Minimization of Torque Deviation of Cylinder Deactivation Engine Through 48V Mild-Hybrid Starter-Generator Control

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Article Minimization of Torque Deviation of Cylinder Deactivation Engine through 48V Mild-Hybrid Starter-Generator Control

Hyunki Shin 1 , Donghyuk Jung 2 , Manbae Han 3,* , Seungwoo Hong 4 and Donghee Han 4

1 Eco-Vehicle Control Design Team, Hyundai KEFICO Corporation, Gunpo 15849, Korea; hyunki.shin@hyundai-keﬁco.com 2 Department of Automotive Engineering, Hanyang University, Seoul 04763, Korea; [email protected] 3 Department of Mechanical and Automotive Engineering, Keimyung University, Daegu 42601, Korea 4 Research & Development Division, Hyundai Motor Company, Hwaseong 18280, Korea; [email protected] (S.H.); [email protected] (D.H.) * Correspondence: [email protected]

Abstract: Cylinder deactivation (CDA) is an effective technique to improve fuel economy in spark ignition (SI) engines. This technique enhances volumetric efficiency and reduces throttling loss. However, practical implementation is restricted due to torque fluctuations between individual cylinders that cause noise, vibration, and harshness (NVH) issues. To ease torque deviation of the CDA, we propose an in-cylinder pressure based 48V mild-hybrid starter-generator (MHSG) control strategy. The target engine realizes CDA with a specialized engine configuration of separated intake manifolds to independently control the airflow into the cylinders. To handle the complexity of the combined CDA and mild-hybrid system, GT-POWER simulation environment was integrated with a SI turbulent combustion model and 48V MHSG model with actual part specifications. The combustion model is essential for in-cylinder pressure-based control; thus, it is calibrated with actual Citation: Shin, H.; Jung, D.; Han, M.; engine experimental data. The modeling results demonstrate the precise accuracy of the engine Hong, S.; Han, D. Minimization of Torque Deviation of Cylinder cylinder pressures and of quantities such as MAF, MAP, BMEP, and IMEP. The proposed control Deactivation Engine through 48V algorithm also showed remarkable control performance, achieved by instantaneous torque calculation Mild-Hybrid Starter-Generator and dynamic compensation, with a 99% maximum reduction rate of engine torque deviation under Control. Sensors 2021, 21, 1432. target CDA operations. https://doi.org/10.3390/s21041432 Keywords: combustion model; cylinder deactivation; engine modeling; in-cylinder pressure; SI Academic Editor: Ruben turbulent flame model; 48V mild-hybrid starter-generator Puche-Panadero

Received: 24 January 2021 Accepted: 16 February 2021 1. Introduction Published: 18 February 2021 Regulations for energy and exhaust emissions are major challenges in the research and development of powertrains. To overcome such challenges, cylinder deactivation Publisher’s Note: MDPI stays neutral (CDA) technology has drawn attention as a way to make engine displacement flexible; the with regard to jurisdictional claims in published maps and institutional affil- process involves deactivating a several cylinders under low-load conditions [1–3]. The iations. CDA deactivates several cylinders with wider throttle openings for compensating the required torque. Wider throttle opening reduces pumping loss and thus improves fuel economy [4–11]. Hybridization also has been demonstrated as a promising method to improve the fuel efficiency and reduce exhaust emission from the internal combustion engine [12–14]. An Copyright: © 2021 by the authors. optimization of several parameters via a genetic algorithm minimizes the brake specific Licensee MDPI, Basel, Switzerland. fuel consumption and nitric oxide emission [15]. The CDA combined with a hybridiza- This article is an open access article distributed under the terms and tion improves fuel efficiency by activating only three cylinders out of the six-cylinder conditions of the Creative Commons engine [16]. Attribution (CC BY) license (https:// Aside from the consideration of the fuel efficiency and exhaust emissions, the success- creativecommons.org/licenses/by/ ful implementation of CDA should suppress adverse effects such as noise, vibration, and 4.0/). harshness (NVH). Such NVH problem results from torque deviation between cylinders

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when activating CDA because activated cylinders must provide more torque to maintain vehicle driving performance. The absence of combustion in the deactivation sequences reduces, therefore, the number of power strokes per revolution and extends the interval between the maximum torque pulses, making it difficult to deliver consistent and smooth brake torque from the engine [17,18]. Overcoming the NVH problems of CDA has been challenging in terms of cost of additional components, calibration efforts, and limited control accuracy. Such drawbacks hinder the realization of CDA in the commercial market. The conventional approach for mitigating NVH problems of CDA engines was to use advanced hardware systems, such as additional torsional dampers and suitable engine mounts [19,20]. Although this method alleviates vibration of the drivetrain, cost and weight increased due to the additional hardware equipment. Unlike such hardware systems used to cope with NVH problems, the Dynamic Skip Fire (DSF) system improves NVH performance by selecting diverse firing sequences through independent control of individual cylinders [21–25]. The high degree of freedom to activate DSF operation increases calibration efforts. To complement this DSF system, an additional motor generator unit was integrated with a 48V electric hybridization [26]. The combined system presented the ability to smooth torque pulsation based on mild-hybrid torque assist; however, the open loop scheme makes it difficult to guarantee accurate control performance without any feedback on the current engine torque and dynamics compensation. For application of the spark ignition (SI) engine model for control purposes, the SI combustion model should strike a balance between model fidelity and computational cost [27]. There have been various types of combustion modeling, which can be grouped into non-predictive models, such as the Wiebe function, and predictive models [28]. Non- predictive models impose a burn rate as a function of crank angle, which means that the burn rate will not be affected by factors such as residual fraction or injection timing. A predictive combustion model would be a good choice for control application because the burn rate will respond appropriately to changes in the variable of interest. One predictive combustion model, the SI turbulent model, predicts the burn rate for homogeneous charges and plays a crucial role in the control application. Even in the high nonlinear conditions where the engine equipped the EGR, water injection, and hydrogen enriched control, the SI turbulent model showed a great fidelity with the computational efficiency [29,30]. The SI turbulent model comprises two subparts of laminar flame speed calculation and entrainment/burn-up. The laminar flame speed is calculated as a function of the equivalence ratio, pressure, temperature, fuel type and dilution effect [31]. The rate of entrained and unburned mixture of fuel and air passing into the flame front through the flame area is proportional to the sum of the turbulent and laminar flame speeds. The burn rate is proportional to the amount of unburned mixture behind the flame front divided by a time constant. This model requires calibration of the four dominant factors of dilution, turbulent flame speed, Taylor microscale length, and flame kernel growth [32–34]. In this study, we propose an in-cylinder pressure based 48V mild-hybrid starter- generator (MHSG) control strategy to reduce engine torque deviation under CDA operations. We use commercial software and combine the SI turbulent model for engine modeling with the 48V MHSG model with actual part specifications. In contrast to conventional CDA valve-train systems, the target engine implements CDA with a novel structure of separated intake and exhaust manifolds [35]. To cope with the complexity of the specialized CDA and 48V electrification, the target engine model was first derived using the SI turbulent model based on actual computer-aided design (CAD) files and engine experimental data. The four parameters of the SI turbulent model were calibrated with the in-cylinder pressures obtained by the actual engine experiment. The engine experiment was conducted in 50 operating points, and 100 cycles of in-cylinder pressure data were obtained for each operating condition. The SI turbulent engine model was designed with a strong correlation of representative air states, cylinder pressure, and engine torque. With this engine model, the proposed algorithm calculates instantaneous torque profiles of individual cylinders Sensors 2021, 21, 1432 3 of 22

Sensors 2021, 21, 1432 3 of 21 this engine model, the proposed algorithm calculates instantaneous torque profiles of in‐ dividual cylinders using in‐cylinder pressure traces. Based on the dynamic compensation, the torque setpoint of the 48V MHSG is derived to modulate the slow characteristics of using in-cylinder pressure traces. Based on the dynamic compensation, the torque setpoint the 48V MHSG from the inherent time delay and response. This is a feedforward control of the 48V MHSG is derived to modulate the slow characteristics of the 48V MHSG from to allow precise control performance with a fast response on a cycle‐by‐cycle basis for the inherent time delay and response. This is a feedforward control to allow precise control practical torque assist with the 48V MHSG. Moreover, the proposed control structure, performance with a fast response on a cycle-by-cycle basis for practical torque assist with where the engine torque is calculated in real‐time based on the in‐cylinder pressure, ef‐ the 48V MHSG. Moreover, the proposed control structure, where the engine torque is fectively reduces the effort needed to calibrate the conventional map‐based open‐loop calculated in real-time based on the in-cylinder pressure, effectively reduces the effort controller under various types of engine operations. Furthermore, the proposed algorithm needed to calibrate the conventional map-based open-loop controller under various types effectively reduces engine torque deviation under the main driving range of the target of engine operations. Furthermore, the proposed algorithm effectively reduces engine CDA operations. torque deviation under the main driving range of the target CDA operations.

2. Experimental Experimental Setup 2.1. Target Target Engine Description The target engine was a 1.6 L gasoline direct injection (GDI) engine, designed with a specialized architecture of separated intake and exhaust manifolds to accommodate the CDA operation [[35].35]. TheThe detaileddetailed working working principle principle of of this this particular particular CDA CDA is illustratedis illustrated in inFigure Figure1. Intake1. Intake manifold manifold 1 is 1 is connected connected to to cylinders cylinders 2 2 and and 3. 3. In In the the same same manner, manner, intake intake manifold 2 is linked to cylinders 1 and 4 to form two different closed airﬂowairflow loops. These twotwo independent loops loops allow the engine to operate with four or two cylinders through control of the intake manifold valve and the three-waythree‐way exhaust valve.

Figure 1. OperationsOperations of the target engine: ( a)) Four Four-cylinder‐cylinder operation; ( b) Two Two-cylinder‐cylinder operation.

As described in Figure 11a,a, four-cylinderfour‐cylinder operationoperation isis realizedrealized byby fullyfully opening opening thethe intakeintake manifold valve between the separated intake manifolds and closing the three three-way‐way exhaust valve. Except Except for for small cylinder cylinder-to-cylinder‐to‐cylinder variations from the air flow flow through an additional throttle, the engine operates as a normal four-cylinderfour‐cylinder engine. On the other hand, under two two-cylinder‐cylinder operation, as shown in Figure 11b,b, thethe intakeintake manifoldmanifold valvevalve is is closed to cut off airflow airflow into intake manifold 2 and the three three-way‐way exhaust valve is opened toto isolate the internal loop of cylinders 1 and 4. This enables deactivation of cylinders 1 and 4, along with the prevention of fuel injection and ignition. Since the closed loop of the deactivated cylinders does not involve a pressure difference between intake and exhaust strokes, the pumping loss can be eliminated simultaneously. strokes, the pumping loss can be eliminated simultaneously. The target engine is equipped with external high-pressure exhaust gas recirculation The target engine is equipped with external high‐pressure exhaust gas recirculation (HP-EGR), variable valve timing (VVT), an intercooler, and a 48V electric supercharger, as (HP‐EGR), variable valve timing (VVT), an intercooler, and a 48V electric supercharger, shown in Table1. The engine is also equipped with a 48V MHSG, which is connected by a as shown in Table 1. The engine is also equipped with a 48V MHSG, which is connected pulley to assist in generating engine power; detailed specifications are provided in Table2. by a pulley to assist in generating engine power; detailed specifications are provided in Table 2.

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Sensors 2021, 21, 1432 4 of 21 Table 1. Specifications of target engine.

Description Specifications Gasoline direct injection (GDI), Inline, Table 1. SpeciﬁcationsEngine type of target engine. Double overhead camshaft (DOHC) Number ofDescription cylinders 4 Speciﬁcations Bore × stroke (mm) Gasoline72 × direct 97 injection (GDI), Inline, Engine type Connecting rod (mm) Double152.2 overhead camshaft (DOHC) Number of cylinders 4 Displacement volume (L) 1.580 Bore × stroke (mm) 72 × 97 CompressionConnecting ratio rod (mm)12:1 152.2 Displacement volume (L)Cylinder deactivation (CDA) with 1.580 separated mani‐ Compression ratiofolds architecture 12:1 ExternalCylinder high‐pressure deactivation EGR (CDA)(HP‐EGR) with separated manifolds architecture Applied technologies Intake/exhaustExternal variable high-pressure valve timing EGR (VVT) (HP-EGR) Applied technologies Intake/exhaustIntercooler variable valve timing (VVT) 48V electric superchargerIntercooler 48V electric supercharger 48V mild‐hybrid starter‐generator (MHSG) 48V mild-hybrid starter-generator (MHSG)

Table 2. Specifications of 48V MHSG. Table 2. Speciﬁcations of 48V MHSG. Description Specifications Description Speciﬁcations Pulley ratio 2.67 Maximum and minimumPulley ratio power ±10 kW 2.67 Maximum and minimum power ±10 kW MaximumMaximum and minimum and minimum torque torque ±100 Nm± 100 Nm

2.2.2.2. Experimental Experimental Conditions Conditions TheThe target target engine was modeled with actual experimental engine data from 50 steady states.states. Figure Figure 22 shows shows the the steady steady states, states, represented represented as value as value of brake of brake mean mean effective effective pres‐ surepressure (BMEP) (BMEP) and andengine engine speed. speed. The The normal normal mode mode of four of four-cylinder‐cylinder operation operation includes includes a totala total of of25 25naturally naturally aspirated aspirated regions, regions, whereas whereas the CDA the CDA mode mode contains contains 15 naturally 15 naturally aspi‐ ratedaspirated and and10 supercharging 10 supercharging areas areas to totrack track the the target target BMEP BMEP values values in in only only two two-cylinder‐cylinder operation.operation. To To derive a precise combustion model, 100 cycles of in in-cylinder‐cylinder pressure data were obtained for each operating condition. The The measured measured pressure signals were sampled everyevery 1 crank angle degree. Depending on on the two two-cylinder‐cylinder or four four-cylinder‐cylinder operation, eacheach spark timing map has been calibrated to produce maximum brake torque to reflect reflect thethe trapped trapped mass influence influence caused by the different activated cylinder configuration.configuration. The HPHP-EGR‐EGR rate, rate, VVT, VVT, spark timing, and intercooler temperature set set-points‐points were fixed fixed at specificspecific target values for each engine operating point.

FigureFigure 2. EngineEngine operating operating conditions: conditions: ( (aa)) Normal Normal mode; mode; ( (bb)) cylinder cylinder deactivation deactivation (CDA) (CDA) mode.

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3. Target Engine Model and 48V MHSG Model 3.3. TargetTarget Engine Engine Model Model and and 48V 48V MHSG MHSG Model Model 3.1.3.1. ModelModel Overview Overview ToTo deal dealdeal with withwith the thethe enormous enormousenormous complexity complexitycomplexity of ofof cylinder cylindercylinder deactivation deactivationdeactivation combined combinedcombined with withwith a aa 48V 48V48V mildmild hybrid hybridhybrid system, system,system, the thethe target targettarget engine engineengine model modelmodel was waswas designed designeddesigned using usingusing GT-POWER GTGT‐‐POWERPOWER simulation. simulation.simulation. In particular,InIn particular,particular, the the the simulation simulationsimulation model modelmodel was waswas derived derived derived based basedbased on 3D onon CAD 3D3D CADCAD files files files to precisely toto preciselyprecisely reflect reflectreflect the geometric information of the specialized engine structure. Figure3 represents the process thethe geometricgeometric informationinformation ofof thethe specializedspecialized engineengine structure.structure. FigureFigure 33 representsrepresents thethe propro‐‐ of importing the actual 3D CAD files into the simulation environment. The discretization cesscess ofof importingimporting thethe actualactual 3D3D CADCAD filesfiles intointo thethe simulationsimulation environment.environment. TheThe discretidiscreti‐‐ process divides a large volume assembly into smaller connected subcomponents. After zationzation processprocess dividesdivides aa largelarge volumevolume assemblyassembly intointo smallersmaller connectedconnected subcomponents.subcomponents. the ensuing procedure of simplification to eliminate unnecessary obstacles with respect AfterAfter thethe ensuingensuing procedureprocedure ofof simplificationsimplification toto eliminateeliminate unnecessaryunnecessary obstaclesobstacles withwith rere‐‐ to the model accuracy, the simulation model analyzes the intake and exhaust flow rates spectspect toto thethe modelmodel accuracy,accuracy, thethe simulationsimulation modelmodel analyzesanalyzes thethe intakeintake andand exhaustexhaust flowflow based on 1D fluid dynamics. The forward and backward discharge coefficients were ratesrates basedbased onon 1D1D fluidfluid dynamics.dynamics. TheThe forwardforward andand backwardbackward dischargedischarge coefficientscoefficients werewere addressed based on the unit experimental test for components of valve types, such as addressedaddressed basedbased onon thethe unitunit experimentalexperimental testtest forfor componentscomponents ofof valvevalve types,types, suchsuch asas throttle, intake manifold valve, and three-way exhaust valve. The 48V electric supercharger throttle,throttle, intakeintake manifoldmanifold valve,valve, andand threethree‐‐wayway exhaustexhaust valve.valve. TheThe 48V48V electricelectric supersuper‐‐ and MHSG were also implemented with the specification values, as shown in the overall chargercharger andand MHSGMHSG werewere alsoalso implementedimplemented withwith thethe specificationspecification values,values, asas shownshown inin thethe model schematics in Figure4. overalloverall modelmodel schematicsschematics inin FigureFigure 4.4.

Figure 3. Process of importing 3D computer-aided design (CAD) ﬁles with discretization. FigureFigure 3.3. ProcessProcess ofof importingimporting 3D3D computercomputer‐‐aidedaided designdesign (CAD)(CAD) filesfiles withwith discretization.discretization.

Figure 4. Schematics of the target engine model. FigureFigure 4. 4.Schematics Schematics of of the the target target engine engine model. model.

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3.2. SI Turbulent Engine Model The in-cylinder pressure is essential information indicating the combustion status of individual cylinders in CDA operations; therefore, the engine model was precisely designed using the SI turbulent flame model of GT-POWER to reflect various in-cylinder conditions such as cylinder geometry, spark location, and mixture characteristics. The SI turbulent flame model calculates the entrained mass of mixture (Me) from a rate proportional to the sum of the turbulent flame speed (ST) and the laminar flame speed (SL). The derivative of burned mass (Mb) is formulated by dividing the difference of Me and Mb by the time constant of the burn rate (τb), as follows [28,36]: dM e = ρ A (S + S ), (1) dt u e T L dM M − M b = e b , (2) dt τb

where ρu is the unburned mixture density, and Ae is the surface area at the flame front location. The four dominant phenomena of dilution, turbulent flame speed, Taylor microscale length, and flame kernel growth determine the flame model [32–34]. The dilution effect of residuals and external EGR is sophisticatedly calibrated with the dilution multiplier (CDE). The CDE scales the dilution effect term (ED) with the burned gas fraction in the unburned zone ( fb). ED is used as a proportional factor to determine SL based on the maximum laminar speed (Bm), laminar speed roll-off value (Bφ), equivalence ratio (φ), and equivalence ratio at maximum speed (φm), with the following formula:

7 ED = 1 − 0.75·CDE· 1 − (1 − 0.75·CDE· fb) , (3)

!α !β 2 Tu p SL = Bm + Bφ(φ − φm) · · ·ED, (4) Tre f pre f

where p is the pressure, Tu is the unburned gas temperature, α and β are temperature exponent and pressure exponent values, and Tre f and pre f are constant values to make p and Tu dimensionless. The flame kernel growth multiplier (CFKG) and the turbulent flame speed multiplier (CTFS) represent magnitude factors of the turbulent flame speed. CFKG has an especially large influence on the initial combustion velocity with the smaller flame radius (R f ), as follows:   0 1 ST = CTFSu 1 − , (5)  R 2  1 + C f FKG Li 0 where u is the turbulent intensity, and Li is the integral length scale. The Taylor length scale multiplier (CTLS) is a parameter that modulates the propagation speed of the burn rate with respect to the Taylor microscale length (λ). The λ is calculated based on Li and the turbulent Reynolds number (Ret). The CTLS factor is multiplied to calibrate the degree of Taylor length scale for the flame propagation:

C L λ = √TLS i , (6) Ret λ τb = , (7) SL To calibrate the combustion model, in-cylinder pressure measurements of the engine experimental data were utilized. The goal of combustion model calibration is to determine the best set of four scale multipliers CDE, CFKG, CTFS, and CTLS. The optimal set was Sensors 2021, 21, 1432 7 of 22

Sensors 2021, 21, 1432 To calibrate the combustion model, in‐cylinder pressure measurements of the engine7 of 21 experimental data were utilized. The goal of combustion model calibration is to determine the best set of four scale multipliers 𝐶, 𝐶, 𝐶, and 𝐶. The optimal set was de‐ rived based on a grid search method using in‐cylinder pressure measurements for a total derived based on a grid search method using in-cylinder pressure measurements for a total of 50 engine operating conditions. of 50 engine operating conditions.

3.3.3.3. 48V 48V MHSG MHSG Model Model FromFrom a control a control point point of of view, view, it it is is important important to to accurately accurately model model the the dynamic dynamic char charac-‐ acteristicsteristics to adequately perform thethe torquetorque assistassist functionfunction ofof thethe 48V48V MHSG.MHSG. TheThe inherentinher‐ entelectromagnetic electromagnetic and and mechanical mechanical features features cause cause specific specific response response times. times. Moreover, Moreover, time timedelay delay also also occurs occurs depending depending on on certain certain periods periods of the of the internal internal control control modules modules and and com- communicationmunication events. events. As As shown shown in Figurein Figure5, these 5, these dynamic dynamic characteristics characteristics were were implemented imple‐ mentedusing using a first-order a first‐ systemorder system with a with time a delay: time delay: 𝐾 𝑇 𝑠 K 𝑒, (8) T (s) = 𝜏𝑠 1 e−Tds, (8) m τs + 1 where the parameter 𝐾 is the DC gain. The time constant (𝜏) and time delay (𝑇) were generatedwhere the with parameter componentK is specification the DC gain. values The using time constant a look‐up (τ table) and (LUT) time for delay the (currentTd) were enginegenerated operating with conditions. component The specification 48V MHSG values model using was a connected look-up table to the (LUT) engine for theflywheel current withengine a certain operating pulley conditions. ratio, rated The power, 48V MHSG and torque model specifications was connected as shown to the engine in Table flywheel 2. with a certain pulley ratio, rated power, and torque specifications as shown in Table2.

FigureFigure 5. Modeling 5. Modeling of the of the48V 48V mild mild-hybrid‐hybrid starter starter-generator‐generator (MHSG) (MHSG) with withfirst‐order ﬁrst-order dynamic dynamic re‐ sponse.response.

3.4.3.4. Modeling Modeling Results Results FigureFigure 6 6provides provides a acomparison comparison of of the the simulation simulation results results and and engine engine experimental experimental measurementsmeasurements under under four four-cylinder‐cylinder and and two two-cylinder‐cylinder engine engine operations. operations. The The four four figures figures showshow the the mass mass air air flow flow (MAF), (MAF), manifold manifold absolute absolute pressure pressure (MAP), (MAP), pressure pressure at upstream at upstream of throttleof throttle (PUT), (PUT), and brake and brake specific specific fuel consumption fuel consumption (BSFC). (BSFC). The performance The performance indices of indices the 2 coefficientof the coefficient of determination of determination (R) and root (R mean) and squared root mean error squared (RMSE) errorare also (RMSE) summarized are also in summarizedTable 3. The representative in Table3. The air representative states of MAF, MAP, air states and PUT of MAF, showed MAP, a strong and PUT correlation, showed 2 witha strong R2 values correlation, over 0.97. withBSFC, R a performancevalues over indicator 0.97. BSFC, of fuel a performance consumption, indicator also presented of fuel 2 anconsumption, accurate trend, also with presented an R2 value an accurate over 0.94 trend, and RMSE with an value R value less than over 2.4 0.94 g/kWh. and RMSE value less than 2.4 g/kWh.

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FigureFigure 6. 6.ModelingModeling results results of of the the air air states states and and brake brake specific speciﬁc fuel fuel consumption consumption (BSFC). (BSFC).

TableTable 3. 3.PerformancePerformance index index of the of modeling the modeling results results for air for states air statesand BSFC: and the BSFC: coefficient the coefﬁcient of deter‐ of minationdetermination (R) and (R root2) and mean root squared mean squared error (RMSE). error (RMSE).

NormalNormal Mode Mode DeactivationDeactivation Mode Mode (Four(Four-Cylinder‐Cylinder Operation) Operation) (Two(Two-Cylinder‐Cylinder Operation) Operation) 𝐑𝟐 R2 RMSERMSE 𝐑𝟐 R2 RMSERMSE MAF MAF (g/s)0.999 0.999 0.019 0.019 0.995 0.995 0.154 0.154 (g/s)MAP (bar) 0.994 0.002 0.983 0.006 MAPPUT (bar) 0.986 0.002 0.973 0.004 BSFC (g/kWh)0.994 0.993 0.002 1.748 0.983 0.941 0.006 2.363 (bar) PUT 0.986 0.002 0.973 0.004 (bar)Figure 7 show modeling results of in-cylinder pressure traces in normal and CDA modes,BSFC respectively. These ﬁgures show ﬁtted results of in-cylinder pressure from the 0.993 1.748 0.941 2.363 combustion(g/kWh) model over a wide range of engine operations. For quantitative comparison of the combustion models, the combustion characteristics were calculated from the cylinder pressure,Figure as 7 shownshow modeling in Figure8 resultsand Table of 4in. The‐cylinder maximum pressure value traces of pressure in normal trace and (PcylMax) CDA modes,and its respectively. crank angle locationThese figures (CaPcylMax) show fitted had results values ofof lessin‐cylinder than 0.6 pressure bar and 0.3from degree, the respectively, showing notable RMSE accuracy. The crank angle location of the mass fraction combustion model over a wide range of engine operations. For quantitative comparison burned 50% (MFB50) and the burn duration difference between MFB90 and MFB10 (MFB90- of the combustion models, the combustion characteristics were calculated from the cylin‐ MFB10) were also precise, with RMSE values of less than 0.5 degree. der pressure, as shown in Figure 8 and Table 4. The maximum value of pressure trace (PcylMax) and its crank angle location (CaPcylMax) had values of less than 0.6 bar and 0.3 degree, respectively, showing notable RMSE accuracy. The crank angle location of the mass fraction burned 50% (MFB50) and the burn duration difference between MFB90 and MFB10 (MFB90‐MFB10) were also precise, with RMSE values of less than 0.5 degree.

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Figure 7. Comparison of the in-cylinder pressure traces: (a) four-cylinder operation; (b) two-cylinder operation. Figure 7. Comparison of the in‐cylinder pressure traces: (a) four‐cylinder operation; (b) two‐cylinder operation.

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FigureFigure 8. Modeling 8. Modeling results results of the of thecombustion combustion characteristics. characteristics.

TableTable 4. Performance 4. Performance index index of the of the modeling modeling results results for for combustion combustion characteristics. characteristics.

Normal NormalMode Mode DeactivationDeactivation Mode Mode (Four‐Cylinder(Four-Cylinder Operation) Operation) (Two‐(Two-CylinderCylinder Operation) Operation) 2 2 𝐑𝟐 R RMSE RMSE 𝐑𝟐 R RMSERMSE PcylMaxPcylMax (bar) 0.972 0.261 0.939 0.590 0.972 0.261 0.939 0.590 (bar)CaPcylMax (deg) 0.560 0.221 0.924 0.299 MFB50 (deg) 0.424 0.253 0.901 0.365 CaPcylMax Burn duration (deg)0.560 0.5000.221 0.4100.924 0.5290.299 0.484 (deg) MFB50 The mean effective0.424 pressure values0.253 of BMEP, indicated0.901 mean effective pressure0.365 (IMEP), (deg) pumping mean effective pressure (PMEP), and friction mean effective pressure (FMEP) Burn duration were also analyzed,0.500 as shown in Figure0.4109. BMEP and IMEP,0.529 which denote the0.484 engine brake (deg) torque and indicated combustion torque, showed precise modeling results with R2 values over 0.99 and RMSE values under 0.04 bar, as detailed in Table5. Both PMEP and FMEP wereThe also mean calculated effective with pressure RMSE valuesvalues belowof BMEP, 0.03 bar.indicated However, mean FMEP effective at some pressure operating (IMEP),points pumping showed amean discrepancy effective compared pressure (PMEP), to the experiment. and friction It mean is caused effective by the pressure limitation (FMEP)of the were linear also regression analyzed, model as shown to estimate in Figure the FMEP. 9. BMEP The and regression IMEP, modelwhich wasdenote based the on enginea least-square brake torque method, and indicated called the combustion Chen-Flynn torque, engine showed friction precise model modeling [28]. Overall, results these 2 withresults R values indicate over that 0.99 the and engine RMSE model values accurately under 0.04 simulates bar, as the detailed various in engine Table conditions5. Both PMEPunder and normal FMEP andwere CDA also operations.calculated with RMSE values below 0.03 bar. However, FMEP at some operating points showed a discrepancy compared to the experiment. It is caused by the limitation of the linear regression model to estimate the FMEP. The regression model was based on a least‐square method, called the Chen‐Flynn engine friction model

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Sensors 2021, 21, 1432 [28]. Overall, these results indicate that the engine model accurately simulates the various11 of 21 engine conditions under normal and CDA operations.

FigureFigure 9. Modeling 9. Modeling results results of ofthe the mean mean effective effective pressure pressure values. values.

TableTable 5. 5.PerformancePerformance index index of ofthe the modeling modeling results results for for mean mean effective effective pressure pressure values. values.

NormalNormal Mode Mode DeactivationDeactivation Mode Mode (Four‐Cylinder(Four-Cylinder Operation) Operation) (Two‐Cylinder(Two-Cylinder Operation) Operation) R R2 RMSERMSE R R2 RMSERMSE BMEP BMEP (bar)0.999 0.9990.005 0.0050.998 0.9980.011 0.011 (bar)IMEP (bar) 0.999 0.014 0.994 0.037 IMEPPMEP (bar) 0.949 0.008 0.861 0.013 0.999 0.014 0.994 0.037 (bar)FMEP (bar) 0.973 0.004 0.260 0.022 PMEP 0.949 0.008 0.861 0.013 4. In-Cylinder(bar) Pressure Based 48V MHSG Control Strategy FMEP 4.1. Controller Overview0.973 0.004 0.260 0.022 (bar) The design objective of the proposed algorithm is to precisely control the 48V MHSG to reduce engine torque deviation under CDA operations. The control algorithm was 4. In‐cylinder Pressure based 48V MHSG Control Strategy designed based on the engine model to efficiently handle the high complexity of the target 4.1.system. Controller Figure Overview 10 shows the overall architecture of the proposed in-cylinder pressure based 48VThe MHSG design controller. objective Theof the controller proposed was algorithm composed is to of precisely (1) engine control torque the calculation, 48V MHSG (2) to 48Vreduce MHSG engine torque torque profile deviation generation, under and CDA (3) dynamicoperations. response The control compensation. algorithm The was control de‐ signedinput based of the on controller the engine is the model in-cylinder to efficiently pressure handle in the the previous high complexity engine cycle, of the and target it can system.calculate Figure the real-time10 shows engine the overall torque architecture in each cylinder. of the In proposed addition, thein‐cylinder target torque pressure profile basedof the 48V 48V MHSG MHSG controller. is generated The usingcontroller the torquewas composed deviations of derived(1) engine from torque the differencecalcula‐ tion,between (2) 48V the MHSG activated torque and profile deactivated generation, cylinders. and (3) In moredynamic detail, response the desired compensation. 48V MHSG torque is calculated every 0.5 degree of the crank angle within one engine cycle. The desired target torque profile can minimize the engine torque deviation in an ideal situation. However, the control strategy requires a rapid response to control the 48V MHSG torque Sensors 2021, 21, 1432 12 of 22

The control input of the controller is the in‐cylinder pressure in the previous engine cycle, and it can calculate the real‐time engine torque in each cylinder. In addition, the target torque profile of the 48V MHSG is generated using the torque deviations derived from the difference between the activated and deactivated cylinders. In more detail, the desired 48V MHSG torque is calculated every 0.5 degree of the crank angle within one engine Sensors 2021, 21, 1432 12 of 22 cycle. The desired target torque profile can minimize the engine torque deviation in an ideal situation. However, the control strategy requires a rapid response to control the 48V MHSGThe control torque input in ofthe the crank controller angle is the domain. in‐cylinder Otherwise, pressure in the the dynamic previous engine response cycle, of 48V MHSG couldand it distort can calculate the torque the real profile.‐time engine Therefore, torque in the each last cylinder. step of In dynamic addition, thecompensation target finally producestorque profile the torqueof the 48V set MHSG‐point is to generated modulate using the the time torque delay deviations and transient derived from response of the the difference between the activated and deactivated cylinders. In more detail, the desired Sensors 2021, 21, 1432 48V MHSG. To alleviate the time delay, the target profile is shifted to 12match of 21 the control 48V MHSG torque is calculated every 0.5 degree of the crank angle within one engine instancecycle. The to desiredthe next target complete torque engineprofile can cycle. minimize The transient the engine response, torque deviation which in is an approximated byideal the situation.first‐order However, time constant, the control compensated strategy requires by a rapida lead response compensator to control which the 48V places a dom‐ inantinMHSG the pole crank torque to angle the in the point domain. crank where angle Otherwise, domain. has fast the Otherwise, dynamicresponse response the characteristics. dynamic of 48V response MHSG of could 48V MHSG distort thecould torque distort profile. the torque Therefore, profile. the Therefore, last step of the dynamic last step compensation of dynamic compensation finally produces finally the torqueproduces set-point the torque to modulate set‐point the to timemodulate delay the and time transient delay response and transient of the response 48V MHSG. of the To alleviate48V MHSG. the timeTo alleviate delay, the the target time profile delay, isthe shifted target to profile match is the shifted control to instance match the to the control next completeinstance to engine the next cycle. complete The transient engine cycle. response, The transient which is response, approximated which by is theapproximated first-order timeby the constant, first‐order compensated time constant, by acompensated lead compensator by a lead which compensator places a dominant which places pole a to dom the‐ pointinant wherepole to has the fastpoint response where has characteristics. fast response characteristics.

Figure 10. Overall process of the proposed 48V MHSG control strategy.

4.2.Figure Engine 10. Overall Torque process Calculation of the proposed 48V MHSG controlcontrol strategy.strategy. The in‐cylinder pressure is important information that allows instantaneous torque 4.2. Engine Torque Calculation calculation4.2. Engine Torquefor the Calculation individual cylinders. As described in Figure 11, the indicated torque of The in-cylinderin‐cylinder pressure is importantimportant informationinformation thatthat allowsallows instantaneousinstantaneous torquetorque the individual cylinders is calculated using the in‐cylinder pressure (𝑃) and the geome‐ calculation for the individual cylinders. As described in Figure 1111,, thethe indicatedindicated torquetorque ofof try.the The individual total indicated cylinders is calculatedtorque applied using the to in-cylinder the crankshaft pressure (𝑇𝑄Pcyl) and𝜃 the is geometry. formulated for each the individual cylinders is calculated using the in‐cylinder pressure (𝑃) and the geome‐ The total indicated𝜃 torque applied to the crankshaft TQind(θ) is formulated for each crank cranktry. The angle total ( indicated) as follows: torque applied to the crankshaft 𝑇𝑄𝜃 is formulated for each angle (θ) as follows: crank angle (𝜃) as follows: 𝑇𝑄𝜃 𝑃𝜃 ⋅ 𝑆 ⋅ 𝑅 ⋅ 𝑠𝑖𝑛𝜃 𝑃 𝜃 ⋅ 𝑆 ⋅ 𝑅 ⋅ 𝑐𝑜𝑠𝜃 ⋅𝑡𝑎𝑛𝛼 , TQind(θ) = Pcyl(θ) · S · R · sin(θ) − Pcyl(θ) · S · R · cos(θ) · tan(α), (9) (9) 𝑇𝑄𝜃 𝑃∑ 𝜃 ⋅ 𝑆 ⋅ 𝑅 ⋅ 𝑠𝑖𝑛𝜃 𝑃 𝜃 ⋅ 𝑆 ⋅ 𝑅 ⋅ 𝑐𝑜𝑠𝜃 ⋅𝑡𝑎𝑛𝛼 , nc (9) wherewhere 𝑛nc isis the the number number of cylinders,of cylinders, and S and, R, and𝑆, 𝑅α ,are and the 𝛼 cross-sectional are the cross area‐sectional of the area of the where 𝑛 is the number of cylinders, and 𝑆, 𝑅, and 𝛼 are the cross‐sectional area of the piston, length of the crank, and connecting rod angle, respectively. piston,piston, length length of of the the crank, crank, and and connecting connecting rod angle, rod respectively. angle, respectively.

Figure 11. In‐cylinder pressure and cylinder geometry.

FigureFigure 11. 11. InIn-cylinder‐cylinder pressure pressure and and cylinder cylinder geometry. geometry.

The inertia torque TQiner(θ) is the part of the engine torque generated from the crankshaft moment of inertia. The formulation is derived as a negative sign with multi-

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Sensors 2021, 21, 1432 13 of 21 The inertia torque 𝑇𝑄𝜃 is the part of the engine torque generated from the crankshaft moment of inertia. The formulation is derived as a negative sign with multi‐ plication of the effective inertia moment (𝐼) and derivative of the instantaneous engine speedplication (𝑁): of the effective inertia moment (Ie f f ) and derivative of the instantaneous engine . speed (N): 2𝜋 𝑇𝑄𝜃 𝐼 ⋅ 2π ⋅𝑁.𝜃, (10) TQ (θ) = −I · 60 · N(θ), (10) iner e f f 60 The friction torque 𝑇𝑄 is approximated as a mean value of one engine cycle. The The friction torque TQ is approximated as a mean value of one engine cycle. The FMEP is calculated based on thef ric Chen‐Flynn engine friction model [28] with a polynomial FMEP is calculated based on the Chen-Flynn engine friction model [28] with a polynomial equation of the PcylMax and a cycle mean value of the engine speed (𝑁), as follows: equation of the PcylMax and a cycle mean value of the engine speed (N), as follows: FMEP 𝐶 𝐶 ⋅PcylMax𝐶 ⋅𝑁 𝐶 ⋅𝑁 , (11) 2 FMEP = C0 + C1 · PcylMax + C2 · N + C3 · N , (11) 𝑛𝑉 𝑇𝑄 n V ⋅FMEP, (12) 2𝜋𝑛c d TQ f ric = − · FMEP, (12) 2πnr where 𝑛 is the number of crankshaft rotations for a complete engine cycle, and 𝑉 is the where nr is the number of crankshaft rotations for a complete engine cycle, and Vd is the engine displacement volume. The coefficients 𝐶, 𝐶, 𝐶, and 𝐶 are derived using the leastengine‐square displacement method. volume. The coefﬁcients C0, C1, C2, and C3 are derived using the least-square method. As shown in Figure 12, the engine brake torque 𝑇𝑄𝜃 is calculated as the sum of As shown in Figure 12, the engine brake torque TQeng(θ) is calculated as the sum of 𝑇𝑄𝜃, 𝑇𝑄𝜃, and 𝑇𝑄 with the following equation: TQind(θ), TQiner(θ), and TQ f ric with the following equation: 𝑇𝑄𝜃 𝑇𝑄𝜃 𝑇𝑄𝜃 𝑇𝑄 , (13) TQeng(θ) = TQind(θ) + TQiner(θ) + TQ f ric, (13)

Figure 12. Calculated engine torques in crank angle domain. Figure 12. Calculated engine torques in crank angle domain. 4.3. 48V MHSG Torque Proﬁle Generation

Based on the calculated engine brake torque, the desired torque proﬁle of the 48V MHSG is generated to eliminate engine torque deviation at each crank angle. Since the sequence of activation and deactivation is repeated every 1/4 cycle in a four-cylinder engine, the deviation can be derived from the brake torque trace shifted by 1/4 cycle, as illustrated in Figure 13. Therefore, the desired proﬁle for the torque assist with 48V MHSG is produced as follows:

1 2π TQ (θ) = · TQ (θ) + TQ θ − − TQ (θ) des 2 eng eng 4 eng (14) 1 1 2π = − ·TQ (θ) + ·TQ θ − 2 eng 2 eng 4

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4.3. 48V MHSG Torque Profile Generation Based on the calculated engine brake torque, the desired torque profile of the 48V MHSG is generated to eliminate engine torque deviation at each crank angle. Since the sequence of activation and deactivation is repeated every 1/4 cycle in a four‐cylinder en‐ gine, the deviation can be derived from the brake torque trace shifted by 1/4 cycle, as il‐ lustrated in Figure 13. Therefore, the desired profile for the torque assist with 48V MHSG is produced as follows: 1 2𝜋 𝑇𝑄 𝜃 ∙𝑇𝑄 𝜃 𝑇𝑄 𝜃 𝑇𝑄 𝜃 2 4 (14) Sensors 2021, 21, 1432 1 1 2𝜋 14 of 21 ∙𝑇𝑄 𝜃 ∙𝑇𝑄 𝜃 2 2 4

FigureFigure 13. 13. CalculationCalculation of of the the desired desired 48V 48V MHSG MHSG torque torque profile proﬁle in in crank crank angle angle domain: domain: (a (a) )Average Average torque;torque; ( (bb)) Torque Torque variation; variation; ( (cc)) Desired Desired 48V 48V MHSG MHSG torque. torque.

4.4. Dynamic Compensation of 48V MHSG Accurate torque assist requires a rapid response of 48V MHSG on a cycle-by-cycle basis; however, the inherently slow characteristics and time delay of the 48V MHSG deteriorate the control accuracy for tracking the target torque waveform. Figure 14 shows the distorted torque waveform without any compensation of dynamic response. The grey dashed line is desired target torque proﬁle, and the blue line is actual torque trajectory which cannot tracking the target torque proﬁle. Sensors 2021, 21, 1432 15 of 22

4.4. Dynamic Compensation of 48V MHSG Accurate torque assist requires a rapid response of 48V MHSG on a cycle‐by‐cycle basis; however, the inherently slow characteristics and time delay of the 48V MHSG dete‐ riorate the control accuracy for tracking the target torque waveform. Figure 14 shows the Sensors 2021, 21, 1432 distorted torque waveform without any compensation of dynamic response. The grey15 of 21 dashed line is desired target torque profile, and the blue line is actual torque trajectory which cannot tracking the target torque profile.

FigureFigure 14. 14. ActualActual response response of ofthe the 48V 48V MHSG MHSG without without dynamic dynamic compensation. compensation.

ToTo resolve resolve this this problem, problem, the the setpoint setpoint applied applied to to the the 48V 48V MHSG MHSG is isfinally finally modulated modulated throughthrough dynamic dynamic compensation compensation of ofthe the desired desired torque torque profile. profile. The The controller controller already already has has twotwo dynamic dynamic characteristic characteristic parameters parameters as as a LUT forfor the the current current engine engine operating operating conditions: condi‐ tions:the timethe time delay delay (Td )(𝑇 and) and time time constant constant (τ) ( explained𝜏) explained in Equationin Equation (8). (8). Figure Figure 15 15 shows shows the thesequential sequential procedures procedures for for the the dynamicdynamic compensation with with the the parameters. parameters. The The signal signal in inFigure Figure 15a 15 representsa represents a desired a desired torque torque profile profile of ofthe the 48V 48V MHSG. MHSG. In In ideal ideal conditions, conditions, thethe desired desired torque torque profile profile can can minimize minimize the the engine engine torque torque deviation deviation from from the the CDA. CDA. Each Each signalsignal in inFigure Figure 15b 15 andb,c shows Figure the 15c control shows instancethe control after instance the compensation after the compensation of the Td and of τ, respectively. After both compensations, the control instance is applied to the 48V MHSG the 𝑇 and 𝜏, respectively. After both compensations, the control instance is applied to thewhich 48V MHSG has a dynamic which has response a dynamic as shown response in Figureas shown 15 d.in ThroughFigure 15d. the Through compensation, the com the‐ pensation,actual torque the actual profile torque in Figure profile 15 ine Figure which 15e is generated which is generated from the from 48V MHSGthe 48V isMHSG almost is identicalalmost identical to the desired to the desired torque profile.torque profile. In the case of the Td compensation, the delay effect is mitigated by matching the In the case of the 𝑇 compensation, the delay effect is mitigated by matching the controlcontrol instance instance to to the the next next complete complete engine engine cycle. The target profileprofile is is further further shifted shifted by by the thedifference difference between between the the 48V 48V MHSG MHSG time time delay delay and and the the current current cycle cycle interval, interval, calculated calculated from the instantaneous engine speed. For the compensation of the τ, the phase-lead compensator from the instantaneous engine speed. For the compensation of the 𝜏, the phase‐lead com‐ is designed to modulate the slow dynamic characteristics. The phase-lead compensator pensator is designed to modulate the slow dynamic characteristics. The phase‐lead com‐ contributes one zero and one pole to the system. The additional zero eliminates the slow pensator contributes one zero and one pole to the system. The additional zero eliminates response of MHSG, which is approximated as a first-order time constant τ, through the the slow response of MHSG, which is approximated as a first‐order time constant 𝜏, pole-zero cancellation. And the additional pole improves the response characteristic of the through the pole‐zero cancellation. And the additional pole improves the response char‐ system as a new dominant pole. The formula of the phase-lead compensator is as follows: acteristic of the system as a new dominant pole. The formula of the phase‐lead compen‐ sator is as follows: τ · s + 1 Tc(s) = Kc , (15) ω𝜏⋅𝑠1·τ · s + 1 𝑇 𝑠 𝐾 , (15) 𝜔∙𝜏⋅𝑠1 where the Kc is control gain to compensate a steady-state error and parameter ω is an atten- whereuation the factor 𝐾 is of control the lead gain compensator to compensate which a hassteady a value‐state between error and 0 to parameter 1. The compensator 𝜔 is an attenuationcontributes factor one of zero the and lead one compensator pole to the which system has at a− value1/τ and between−1/ωτ 0 to, respectively. 1. The compen After‐ satorthe initialcontributes value one search zero based and on one the pole pole-zero to the cancelation,system at − the1/𝜏 Kandc and −1/ω𝜔𝜏values, respectively. fine-tuned Afterto offset the initial the time value constant search of based the 48V on MHSG the pole specifications.‐zero cancelation, These valuesthe 𝐾 are and also 𝜔 generated values as a LUT according to the current engine operating condition.

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Sensors 2021, 21, 1432 16 of 21 fine‐tuned to offset the time constant of the 48V MHSG specifications. These values are also generated as a LUT according to the current engine operating condition.

FigureFigure 15. 15. ProceduresProcedures of of the the dynamic dynamic compensation compensation for for time time delay delay and and time time constant: constant: (a ()a )Desired Desired torque;torque; (b ()b Compensation) Compensation of of time time delay; delay; (c ()c Compensation) Compensation of of lead lead compensator; compensator; (d (d) )Application Application of of dynamicdynamic response response in in 48V 48V MHSG; MHSG; (e ()e Actual) Actual response response of of 48V 48V MHSG. MHSG.

4.5.4.5. 48V 48V MHSG MHSG Control Control Results Results AsAs shown shown in inFigure Figure 16, 16the, theperformance performance of the of proposed the proposed control control algorithm algorithm was eval was‐ uatedevaluated according according to the to reduction the reduction rates ratesof the of torque the torque deviations, deviations, peak‐ peak-to-peakto‐peak values values of the of enginethe engine torque torque traces, traces, and average and average power power of the of 48V the MHSG 48V MHSG without without any regeneration. any regeneration. Fig‐ ureFigure 17a shows17a shows the control the control results results for for48V 48V MHSG MHSG at constant at constant engine engine speed speed of of 1000 1000 rpm, rpm, BMEPBMEP of of 2 2 bar. bar. Compared toto the the results results without without 48V 48V MHSG MHSG torque torque assistance, assistance, the proposedthe pro‐ algorithm reduced the engine torque deviation by 98% and the peak-to-peak value by posed algorithm reduced the engine torque deviation by 98% and the peak‐to‐peak value 26%. In this operating area, the average power of 48V MHSG was 3.54 kW. These results by 26%. In this operating area, the average power of 48V MHSG was 3.54 kW. These re‐ demonstrate that the proposed control algorithm effectively reduces torque fluctuation sults demonstrate that the proposed control algorithm effectively reduces torque fluctua‐ between the activated and deactivated cylinders under CDA operations. Moreover, they tion between the activated and deactivated cylinders under CDA operations. Moreover, indicate that the specifications of 48V MHSG are sufficient to mitigate torque variations in this engine operating condition, with working range of the 48V MHSG torque and power within rated values of 100 Nm and 10 kW. On the other hand, the results presented in Figure 17b show relatively small reduction rates of 38% and 10% in the deviation and

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they indicate that the specifications of 48V MHSG are sufficient to mitigate torque varia‐ tions in this engine operating condition, with working range of the 48V MHSG torque and power within rated values of 100 Nm and 10 kW. On the other hand, the results presented in Figure 17b show relatively small reduction rates of 38% and 10% in the deviation and peak‐to‐peak indices, despite the MHSG consumes a larger average power of 6.9 kW. This is because torque variation was not completely eliminated in this engine operating area at an engine speed of 3000 rpm and BMEP of 2 bar, due to the limited power of the 48V MHSG. Figure 18 summarize the control results for each engine operating condition. Torque deviations were calculated with a maximum decrease rate of 98% at an engine speed of 1000 rpm and BMEP of 2 bar, and a minimum reduction rate of 0.1% in the engine opera‐ tion at an engine speed of 4000 rpm and BMEP of 7 bar. For the reduction rate in peak‐to‐ peak values, a maximum of 26% and minimum of 0.2% were derived under operation with an engine speed of 1000 rpm, BMEP of 2 bar, area at engine speed of 4000 rpm, and BMEP of 4 bar. The average power of the 48V MHSG was proportional to engine speed Sensors 2021, 21, 1432 and BMEP in the range of 1.71 kW to 9.67 kW, and it converged to 48V MHSG’s maximum17 of 21 power of 10 kW. These analysis results indicate that the proposed algorithm practically decreases the torque deviations of the CDA engine with 48V MHSG specifications, mainly peak-to-peakunder low engine indices, speed despite and theload MHSG conditions. consumes In other a larger words, average the proposed power of controller 6.9 kW. This pro is‐ becausevides effective torque performance variation was under not completely the primary eliminated target driving in this area engine of operatingCDA operations. area at an engine speed of 3000 rpm and BMEP of 2 bar, due to the limited power of the 48V MHSG.

Figure 16. Performance index to evaluate the proposed controlcontrol strategy.strategy.

Figure 18 summarize the control results for each engine operating condition. Torque deviations were calculated with a maximum decrease rate of 98% at an engine speed of 1000 rpm and BMEP of 2 bar, and a minimum reduction rate of 0.1% in the engine operation at an engine speed of 4000 rpm and BMEP of 7 bar. For the reduction rate in peak-to-peak values, a maximum of 26% and minimum of 0.2% were derived under operation with an engine speed of 1000 rpm, BMEP of 2 bar, area at engine speed of 4000 rpm, and BMEP of 4 bar. The average power of the 48V MHSG was proportional to engine speed and BMEP in the range of 1.71 kW to 9.67 kW, and it converged to 48V MHSG’s maximum power of 10 kW. These analysis results indicate that the proposed algorithm practically decreases the torque deviations of the CDA engine with 48V MHSG speciﬁcations, mainly under low engine speed and load conditions. In other words, the proposed controller provides effective performance under the primary target driving area of CDA operations. Sensors 2021, 21, 1432 18 of 22

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Figure 17. 48V MHSG control results: (a) engine speed of 1000 rpm and brake mean effective pressure Figure 17. 48V MHSG control results: (a) engine speed of 1000 rpm and brake mean effective (BMEP) of 2 bar; (b) engine speed of 3000 rpm and BMEP of 2 bar. pressure (BMEP) of 2 bar; (b) engine speed of 3000 rpm and BMEP of 2 bar.

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FigureFigure 18. 18. ReductionReduction rate rate with with respect respect to engine to engine operating operating conditions: conditions: (a) the (a )torque the torque deviations; deviations; (b()b the) the peak peak-to-peak‐to‐peak values; values; (c) ( cthe) the average average power power consumptions. consumptions.

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5. Conclusions In this paper, an in-cylinder pressure based 48V MHSG control strategy was proposed for minimizing engine torque deviation in the CDA engine. To deal with the significant complexity of the integrated system of CDA and mild-hybrid electrification, the proposed control algorithm was designed in a simulation environment. The SI turbulent engine model was derived based on 3D CAD data to implement the geometric information of the particular structure with a separated intake and exhaust manifolds. The model included a combustion model that was finely calibrated using in-cylinder pressure measurements, and a 48V MHSG model with dynamic characteristics based on detailed specifications. The modeling results of BMEP and IMEP showed a precise accuracy, with RMSE values under 0.04 bar. PcylMax and CaPcylMax presented RMSE values of less than 0.6 bar and 0.3 degree, respectively. The performance of the proposed 48V MHSG control algorithm was analyzed with respect to the engine operating range. The reduction rate of the torque deviations and peak-to-peak values were calculated and found to have maximum values of 98% and 26%, respectively. At the maximum reduction rate the average power of 48V MHSG was 3.54 kW without any regeneration. These results demonstrate that the proposed strategy effectively reduced engine torque deviations through accurate control of the 48V MHSG, under target CDA operations of low engine speed and load conditions. As a follow-up research, the proposed 48V MHSG control algorithm which was evalu- ated through a simulation will be implemented into an actual vehicle for the investigation of NVH issues during the mode transition such as four-cylinder to two-cylinder mode transition, and vice versa. In addition, battery management considering regenerative braking will be considered to analyze fuel efficiency while running specific driving cycles such as NEDC and WLTP.

Author Contributions: Methodology, H.S., D.J., S.H. and D.H.; Writing—original draft, H.S. and D.J.; Writing—review & editing, M.H.; Supervision, M.H.; Conceptualization, S.H. and D.H. All authors have read and agreed to the published version of the manuscript. Funding: This work was financially supported by the Industrial Strategy Technology Development Program (No. 10039673, 10060068, 10079961, 10080284), the International Collaborative Research and Development Program (N0001992) under the Ministry of Trade, Industry and Energy (MOTIE Korea), and National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (No. 2011-0017495). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest.

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