ derivative θ = 0. Thus, the error dynamics of the states can be written as F˙˜ = (A − LC) F˜ + θ˜ − σ.

(23)

Define a linear combination of F˜ and θ˜ by assuming that there exists a time-varying matrix ϒ(t) ∈ 3 × z˜ = F˜ − ϒ(t)θ˜ .

(26)

ϒ˙ = (A − LC)ϒ +

(27)

and

then (25) can be simplified as z˙˜ = (A − LC)˜z .

−k2 (Wc + WHEGR ) F˜22 −k3 Weo F˜32 − l F˜32 1 1 = − k1 Wc − k2 Wc F˜12 − k2 Wc ( F˜1 − F˜2 )2 2 2

1 −k2 Wc + WHEGR F˜22 − (k3 Weo + l) F˜32 . (20) 2

RT1 1 1 RT2 > k2 = . P1 V1 2 2 P2 V2

σ = ϒ θ˙ˆ = −ϒ θ˙˜

(19)

Select L 1 = k1 WLEGR , L 2 = k2 WHEGR +k3 We , and L 3 = l, where l > 0 being the tunable observer gain. Then, (19) becomes

k1 =

Select

(24)

(28)

At the beginning of this section, using classical observer design method, it has been guaranteed that (A − LC) is Hurwitz, thus z˜ (t) → 0 when t → ∞. Although the state estimation error F˜ and the combination estimation error z˜ = F˜ −ϒ(t)θ˜ have been proved to be stable, the convergence of θ˜ still needs further investigation as ϒ(t) is a time-varying matrix. It is natural to assume that the parameter estimation dynamics is proportional to that of the output error, and it can be written in such a form ˆ θ˙ˆ = (t)(y − C F) (29) where (t) is a positive time-varying matrix, whose exact form will be specified. Since θ˙ = 0, then ˆ = −(t)C F. ˜ θ˙˜ = −θ˙ˆ = −(t)(y − C F)

(30)

Substituting F˜ = z˜ + ϒ(t)θ˜ into (30) gives θ˙˜ = −(t)C(˜z + ϒ θ˜ ) = −(t)C z˜ − (t)Cϒ θ˜ .

(31)

It has been shown that z˜ will converge to zero; the next step is to properly choose (t) to make sure that the homogeneous part is stable. Clearly, a suitable choice would be (t) = (Cϒ)T

(32)

where is an arbitrary positive matrix. This selection can be proved to be reasonable by applying the following lemma. Lemma 1 [26]: φ(t) ∈ m × p is a bounded and piecewise continuous matrix, ∈ p × p is any symmetric positivedefinite matrix. Given positive constants T , α, and β, if ∀t such that t +T αI ≤ φ T (τ )φ(τ )dτ ≤ β I. (33) t

Then, the system x(t) ˙ = − φ T (t)φ(t)x(t)

(34)

is globally exponentially stable. See [27, Th. 2.16] for a classical proof of this lemma. In this paper, φ = Cϒ, where C = [0 0 1] is a constant matrix, ϒ is piecewise continuous and bounded, as


85

= [0 0 −k3 W f ]T in (27) is piecewise continuous and bounded. Therefore, the autonomous part in (31) θ˙˜ = − (Cϒ)T Cϒ θ˜

(35)

is globally exponentially stable. However, the convergence of the nonautonomous system in (31), which now can be rewritten as θ˙˜ = − (Cϒ)T Cϒ θ˜ − (Cϒ)T C z˜

(36)

and it requires further support from the following lemma. Lemma 2 [26]: If the autonomous linear time-varying system x(t) ˙ = H (t)x(t)

(37)

is globally exponentially stable, u(t) is bounded and can be integrated, and when t → ∞, u(t) → 0, then x(t) driven by u(t) through the ordinary differential equation (ODE) system x(t) ˙ = H (t)x(t) + u(t)

(38)

where x(t) is bounded and also converges to zero. Moreover, if u(t) vanishes exponentially fast, then x(t) also vanishes exponentially fast. A short proof of this lemma is given below. Proof of Lemma 2 [26]: Brockett [28] has proved that if H (t) is Hurwitz, u(t) is bounded and converges to zero, then x(t) is bounded and will converge to zero. One step further, the lemma states that if u(t) converges exponentially, and then x(t) also converges exponentially. Now, let (t, τ ) be the transition matrix, thus the solution of the ODE system can be written as t (t, τ )u(τ )dτ. (39) x(t) = (t, t0 )x(t0 ) + t0

Since u(t) vanishes exponentially, ∃ k1 > 0 and λ1 > 0, such that u(t) ≤ k1 e−λ1 (t −t0 ) . In addition, the autonomous system is exponentially stable, which implies that ∃ k2 > 0 and λ2 > 0, such that (t, τ ) ≤ k2 e−λ2 (t −t0 ) . Therefore t x(t) ≤ (t, t0 )x(t0 ) + (t, τ )u(τ )dτ t0 t ≤ k2 e−λ2 (t −t0 ) x(t0 ) + k1 k2 e−λ1 (t −t0 ) e−λ2 (t −t0 ) dτ t0 t −λ2 (t−t0 ) x(t0 )+k1 k2 e−λ2 (t−t0 ) e(λ2−λ1 )(τ−t0 ) dτ. ≤ k2 e t0

(40) If λ1 = λ2 , then x(t) ≤ k2 e−λ2 (t −t0) x(t0 ) + k1 k2 e−λ2 (t −t0 ) (t − t0 ).

(41)

If λ1 = λ2 , then e−λ1 (t −t0) − e−λ2 (t −t0 ) x(t) ≤ k2 e−λ2 (t −t0 ) x(t0 ) + k1 k2 λ2 − λ1 k k 1 2 −λ1 (t−t0 ) +e−λ2 (t−t0 ) . ≤ k2 e−λ2 (t−t0 ) x(t0 )+ λ −λ e 2 1 (42)

Fig. 3.

State estimation results from simulation.

It can be seen that x(t) decays exponentially in both cases. By combining the results obtained through Lemmas 1 and 2, conclusion can be made that the parameter estimation error is globally exponentially stable. To sum up, the adaptive observer can be designed as ϒ˙ = (A − LC)ϒ + (43) ˙ˆ T ˆ ˆ ˆ F = A F + Bu + θ + [L + ϒ (Cϒ) ](y − C F) (44) ˆ (45) θ˙ˆ = (Cϒ(t))T (y − C F). To obtain a satisfactory convergence behavior, the constant can be replaced by a positive-definite time-varying variable [29] ˙ = − (Cϒ)T (Cϒ) + λ .

(46)

This computation method is similar to the classical recursive least-squares algorithm with an exponential forgetting factor λ > 0. In both simulation and experiment, the observer parameters are tuned as ⎧ λ = 0.5 ⎪ ⎪ ⎪ ⎪ ⎪ (0) = 1 ⎪ ⎪ ⎪ ⎨ϒ(0) = [0, 0, 0]T (47) T ⎪ F(0) = [0, 0, 0] ⎪ ⎪ ⎪ ⎪ ⎪ θ (0) = 3.115 ⎪ ⎪ ⎩ L = [k1 WLEGR , k2 WHEGR + k3 We , 500]T. IV. S IMULATION S TUDIES To validate the performance of the adaptive observer, a high-fidelity engine model is first built in GT-power with all

86

Fig. 4.


Parameter estimation results from simulation.

the major components shown in Fig. 1. Fuel models are also carefully developed. Fuel property parameters of diesel (B0) are defined in the GT-power library, but biodiesel (B100) is not a standard fuel type in this software fuel library. The parameters of biodiesel are adopted from [30]. During the simulations, the engine speed is kept at a constant speed of 1000 r/min. At each operating point, VGT position, EGR valve angle, and fuel injection strategy including common rail pressure, injection duration, and timing are kept identical for both fuels, so that the comparison can be fairly conducted. This is also to simulate what conventional ECUs would do when the engine is fueled with biodiesel blends but the ECU control algorithms are not modified accordingly. Fig. 3 shows the observer performance when the EGR levels are changing. Before 100 s, the LEGR valve is closed, but the HEGR valve is varying among different levels; and after that, the HEGR valve is closed while the LEGR valve is varying. Once the observer is turned ON, the estimated values rapidly converge to and keep tracking the true values throughout the process it both cases. As F1 is the oxygen fraction in the air-path section before the inlet of HEGR, only the variation of LEGR has an influence on it. When EGR valve angles are increased, more inert gases are recirculated back to the intake manifold, which then reduce both the intake and exhaust oxygen fractions. In addition, it can be observed that the exhaust oxygen fraction for B100 is higher than that of B0, which is expected as B100 is oxygenated and it has a smaller oxygen consumption factor. When both EGR valves are closed, the intake oxygen fractions are the same for both fuels. When EGR is introduced, both will decrease; however, EGR is less effective in the B100 case in terms of reducing the intake oxygen fraction. At a higher EGR level, the difference between B0 and B100 is enlarged. This phenomenon is particularly helpful for explaining the NO@ emission increase caused using biodiesel, especially using biodiesel in modern diesel engines, in which a high level of EGR is more frequently employed. Thus, it is potentially useful to monitor the oxygen fraction in the intake manifold for the purpose of controlling and reducing the NOx emission increase caused by biodiesel.

Fig. 5.

Gradual variation profile of EGR levels.

The parameter estimation performance is shown in Fig. 4. To better demonstrate the estimation results, blend level is used as the output of the parameter estimation instead of θ , which ranges from 2.89 to 3.34, as shown in Table I. The output can be simply translated by BL = (θ − g1 )/g2 × 100. For both cases, the initial values of estimation are set at θ (0) = 3.115, or equivalently at the level of B50. It can be observed that once the observer is enabled, the estimation can gradually converge to the true blend levels. During transient stages when the EGR levels are varying, the estimation will temporally diverge from the target. This is because the estimation is conducted by realtime monitoring and comparing intake and exhaust oxygen fractions, which can be affected by the gas transportation delays. After the EGR valve is opened, it takes some time for the exhaust gas to recirculate back to the intake manifold and mix with the fresh charge. Similarly, after the EGR valve is closed, it also requires some buffer time before all the residual EGR left in the air path to purge out. In the statespace model represent by (10), transportation delays are not yet modeled. That is why the spikes appear during either valveopen or valve-close stage, and the directions of the spikes are correspondingly opposite. In addition, when the step change of EGR level is higher, the modeling error becomes larger, which leads to a higher magnitude of deviation. However, after the system reaches steady states, the estimation can rapidly trace back to the true value. To further investigate the influence of EGRs transportation delay on the performance of the observer, simulation is conducted again for the same EGR set points but with a gradually changing profile, as shown in Fig. 5. The result in Fig. 6 shows that the estimation error during transient stage is much smaller compared with the previous result. In addition, this result confirms that the error is caused by the gas transportation delay. In practice, as the fuel blend level does not change during an estimation cycle, intuitively the sudden divergence of the estimation can be smoothed out by simply averaging the estimation result during an estimation cycle.


Fig. 7. Fig. 6.

Parameter estimation with gradual EGR variation. TABLE II K EY PARAMETERS OF THE T EST E NGINE G EOMETRY

V. E XPERIMENTAL R ESULT The designed adaptive observer is also validated on a fourstroke medium-duty diesel engine, whose geometry parameters are given in Table II. The schematic diagram of the test engine has been shown in Fig. 1. An AVL fuel balance system is used to precisely measure the fuel flow rate and to maintain a constant fuel temperature. The signals of MAP and MAF rate are obtained from the ECU. The test bench setup is shown in Fig. 7. The engine is equipped by a dual-loop EGR system, HP throttle, and VGT. To provide the backpressure for the LEGR, an exhaust valve with a constant opening area is placed at the end of tailpipe. The temperatures and pressures in the intake and exhaust manifolds of the diesel engine are measured by thermocouples and pressure sensors. The oxygen fractions in the intake and exhaust manifolds are measured by wideband λ sensors, while there is no measurement for F1 . These sensors are commonly used for the purpose of air-path modeling. Compared with measuring actual mass flow rates through EGR valves, these signals are much easier to access. All these data are recorded at a rate of 10 Hz via a dSPACE MicroAutoBox data acquisition system. In the experiments, the engine runs at a constant speed, i.e., 1000 r/min, and the fuel injection amount is 28.5 mg per cylinder per cycle. The pedal position instead of engine torque is used to define each operating point. Because the LHV

87

Experimental system setup.

of biodiesel is about 13% lower than that of diesel’s, if the engine torque values are matched, the engine controller would require longer injection duration or higher rail pressure for biodiesel to attain the same torque level. However, to compare and model different ignition quality and combustion process, it is reasonable to keep the fuel injection amount and injection strategy the same for different fuels. In addition, from the control point of view, pedal position is actually used as an input command to the ECU, in which the injection strategy including injection pressure, duration, and timing are stored in maps developed from calibrations with respect to the conventional diesel fuel. In reality, no matter how the fuel properties change, the ECU can only respond to the pedal position signal and give corresponding injection profile. Unlike in the simulation, the measurement of each sensor in the experiment is contaminated by noises, which can affect the performance of the observer. To show some properties of the proposed adaptive observer with the presence of the measurement noises, rewrite the system with noises as [26] F˙ = A(t)F + B(t)u + (t)θ + ω(t) θ˙ = ε(t) y = C(t)x + v(t)

(48)

where ω(t) ∈ 3 , ε(t) ∈ , and v(t) ∈ are state, parameter, and observation noises, respectively, and they are all bounded. Then, the state and parameter estimation errors F˜ = Fˆ − F and θ˜ = θˆ − θ are bounded as well. Let z˜ = F˜ − ϒ θ˜ , the error dynamics can be written as [26] z˙˜ = (A − LC)˜z − ω + Lv + ϒε θ˙˜ = − ϒ T C T C(˜z + ϒ θ˜ ) + ϒ T C T v − ε.

(49) (50)

Similar to the proof in Section III, z˜ and θ˜ are bounded according to Lemma 2. In addition, assume that the averages Eω = 0, Eε = 0, and Ev = 0, and ω, ε, v are independent of A, L, C, and , so that d(E˜z ) = (A − LC)E˜z dt d(Eθ˜ ) = − ϒ T C T C(E˜z + ϒEθ˜ ). dt

(51) (52)

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Fig. 9.

Fig. 8.

Blend-level estimation result from experiment.

State estimation result from experiment.

It can be seen that the dynamics of E˜z and Eθ˜ are identical ˜ It can be concluded that when the to those of z˜ and θ. system is corrupted by centered noises, E F˜ and Eθ˜ will exponentially converge to zero. This does not mean that the estimated states Fˆ or θˆ will converge to the true values. Instead, the estimated values will oscillate around true values when centered noises of measurement are present. However, this conclusion above indicates that better estimation can be obtained by averaging the transient outputs of the adaptive observer. In practice, the fuel blend level only changes when the vehicle fuel tank is refueled, which typically happens after several hundreds of miles of driving. Thus, the blend level only needs to be identified after each refuel instead of being monitored all the time. By averaging the estimated blend level within a short period, a constant value of estimated blend level will be provided to the engine controller, which will make adaption to the combustion strategy based on the fuel types. The test results, given in Figs. 8 and 9, show some similarities to the simulation in Section IV. Comparing the measured and estimated oxygen fractions in both intake and exhaust manifolds, it can be seen that the observer is able to conduct accurate estimation of the system states. In addition, between these two fuels, the differences of oxygen fraction in both the intake and exhaust manifolds can be seen. The estimation of the blend level is shown in Fig. 9. Similarly, the initial values are set to B50 for both fuels. Compared with the simulation results, the estimations in experiment are clearly contaminated by measurement uncertainties

Fig. 10.

Measurements of the MAF sensor.

and noises. In addition, it can be observed that the spikes of estimated signal occur during transients are higher than those in the simulation, which is probably caused by more severe transient changes of EGR. However, the averages of the estimation still track the true values closely, which is expected based on the robust analysis above. The fuel injection amount and intake mass flow rate are two important system inputs for the engine and the decisive factors for state and parameter estimations. In industry, a lot of efforts have been made to ensure precisely controlling and monitoring of the fuel injection amount in the common-rail system of a diesel engine. Therefore, it is believed by the authors that the fuel injection information from the ECU is reliable and the main uncertainty comes from the measurement of mass airflow rate. Fig. 10 shows the measured signals from the MAF sensor, and it can be seen that the magnitude of the noise reaches about 10% of the mean value of the measured signal. The measurement drift of the MAF sensor may cause the offsets of the parameter estimation.


VI. C ONCLUSION In this paper, an oxygen fraction dynamic model is built for a biodiesel-compatible engine equipped with a dual-loop EGR system. The model takes the oxygen content in biodiesel and its lower oxygen consumption feature into consideration. Based on the model, an adaptive observer is designed for the joint estimation of air-path oxygen fractions and biodiesel– diesel blend level. Both simulation and experimental validations are presented to demonstrate the performance of the adaptive observer. The estimation errors during transients are analyzed and verified by a particular operation pattern. In the experiment, due to the measurement noise, the parameter estimation oscillates around the true value. However, it is suggested by the theoretical analysis of robustness that the problem can be remedied by taking the average of the estimated signal. With the capability of simultaneously estimating the air-path oxygen fractions and biodiesel blend level, the observer will be useful for adaptive control of combustion and emission in biodiesel-compatible engines.

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Junfeng Zhao (S’14) received the B.E. degree in electronics engineering from Tsinghua University, Beijing, China, and the M.S. degree in mechanical engineering from the University of British Columbia, Vancouver, BC, Canada, in 2007 and 2010, respectively. He is currently pursuing the Ph.D. degree with the Department of Mechanical and Aerospace Engineering, Ohio State University, Columbus, OH, USA. His current research interests include dynamic system modeling, nonlinear system estimation and control, alternative fuel vehicle control, and hybrid powertrain control and optimization.

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Junmin Wang (M’06) received the B.E. degree in automotive engineering and the M.S. degree in power machinery and engineering from Tsinghua University, Beijing, China, the second and third M.S. degrees in electrical engineering and mechanical engineering from the University of Minnesota–Twin Cities, Minneapolis, MN, USA, and the Ph.D. degree in mechanical engineering from the University of Texas at Austin, Austin, TX, USA, in 1997, 2000, 2003, and 2007, respectively. He was involved in full-time industrial research with Southwest Research Institute, San Antonio, TX, USA, from 2003 to 2008. In 2008, he joined Ohio State University, Columbus, OH, USA, and founded the Vehicle Systems and Control Laboratory. He has authored and co-authored more than 170 peer-reviewed journal and conference papers and

holds 11 U.S. patents. His current research interests include control, modeling, estimation, and diagnosis of dynamical systems, specifically for engine, powertrain, aftertreatment, hybrid, flexible fuel, alternative / renewable energy, (electric) ground vehicle, transportation, sustainable mobility, energy storage, and mechatronic systems. Dr. Wang serves as an Associate Editor for the IEEE T RANSAC TIONS ON V EHICULAR T ECHNOLOGY , IFAC Control Engineering Practice, ASME Transactions Journal of Dynamic Systems, Measurement and Control, and SAE International Journal of Engines. He was the recipient of the SAE Ralph R. Teetor Educational Award in 2012, the National Science Foundation CAREER Award in 2012, the 2009 SAE International Vincent Bendix Automotive Electronics Engineering Award in 2011, the Office of Naval Research Young Investigator Program Award in 2009, and the ORAU Ralph E. Powe Junior Faculty Enhancement Award in 2009.