common rail injection system iterative learning control ... - Springer Link

International Journal of Automotive Technology, Vol. 12, No. 2, pp. 149−157 (2011)

DOI 10.1007/s12239−011−0019−7

Copyright © 2011 KSAE 1229−9138/2011/057−01

COMMON RAIL INJECTION SYSTEM ITERATIVE LEARNING CONTROL BASED PARAMETER CALIBRATION FOR ACCURATE FUEL INJECTION QUANTITY CONTROL F. YAN and J. WANG

*

Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio 43210, USA (Received 17 May 2010; Revised 9 July 2010)

ABSTRACT−This paper presents an accurate engine fuel injection quantity control technique for high pressure common rail

(HPCR) injection systems by an iterative learning control (ILC)-based, on-line calibration method. Accurate fuel injection quantity control is of importance in improving engine combustion efficiency and reducing engine-out emissions. Current Diesel engine fuel injection quantity control algorithms are either based on pre-calibrated tables or injector models, which may not adequately handle the effects of disturbances from fuel pressure oscillation in HPCR, rail pressure sensor reading inaccuracy, and the injector aging on injection quantity control. In this paper, by using an exhaust oxygen fraction dynamic model, an on-line parameter calibration method for accurate fuel injection quantity control was developed based on an enhanced iterative learning control (EILC) technique in conjunction with HPCR injection system. A high-fidelity, GT-Power engine model, with parametric uncertainties and measurement disturbances, was utilized to validate such a methodology. Through simulations at different engine operating conditions, the effectiveness of the proposed method in rejecting the effects of uncertainties and disturbance on fuel injection quantity control was demonstrated.

KEY WORDS: Common rail injection system, Iterative learning control, Fuel injection quantity control, Diesel engines

NOMENCLATURE k α α ϕ ηv λ

K

int

K

exh

s

ρ ∆P

fuel

θ(t) A c d ET F cyl

d,cyl

i

F

e

F F k

c

ec

m m m

c

e

: index of engine cycle : piston surface area effective parameter : piston surface area effective parameter : engine crank angle : engine volumetric efficiency : Stoichiometric oxygen fuel mass ratio for complete combustion : fuel density : pressure difference between common rail and incylinder pressures : uncertainty parameter to be calculated : area of the total outflow section : fuel flow discharge coefficient : in-cylinder charge density during valve overlapping : injection duration : oxygen fractions of the gases in intake manifold at IVC : oxygen fractions of the gases in exhaust manifold at IVC : oxygen fractions of the gases in cylinder at IVC : oxygen fractions of the gases out of cylinder : index of engine cycle

ic

m

ec

m

ce

m ∆m f

restV

∆m

restB

N p p R T T V V W i

e

i

e

i

e

c

: mass of gas in the cylinder at IVC : mass of gas in exhaust manifold at IVC : mass of gas from intake manifold to cylinder per cycle : mass of gas from exhaust manifold to cylinder per cycle : mass of gas from cylinder to exhaust manifold per cycle : fuel mass quantity per cylinder per cycle : mass from exhaust manifold to cylinder caused by the volume change : mass from exhaust manifold to cylinder caused by the pressure difference : engine speed (rpm) : pressure in intake manifold : pressure in exhaust manifold : ideal gas constant : temperature in intake manifold : temperature in exhaust manifold : volume of intake manifold : volume of exhaust manifold : mass flow rate through cylinder

1. INTRODUCTION With the consistently-increasing demands on vehicle fuel

*Corresponding author. e-mail: [email protected] 149

150

F. YAN and J. WANG

economy and pollutions worldwide, precise engine control is becoming imperative for improving engine combustion fuel efficiency and reducing engine-out emissions (Benajes et al., 2010; Wang, 2008b; Seykens et al., 2005; Tsutsumi, et al, 2009; Lee and Huh, 2010). The engine combustion process is mainly determined by the in-cylinder conditions (ICCs) and fuel injection strategies. To achieve the desired combustion on a cycle-by-cycle basis, seamless combinations of advanced air-path control techniques and precise fuel injection control are critical (Wang and Chadwell, 2008; Wang 2008a; Wang 2008b). As the control through fuel-path is much faster than that of the air-path and the combustion process is very sensitive to the fuel injection, accurate fueling control is thus necessary (Benajes et al., 2010). High pressure common rail (HPCR) fuel injection systems, typically employed in light- and medium-duty Diesel engines, provide an effective way in fuel injection quantity and injection timing control primarily due to their high rail pressure (Huhtala and Vilenius, 2001; Stumpp and Ricco, 1996). Through HPCR systems, typically, fuel injection per cycle per cylinder can be controlled based on a pre-calibrated table or injector models. However, HPCR pressure oscillation, HPCR pressure sensor reading inaccuracy, and the injector aging can all cause fuel injection quantity error (Alzahabi and Schulz, 2008; Baumann and Kiencke, 2006). It is therefore desirable to have some on-line adaptive correction methods for reducing such effects. To a large extent, the imprecise of the fuel injection are caused by periodical disturbance (the oscillation effect of HPCR pressure) and quasi-constant inaccuracy (HPCR pressure sensor reading inaccuracy and the injector aging). This type of disturbance can be effectively rejected by iterative learning control (ILC) algorithms (Chien, 1998; Chien, et al, 2007). By combining the information of previous control signal and the feedback error, an updated control law can be generated to reduce the effect of system variations/ uncertainties without exactly knowing the system dynamics (Norrlof and Gunnarsson, 2001; Norrlof, 2004). In this paper, an ILC-based HPCR injection system on-line parameter calibration algorithm is presented. To generate the error used in the ILC algorithm, an oxygen mass fraction model, based on the engine breathing process, is introduced. An ILC on-line calibration control law can then be devised to reduce the effect of the periodical HPCR pressure disturbance and slowly varying uncertainties (pressure sensor reading inaccuracy and fuel injector parameter uncertainties). The algorithm can help to achieve accurate injection quantity control without additional hardware. Such an algorithm can also be applied for injection system on-board fault diagnosis purposes. The arrangement of the rest of this paper is as follows. In section II, the oxygen mass fraction model is presented. Section III describes a fuel injection on-line parameter calibration algorithm based on the enhanced ILC (EILC) method and the convergence criterion. In section IV, the validation of the on-line calibration method is shown by applying it to a high-fidelity GT-Power engine model, which is

an industrial standard simulation package and is able to simulate the one-dimensional wave dynamics and heat transfer throughout the engine systems. Conclusive remarks are provided in the end.

2. OXYGEN MASS FRACTION MODEL The aim of this model is to generate a nominal exhaust oxygen mass fraction with respect to the desired fuel injection. By comparison between the nominal value and the one measured from a lambda sensor installed in the exhaust manifold of a real engine, a base error can be derived for disturbance rejection purpose in ILC. Here a single-input-single-output (SISO) dynamic model is proposed through the engine breathing and gas exchanging process (Yan and Wang, 2010). Respectively, the input is the fuel injection quantity and the output is the exhaust oxygen mass fraction. For lean-burn engines such as Diesel engines, the oxygen mass fraction in exhaust gas is considerable. The combustion is assumed complete, i.e. the fuel injected into the cylinder is completely burned. Only the in-cylinder oxygen mass fraction at the crank angle of intake valve closing (IVC), which is before the occurrence of combustion for each cylinder/cycle, is considered as the other state. The dynamic models were developed based on the mass conservation and are described by the following difference equations as: mc( k + 1 )Fc( k + 1)= (mc ( k ) + mf( k ))Feo( k ) + m ic ( k ) F i ( k ) + m ec ( k ) F e ( k + 1 ) – m ce ( k ) F eo ( k ) ,

(1)

me(k + 1)Fe( k + 1) = mce(k)(Feo(k) – Fe(k)) + me(k)Fe(k) ,

(2)

where k is the index of engine cycle, mc(k) and are the mass of charge in the cylinder and in the exhaust manifold at the kth IVC, respectively. mic(k), mec(k), and mce(k) are the mass of charge from intake manifold to cylinder, from exhaust manifold to cylinder, from cylinder to exhaust during the period right after the kth IVC. Fi(k), Fe(k), Fc(k) and Feo(k) are the oxygen fractions of the gases in intake manifold, in exhaust manifold, in cylinder, and out of cylinder after combustion at or right after the kth IVC, respectively. mf(k) is the mass of injected fuel after the kth IVC. Figure 1 illustrates the evolving process. The oxygen fraction of the gas after combustion can be derived by: ( mc( k ) + mf( k ) )Feo( k ) = mc ( k )Fc ( k ) – mf( k )λs,

(3)

i.e. f ( k )λ S ----------------, Feo( k ) = -m----c--(--k---)--F----c-(---k--)---–----m mc ( k ) + mf ( k )

(4)

where λs is the stoichiometric oxygen fuel mass ratio for complete combustion.

COMMON RAIL INJECTION SYSTEM ITERATIVE LEARNING CONTROL BASED PARAMETER

C

7

mce λs . m m m

151

(16)

= – ------- ⋅ --------------e c+ f

Here, we denote mce, mec, mic, mc, me, mf as mce(k), mec(k), mic(k), mc(k) (or mc (k+1)), me(k) (or me (k+1)), mf(k)

respectively for simplicity. As illustrated above, the oxygen fraction can be described as a discrete linear parameter-varying system with C = ( C C C C C C C )T . 1

2

3

4

5

6

7

(17)

The system states are: Figure 1. Engine breathing and gas exchanging process from the kth IVC to (k+1)th IVC. It is assumed that the mass of inlet gas equals to that of outlet gas for both the cylinder and the exhaust manifold in each cycle (Wang, 2008b; Ammann et al., 2003), i.e., mce( k ) = mic( k) + mec ( k ) + mf( k) .

(5)

So, mc(k + 1 ) = mc(k) + mf(k) + mic(k) + mec(k) – mce( k) = mc(k) ,

(6)

and also me ( k + 1 ) = me ( k ) ,

(7)

x = [ Fc Fe ]T .

System input is: u = mf .

F c ( k + 1 ) = C Fc ( k ) + C F e ( k ) + C Fi ( k ) + C m f ( k ) ,

(8)

Fe ( k + 1 ) = C Fc ( k ) + C Fe ( k ) + C mf ( k ) ,

(9)

1

2

5

6

3

7

4

where, C

1

mce mce mec , m m m m m

= 1 – --------------- + ------- ⋅ --------------c+ f e c+ f

(10)

mce ⎞ ec ⎛ ------- ⋅ 1 – -------- , C =m mc ⎝ mem⎠

(11)

ic ------ , C =m mc

(12)

2

3

C C C

4

5

6

λs mce m m m

λs mec mce λs , m m m m m

= -------------------------- – ----- – ------- ⋅ ------- ⋅ --------------c( c + f) c c e c+ f

(13)

(19)

System output is: y = Fe .

(20)

With the assumption that the density of in-cylinder charge at IVC is considered the same as the one in intake manifold (Killingsworth et al., 2006; Koehler and Bargende, 2004), and can be approximated, by the ideal gas law, as below: ---- , mc = p----i-V----IVC RTi

(21)

---- . me = p-----V RT

(22)

6

Thus, the resultant dynamic models are given as follows:

(18)

6

6

By the speed-density equation, the mass flow rate into the engine cylinder, Wic, can be calculated as: η v p i V IVC ---------------------- . Wic = N 120 RT i

(23)

Then, the mass into cylinder per cycle, mic, can be generated as: ---- . mic = η----v--p---i-V----IVC RTi

(24)

Here, pi, pe and Ti, Te are pressures and temperatures of intake manifold and exhaust manifold, respectively. ηv is the engine volumetric efficiency. R is the ideal gas constant. In what follows, the mass flow from exhaust manifold to cylinder during intake and exhaust valve overlapping period are derived by using the model developed in (Koehler and Bargende, 2004):

mce mc , m m m

(14)

mec = ( ∆mrestV + ∆mrestB ) .

mce , me

(15)

where ∆mrestV and ∆mrestB are the mass flow caused by the

= ------- ⋅ --------------e c+ f

= 1 – -------

(25)

152

F. YAN and J. WANG

volume change and pressure difference, respectively. The two terms can be written as:

3. HPCR FUEL INJECTION PARAMETER ON-LINE CALIBRATION

∆mrestV = di ⋅ K1 ,

(26)

dt K , ∆mrestB = SGN( pe – pi )AK 2diABS( pe – pi) ⋅ -----dϕ 2

(27)

3.1. Injector Model The predicted exhaust manifold oxygen fraction can be generated by the oxygen fraction model presented in section 2 based on the desired fuel injection amount and the signals measured on the engine. Thus, the difference between the predicted exhaust manifold oxygen fraction and the one measured from the engine can be chosen as the base error in the injector model parameter on-line calibration algorithm. The HPCR injection mass quantity can be modeled by (Lino et al., 2005, 2007):

where EVC dv αKexh2 dϕ , K1 = ∫IVO -----⋅ ----------------------------dϕ αKexh2+ αKint2

(28)

αK_exh ⋅ αK_int EVC - dϕ , K2 = ∫IVO ----------------------------------αK_exh + αK_int

(29)

mce = mic + mec .

(30)

2

2

Here, di is the in-cylinder charge density during valve overlapping, and can be approximated by the intake manifold charge density calculated through ideal gas law. ABS(pe-pi) denotes the absolute value of pressure difference between intake manifold and exhaust manifold. AK is the piston surface area. αKint and αKexh are piston surface area effective parameters. ϕ is the crank angle. The intake and exhaust manifold signals (including pressures, temperatures, and oxygen fractions) can be obtained by sensors and/or air-path observers (Wang, 2008a; Wang, 2008b) for calculating the predicted exhaust manifold oxygen fraction based on the desired (commanded) fuel injection quantity. Such intake and exhaust manifold sensors are available on some new engine platforms. As the effectiveness of the method proposed in this paper relies on the accuracy of the exhaust oxygen mass fraction model, the parameters in the model need to be carefully calibrated. Figure 2 illustrates the comparison of the foregoing discrete dynamic model with a high-fidelity, one-dimensional computational, GT-Power engine model. As it indicates, the dynamic model can well predict the exhaust oxygen fractions in both the steadystate and transient conditions with varying oxygen fractions and engine speed.

∆p- , mf = ρfuel ⋅ sgn( ∆P) ⋅ cd cyl ⋅ Acyl ⋅ ET ⋅ 2---------ρfuel ,

(31)

where Acyl is the area of the total outflow section, cd,dyl is the fuel flow discharge coefficient, ET is the injection duration commanded to the injector, and ∆P is the pressure difference between common rail and in-cylinder pressures. ρfuel is the fuel density. The injection model (31) can be used to generate the injection duration with the information of the desired fuel quantity and the pressure difference between HPCR and cylinder pressures. However, the pressure difference reading may not be accurate due to the sensor bias, and the injector parameters may change with injector aging and environmental conditions. These uncertainties/variations will affect the actual fuel injection quantity. To ensure the injection quantity control accuracy, an uncertainty parameter θ(k) is introduced in the injector model and it will be calibrated on-line. Thus, the injection model (31) can be modified as: ∆P- , mf = θ( k ) ⋅ ρfusl ⋅ sgn n( ∆P) ⋅ cd cyl ⋅ Acyl ⋅ ET ⋅ 2----------ρfusl ,

(32)

where, the nominal value of θ(k) is 1.0. 3.2. ILC and EILC Here, ILC and Enhanced ILC algorithms are briefly reviewed. The ILC algorithm in (Chien, 1998; Chien et al., 2007) can be written as: ui ( n ) = ubi ( n ) + ufi( n) .

(33)

where ufi(n) is the feedforward control in the form of: ufi ( n ) = Σij –=mi – 1Gjuj( n) + Σij –=mi – 1Lj( n)ej( n + 1) ,

(34)

and ubi ( n) is the feedback controller in the form of: Figure 2. Comparison of the exhaust manifold oxygen fraction model with a high-fidelity GT-Power engine model.

zi ( n + 1 ) = p ( zi ( n ) ) + q ( zi ( n ) ) ei ( n ) ,

(35)

ubi ( n) = r ( zi ( n ) ) + s ( zi( n) ) ei( n) .

(36)

COMMON RAIL INJECTION SYSTEM ITERATIVE LEARNING CONTROL BASED PARAMETER Here, e (n) denotes the tracking error between the desired and system outputs at time n in iteration i. G and L denote the forgetting factor and learning gain operator. In the basic ILC, G is chosen as 1. e (n) is the current tracking error and p, q, r and s are the functions for bounded conditions. Essentially, the ILC includes the information from previous control signal (feed-forward) and the feedback signal. So, by choosing m = i−1, G = 1, r(·) = 0, and s(·) = K , in (34)~(36), one of the basic controller, Dtype ILC (Chien et al., 2007), can be derived as: i

j

j

j

i

j

p

u ( n ) = u ( n ) + Le ( n + 1 ) + k e ( n ) , i–1

i

i –1

p

(37)

i

In ILC, the control law includes the control signal and the error signal in the last iteration. However, the convergence of the ILC in (37) requires identical initial condition, which may not be satisfied in the highly nonlinear engine systems (Chien, 1998). Thus, in this paper, the enhanced ILC (Chien et al., 2007) is employed to release the identical initial condition requirement. The control law is given as: u ( n ) = u ( n ) + Le ( n + 1) + K[ e ( n ) – e ( n) ] . i–1

i

i–1

(38)

i–1

i

Here K is the compensation gain and K[e (n)−e (n)] term compensates the state difference between two iterations at time n. Thus there is no requirement for the same initial conditions for all iterations as that in normal ILC (Chien, 1998). i

i-1

3.3. EILC-based On-line Fuel Injection Parameter Calibration In the EILC algorithm (38), the was chosen by the difference of the oxygen fraction ∆F , and the ∆θ = θ(k)−1 as the u in (38). Each of the iterations contains 10 engine cycles. To keep consistent with the EILC algorithm, we use ∆F (z), ∆θ (z), to represent ∆F (z) in i th iteration. Thus, the EILC algorithm in (38) can be written as e

e,i

i

e

∆θi( n) = ∆θi – 1( n ) + L ∆Fe i – 1( n + 1 ) + K [∆Fe i( n) – ∆Fe i – 1( n) ] ,

,

,

(39)

As can be seen from the simulation scheme in Figure 3, the input signal is the desired fuel injection quantity. The nominal values of the injector model parameters can be

153

obtained by injector calibration and measurement from the rail pressure sensor. By applying the EILC, a compensating value ∆θ can be generated, and it can be used in the injector model to generate the adjusted injection duration signals for delivering accurate injection quantity to the cylinders. 3.4. Convergence Criterion and Parameters Selection In EILC, the parameters, L and K used in (39) can be chosen by the following convergence criterion, which is similar to the one for linear time-invariant (LTI) systems as proposed in (Chien et al., 2007). Considering the model generated in Section 3, the actual dynamics of oxygen fraction can be written as: Fc(k + 1) = C1Fc(k) + C2Fe(k) + C3Fi(k) + C4(mf( k) + d(k)) , (40) Fe ( k + 1 ) = C 5 Fc ( k ) + C 6 Fe ( k ) + C7 ( m f ( k ) + d ( k ) ) ,

(41)

where m (k) is the desired injection fuel amount, d(k) is the disturbance caused by fuel pressure oscillation and etc. The dynamics of oxygen fraction generated by the comparison model is: Fˆ (k + 1) = C Fˆ (k) + C Fˆ (k) + C Fˆ (k) + C (m ( k) + ∆m ( k) ),(42) f

1

c

c

2

3

e

i

4

f

f

Fˆ e(k + 1) = C5Fˆ c(k) + C6Fˆ e(k) + C7( mf(k) + ∆mf(k)) ,

(43)

where m (k) is the adjusted fuel amount and can be written as: f

∆mf ( k ) =∆θ ( k ) ⋅ ρfuel ⋅ sgn ( ∆P ) ⋅ cd cyl ⋅ Acyl ⋅ ET ∆P- = γ ∆θ ( k ) ⋅ 2----------ρfuel ,

(44)

Denote ∆F (k) = F (k) – Fˆ (k ) and ∆F (k) = F (k) – Fˆ (k) . Then one can get: e

e

e

c

c

c

∆Fc( k + 1 ) = C1∆Fc( k ) + C2∆Fe( k ) + C4( d( k ) – ∆mf( k ) ) ,

(45)

∆Fe( k + 1 ) = C5∆Fc( k ) + C6∆Fe( k ) + C7( d( k ) – ∆mf( k ) ) .

(46)

Here, we denote

Figure 3. Block diagram of the fuel injection on-line parameter calibration system.

154

F. YAN and J. WANG

φ ( C ) = ⎛⎝

By choosing and satisfying Equation (54), as indicated in ∆F , ( ω ) < 1 , i.e., ∆F will converge. The convergence (53), -----------------------

C1 C2⎞ , C5 C6⎠

e i

F , – 1( ω )

∆

e

e i

Then a z-form transfer function of the system can be derived as:

of ∆F will lead to the correction of fuel injection amount. Here we do not provide the proof of the detectability. It can be easily realized that, in real engineering practice, with the other conditions being the same, the injection fuel amount and exhaust oxygen mass fraction are one-to-one correspondence, i.e., when error of the latter converges to zero, the former can be corrected as well.

G(C, z ) = H( zI – φ (C))–1T(C) .

4. SIMULATION STUDIES

T ( C ) = C4 , C7 H = [01] .

e

(47)

i.e.

(48)

Fe (z ) = ( d( z) – γ ∆θ (z ) )G( C, z) = d( z )G( C, z ) – γ ∆θ (z )G( C, z )

By taking z-transform of (39), we can get: z = ∆θ – 1(z) + zL∆F

∆θ i ( )

i

e, i – 1 (

z) + K[∆F (z) – ∆F e, i

e, i – 1 (

z)] .

(49)

As the transfer function G(C,z) depends on the parameter vector C, to distinguish the difference between G in i th and (i−1) th iterations in one expression, we use G and G − , respectively. Inserting (49) to (48) and denoting ∆F as ∆F in the th iteration lead to: i

1

i

e

e,i

∆F ( z ) = d ( z ) G ( z ) – γ ∆θ ( z ) G ( z ) = d ( z ) G ( z ) – γ G ( z ) ∆θ ( z ) (50) –γLzG (z)∆F (γK[G (z)∆F (z) – G (z)∆F (z) ]) e, i

i

i

e, i – 1

i

i

i

i

e, i

i–1

i

e, i – 1

i

By rearrangement of (50), one can get

1 + γKG (z))∆F (z) = d(z)G (z) – γG (z)∆θ (z) –(γLzG (z) – γKG (Z))∆F (z)

(

i

e, i

i

i

i–1

i

(51)

e, i – 1

i

Consequently, by considering Equation(48), one can have:

–γG (z)∆θ – 1(z) + d(z)G (z-) γ------------------------------------------F (z)- --------------------------------------------------------------LzG (z) – γKG (z)--------------------F – 1(z) = ∆F – 1(z)(1 + γKG (z)) – (1 + γKG (z)) –γG (z)∆θ – 1(z) + dzG (z) = -----------------------------------------------------------------------------------------------------------–(γ G – 1(z)∆θ – 1(z) + d(z)G – 1(z))(1 + γKG (z)-) – γ LzG ( z ) – γ KG ( z ) G (z) ------------------------------------------- = G-----------------------------------------------– ( 1 + γ KG ( z ) ) – 1 ( z ) ( 1 + γ KG ( z ) ) γ LzG ( z ) – γ KG ( z ) ------------------------------------------(52) ( 1 + γ KG ( z ) ) Evaluating (49) on the unit cycle z = e ω leads to: ∆F ( ω ) = ----------------------∆F – 1 ( ω ) ω G (ω ) γ Le G ( ω ) – γ KG ( ω ) ---------------------------------------------------------------------------------------------------, (53) – G – 1(ω )(1 + γKG (ω )) ( 1 + γ KG ( ω ) ) ∆ ∆

e, i

i

e, i

i

i

e, i

i

i

i

i

2

d,cyr

fuel

-8

2

cyl

i

i

i

i

i

i

i

i

4.2. Case 1-Fuel Injection Parameter Uncertainty and Disturbance Rejection 4.2.1. Simulation conditions To evaluate the parameter calibration algorithm, a “real” engine, including injection system, was constructed with the typical parameters: HPCR high-frequency pressure oscillation as shown in Figure 4 (one periodical disturbance was set 8 times of fuel injection frequency to simulate the circumstance of a 8-cylinder engine, i.e. 80 Hz with a magnitude of 15 MPa for 1200 rpm engine speed; another low frequency disturbance was added with 2 Hz frequency and 15 MPa magnitude); the fuel flow discharge coefficient c = 0.75; the fuel density ρ = 850 kg/m ; the area of injection section A = 2×10 m . Whereas, the parameters of injector model with the uncertainty and variations were

i

i

i

i

4.1. Simulation Setup In this section, a high-fidelity, 1-D computational, GTPower engine model is utilized to evaluate the on-line injection quantity correction algorithm. GT-Power is an industrial standard computational simulation package and is able to simulate the one-dimensional wave dynamics and heat transfer throughout the engine systems. In the GTPower combustion model, the fuel injection quantity was assumed to be precise.

i

i

i

i

j

e, i

e, i

j

i

i

i

i

i

i

Thus, the convergence criterion is derived as: ω G (ω ) γ Le G ( ω ) – γ KG ( ω ) ---------------------------------------------------------------------------------------------------– < 1, ∀ω . G (ω )(1 + γKG (ω )) ( 1 + γ KG ( ω ) ) j

i

i–1

i

i

i

i

(54)

Figure 4. HPCR pressure variation.

COMMON RAIL INJECTION SYSTEM ITERATIVE LEARNING CONTROL BASED PARAMETER

Figure 5. Error convergence. assumed as: HPCR pressure sensor reading p = 150 MPa; the fuel flow charge coefficient cd,cyi = 0.71; the fuel density ρfuel = 870 kg/m ; the area of injection section Acyl = 1.9×10 m. Thus, without the active fuel injection system parameter online calibration, the actual fuel injection quantity delivered into GT-Power combustion model will be different from the desired one due to the unknown uncertainties. To evaluate the developed injection system parameter on-line calibration algorithm, co-simulations within Matlab/SIMULINK and GTPower were conducted. The parameters in the controller were chosen as: L = -1.2, K =-1.2. 2

8

155

Figure 7. Desired and actual fuel injection quantities during the injection model parameter on-line calibration.

-

2

4.2.2. Simulation results The predicted exhaust manifold oxygen fraction, Femodel in Figure 5, was modeled based on the desired injection quantity and measured intake and exhaust manifold signals according to the oxygen mass fraction model in section II. The difference between this predicted exhaust manifold oxygen fraction and the measured one is related to the injection quantity error. Therefore, such an oxygen fraction difference can provide an error signal in EILC algorithm. In the simulation, the uncertainty parameter θ(t) on-line calibration was initiated at the 110 engine cycle. As can be th

Figure 6. Model uncertainty parameter adjustment.

seen from Figure 5, the error between the predicted and measured exhaust manifold oxygen fractions was rendered to zero after the algorithm was applied. Figure 6 shows that the uncertainty parameter of the injection model, θ(t), was actively calibrated after the EILC-based parameter calibration algorithm was activated. Figure 7 shows that the desire fuel injection amount is 20 mg, whereas the actual injection amount before EILC algorithm correction was around 22.3 mg, with oscillation. After parameter on-line calibration was started, the actual fuel injection quantity was adjusted to the desired value (20 mg) by updating the uncertainty parameter in the injector model (32) and thus the corresponding injection duration for the injector. 4.3. Case 2-Effects of Engine Signal Measurement Inaccuracy 4.3.1. Simulation conditions The proposed on-line parameter calibration method is based on signals (temperature, pressure, and oxygen fraction) measured in intake and exhaust manifolds. The accuracies of such measurements will affect the oxygen fraction model

Figure 8. HPCR pressure variation.

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F. YAN and J. WANG

Figure 9. Intake manifold oxygen fraction signals. and therefore the performance of the on-line parameter calibration. To show the effects by inaccurate measurements, another simulation was conducted at a different operation condition (different EGR opening and engine speed, i.e. 1800 rpm) with measurement signal uncertainties/noise. The parameters in the “real” engine, including injection system, were set as follows: the fuel flow discharge coefficient c = 0.8; the fuel density ρ = 835 kg/m ; the area of injection section A = 1.8×10 m . The HPCR pressure is indicated as Figure 8. Comparing to the previous case, two periodical disturbances (one is with a frequency of 60 Hz and a magnitude of 12 MPa; the other is with 3 Hz frequency and a magnitude of 16 MPa) for 1800 rpm engine speed were added to the HPCR pressure. The parameters of injector model with the uncertainty and variations were assumed as: HPCR pressure sensor reading p = 150 MPa; the fuel flow charge coefficient c = 0.71; the fuel density ρ = 870 kg/m ; the area of injection section A = 1.9×10 m . To be noted, comparing to the sensor pressure reading 150 MPa, the real HPCR pressure 2

d,cyl

fuel

-8

2

cyl

d,cyl

2

fuel

-8

2

Figure 11. Desired and actual fuel injection quantities during the injection model parameter on-line calibration with measurement inaccuracies. has a mean value of 135 MPa, i.e. 15 MPa bias value was included. To evaluate the influence of inaccurate manifold signals, a measurement uncertainty with a bias value of -0.02 was added to the actual intake manifold oxygen fraction (Figure 9) and a noise signal was added to the exhaust manifold pressure as indicated in Figure 10. 4.3.2. Simulation results By the same on-line calibration design method, the simulation result is shown in Figure 11. As it indicates, the inaccurate measurement signals affect the correction of fuel injection quantity to a certain extent. This simulation shows that the performance of the proposed method is related to engine measurement signal accuracies.

cyl

Figure 10. Exhaust manifold pressure signals.

5. CONCLUSIONS

In this paper, a HPCR injection system on-line parameter calibration method based on the EILC algorithm was developed for accurate fuel injection quality control of Diesel engines. Such an algorithm can significantly reduce the effects of periodical disturbance and uncertainties (such as the HPCR pressure sensor uncertainty and variations associated with injector aging and fuel properties) on the fuel injection quantity control accuracy. Simulations using a high-fidelity GT-Power engine model with added disturbance and uncertainties were utilized to demonstrate the effectiveness of the developed algorithm. It was observed that, by the on-line calibration, the actual HPCR fuel injection quantity can be precisely controlled around the desired value. However, the effectiveness of the proposed method relies on accurate engine signal measurements as indicated in simulation case 2.

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