Impact of Electrically Assisted Turbocharger on the Intake Oxygen Concentration and Its Disturbance Rejection Control for a Heavy-duty Diesel Engine

Abstract

The electrically assisted turbocharger (EAT) shows promise in simultaneously improving the boost response and reducing the fuel consumption of engines with assist. In this paper, experimental results show that 7.8% fuel economy (FE) benefit and 52.1% improvement in transient boost response can be achieved with EAT assist. EAT also drives the need for a new feedback variable for the air system control, instead of the exhaust recirculation gas (EGR) rate that is widely used in conventional turbocharged engines (nominal system). Steady-state results show that EAT assist allows wider turbine vane open and reduces pre-turbine pressure, which in turn elevates the engine volumetric efficiency hence the engine air flow rate at fixed boost pressure. Increased engine air flow rate, together with the reduced fuel amount necessary to meet the torque demand with assist, leads to the increase of the oxygen concentration in the exhaust gas (EGR gas dilution). Additionally, transient results demonstrate that the enhanced air supply from the compressor and the diluted EGR gas result in a spike in the oxygen concentration in the intake manifold (X_oim) during tip-in, even though there is no spike in the EGR rate response profile. Consequently, there is Nitrogen Oxides (NOx) emission spike, although the response of boost pressure and EGR rate is smooth (no spike is seen). Therefore, in contrast to EGR rate, X_oim is found to be a better choice for the feedback variable. Additionally, a disturbance observer-based X_oim controller is developed to attenuate the disturbances from the turbine vane position variation. Simulation results on a high-fidelity GT-SUTIE model show over 43% improvement in disturbance rejection capability in terms of recovery time, relative to the conventional proportional-integral-differential (PID) controller. This X_oim-based disturbance rejection control solution is beneficial in the practical application of the EAT system.

1. Introduction

Modern diesel engines are normally equipped with a variable-geometry turbocharger (VGT) or fixed geometry turbocharger (FGT) [1,2]. However, the FGT, and to a lesser extent VGT, suffer from an undesired response dynamic caused by the sluggish turbine power response, popularly known as turbo-lag. Turbo-lag is observed through the slow boost pressure ($p_2$) and torque responses, leading to undesired transient emissions spikes and fuel penalty. In addition, the poor transient boost response, together with smoke limited fueling, also leads to poor drivability performance [3]. Moreover, part of the exhaust energy is also wasted, either through the exhaust bypass valve or widely opened VGT vane, to avoid over-boost at high engine load conditions. This results in the thermodynamic efficiency penalty for engines equipped with conventional turbochargers.

The electrically assisted turbocharger (EAT) is promising in enhancing boost response and recovering exhaust energy [4,5,6,7,8,9,10,11]. By mounting an electrical motor/generator (referred to as TEMG in this paper) in the shaft of conventional turbocharger, EAT is capable of bi-directional energy transfer. The EAT can assist the compressor via the motor mode for enhanced boost response at the early stage of tip-in, and recover the exhaust energy via the generator mode to avoid over-boost. The schematic of the diesel engine equipped with EAT is shown in Figure 1. The benefits of EAT are summarized as below:

(1)

Improved boost response allows enhanced engine torque response [12,13], and enables down-speeding and downsizing [14,15]. Improvements of fuel economy (FE) can also be achieved mainly by reduced pumping losses. In a drive cycle simulation by Zhao et al. [16], a 6.44% fuel-saving was reported for a Hybrid electric vehicle equipped with EAT assisted diesel engine.

(2)

Better utilization of exhaust enthalpy during regen mode via energy recuperation from turbocharger (TC) braking.

(3)

Lower pre-turbine pressure ($p_3$) and thereby lower pumping loss can be achieved through reduced VGT throttling during assist mode. This improves the thermal efficiency of the engine [17].

(4)

Proper use of assist and regen modes allows the TC to operate in optimal efficiency region [14].

(5)

Improved regulation of intake oxygen concentration (X_oim). Compared to the conventional variable geometry turbocharger-exhaust gas recirculation (VGT-EGR) system, EAT offers additional control degree of freedom and therefore brings a direct result of improved manipulations of $p_3$ and $p_2$. This helps to improve EGR inert quality and reduce transient soot/Nitrogen Oxides (NOx) emissions [18].

For a tip-in maneuver with the EAT system, a fast boost response can be achieved in assist mode without the need for an equivalent increase in exhaust turbine power. Therefore, a wider open VGT vane position can be held for optimal turbine efficiency, relative to the unassisted VGT-EGR air-path system (referred to as nominal system in this paper henceforth) [19]. A wider open vane position leads to a decrease in the exhaust manifold pressure. The simultaneous decrease in $p_3$ and increase in $p_2$ reduce the ($p_3-p_2$) margin which impacts both FE and the ability to flow high pressure EGR (HP-EGR).

Using the intake oxygen concentration as feedback variable was attempted by Nakayama et al. [20], Shutty et al. [21], and Millo et al. [22], for conventional VGT-EGR diesel engines. For engines equipped with EAT, however, fast boost response leads to increased fresh air flow relative to the nominal system, and wider open VGT vane position improves the engine volumetric efficiency for increased engine mass flow rate. Those two facts lead to increased dilution of the HP-EGR gas relative to the nominal system, which distinguished from conventional VGT-EGR engine. Therefore a higher HP-EGR flow rates may be of necessity to keep the intake oxygen concentration well matched with any hard constraints on engine out emissions. In other words, the EGR rate (X_EGR), as popularly used in the conventional VGT-EGR system, might not be an appropriate output for control for EAT [3]. So far no experimental assessment results are reported on the selection of control output variables for EAT assisted engines, according to the authors’ best knowledge.

Regarding the control of X_oim, the traditional proportional–integral–derivative (PID) algorithm is fairly straightforward to use and consequently is of great popularity. For instance, Park [23] proposed a PID controller for X_oim control in a 2.2 L turbocharged passenger car diesel engine, where the proportional gain was determined according to the current NOx level. In another approach, Chen et al. [24] proposed an implicit PI-based X_oim controller by tracking the air-fuel ratio in the tail pipe.

However, the PID controller suffers from the time-consuming parameter tuning and gain-scheduling [25], and shows as poor robustness against operating condition variations and external disturbances. For EAT-assisted diesel engines, the transient response of the air system is much faster relative to the conventional VGT-EGR system. The frequent VGT vane position optimization also introduces a lot of disturbances to the X_oim controller. Those facts drive the need for an advanced control solution for X_oim with faster response and improved robustness against uncertainties.

In this paper, the benefits from using the X_oim as control output is assessed experimentally on a heavy duty Diesel Engine test bench. Then, an active disturbance rejection control [25,26] based X_oim controller (OADRC) is proposed, assisted by an existing X_oim observer [23]. The superiority of the proposed controller, against the conventional PID controller, is validated based on a previously calibrated high fidelity GT-SUITE simulation model [27].

The rest of the paper is organized as follows. The system layout and the experiment setup as well as the simulation platform used in this study are discussed briefly in Section 2. Experimental investigation on the fuel economy benefit and discussion on the selection of feedback variable for the HP-EGR system are provided in Section 3. The impact of EAT on X_oim control is analyzed in Section 4. The X_oim controller is developed and validated in Section 5 and Section 6 respectively. Finally, the conclusions are summarized in Section 7.

2. Experiment Setup and Simulation Platform

A modern heavy-duty diesel engine equipped with common-rail injection system, HP-EGR and VGT, was used for the experimental evaluation. The engine specifications are tabulated in

Table 1. Engine specifications.

Variable	Value
Displacement (liter)	6.7
Cylinders	V8
Compression ratio	16.2
Maximum injection pressure (MPa)	200
Bore (mm)	99
Stroke (mm)	108
Bore/Stroke Ratio	0.92
Maximum torque (Nm)/speed (rpm)	1166/2600
Rated power (kW)/speed (rpm)	328/2800

. Note that the original variable geometry turbocharger was replaced by the EAT and the specifications are listed in

Table 2. EAT specifications.

Variable	Value
Operating voltage (V)	200~400
Maximum power (kW)	17  kW in continuous mode and 23  kW in intermittent mode
Shaft speed (krpm)	0~140
Type of cooling	water and oil cooling

.

The schematic diagram of the experimental platform is shown in Figure 2, where all the variables are explained in Nomenclature. The test bench is shown in Figure 3. The specifications of the test bench are listed in

Table 3. Specifications of test bench.

Num	Device	Specifications
1	AVL INDYS22 AC electric dynamometer	Max speed/power	8000 rpm/200 kW
2	AVL 735S/753 C fuel mass flow meter	Max measuring fuel consumption	125 kg/h
		Max measuring frequency	20 Hz
3	KWELL EVS-80-800 Battery Simulator	Max output voltage	800 V
		Rated power	80 kW
4	Bosch LSU 4.9 oxygen sensor	Measuring range	lambda 0.65–∞
5	Continental SNS14 NOx sensor	Measuring accuracy	±10% from 100 ppm to 1500 ppm

.

A high-fidelity simulation model was established in GT-SUITE [28]. The performance of the model was validated against experimental data from a FTP-75 test cycle. Validation results are shown in Figure 4. Model accuracy results are summarized in

Table 4. Estimation error of the GT-SUITE model.

Variable	GT-SUITE Model
p2	1.8% points has error > 5 kPa
p3	2.9% points has error > 10 kPa
${\dot{m}}_c$	3.3% points has error > 0.01 kg/s
${\displaystyle \int P_{Eng}}dt$	Xerror = 6.7%

. The relative error (X_error) is defined as in Equation (1), where y_meas is the measured value in the experiment, y_model is the estimated value obtained from the GT-SUITE model.

$$X_{error}=\frac{y_{meas}-y_{model}}{y_{meas}}\times 100\%$$

(1)

3. Experimental Assessment on the Benefits from Using X_oim as Control Output Variable

3.1. Steady-State Investigation

In this section, steady-state experiment was carried out on the test bench to assess the superiority of regulating X_oim in terms of NOx emission reduction relative to the EGR rate. The impact of EAT on the HP-EGR flow and fuel efficiency were also investigated. The operating conditions were tabulated in

Table 5. Test case set-up for steady-state investigation of assist power.

Test case	NEng	TEng	p2	Xoim	uVGT	uHP-EGR	PTEMG
-	rpm	Nm	bar	%	%	%	kW
Case1	1400	265	1.24	15.5	Sweep from 15% to 55% open	Closed-loop control to maintain Xoim	Closed-loop control to maintain p2

. Note that in this paper 100% is fully open and 0% is fully closed for both the VGT vane and EGR valve.

From the results shown in Figure 5, the following observations are clear:

• When the VGT vane open is less than 22%, the electrical regeneration (E-regen) mode is turned on to brake the turbine in order to avoid over-boost. The electrical power in regeneration is about 0.46 kW at the cost of 45 kPa increase in $p_3-p_2$, compared to the nominal system. Consequently, 12.1% increase in fuel consumption is seen with E-regen compared to the nominal system.
• When the VGT vane is greater than 37% open, there is X_oim surplus even though the HP-EGR valve (the blue triangle curve) is already 100% open. This is a direct effect of reduced $p_3-p_2$ caused by wide VGT vane open, which limits the HP-EGR flow capability.
• For VGT vane ranging from 22% to 37%, with increasing VGT vane position, the assist power increases (from 0 kW to 0.78 kW) to compensate for the turbine power deficit in order to maintain the boost pressure. Consequently, the pumping loss (indicated by $p_3-p_2$) decreases (from 4.22 kW to 0.86 kW) due to reduced $p_3$. Lower p₃ and unchanged p₂ elevates the thermodynamic efficiency (${\eta }_e$) of the engine (8.5% improvement) through pumping loss reduction. This allows less fuel injection to maintain the desired torque, relative to the nominal system.
• With VGT vane increasing from 22% to 37%, the incremental benefit in fuel economy decreases, since $p_3-p_2$ gradually converges when the VGT open approaches 37%. The fuel saving with VGT vane 37% open is 7.8%, relative to the nominal system. Note that here the electrical energy is assumed to be free in the driveline electrical regeneration during vehicle braking. Therefore, the cost for the electrical power is neglected when evaluating the fuel economy.
• It should be noted that equivalent brake-specific fuel consumption (Eq_BSFC), as defined in Equation (2), can also be used to evaluate the efficiency of the system when the cost of assist power has to be taken into consideration [3]. In Equation (2), t₀ and t_f are the time stamps of the start and end of the current test respectively, $W_{Eng}$ is the engine work output, $W_{TEMG}^{assist}$ and $W_{TEMG}^{regen}$ are defined as $W_{TEMG}^{assist}={\displaystyle {\int }_{t_0}^{t_f}\max (0,P_{TEMG})dt}$ and $W_{TEMG}^{regen}=\left|{\displaystyle {\int }_{t_0}^{t_f}\min (0,P_{TEMG})dt}\right|$ respectively. In terms of Eq_BSFC, the fuel economy benefit from using EAT is 5.9% relative to the conventional VGT-EGR engine.

  $$Eq\_BSFC=\frac{{\displaystyle {\int }_{t_0}^{t_f}{\dot{m}}_{fuel}dt}}{W_{Eng}-W_{TEMG}^{assist}+W_{TEMG}^{regen}}$$

  (2)

In addition to FE improvement, another impact of reduced $p_3-p_2$ is the improvement in the volumetric efficiency ${\eta }_{vol}$ of the engine, as calculated according to Equation (3), where N_Eng is the engine speed, V_Eng is the engine displacement, M is the molar mass of gas in intake manifold, and p₂ and T₂ are intake manifold pressure and temperature, respectively. The engine mass flow rate ${\dot{m}}_{Eng}$ can be calculated based on Equation (4),where oxygen concentration in the recirculated exhaust gas (X_oegr) and X_oim are measured by the UEGO sensors, fuel injection rate ${\dot{m}}_{fuel}$ is obtained from the AVL 735 S fuel mass flow meter, X_oair is oxygen concentration in the air, AFR is air-fuel ratio. From Figure 6, it is seen that up to 13.6% improvement in ${\eta }_{vol}$ is achieved with 1.01 kW E-assist power ($P_{TEMG}$) relative to the nominal system. This is primarily attributed to the decrease in p₃ − p₂, as clearly explained in the Equation (5) proposed in [29], where $C_{{\eta }_{vol}}(N_{Eng})$ is an engine speed dependent factor, $r_c$ is compression ratio. Obviously, the decrease in $p_3-p_2$ helps increasing ${\eta }_{vol}$.

The increase in-cylinder charge amount caused by increased ${\eta }_{vol}$, together with reduced fuel amount (shown in Figure 5), elevates the oxygen concentration in the HP-EGR gas (EGR dilution), i.e., the increasing X_oegr as shown in Figure 6. Therefore, a 7.5% increase in EGR rate (from 36.30% in nominal system to 39.03% in EAT system) at 37% VGT open is needed to maintain the X_oim and NOx emission, relative to the nominal system (22% VGT vane open), as shown in Figure 7. This can be understood via the mathematical expression for X_EGR shown in Equation (6) [30], where ${\dot{m}}_{HP,EGR}$ is the HP-EGR mass flow rate. It is clearly seen from Equation (6) that the desired X_EGR increases with increasing X_oegr with X_oim fixed and X_oair being a constant.

$${\eta }_{vol}={\dot{m}}_{Eng}\cdot \frac{120}{N_{Eng}}\cdot \frac{R{T}_2}{p_2{V}_{Eng}M}$$

(3)

$${\dot{m}}_{Eng}=\frac{{\dot{m}}_{fuel}(AFR X_{oair}+X_{oegr})}{X_{oim}-X_{oegr}}$$

(4)

$${\eta }_{vol}(p_2,p_3)=C_{{\eta }_{vol}}(N_{Eng})\frac{r_c-{\left(\frac{p_3}{p_2}\right)}^{1/\gamma }}{r_c-1}$$

(5)

$$X_{EGR}=\frac{{\dot{m}}_{HP-EGR}}{{\dot{m}}_{Eng}}=\frac{X_{oair}-X_{oim}}{X_{oair}-X_{oegr}}$$

(6)

The primary reason to regulate X_oim is that X_oim has much higher correlation with NOx emission than X_EGR and X_oegr in the EAT system, as shown in Figure 8. For EAT assisted air system, the HP-EGR is diluted due to elevated engine mass flow rate, which is not taken into account in the conventional EGR rate based control. In contrast, the X_oim based control is able to maintain X_oim using increased X_EGR, which is beneficial for NOx control for EAT assisted air system.

Therefore, steady-state results show that X_oim is a better control output for the air system relative to the X_EGR in EAT assisted air system in diesel engines.

3.2. Transient Results Analysis

In addition to the steady-state experiment, transient tests were also carried out on the test bench under the operating conditions shown in

Table 6. Test case set-up for transient investigation of assist power.

Test Case	NEng	TEng	uVGT	uHP-EGR	PTEMG
-	rpm	Nm	%	%	kW
Case1	1200	120→260	56→36	24→14	0
Case2	1200	120→260	56→36	24→14	Closed-loop control to trace NT

. The three actuators were manipulated as shown in Figure 9.

For conventional VGT-EGR system, as shown in Figure 10, the settling time for p₂ is about 4.6 s. Consequently, there is X_oim undershoot in the time period from 31.6 s to 36 s, where the X_EGR response is smooth. In the process of tip-in, there is a slight NOx spike.

For the EAT assisted engine, the p₂ response is significantly enhanced with the settling time shorten to 2.2 s (52.1% improvement relative to the nominal system without E-assist), as shown in Figure 11. This implies enhanced fresh air or oxygen response. Consequently, there is a X_oim spike shown in the time period from 32.8 s to 34.8 s. Therefore, it is not surprising to see a NOx spike in the same time interval. What is interesting is that the X_EGR response is still smooth without any overshoot or undershoot. This implies that there is no sign of oxygen surplus by observing the EGR rate for EAT assisted engines. This makes it difficult to suppress the NOx spike by controlling the EGR rate since the EGR rate based control is not able to take into account the EGR dilution caused by VGT vane position optimization with EAT. Therefore, transient results confirmed that X_oim is a better control output in the air system of EAT assisted engines, relative to EGR rate, since the NOx spike can be removed by simply avoiding the X_oim overshoot.

4. Theoretical Analysis of the Impact of EAT on X_oim Control

From the aforementioned analysis, both steady-state and transient response confirmed the superiority of using X_oim as the control output for EAT assisted engines. However, interactions, between the electrical power of EAT and the states in the intake and exhaust manifolds, bring up complex disturbances to the X_oim control loop. This will be investigated based on the fundamentals of the boosting system in this section.

Based on the mass conservation of the intake manifold, the X_oim dynamics can be modeled as [27]:

$${\dot{X}}_{oim}=\frac{R{T}_2}{p_2{V}_{im}}({\dot{m}}_C{X}_{oair}+{\dot{m}}_{HP-EGR}{X}_{oegr}-{\dot{m}}_{Eng}{X}_{oim})$$

(7)

where ${\dot{m}}_C$ is the compressor mass flow rate, ${\dot{m}}_{HP-EGR}$ is the HP-EGR mass flow rate, ${\dot{m}}_{Eng}$ is the engine mass flow rate, $V_{im}$ is the volume of intake manifold. At steady-state condition, ${\dot{m}}_{Eng}$ can be approximated by the sum of ${\dot{m}}_{HP-EGR}$ and ${\dot{m}}_C$. Detailed discussion about the unknown terms, namely ${\dot{m}}_C$, ${\dot{m}}_{HP-EGR}$ and $X_{oegr}$, are shown below. This purpose of the following analysis is to understand the impact of EAT assist on the X_oim control from the perspective of physics.

1. The compressor mass flow rate ${\dot{m}}_C$ can be obtained from the definition of the compressor efficiency (${\eta }_C$) in [29], as shown in Equations (8) and (9).

$$P_{C,ideal}={\dot{m}}_C\Delta h_{0s}={\dot{m}}_C{c}_{p,c}{T}_1\left\{{\left(\frac{p_2}{p_1}\right)}^{\frac{\gamma -1}{\gamma }}-1\right\}$$

(8)

$${\eta }_C=\frac{P_{C,ideal}}{P_C}=\frac{{\left(\frac{p_2}{p_1}\right)}^{\frac{\gamma -1}{\gamma }}-1}{\frac{T_2}{T_1}-1}$$

(9)

where $c_{p,c}$ is the specific heat capacity of air, $p_1$ and T₁ are pre-compressor pressure and temperature, respectively, $P_{C,ideal}$ is the isentropic power for compressing the air from $p_1$ to $p_2$, i.e., power requirement during an isentropic process, and $P_C$ is the actual power that the compression process consumes, which can be approximated by the steady-state energy balance relation:

$$P_C=P_T+P_{TEMG}-P_{Loss}$$

(10)

where $P_T$ is the turbine power, $P_{Loss}$ is the mechanical loss of the EAT. Based on Equations (8)–(10), the compressor mass flow rate is modeled as function of $P_{TEMG}$ as below:

$${\dot{m}}_C=\frac{{\eta }_C(P_T+P_{TEMG}-P_{Loss})}{c_{p,c}{T}_1\left({\left(\frac{p_2}{p_1}\right)}^{1-\frac{1}{k}}-1\right)}\equiv g_{{\dot{m}}_C}(P_{TEMG},P_T,p_2)$$

(11)

2. The HP-EGR flow rate ${\dot{m}}_{HP-EGR}$ can be estimated by the model proposed in [29] as:

$${\dot{m}}_{HP-EGR}={\theta }_{HP-EGR}\frac{A_{HP-EGR}{C}_D{p}_3}{\sqrt{R{T}_3}}\sqrt{1-{\left(\frac{p_2}{p_3}\right)}^2}$$

(12)

where ${\theta }_{HP-EGR}$ is the HP-EGR valve position, $C_D$ and $A_{HP-EGR}$ are the flow coefficient and cross-sectional area of the HP-EGR valve, respectively, $p_3$ and $T_3$ are exhaust manifold pressure and temperature respectively.

The $p_3$ in Equation (12) can be obtained through the turbine efficiency definition and the Equation (10) as show in Equation (13) [29]:

$$P_T=P_C+P_{Loss}-P_{TEMG}={\eta }_{tm}{\dot{m}}_T{c}_{p,e}{T}_3\left(1-{\left(\frac{p_4}{p_3}\right)}^{1-\frac{1}{k}}\right)$$

(13)

where ${\eta }_{tm}$ is the turbine efficiency, ${\dot{m}}_T$ is the turbine mass flow rate, $c_{p,e}$ is the specific heat capacity of exhaust gases, and $p_4$ is the post-turbine pressure. Specifically, the $p_3$ model shown in Equation (14) as:

$$p_3=p_4{\left(1-\frac{P_C+P_{Loss}-P_{TEMG}}{{\eta }_{tm}{\dot{m}}_T{c}_{pe}{T}_3}\right)}^{1-\frac{1}{k}}\equiv g_{p_3}(P_{TEMG},P_C,T_3,{\dot{m}}_T)$$

(14)

Substituting Equation (14) into Equation (12) transforms the HP-EGR flow model into:

$$\begin{array}{ll}{\dot{m}}_{HP-EGR}& ={\theta }_{HP-EGR}\frac{A_{HP-EGR}{C}_D{g}_{p_3}(P_{TEMG},P_C,T_3,{\dot{m}}_T)}{\sqrt{R{T}_3}}\sqrt{1-{\left(\frac{p_2}{g_{p_3}(P_{TEMG},P_C,T_3,{\dot{m}}_T)}\right)}^2}\\ & \equiv {\theta }_{HP-EGR}{g}_{{\dot{m}}_{HP-EGR}}(P_{TEMG},p_2,{\dot{m}}_T,T_3)\end{array}$$

(15)

It can be inferred that increased assist power (P_TEMG) reduces the EGR flow rate through reduced pressure differential (or p₃) across the EGR value, as shown in Equation (14).

3. The $X_{oegr}$ can be approximated as the engine outlet port oxygen concentration ($X_{ocyl\_out}$), which is estimated based on [27]:

$$X_{oegr}\approx X_{ocyl\_out}=\frac{{\dot{m}}_{Eng}{X}_{oim}-{\dot{m}}_{fuel}AFR{X}_{oair}}{{\dot{m}}_{Eng}+{\dot{m}}_{fuel}}$$

(16)

where $AFR$ is the air-to-fuel ratio, ${\dot{m}}_{Eng}$ and ${\eta }_{vol}$ can be estimated by Equations (3) and (5) respectively. By substituting Equations (3), (5), and (14) into Equation (16), the $X_{oegr}$ can be modeled as a function of $P_{TEMG}$ as:

$$\begin{array}{ll}{X}_{oegr}& =\frac{g_{{\eta }_{vol}}(N,p_2,g_{p_3}(P_{TEMG},P_C,T_3,{\dot{m}}_T))N_{Eng}{p}_2{V}_{Eng}}{120R{T}_2({\dot{m}}_{Eng}+{\dot{m}}_{fuel})}{X}_{oim}-\frac{{\dot{m}}_{fuel}AFR{X}_{oair}}{{\dot{m}}_{Eng}+{\dot{m}}_{fuel}}\\ & \equiv g_{X_{oegr}}(P_{TEMG},N,p_2,{\dot{m}}_{fuel},{\dot{m}}_{Eng})\end{array}$$

(17)

Finally, substituting Equations (11), (15), and (17) into Equation (7), the $X_{oim}$ model is derived as below:

$$\begin{array}{l}{\dot{X}}_{oim}=\frac{R{T}_2}{p_2{V}_{im}}({\dot{m}}_C{X}_{oair}+{\dot{m}}_{HP-EGR}{X}_{oegr}-{\dot{m}}_{Eng}{X}_{oim})\\ =\frac{R{T}_2}{p_2{V}_{im}}[g_{{\dot{m}}_C}(P_{TEMG},P_T,p_2)X_{oair}+ {\theta }_{HP-EGR}{g}_{{\dot{m}}_{HP-EGR}}(P_{TEMG},p_2,{\dot{m}}_T,T_3)\times g_{X_{oegr}}(P_{TEMG},N,p_2,{\dot{m}}_{fuel},{\dot{m}}_{Eng}) -{\dot{m}}_{Eng}{X}_{oim}]\end{array}$$

(18)

It should be noted that the turbine and compressor efficiency are implicitly used in Equation (18), both of which vary with the operating point. For simplicity, they are read in turbine and compressor maps respectively, which are extrapolated from manufacturer’s data.

By observing Equation (18), it is clear that the EAT assisting power affects the $X_{oim}$ dynamic primarily from three different aspects:

• Enhanced air response through the term ${\dot{m}}_C=g_{{\dot{m}}_C}(P_{TEMG},P_T,p_2)$, since P_TMEG increased the compressor power.
• HP-EGR flow deficit when the pressure differential across the HP-EGR valve is insufficient as illustrated by ${\dot{m}}_{HP-EGR}={\theta }_{HP-EGR}{g}_{{\dot{m}}_{HP-EGR}}(P_{TEMG},p_2,{\dot{m}}_T,T_3)$, as P_TEMG affects the upstream pressure of the EGR valve.
• EGR gas dilution due to increased engine mass flow rate from elevated volumetric efficiency as indicated by $X_{oegr}=g_{X_{oegr}}(P_{TEMG},N,p_2,{\dot{m}}_{fuel},{\dot{m}}_{Eng})$, since P_TEMG leads to increased fresh air flow and reduces the fuel consumption.

Clearly, in order to attenuate the disturbances caused by the additional control degree of freedom ($P_{TEMG}$), an advanced disturbance rejection solution becomes necessary, as will be discussed in Section 5.

5. X_oim Controller Development

Since the universal oxygen sensor is mounted only on the exhaust side (UEGO), a X_oim observer is necessary. In this paper, the X_oim observer based on the measured $p_2$, X_oegr, and estimated ${\dot{m}}_C$, proposed by Park in [23], is used. A brief introduction and experimental validation are provided in the Appendix A for completeness. Then, an active disturbance rejection controller of oxygen concentration in intake manifold (OADRC) was developed with the control structure shown in Figure 12.

For OADRC controller derivation, Equation (18) is rewritten into Equation (19):

$$\begin{array}{ll}{\dot{X}}_{oim}& =\frac{R{T}_2}{p_2{V}_{im}}[g_{{\dot{m}}_C}(P_{TEMG},P_T,p_2)X_{oair}+\\ & {\theta }_{HP-EGR}{g}_{{\dot{m}}_{HP-EGR}}(P_{TEMG},p_2,{\dot{m}}_T,T_3)g_{X_{oegr}}(P_{TEMG},N,p_2,{\dot{m}}_{fuel},{\dot{m}}_{Eng})\\ & -{\dot{m}}_{Eng}{X}_{oim}]\\ & ={\theta }_{HP-EGR}\frac{R{T}_2}{p_2{V}_{im}}{g}_{{\dot{m}}_{HP-EGR}}(P_{TEMG},p_2,{\dot{m}}_T,T_3)g_{X_{oegr}}(P_{TEMG},N,p_2,{\dot{m}}_{fuel},{\dot{m}}_{Eng})+\\ & \frac{R{T}_2}{p_2{V}_{im}}[g_{{\dot{m}}_C}(P_{TEMG},P_T,p_2)X_{oair}-{\dot{m}}_{Eng}{X}_{oim}]\\ & ={\theta }_{HP-EGR}{b}_0+f\end{array}$$

(19)

where $b_0=\frac{R{T}_2}{p_2{V}_{im}}{g}_{{\dot{m}}_{HP-EGR}}(P_{TEMG},p_2,{\dot{m}}_T,T_3)g_{X_{oegr}}(P_{TEMG},N,p_2,{\dot{m}}_{fuel},{\dot{m}}_{Eng})$ is the control input gain, and $f=\frac{R{T}_2}{p_2{V}_{im}}[g_{{\dot{m}}_C}(P_{TEMG},P_T,p_2)X_{oair}-{\dot{m}}_{Eng}{X}_{oim}]$ is denoted as the “total disturbance”. It is clear that estimation errors in engine flow rate and HP-EGR flow rate as well as the external disturbance are all lumped as total disturbance.

Equation (19) is then rewritten in the state space form for ESO derivation, as shown in Equation (20):

$$\{\begin{array}{l}\dot{x}=Ax+Bu+E\dot{f}\hfill \\ y=Cx\hfill \end{array}$$

(20)

where $A=\left[\begin{array}{ll}0& 1\\ 0& 0\end{array}\right]$, $B=\left[\begin{array}{l}{b}_0\\ 0\end{array}\right]$, $C={\left[\begin{array}{l}1\\ 0\end{array}\right]}^T$, $E=\left[\begin{array}{l}0\\ 1\end{array}\right]$, i.e., $x={[\begin{array}{ll}y& f\end{array}]}^T$, $\{\begin{array}{l}{x}_1=X_{oim}\\ x_2=f\end{array}$ are the states, $y=x_1$ is the output, $u$ is the input ($u={\theta }_{HP-EGR}$), namely the HP-EGR valve position.

Based on Equation (20), a linear first order extended state observer (ESO) is designed as in Equation (21), following the method shown in [31],

$$\{\begin{array}{l}\dot{\widehat{x}}=A\widehat{x}+Bu+L\left(y-\widehat{y}\right)\hfill \\ \widehat{y}=C\widehat{x}\hfill \end{array}\Rightarrow \{\begin{array}{l}\dot{\widehat{x}}=\left(A-LC\right)\widehat{x}+[\begin{array}{ll}B& L\end{array}]\left[\begin{array}{l}u\\ y\end{array}\right]\hfill \\ \widehat{y}=C\widehat{x}\hfill \end{array}$$

(21)

where $L=\left[\begin{array}{l}{\beta }_1\\ {\beta }_2\end{array}\right]$ is the tunable observer gain matrix, $A-LC=\left[\begin{array}{ll}-{\beta }_1& 1\\ -{\beta }_2& 0\end{array}\right]$, and $\{\begin{array}{l}{\widehat{x}}_1={\widehat{X}}_{oim}\\ {\widehat{x}}_2=\widehat{f}\\ y={\widehat{x}}_1\end{array}$ are the observed states and output (measurement) estimate, respectively.

The tuning of $L$ matrix is addressed using the bandwidth parameterized method proposed by Gao [31]. This is briefly introduced here for completeness. The characteristic polynomial for the ESO system, Equation (21), is $s^2+{\beta }_{1}s+{\beta }_2=0$. Since ${\beta }_1$ and ${\beta }_2$ are design variables, these can be chosen to make the ESO state space Hurwitz stable. If we recognize that the characteristic polynomial may be expressed as a damped second order system, that is: $s^2+{\beta }_{1}s+{\beta }_2\equiv s^2+2\xi {\omega }_{o}s+{\omega }_o{}^2$ with $\xi$ and ${\omega }_o$ being the damping coefficient and the natural frequency (bandwidth) of the ESO system respectively, the ESO observer gains, ${\beta }_1$ and ${\beta }_2$ are then easily determined by choosing a system bandwidth and damping as follows:

$$\{\begin{array}{l}{\beta }_1=2\xi {\omega }_o\\ {\beta }_2={\omega }_o{}^2\end{array}$$

(22)

Both $\xi$ and ${\omega }_o$ can be time varying and a dynamic selection for ${\omega }_o$ is allowed. For simplicity, the damping ratio $\xi$ is fixed at 1 in this paper. Hence, the eigenvalues for $A-LC$ in Equation (21) are determined by the system bandwidth ${\omega }_o$. After convergence of ESO, ${\widehat{x}}_1\to x_1\to X_{oim}$, ${\widehat{x}}_2\to x_2\to f$, and then observed value of disturbance $\widehat{f}$ will approach the actual disturbance $f$, which realizes the observation of the total disturbance of the system.

With the state observer properly designed, the plant is reduced to an integrator

$${\dot{X}}_{oim}=b_{0}u+f=b_{0}u+\widehat{f}+(f-\widehat{f})\approx u_0$$

(23)

which is easily controlled by a P (proportional) controller

$$u_0=k_p(r-{\widehat{x}}_1)$$

(24)

where $r$ is the set-point for the desired intake oxygen concentration, ${\widehat{x}}_1$ is the observed value of oxygen concentration in intake manifold, $k_p$ is the proportional gain, which is selected to place the pole of the closed-loop system at the controller bandwidth ${\omega }_c$.

Finally, the control input, namely the HP-EGR valve position can be obtained as:

$$u=\frac{u_0-{\widehat{x}}_2}{b_0}=\frac{u_0-\widehat{f}}{b_0}$$

(25)

So far, the active disturbance rejection controller of oxygen concentration in intake manifold of the diesel engine equipped with EAT has been designed and the validation will be discussed in the next section.

6. Simulation Validation of the Proposed X_oim Controller

The OADRC controller was validated through the co-simulation between GT-SUITE and Matlab/Simulink. Compared with the traditional PID algorithm, the response speed and disturbance rejection ability of the OADRC controller were evaluated. Four evaluation metrics were proposed to quantify the control performance, including the settling time (defined as the time required for the response curve of intake oxygen concentration to reach and stay within a range of ±2% of the final intake oxygen concentration, denoted as $T_S$), steady-state error (defined as the difference between the desired intake oxygen concentration and the actual intake oxygen concentration when the response has reached steady state, denoted as $E_{SS}$), overshoot (defined as the maximum peak value of the actual intake oxygen concentration measured from the desired intake oxygen concentration, denoted as $M_P$) and recovery time (defined as the time it takes to recover to its prior intake oxygen concentration, denoted as $T_R$).

6.1. Intake Oxygen Concentration Step Response Test

To evaluate the tracking performance of the OADRC controller, a continuous step change of intake oxygen concentration were carried out at 1500 rpm engine speed and 18 mg/cycle fuel injection rate, with 80% VGT vane open. The desired X_oim ($X_{oim}^{des}$) was changed step by step as shown in Figure 13, with the demonstration of the control effect of OADRC controller and the total disturbance observed by the ESO. The estimated intake oxygen concentration in the first plot was the real-time output of the oxygen concentration observer mentioned in Appendix A.

In the step response test of X_oim shown in Figure 14, it is seen that the proposed solution offers faster response compared to that of PID controller. The specific improvement is tabulated in

Table 7. Comparison between OADRC and proportional-integral-differential (PID) controller with step changes of intake oxygen concentration.

Item	OADRC	PID	Improvement with OADRC
Average TS (s)	1.21	2.07	41%
Maximum TS (s)	1.5	2.35	36%
Average ESS (%)	0.05	0.05	0
MP (%)	0	0	0

.

6.2. Disturbance Rejection Capability Test

In order to evaluate the disturbance rejection ability, the N_T steps from 20,000 rpm to 15,000 rpm and then to 10,000 rpm by manipulating the P_TEMG, as shown in Figure 15. It is observed that the maximum deviation of X_oim from $X_{oim}^{des}$ is reduced by 15.6% using the proposed controller compared to the PID controller, in the time period from 8.1 s to 10.6 s. Detailed performance metrics are provided in

Table 8. Disturbance rejection performance comparison with step change of N_T.

Item	OADRC	PID	Improvement with OADRC
Average MP (%)	0.24	0.31	22.6%
Maximum MP (%)	0.27	0.32	15.6%
Average TR(s)	1.96	3.47	43.5%
Maximum TR(s)	2.48	4.5	44.9%

.

Another disturbance to X_oim comes from the VGT vane position, due to its influence on $p_3$, i.e., the upstream pressure of the HP-EGR valve. In Figure 16, the VGT vane position steps from 30% to 60% open, it is clear that the proposed solution shows reduced maximum X_oim deviation from the target and takes shorter time to converge to $X_{oim}^{des}$. Detailed performance assessment are available in

Table 9. Disturbance rejection performance comparison with step change of VGT vane.

Item	OADRC	PID	Improvement with OADRC
MP (%)	6.18	6.19	0.2%
TR (s)	1.58	2.02	21.8%

.

7. Conclusions

In this paper, experimental assessment on the impact of EAT on the air system control was conducted, based on a 6.7 L diesel engine. A disturbance rejection controller for the EAT air system was proposed and validated in simulation.

(1)

At 265 Nm engine load and 1400 rpm engine speed condition, up to 7.8% FE benefit can be achieved with the assist function of EAT(assuming the electrical energy is free in the driveline electrical regeneration during vehicle braking), through the reduction of pumping loss from wider VGT vane open, relative to the nominal system. Further FE benefit is limited by the HP-EGR deficit from over-reduced p₃ (low HP-EGR flow capability).

(2)

Transient boost response with EAT assist is improved by 52.1% relative to the nominal system. The new dynamics of p₂ introduced by EAT must be considered to avoid intake oxygen concentration overshoot and NOx spike. The EGR requirements should be reconsidered because of the excess fresh air from a fast boost response.

(3)

The EGR flow-based control objective should be transformed into the intake oxygen concentration-based control objective, which aligns well with the EAT system and the associated control design. EAT assist improved the volumetric efficiency of the engine (by up to 13.6% with 1.01 kW E-assist power at 265 Nm engine load and 1400 rpm engine speed in this paper), thereby increased the engine mass flow rate. This leads to HP-EGR gas dilution. EGR dilution and enhanced boost response makes the conventional EGR rate-based air system control not applicable to EAT system. Experimental results confirmed that X_oim works better as the control output for EAT system than EGR rate for NOx control.

(4)

In order to attenuate the disturbances from EAT on X_oim, a disturbance rejection based controller was proposed and validated in a high-fidelity GT-SUITE model. Results showed over 36% improvement in settling time and over 43% improvement in recovery time, relative to the conventional PID controller.