Intake Air Mass Observer Design Based on Extended Kalman Filter for Air-Fuel Ratio Control on SI Engine

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Article Intake Air Mass Observer Design Based on Extended Kalman Filter for Air-Fuel Ratio Control on SI Engine

Lei Meng , Jie Luo, Xu Yang * and Chunnian Zeng *

School of Automation, Wuhan University of Technology, Wuhan 430070, China * Correspondence: [email protected] (X.Y.); [email protected] (C.Z.)

Received: 13 August 2019; Accepted: 3 September 2019; Published: 6 September 2019

Abstract: Air-fuel ratio (AFR) control is important for the exhaust emission reduction while using the three-way catalytic converter in the spark ignition (SI) engine. However, the transient cylinder air mass is unable to acquire by sensors directly and it may limit the accuracy of AFR control. The complex engine dynamics and working conditions make the intake air estimation a challenge work. In this paper, a novelty design of intake air observer is investigated for the port-injected SI engine. The intake air dynamical modeling and the parameter fitting have been carried out in detail. Extended Kalman Filter (EKF) has been used to optimize the instantaneous cylinder charge estimation and minimize the effort of pump gas fluctuation, random noise, and measurement noise. The experiment validation has been conducted to verify the effectiveness of the proposed method.

Keywords: intake air mass observer; Extended Kalman Filter; air-fuel ratio control; SI engine

1. Introduction The spark ignition (SI) engine emission is reduced by using the three-way catalytic converter (TWC) based on electronic fuel injection control to meet the strict emission requirements. However, the conversion efficiency of TWC depends on the engine air-fuel ratio (AFR) significantly. The maximum converter efficiency and fuel economy could be guaranteed by regulating the AFR at a very narrow band around the stoichiometric value. One of the important practical aspects for the accurate AFR control is the correct intake air mass estimation in the engine cylinder [1]. However, the transient cylinder air mass is difficult to measure by sensors, due to the intake manifold dynamics. Practically, there are two kinds of method for the intake air measurement on production engines. Using the mass air flow (MAF) sensor that was installed before the throttle can directly measure the mass flow entering the intake system, but the result has a tremendous error against the actual cylinder air mass under the transient state. The other method is using the manifold air pressure (MAP) sensor to calculate the cylinder air mass based on the speed-density approach, which is widely used on the existing engine control system, has a faster response time, and costs less. Both of the technical methods mentioned above could not directly acquire the instant cylinder air mass. In addition, the complex engine working conditions and tremendous measurement noise make the cylinder air mass estimation a challenging task and have captured enormous attention recently. On the production engine management system, the intake air mass estimation is based on the well-calibrated look-up tables at different engine operating states. However, the dramatic change of intake dynamics and parameter varying makes a challenging problem for the traditional air estimation. Many approaches have been proposed in the literature on the air charge estimation to improve the accuracy at both the transient and steady state [2,3]. Hendricks [4] has emphasized that the pressure transducer response time existed and it was impossible to follow rather slow throttle angle transients and proposed the necessary of intake air observer to eliminate the sensor response characteristic.

Energies 2019, 12, 3444; doi:10.3390/en12183444 www.mdpi.com/journal/energies Energies 2019, 11, x FOR PEER REVIEW 2 of 12

Energiescharacteristic.2019, 12, 3444 An adaptive observer is proposed to estimate the intake oxygen concentration of a2 lean- of 12 burn engine while using existing sensors with minimum computational load [5]. The research [6] proposed an air mass flow estimator design with model bias correction for a turbocharged diesel Anengine adaptive by off-line observer calculation. is proposed An to in-cylinder estimate the air intake mass oxygen observer concentration was implemented of a lean-burn in [7],engine which whilecombined using the existing feedforward sensors neural with minimumstatic model computational and a linear load parameter [5]. The varying research (LPV) [6] proposedpolytopic anobserver. air mass Some flow air estimator charge observers design with have model been reported bias correction in [8,9] on for the a turbocharged SI engine and dieselthe experimental engine by oresultsff-line calculation.showed that An the in-cylinder input estimation air mass techniqu observeres could was implemented enhance the incontrol [7], which performance. combined Using the feedforwardthe Kalman neuralfilters to static develop model the and intake a linear air parametermass observer varying have (LPV) been polytopicreported an observer. effective Some way air to chargesolve the observers problem, have as it been is difficult reported to obtain in [8,9 ]measurements on the SI engine in time and thefor experimentalthe accurate cylinder results showedair mass thatflow the [6,10,11] input estimation. Although techniques there was couldsome enhancework about the controlthe engine performance. air charge, Using the complex the Kalman intake filters air todynamics develop and the accurate intake air AFR mass control observer demand have still been arou reportedsed interest an eff forective the wayresearch to solve of accurate the problem, intake asair it estimation. is difficult to obtain measurements in time for the accurate cylinder air mass flow [6,10,11]. AlthoughIn this there paper, was a somenovelty work design about of detailed the engine air aircharge charge, estimation the complex observer intake is investigated air dynamics for and the accurateport-injected AFR controlSI engine. demand The intake still aroused air dynamica interestl for modeling the research and ofthe accurate parameter intake fitting air estimation. have been carriedIn this out. paper, Extended a novelty Kalman design Filter of detailed(EKF) has air b chargeeen used estimation to optimize observer the instantaneous is investigated cylinder for the port-injectedintake air estimation. SI engine. TheFurthermore, intake air dynamicalthe experime modelingntal validation and the parameter invested fittingthe effectiveness have been carried of the out.proposed Extended intake Kalman air mass Filter observer (EKF) design has been method. used to optimize the instantaneous cylinder intake air estimation. Furthermore, the experimental validation invested the effectiveness of the proposed intake air2. Air mass Path observer Modelling design of method. the SI Engine

2. Air Path Modelling of the SI Engine 2.1. System Description of the Engine Air Path 2.1. SystemFor the Description port injected of the SI engine, Engine AirFigure Path 1 shows a brief structure of the entire system. The SI engine α is controlled,For the port followed injected by SI the engine, throttl Figuree movement1 shows aand brief the structure position of angle the entire ( ) system.affects the The relative SI engine air ismass controlled, supply. followedAt different by engine the throttle operation movement conditio andns, thethe positionintake air angle passes (α through) affects the throttle relative and air massgoes supply.into the Atcylinder different during engine the operation inlet valves conditions, opening. the The intake electronic air passes control through unit (ECU) the throttle calculates and m goesand controls into the cylinderthe fuel injection during theamount inlet valves( fcmd ) opening.based on the The intake electronic air mass control and unit AFR (ECU) control calculates strategy. . andThe controlsair and theinjected fuel injectionfuel mix amountin the intake (m f cmd manifold) based on in the front intake of the air intake mass and valves, AFR and control then strategy. the gas Themixture air and enters injected the engine fuel mix cylinder. in the The intake mixture manifold is ig innited front by ofthe the spark intake plug valves, to release and thenthe chemical the gas mixtureenergy and enters produces the engine the cylinder.engine output The mixture torque. isUs igniteding theby exhaust the spark gas plugoxygen to release(EGO) sensor the chemical before φ energythe TWC and to produces measure the the engine exhaust output oxygen torque. content Using the ( exhaustexh ) for gasrepresenting oxygen (EGO) the sensorAFR during before thethe TWCcombustion to measure process the can exhaust provide oxygen the fe contentedback ( φofexh the) for fuel representing and the air themixing AFR ratio. during In addition, the combustion engine processfueling cancontrol provide is a the fundamental feedback of theissue fuel in and SI theengine air mixingand has ratio. to depend In addition, on enginethe cylinder fueling air control mass isestimation, a fundamental which issue also in has SI a engine strong and impact has toon dependthe combustion, on the cylinder efficiency, air mass and emission estimation, performances which also hasof the a strong SI engine. impact on the combustion, efficiency, and emission performances of the SI engine.

FigureFigure 1.1. StructureStructure ofof thethe SISI engineengine airair path.path.

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However, the cylinder air mass, which is controlled by the inlet and outlet valves, is difficult to However, the cylinder air mass, which is controlled by the inlet and outlet valves, is difficult to directly obtain and have event-based dynamics that are based on the crank angle domain. There are directly obtain and have event-based dynamics that are based on the crank angle domain. There are two two main implementation challenges. One is because the engine working conditions are really main implementation challenges. One is because the engine working conditions are really complicated complicated and defined by both the engine speed and load. During the transient operation, the air and defined by both the engine speed and load. During the transient operation, the air mass through mass through the throttle may be different from the cylinder air mass. At the steady operating the throttle may be different from the cylinder air mass. At the steady operating conditions, the intake conditions, the intake air mass can be dynamically balanced. The other is because the intake pressure air mass can be dynamically balanced. The other is because the intake pressure that is measured by the that is measured by the sensor is fluctuated, even at the steady state because of the valve movement. sensor is fluctuated, even at the steady state because of the valve movement. As the pressure signal As the pressure signal recorded by the oscilloscope, as shown in Figure 2, using the sensor installed recorded by the oscilloscope, as shown in Figure2, using the sensor installed in the intake manifold in the intake manifold with a fluctuated signal during each cycle is a challenge for predicting the with a fluctuated signal during each cycle is a challenge for predicting the actual cylinder air mass. actual cylinder air mass. The transient air mass flow through the intake valve is difficult to measure The transient air mass flow through the intake valve is difficult to measure directly by sensors, and the directly by sensors, and the cylinder air must be estimated while using the control observer. In this cylinder air must be estimated while using the control observer. In this work, the intake air observer work, the intake air observer is developed based on commonly used MAP sensor on the car, and one is developed based on commonly used MAP sensor on the car, and one MAF sensor is additionally MAF sensor is additionally installed to calibrate the parameters at steady state. installed to calibrate the parameters at steady state.

10 1.8 CA One Working Cycle MAP 1.7 1.6 ）

1.5 ） V

0 V

（ 1.4 （

1.3 MAP Sensor

Crankshaft Sensor Crankshaft 1.2 -10 1.1 25 50 75 100 125 150 Time（ms） FigureFigure 2. The 2. The recorded recorded air airpressure pressure signal. signal.

Moreover,Moreover, the the accurate accurate parameters parameters of ofthe the intake intake air air path path are are usually usually difficult difficult to todetermine determine with with certainty.certainty. The The modeling modeling of ofthe the intake intake path path of ofthe the SI SIengine engine and and the the parameter parameter fitting fitting are are the the significant significant basisbasis for for the the observer observer design. design.

2.2. Mathematical Description of the Intake Air Path 2.2. Mathematical Description of the Intake Air Path FromFrom the the SI SIengine, engine, it is it isdifficult difficult to toderive derive th thee precise precise model model for for the the control control purpose. purpose. The The engine engine systemsystem is isa highly a highly nonlinear nonlinear and and multi-variable multi-variable system. system. The The mean mean value value engine engine model model (MVEM) (MVEM) is is suitablesuitable for for real-time real-time simulation simulation and and it has it has acceptab acceptablele accuracy accuracy for for representing representing engine engine dynamics dynamics for for thethe control control application application [12,13] [12,13].. Additionally, Additionally, MVEMMVEM hashas been been shown show ton to be be quite quite accurate accurate for thefor intakethe intakeair mass air mass observer observer design design [2]. It [2] describes. It describes the physical the physical engine engine dynamics dynamics on the on time the scaletime ofscale several of severalengine engine events events without without the cycle-to-cycle the cycle-to-cycle characteristics. characteristics. In this section, In this the section, intake airthe mathematical intake air mathematicaldescription ofdescription the SI engine of the is specificallySI engine is analyzedspecifically based analyzed on MVEM. based on MVEM. The intake air dynamics expresses the filling behavior in the manifold with the air mass via the The intake air. dynamics expresses the filling behavior in the manifold with the .air mass via the throttle plate (m ) inlet, while at the same time drawing air mass into the cylinder (m ). The manifold throttle plate ( m at ) inlet, while at the same time drawing air mass into the cylinderap ( m ). The pressure state equationat is acquired based on the ideal gas law [14,15]: ap manifold pressure state equation is acquired based on the ideal gas law [14,15]: . RT . . RT man pman =−= man ()mat map (1) pmmmanV at ap V man − (1) man where R is the gas constant of fresh air 287 J/(kg∙K) and Vman is the volume of the intake manifold (L).

Tman is the manifold air temperature (K) and pman is the manifold air pressure (kPa). The throttle air mass flow can be physically modeled as two separated parallel isentropic flows [16]:

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where R is the gas constant of fresh air 287 J/(kg K) and Vman is the volume of the intake manifold (L). · Tman is the manifold air temperature (K) and pman is the manifold air pressure (kPa). The throttle air mass ﬂow can be physically modeled as two separated parallel isentropic ﬂows [16]:

 . . pamb  mat = mat1 β1(α)β2(pr)  √Tamb  pman  pr =  pin  2  β1(α) = 1 a1 cos(α) + a2 cos (α)  − 1 p p p   ( pr 1 pr 2 ) , if (pr pc)   pn (2)  β2(pr) =  − ≥   1 , if (p < p )  r c  ( 1 )  p1 p p  pc = 2− 1  p2  p p p  pn = pc 1 pc 2 − . where pr is the ratio of air pressure before and after the throttle plate, mat1 is a fitting constant, α is the throttle opening angle(degree), β1(α), β2(pr) are the empirical equations, pamb and Tamb are the ambient air pressure and temperature, and a1, a2, p1, p2, pn, pc are constant parameters that have been found in [16]. It is difficult to use the ideal gas law to calculate the real intake air mass in the cylinder because the cylinder pressure and temperature cannot be measured in practice. Accordingly, volumetric efficiency (ev) is introduced to observe the amount of air in each cylinder by the pressure and temperature measured in the manifold. Using the speed density formula:

. Vd Vd map = (ev pman)n = (si pman yi)n (3) 120RTman · 120RTman · − where Vd is the engine displacement (L), n is the engine velocity (RPM), and si, yi are speed dependent ﬁtting parameters and they should not change much over the engine operating range. Above all, the mathematical description of the intake air path could be modeled by Equations (1)–(3). It is obvious that the model structure matches the experience that the intake air is diﬀerent at each working condition determined by the throttle opening angle (α) and engine speed (n).

2.3. SI Engine AFR Control Problem Formulation The AFR control purpose is to regulate the air-fuel mixture ratio at a proper value under different . working conditions. It should be noted that the fuel mass flow rate in the cylinder (m f cyl) needs to . adapt the cylinder intake air mass flow rate (map) based on the definition of AFR, the parameters are determined by:  .  map  AFR = .  m  f cyl (4)  λ = AFR = 1  AFRs φ The AFR controlling strategy is complicated and the design objective is to track a desired air-fuel ratio (φre f ) at different working conditions that have the ability of rejecting disturbances. φre f is the stoichiometric value for calibration requirements in practice. It is a challenging work to handle the control problems of parameter uncertainties and variations, the time-delay and nonlinearities, the large modeling uncertainties and unknown dynamics, and the wide operating range and complex working conditions. The adaptive AFR controller was introduced to overcome the control problems that are mentioned above [17]. From the definition in Equation (4), the in-cylinder air mass estimation is a crucial part for the fuel injection calculation and it affects the AFR control results. As a consequence, the accurate intake air mass observation is a key solution in order to regulate the AFR at expected value using the advanced control method. Energies 2019, 12, 3444 5 of 12

3. Observer-Based Intake Air Mass Estimation

3.1. Discrete Sampling Based on Engine Operation Cycle Although the dynamic engine operation process is a continuous-time system, the digital controller should obtain the system at the discrete-time domain for the control applications. The movement of the inlet and outlet valves are based on the camshaft in each engine working cycle that corresponded to four-stroke events. Consequently, the sampling time is not constant and is varied by the engine speed. On the other hand, the timing is constant in rotation domain that also can be treated as crank-angle based sampling. For the four-cylinder engine discussed in this paper, the engine speed can be:

1 dθ n = (5) 6 dt where θ is the crank angle (◦) and n is the engine velocity (RPM). In addition, to transform the time-domain diﬀerential equation into the crank-angle domain, note that:

dx dx = 6n (6) dt dθ

Therefore, the event-based sampling can be implemented each 720◦ crank angle each engine cycle and the sampling time can be T = 120/n.

3.2. Model Parameter Fitting Based on Equations (1) and (3), the air pressure in the intake manifold can be:

. RTman . . RTman . Vdn pman = mat map = mat (sipman yi) (7) Vman − Vman − 120Vman − assuming k = RTman and k = Vdn , we have the intake air mass equation: t Vman n 120Vman ( . . . p = ktmat kn(sipman yi) = ktmat knsipman + kn yi = knsipman + u man . − − − − (8) u = ktmat + kn yi where u is assumed as the system input. Accordingly, the discrete air mass model can be:

pman(k + 1) = (1 Tkns )pman(k) + Tu(k) (9) − i

As the air pressure in the manifold changes much faster than the engine speed, kn, kt, u can be treated as constant at each sampling point. Based on Equation (2), while using the MAF and MAP . sensor, the mat can be ﬁtted using the experiment data at the diﬀerent engine speed as the result in Figure3. Energies 2019, 11, x FOR PEER REVIEW 6 of 12

Energies 2019, 12, 3444 6 of 12 Energies 2019, 11, x FOR PEER80 REVIEW 6 of 12 800r/min y=38.3519*x+3.0693 1000r/min 7080 1200r/min 1400r/min 800r/min y=38.3519*x+3.0693 60 1600r/min1000r/min 70 1800r/min1200r/min 2000r/min1400r/min 50 2500r/min1600r/min 60 3000r/min1800r/min 3500r/min2000r/min 4050 4000r/min2500r/min 4500r/min3000r/min

m3500r/minat1fitting 3040 4000r/min 4500r/min m fitting 2030 at1

1020 0 100.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 p amb βαβ() ( ) 0 12pr T 0.0 0.5 1.0 1.5amb 2.0 2.5 3.0 3.5 4.0 4.5 5.0 p amb βαβ() (p ) Figure 3. The experimental fittingT result12 of throttler air mass parameter m . amb at . Figure 3. The experimental fitting result of throttle air mass parameter mat. Figure 3. The experimental fitting result of throttle air mass parameter mat . It is obvious that the mat was linear at each engine speed condition when . It is obvious that the m was linear at each engine speed condition when (p / √T )β (α)β (p ) ()p Tpβαβ() ( ) wasat at a small value, and then m reached to a maximumamb value.amb 1 In order2 r to ambIt ambis 12obvious r that the. m was linear atat each engine speed condition when was at a small value, and then mat reachedat to a maximum value. In order to find out the maximum find out the maximum. throttle air mass m at each engine speed, we obtained the fitting throttle()p airTp massβαβ()matmax (at ) each engine speed, weat obtainedmax m the fitting experimental result, as shown in amb amb12 r was at a small value, and then at reached to a maximum value. In order to Figureexperimental4. result, as shown in Figure 4.  find out the maximum throttle air mass mat max at each engine speed, we obtained the fitting experimental result, as shown80 in Figure 4. Experiment Data 7080 Fitting Result 60 Experiment Data 70 Fitting Result 50 ） 60 y=2.991 *x-4.988 g/s 4050 （） y=2.991 *x-4.988

g/s 3040 （ 2030

1020 0 100.0 5.7 11.4 17.1 22.8 28.5 pn 0 amb 1000 T 0.0 5.7 11.4amb 17.1 22.8 28.5 . pnamb Figure 4. matmax fitting results relative to engine speed and ambient temperature. Figure 4. m fitting results relative1000 to Tengine speed and ambient temperature. at max amb . As the result, the air mass passes the throttle mat(α, pman, n) at different operation points can be Figure 4. m at max fitting results relative to mpnengine (,α speed ,) and ambient temperature. estimated,As the as below:result, the air mass passes the throttle at man at different operation points can be  . pamb estimated, as below:  mat = 38.3519 β1(α)β2(pr) + 3.0693 As the result, the air mass passes the √throttleTamb mpn (,α ,) at different operation points can be  . pambN at man  matmax = 2.991 4.988 (10) estimated, as below:  1000 √Tamb −  . . .  mat(α, pman, n) = min(mat, matmax) In addition, MAF measurement can be used to represent the in-cylinder air mass at the steady state. Based on the Equation (3), the experimental data that are shown in Figure5 indicate that s pman y is i − i linear at the different engine load if the engine speed remains steady, and so that the si and yi can be treated as constant. The fitted si and yi alone with the engine speed is shown in Figure6.

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Energies 2019, 11, x FOR PEER REVIEW 7 of 12  p  =+amb βαβ() ( ) mpat38.351912 r 3.0693 Tp  =+ambamb βαβ() ( ) mp at38.351912 r 3.0693  pNT  =−ambamb m at max 2.991 4.988 (10)  1000pNT  =−ambamb m at max 2.991 4.988 (10) mpn(,α ,) =1000 min(, mmT )  at manamb at at max mpn(,α ,) = min(, mm )  at man at at max In addition, MAF measurement can be used to represent the in-cylinder air mass at the steady state. Based on the Equation (3), the experimental data that are shown in Figure 5 indicate In addition, MAF measurement can be used to represent the in-cylinder air mass at the steady that sip - y is linear at the different engine load if the engine speed remains steady, and so that state. manBased oni the Equation (3), the experimental data that are shown in Figure 5 indicate that sip - s y s y man the i and i can be treated as constant. The fittedi and i alone with the engine speed is sshown y yi is linear at the different engine load if the engine speed remains steady, and so that the i and i inEnergies Figure2019 6. , 12, 3444 7 of 12 can be treated as constant. The fittedsi and yi alone with the engine speed is shown in Figure 6.

100 100 800r/min 1000r/min 800r/min 1200r/min1000r/min 80 1400r/min1200r/min 80 1600r/min1400r/min 1800r/min1600r/min 2000r/min1800r/min 2500r/min2000r/min 60 3000r/min2500r/min 60 3500r/min3000r/min (kPa) i 4000r/min3500r/min (kPa) i -y 4500r/min4000r/min -y 4500r/min man 40 fitting results p i man 40 fitting results s p i s 20 20

0 0 20 30 40 50 60 70 80 90 100 20 30 40p 50 (kPa) 60 70 80 90 100 manp (kPa) man Figure 5. The fitting result of sip - y alone with the intake pressure. FigureFigure 5.5. The ﬁttingfitting resultresult ofof sispmanpman - iy alone alone withwith thethe intakeintake pressure.pressure. i man− ii 1.15 1.15 si -6.0 si -6.0 1.10 yi 1.10 yi -6.5 -6.5 1.05 -7.0 1.05 -7.0 1.00 -7.5 i 1.00 -7.5 i s y i i

s 0.95 -8.0 y 0.95 -8.0 0.90 -8.5 0.90 -8.5 -9.0 0.85 -9.0 0.85 -9.5 0.80 -9.5 0.80500 1000 1500 2000 2500 3000 3500 4000 4500 5000 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Engine Speed（r/min） Engine Speed（r/min） Figure 6. The calculated si and yi alone with the engine speed. Figure 6. The calculated si and yi alone with the engine speed. Figure 6. The calculated si and yi alone with the engine speed. For the intake air mass mathematical model in Equation (8), all of the parameters are obtained For the intake air mass mathematical model in Equation (8), all of the parameters are obtained usingFor the the data intake ﬁtting air method, mass mathematical as mentioned model above. in Equation (8), all of the parameters are obtained using the data fitting method, as mentioned above. 3.3.using Intake the data Air Mass fitting Observer method, as mentioned above.

We use a time-varying extended Kalman predictor [18] for the optimal estimation of the intake manifold air pressure, which can minimize the eﬀort of pump gas ﬂuctuation, random noise, and measurement noise. We consider the system description in Equation (6), the state space model is then given as follows at the sampling time T = 120/n: ( pˆman(k + 1) = Fapˆman(k) + Gau(k) + Ka[pman(k) pˆman(k)] − (11) z(k) = pˆman(k)

where Fa = 1 Tknsi is the state-transition vector, Ga = T is the control-input vector, and Ka is the − T Kalman gain matrix. The predicted covariance estimate is P(k + 1/k) = Fa(k)P(k/k)Fa (k) + Q(k), the 1 near-optimal Kalman gain is Ka(k + 1) = P(k + 1/k)[P(k + 1/k) + R(k)]− , and then update the state estimate by pˆman(k + 1) = pˆman(k + 1/k) + Ka(k + 1)[pman(k + 1) pˆman(k + 1/k)]. Q and R are the − k k Energies 2019, 11, x FOR PEER REVIEW 8 of 12

3.3. Intake Air Mass Observer We use a time-varying extended Kalman predictor [18] for the optimal estimation of the intake manifold air pressure, which can minimize the effort of pump gas fluctuation, random noise, and measurement noise. We consider the system description in Equation (6), the state space model is then given as follows at the sampling time T = 120/n:

 ∧∧ ∧ pk(+=1 ) FpkGukKpkpk () + () + () − ()  manaaaman man man   (11)  ∧ zk()= p () k  man =− = where Fani1 Tk s is the state-transition vector, GTa is the control-input vector, and Ka is the (+= ) () ( )T () + () Kalman gain matrix. The predicted covariance estimate is P kkFkPkkFkQk1/aa / , the − Energies 2019, 12, 3444 ()()()()+= + ++ 1 8 of 12 near-optimal Kalman gain is Ka k11/1/ Pk k Pk k Rk , and then update the state ∧∧ ∧ pk()+=11/111/ pk ( + kKk ) + () + pk () +− pk ( + k ) Q R estimate by man man a man man . k and k are the covariance matrices of the zero mean multivariate Gaussian state and observation noises, respectively. Thecovariance in-cylinder matrices air mass of prediction the zero canmean be obtained multivariate based onGaussian Equation state (3): and observation noises, respectively. The in-cylinder air mass prediction can be obtained based on Equation (3): Z tic ^ . 30 V V tic 30 VVd d mˆ ap = m==apdt = dd(()si ⋅−=⋅−pˆˆˆman yi)n = ()(si pˆman yi) (12) mmdtap ap spynspy i man i i man i (12) t tio n 120nRT120RTman · − 4 RT4RTman · − io man man where t t and t t are the intake valve opening and closing time, which has a diﬀerent value along where icic and ioio are the intake valve opening and closing time, which has a different value along withwith thethe engineengine speedspeed at at 180 180°◦ crank crank angle.angle. AsAs mentionedmentioned above,above, thethe solvingsolving processprocess ofof thethe intakeintake airair observerobserver isis asas thethe calculatingcalculating stepssteps thatthat areare shown shown in in Figure Figure7 7based based on on Equations Equations (8)–(12). (8)–(12).

Initialize Qk () and Rk()

Calculate F a and u

Predict the intake pressure of step k+1 based on the value of step k: ∧∧ (+= ) () () + () pkman 1/ kFkpkGukamana

Calculate the predicted covariance estimate: (+= ) () ( )T () + () P kkFkPkkFkQk1/aa /

Calculate the Kalman gain: ()()()()+= + + + −1 Ka k11/1/ Pk k Pk k Rk

Update the intake air pressure state: ∧∧ ∧ pk()+=11/111/ pk ( + kKk ) + () + pk () +− pk ( + k ) man man a man man

Update the predicted covariance: ()()()++=− + + P kk1/ 1 IKkPkka 1 1/

Update the cylinder air mass =+ kk1 FigureFigure 7.7. TheThe calculatingcalculating stepssteps ofof thethe intakeintake airair observer.observer.

4. Experimental Veriﬁcation

4.1. Experimental Test Bench The experimental validation was conducted on a SGMW B15 engine test bench to verify the eﬀectiveness of the illustrated intake air mass observer and the prediction results of cylinder intake ﬂow. The engine geometry dimensions are listed in Table1. Figure8 shows the control system scheme of the engine test bench. A BOSCH HFM5 MAF sensor was installed in front of the throttle plate. The other necessary sensors and actuators were using the original OEM parts for the engine control application. The engine ECU was implemented on a Freescale MC9S12XDP512 based controller. An ATI Vision based calibration system was established to acquire the control parameter online updating and internal data logging [17]. Energies 2019, 11, x FOR PEER REVIEW 9 of 12

4. Experimental Verification

4.1. Experimental Test Bench The experimental validation was conducted on a SGMW B15 engine test bench to verify the effectiveness of the illustrated intake air mass observer and the prediction results of cylinder intake flow. The engine geometry dimensions are listed in Table 1. Figure 8 shows the control system scheme of the engine test bench. A BOSCH HFM5 MAF sensor was installed in front of the throttle plate. The other necessary sensors and actuators were using the original OEM parts for the engine control application. The engine ECU was implemented on a Freescale MC9S12XDP512 based controller. An Energies 2019, 12, 3444 9 of 12 ATI Vision based calibration system was established to acquire the control parameter online updating and internal data logging [17]. Table 1. SGMW B15 Engine Speciﬁcations. Table 1. SGMW B15 Engine Specifications.

ParameterParameter Type Type Value Value EngineEngine Type Type SI, 4 cylinders, SI, 4 cylinders, In-line In-line DisplacementDisplacement (liters) (liters) 1.485L 1.485L CompressionCompression Ratio Ratio 10.2:1 10.2:1 BoreBore (mm) (mm) 74.7 74.7 StrokeStroke (mm) (mm) 84.7 84.7 Maximum torque 146 N m/3600–4000 RPM Maximum torque 146 N∙m/3600–4000· RPM Maximum power 82 kW/5800 RPM Maximum power 82 kW/5800 RPM

FigureFigure 8. The8. The control control system system schemescheme of of the the engine engine test test bench. bench.

4.2. The4.2. Experimental The Experimental Results Results The ECUThe ECU controller controller was was set set as as open-loop open-loop controlcontrol st strategyrategy mode mode for for the the observer observer test testverification, verification, and theand CCPthe CCP calibration calibration software software is used used toto collect collect real-time real-time parameters parameters inside the inside controller. the controller. The The dynamometerdynamometer was set at a a constant constant load load of of 40 40 N N∙mm and and the the engine engine speed speed fluctuated fluctuated between between about about · 1200 r1200/min. r/min. and and 3000 3000 r/min. r/min. by by applying applying an 8%–16 8–16%% squaresquare wave wave disturbance disturbance to the to thethrottle throttle valve. valve. The intakeThe intake air pressure air pressure was was averaged averaged to to four four timestimes an engine engine cycle cycle toto reduce reduce thethe effect eff ofect pump of pump loss. loss. Figure 9 shows the experimental results. FigureEnergies9 shows 2019, the11, x experimentalFOR PEER REVIEW results. 10 of 12 ）

（ 40 30 ） 20 10 0 4000 r/min （ 3000 Throttle Position Throttle

） 2000 1000 kPa

（ 0 100 Observed Value

75 Measured Value Engine Speed

50 25 0 30.0 ）

Observed Value g/s Measured Value 22.5 （ 15.0

Intake Air Pressure Intake 7.5 0.0 0 20406080100120Mass Air （） Time s FigureFigure 9. Experimental9. Experimental results results ofof the intake intake air air mass mass observation. observation.

It can be seen that the observed value of intake air pressure using the Kalman filter had a better noise suppression than the measured value. The air flow at the engine intake valve could not be directly measured by sensors. Accordingly, in the experiment, the cylinder air that was predicted by the observer was compared with the intake air flow measurements by the installed HFM5 sensor. In Figure 9, it was obvious that the intake air pressure increased when the engine speed decreased and the pressure decreased when the engine speed increased at the constant throttle position. This followed the physical properties of the SI engine. It also showed that the air mass estimated by the observer responded faster when compared with the measured value by MAF sensor when the throttle position changed at transient. There was a certain difference between the measured and observed air mass, the main reason might be the response speed of the sensor, the installation position and the measurement characteristic that determined the measured value was not equal to the transient intake air mass flow through the inlet valve. Furthermore, there was some inevitably certain error that existed in the parameter fitting process of the observer design to cause the error. However, in general, the prediction results from the observer can effectively describe the intake dynamics and achieve satisfactory prediction accuracy, which can be used to observe the cylinder intake air mass in the air- fuel ratio control application. The air-fuel ratio error that was caused by the observer could be compensated by the feedback control method. For the AFR control application, a comparable experimental result is shown in Figure 10. The ECU controller was designed differently about the control algorithm by using the measured intake air pressure based on Equation (3) and using the intake air mass observer. The engine speed was fixed at 1500 RPM and the throttle position fluctuated near 6% to conduct the intake air mass varying. The exhaust AFR was measured by the UEGO sensor and then recorded by the calibration system. It was obvious that the exhaust AFR has a better noise suppression while using the observer method and the transient overshoot was less. However, the fluctuation of the AFR was remarkable, because the open-loop controller could not overcome the AFR variation based on the engine dynamics. Using the extended Kalman predictor for intake air mass observation has a reasonable optimization for the AFR control application.

Energies 2019, 12, 3444 10 of 12

It can be seen that the observed value of intake air pressure using the Kalman filter had a better noise suppression than the measured value. The air flow at the engine intake valve could not be directly measured by sensors. Accordingly, in the experiment, the cylinder air that was predicted by the observer was compared with the intake air flow measurements by the installed HFM5 sensor. In Figure9, it was obvious that the intake air pressure increased when the engine speed decreased and the pressure decreased when the engine speed increased at the constant throttle position. This followed the physical properties of the SI engine. It also showed that the air mass estimated by the observer responded faster when compared with the measured value by MAF sensor when the throttle position changed at transient. There was a certain difference between the measured and observed air mass, the main reason might be the response speed of the sensor, the installation position and the measurement characteristic that determined the measured value was not equal to the transient intake air mass flow through the inlet valve. Furthermore, there was some inevitably certain error that existed in the parameter fitting process of the observer design to cause the error. However, in general, the prediction results from the observer can effectively describe the intake dynamics and achieve satisfactory prediction accuracy, which can be used to observe the cylinder intake air mass in the air-fuel ratio control application. The air-fuel ratio error that was caused by the observer could be compensated by the feedback control method. For the AFR control application, a comparable experimental result is shown in Figure 10. The ECU controller was designed differently about the control algorithm by using the measured intake air pressure based on Equation (3) and using the intake air mass observer. The engine speed was fixed at 1500 RPM and the throttle position fluctuated near 6% to conduct the intake air mass varying. The exhaust AFR was measured by the UEGO sensor and then recorded by the calibration system. It was obvious that the exhaust AFR has a better noise suppression while using the observer method and the transient overshoot was less. However, the fluctuation of the AFR was remarkable, because the open-loop controller could not overcome the AFR variation based on the engine dynamics. Using the extendedEnergies 2019 Kalman, 11, x FOR predictor PEER REVIEW for intake air mass observation has a reasonable optimization for the11 AFR of 12 control application.

Throttle Position 8.5 6.8 5.1 (%) 3.4 18.7 Throttle Position Throttle Directly Calculation 17.0 Observer Based

AFR 15.3 13.6

0 5 10 15 20 25 30 35 40 45 50 55 60

Time (s) FigureFigure 10. 10.Experimental Experimental results results of of di differentﬀerent intake intake air air mass mass estimation. estimation.

5. Conclusions 5. Conclusions AnAn intake intake air air mass mass observer observer design design that wasthat basedwas based on extended on extended Kalman Kalman filter for filter the port-injected for the port- SIinjected engine isSI presented engine is inpresented this work. in Tothis estimate work. To the estimate cylinder the air masscylinder for theair AFRmass controlfor the application,AFR control theapplication, air path dynamics the air path modeling dynamics and modeling air mass observerand air mass design observer were implementeddesign were implemented based on MVEM. based Theon parametersMVEM. The of parameters the model of were the model carried were out bycarrie thed experimental out by the experimental data fitting data method. fitting A method. detailed A analysisdetailed of analysis the observer of the design observer was design introduced was in whiletroduced using while the extendedusing the Kalmanextended filter Kalman method. filter Themethod. comparative The comparative experiments experiments were conducted were on conduc an engineted teston benchan engine to validate test bench the performance to validate ofthe theperformance proposed intake of the air proposed mass observer. intake air mass observer. The experiment results could show that the proposed intake air mass observer is effective for the cylinder air mass estimation, which is unable to be directly measured by sensors. Although the computation process became more complicated, using the intake air mass observer based on the extended Kalman filter could obtain the acceptable estimated cylinder air mass for the AFR control application and also have a better response time when compared with the MAF sensor. Future work will involve the intake air observer with the optimal AFR control for SI engine at different operating conditions.

Funding: This research was funded by National Natural Science Foundation of China, grant number 61903287 and Fundamental Research Funds for the Central Universities, grant number WUT: 2018IVA109. This work also supported by Nature Science Foundation of Hubei Province, grant number 2018CFB303.

Conflicts of Interest: The authors declare no conflict of interest.

References

Energies 2019, 12, 3444 11 of 12

The experiment results could show that the proposed intake air mass observer is effective for the cylinder air mass estimation, which is unable to be directly measured by sensors. Although the computation process became more complicated, using the intake air mass observer based on the extended Kalman filter could obtain the acceptable estimated cylinder air mass for the AFR control application and also have a better response time when compared with the MAF sensor. Future work will involve the intake air observer with the optimal AFR control for SI engine at different operating conditions.

Author Contributions: All authors have cooperated for the preparation of the work. conceptualization, L.M. and X.Y.; methodology, L.M. and C.Z.; software and validation, L.M. and J.L.; writing—Original draft preparation, L.M. and X.Y.; writing—Review and Editing, J.L. and X.Y. Funding: This research was funded by National Natural Science Foundation of China, grant number 61903287 and Fundamental Research Funds for the Central Universities, grant number WUT: 2018IVA109. This work also supported by Nature Science Foundation of Hubei Province, grant number 2018CFB303. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

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