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Robust, Cost-Optimal and Compliant Engine and Aftertreatment Operation using Air-Path Control and Tailpipe Emission Feedback.

INTRODUCTION

With the introduction of heavy-duty diesel Euro-VI emission regulations in 2013/2014, again a major step in the reduction of pollutant emissions was made. These European standards contain more real-world emission focus by stricter OBD requirements, off-cycle emission limits (OCE), In-Service Conformity testing (ISC), and extended emission durability life-time periods. Also, new Type Approval (TA) cycles (World Harmonized Transient and Steady-state Test Cycle, WHTC and WHSC respectively) with tighter limits [1] were introduced.

In addition to this, significant C[O.sub.2] reduction has been set as a main target by the European Commission and Environmental Protection Agency (EPA), like in [2] and [3] to further reduce C[O.sub.2] footprints from heavy-duty trucks. Heavy-duty truck manufacturers face a strong challenge to comply to these standards and simultaneously develop engines, which have low operational cost and good performance. To meet these requirements, the vast majority apply both Exhaust Gas Recirculation (EGR) and exhaust gas aftertreatment system, which contains a Diesel Particulate Filter (DPF) and urea-based Selective Catalytic Reduction (SCR) system. Exceptions exist from Iveco and Scania, who offer SCR-only solutions [4], [5]. However, they all need to deal with engine and aftertreatment interaction under real-world circumstances, which is challenging and not straightforward, due to the growing number of sensors, actuators, sub-systems and extensive variety of operating conditions. This sets new targets for on-road performance robustness while maintaining low operational cost.

TNO has been developing an integrated control strategy for engine and aftertreatment, called Integrated Emission Management (IEM), for several years. This model-based control strategy continuously (in real-time) minimizes fuel and urea consumption within the emission constraints. Engine air-path settings are determined based on the actual state of engine and aftertreatment. Several IEM topics have been addressed the past years, ranging from concept demonstration [6], experimental demonstration [7] and real-world cycle performance evaluation using ISC [8].

This work is a direct extension of previous work [8], focusing on the robustness under real-world circumstances. A sensitivity analysis is conducted in the form of a Monte Carlo simulation study, to introduce sensor and actuator uncertainties in the system and evaluate the system performance by calculating the ISC factor (Conformity Factor, CF). To guarantee real-world robustness in terms of tailpipe emissions, the IEM strategy is extended with a feedback loop from the tailpipe N[O.sub.x] sensor that controls the emission output from the system. Such an extension is made without significantly compromising on the performance of the system in terms of fuel consumption.

In terms of a control problem, the disturbances acting on the system are at different time scales as shown in Figure 1. Production tolerances and sensor offsets act as constant disturbances (frequency is 0 Hz) on the system while ageing of the system occurs over longer durations. A typical drive cycle lasts from a few hours to a few days. Climatic effects also occur over a similar time scale. Different time scales of disturbances provide a challenge from a control perspective. That is, it is challenging to design a single control system that is capable of being robust towards disturbances over all time scales. In this paper, focus is made on studying the sensor and actuator effects (short time scales) over a drive cycle. System ageing effects and changes in climatic conditions have not been considered here.

This paper is organized as follows: first a brief description of the IEM strategy is given, together with its control approach. Second, the simulation set-up, containing descriptions of the applied engine and aftertreatment models, high-level and low-level controls and real-world cycles. Subsequently, the Monte Carlo method is described, including the applied sensor and actuator tolerances. The results of this Monte Carlo study are described afterwards. Then, the novel tailpipe N[O.sub.x] feedback in the IEM control strategy is described. The performance of the extended IEM strategy, evaluated by again a Monte Carlo study is successively described. The final section contains the conclusions and outlook for future work.

IEM MODEL BASED OPTIMAL CONTROL STRATEGY

The main idea behind the development of the IEM control strategy is to integrate the control of the engine and aftertreatment components, thereby extracting performance benefits from the overall powertrain. The IEM strategy, thus acts as a supervisory controller, that, based on the current state of the aftreatment system, adjusts the engine settings, such that the fuel and Adblue costs are minimized and the emission levels are kept below the legislative limits.

The layout of the IEM strategy and its interaction with low-level controllers is shown in Figure 2. The IEM is a model based control strategy. Models of the engine and aftertreatment system are used to formulate a cost function that is optimised in real-time in the optimiser. For real-time implementation, the models should be able to run and process calculations quickly. For this purpose, a steady-state implementation of the dynamic engine model from [9] is used.

Model Improvements

The IEM control architecture is similar to the one presented in previous publications [7], [8] and [10]. An extension has been made to the aftertreatment model inside the IEM strategy. Previous versions of the IEM strategy included steady-state efficiency maps of the SCR system as can be seen in Figure 3. However, the use of efficiency maps resulted in differences between actual and modelled SCR efficiencies. This is illustrated in Figure 4. It can be observed that the cumulative tailpipe N[O.sub.x] value of the IEM model and the actual value diverges throughout the cycle. Another factor to be considered is that the steady-state maps cannot adapt themselves to system ageing, which is also shown in Figure 4. Ageing of the SCR catalyst is simulated here by adapting the calibration parameters related to adsorption and desorption reaction kinetics and the ammonia storage capacity of the catalyst. In Figure 4, the actual value of tailpipe N[O.sub.x] for an aged SCR system (30% aged) is much higher than that for a new SCR system. However, the IEM model predicted tailpipe N[O.sub.x] value does not show a difference between the new and aged systems.

The error in prediction for a new SCR system is 26.4% and for an aged SCR system is 35.7%. This means that the IEM model assumes a different tailpipe N[O.sub.x] emission compared to the actual value, resulting in model errors, which affect the performance of the optimal controller.

In order to improve accuracy of prediction of the efficiency of the SCR in the IEM strategy(and thus improve the tailpipe N[O.sub.x] prediction accuracy), the efficiency maps of the SCR is replaced by feedback signals from the low-level urea dosing controller. The urea dosing controller uses a dynamic SCR storage model to determine the amount of Adblue dosing required by the system. Efficiency of the SCR can be calculated by this model and this signal is used by the IEM controller. The updated SCR model inside the IEM strategy is presented in Figure 5.

The current efficiency of the SCR, [[eta].sub.scr,t], is calculated in the low-level controller. Inside the IEM controller, the current SCR efficiency is used to predict the SCR efficiency at the next time step, given the temperature, space velocity and pre-SCR N[O.sub.2]-N[O.sub.x] ratio at the next step from the engine model inside the IEM controller. This is done through the use of the first order Taylor series expansion as shown in Equation (1). The derivatives of the SCR efficiency with respect to temperature, space velocity and N[O.sub.2]-N[O.sub.x] ratio are based on offine maps.

The efficiency of the SCR as predicted by the IEM controller needs to be calculated several times at each time step corresponding to the chosen air path setting of the engine model (which subsequently affects the space velocity of exhaust gas and DOC efficiency). This requires that the SCR efficiency calculation needs to be done very quickly. This prevents the usage of high fidelity SCR models inside the IEM which would have been ideally desirable. The usage of Taylor series expansion is an approximation which is computationally less expensive while being accurate enough for this purpose.

Using this model update, the plot shown in Figure 4 is recomputed and is presented in Figure 6. It can now be seen that the model predicted error in tail-pipe N[O.sub.x] has been reduced to 8.2% for a new SCR system and to 7.1% for an aged SCR system. The error, however, has not yet converged to zero. A possible reason for this is the use of Taylor series approximation for calculation of the new efficiency, which is accurate only in a region close to the current SCR efficiency. A possible way to overcome this is to use physics based models of the SCR inside the IEM controller, but this comes at the cost of additional computational effort.

IEM and Optimal Control

The IEM strategy is steeped in the concept of the optimal control theory and uses the Pontryagin's Minimum Principle in order to minimize a cost function - fuel and Adblue costs, under the constraints of emission limits set by legislation. Thus, the following objective function can be formulated:

[mathematical expression not reproducible] (2)

Subject to:

[mathematical expression not reproducible] (3)

Where,

* [[pi].sub.fuel] is the fuel price [[euro]/kg];

* [[pi].sub.adblue] is the Adblue price [[euro]/kg];

* [P.sub.d] is the power required for the drive cycle [kW];

* [mathematical expression not reproducible] is the legislative emission limit for TA cycle [g/kWh]

Table 1 lists the fluid prices used in this study. The prices are taken from [11] and [12]:

The fuel quantity, [W.sub.fuel] used, is determined by a low-level fuel path controller, while the desired Adblue quantity, [W.sub.Adblue] is calculated assuming all of the injected urea is available for conversion of engine out NO emissions. Using this assumption, W[A.sub.dbl] is determined as:

[mathematical expression not reproducible] (4)

Where, 2.0067 represents the stoichiometry between urea and N[O.sub.x] gas. The [W.sub.NOx,eo] term in Equation (4) is determined from the engine model inside the IEM strategy as shown in Figure 2. Using Equations (2) and (3), a Hamiltonian is formulated wherein, the objective function is augmented with state dynamics and constraints using Lagrange parameters. The following Hamiltonian function is obtained:

H(x,u) = ([[pi].sub.fuel] * [W.sub.fuel(x,u) + [[pi].sub.adblue] *[W.sub.adblue](x,u))+ [[lambda].sup.T] * f(x,u) (5)

With state dynamics f(x, u) and Lagrange parameters: [[lambda].sup.T] = [[[lambda].sub.1]; [[lambda].sub.2]; [[lambda].sub.3]].

The state dynamics are given by:

[mathematical expression not reproducible] (6)

With states : [mathematical expression not reproducible]

In order to minimize the above Hamiltonian, optimal trajectories of the Lagrange parameters have to be determined. This means that the drive cycle needs to be known a priori which is not possible in a real time implementable situation. In order to have a real-time implementable controller, approximations of the Lagrange parameters have been used through application of heuristic rules. The heuristic rules and the physical interpretation of the applied Lagrange parameters have been detailed in [7], [8] and [10].

SIMULATION SETUP

In the previous work [8], the performance of the Integrated Emission Management strategy in real-world conditions is studied and compared with a state-of-the-art Euro-VI strategy, containing several discrete engine calibrations to enable the desired N[O.sub.x] conversion in the SCR as well as low fuel consumption when N[O.sub.x] conversion is sufficient. As an extension of this, the robustness of the IEM strategy to sensor and actuator tolerances is studied. This paper covers the findings of this analysis, while also providing an extension to the IEM strategy to make the controller robust towards such tolerances.

Figure 7 shows the simulation setup used for this study. The IEM controller block has been previously explained. The other controller and simulation models are explained in the next section. The virtual engine model and the virtual aftertreatment models used here represent an engine and aftertreatment system and are validated high fidelity models. The control models used in the IEM strategy consist of low fidelity physics based models and map based models.

System Description

Dynamic Engine Model

The dynamic Mean Value Engine Model (MVEM) used, is similar to the one presented in [8] and is used as a virtual engine. This model is based on [9] and has been updated to include the effects of heat transfer in the downpipe between the engine and the aftertreatment system. The engine model represents a 375 kW, Euro-VI Heavy Duty (HD) diesel engine and is equipped with cooled high pressure Exhaust Gas Recirculation (EGR), Variable Turbine Geometry (VTG), with intercooler, Back Pressure Valve (BPV), and a common rail fuel injection system.

Aftertreatment Model

For this study, validated aftertreatment models of Diesel Oxidation Catalyst (DOC), Diesel Particulate Filter (DPF), Selective Catalytic Reductor (SCR) and AMmonia OXidation catalyst (AMOX) are used. Also included in this study is a model of urea injection upstream of the SCR and its decomposition through the thermolysis reaction. Active regeneration of the DPF has not been considered, hence, diesel injection into the aftertreatment line has not been modelled in this study. An overview of the applied aftertreatment models has been presented in [13].

Control Description

The control architecture used in this study is divided into two layers - a lower level control layer including air and fuel path controllers for the engine and the urea injection controller for the SCR system, and a higher level control layer consisting of the IEM control strategy and an aftertreatment state monitor. Since there is no active DPF regeneration used, the HC dosing controller has been neglected. The IEM strategy has been explained previously. The other controllers used are explained below.

Air-Path Controller

The air-path controller translates the exhaust manifold pressure ([p.sub.em]) and engine-out N[O.sub.x] emission setpoints into EGR, VTG and BPV positions. In case of the baseline strategy, the setpoints are determined by several discrete engine calibrations, while for the IEM strategy, the setpoints are provided from the IEM controller.

Fuel Path Controller

The torque controller determines the quantity of fuel to be injected. This is done by calculating the difference between the actual engine torque and the requested engine torque (from the drive cycle) and translating this difference into a desired fuel injection value. In order to avoid excessive smoke, the torque controller also uses a smoke limiter that sets a lower bound on the air-fuel equivalence ratio in the cylinder to a value of 1.1. Injection timing calculation has not been implemented in the current work.

Urea Dosing Controller

The urea dosing controller controls the amount of Adblue injected into the exhaust line. The urea dosing controller makes use of an online storage model that dynamically predicts the quantity of ammonia stored on the catalyst. The urea dosing controller is essentially a PID controller with an anti-windup that tries to minimise the error between the stored ammonia ([theta]) on the catalyst and a reference storage line ([[theta].sub.ref]). The reference line has been calibrated, such that the tailpipe N[O.sub.x] as well as ammonia slip are within legislative limits [10]. The ammonia storage reference calibration has been shown in Figure 9.

AT State Monitor

The AT state monitor is a standard high level control strategy that deals with interaction between the engine and aftertreatment system. Depending on the state (temperature) of the aftertreatment system and the tailpipe N[O.sub.x] emissions, the AT state monitor adjusts the air and fuel path settings of the engine in several discrete steps that aims to operate the aftertreatment system in a desirable efficiency range to bring about sufficient emission reduction. The AT state monitor forces the engine to operate in a low efficiency mode (high fuel consumption, low engine-out N[O.sub.x] emissions) when the aftertreatment system cannot bring sufficient emission reduction, while it switches the engine to a high efficiency mode when the aftertreatment system has a high efficiency.

In the case of the baseline control strategy, the AT state monitor provides the air and fuel path settings to the engine. In the case of a the IEM control strategy, the AT state monitor provides only fuel path settings to the engine, while the air path settings are provided by the IEM strategy.

Real-World Cycles

One of the objectives of this study is to analyse the robustness of the IEM control strategy in real-world conditions in addition to the type approval test conditions. For this purpose, two drive cycles were chosen as inputs to the system - the WHTC representing the type approval test cycle and a real-world cycle representing urban driving conditions. The cycle specifications are described in Table 2.

SENSITIVITY ANALYSIS USING MONTE CARLO SIMULATIONS

For the IEM control strategy, the accuracy of the model used for formulation of the cost function plays an important role in the optimal set-points specified to the air management controller. Furthermore, the structure of the IEM controller is such that it acts like an "open-loop" controller. By this, it is meant that the IEM strategy is oblivious to whether the specified setpoints have been realized by the low-level controller or if the efficiency of the aftertreatment system is as predicted, and consequently, if the tailpipe emissions are within legislative limits. During real-world operations, several factors may contribute towards discrepancies between the actual powertrain and the modelled powertrain, the most important of which are sensor accuracies, actuator/injector accuracies and the effect of system ageing. In this work, these factors are classified as disturbances to the IEM powertrain model. In order to determine the effect of these disturbances on the IEM strategy, a sensitivity study, through Monte Carlo simulations, is made. In Monte Carlo simulations, uncertainties in the inputs are represented by a probability distribution and by randomly picking points from this distribution, the input is biased and the effect of this bias on the output is measured. Combined with statistical methods, such as regression analyses, the effect of input disturbances on the controller performance can be quantified.

Regression models involve the following variables:

1. Unknown parameter [beta];

2. Independent variables X; and

3. Dependent variables Y.

The aim of the regression model is to relate Y to X and [beta], such that:

Y = f(X,[beta]) =[[beta].sub.0]+ [[beta].sub.1][X.sub.1] + [[beta].sub.2][X.sub.2] + -[[beta].sub.n][X.sub.n] (7)

A necessary condition for obtaining an accurate regression model is that the number of simulations should be at the least equal to the number of input variables. Mathematically, this condition is equivalent to the matrix [X.sup.T]X being invertible (X being the vector of input variables). That is,

det([X.sup.T]X) [not equal to] 0 (8)

A generalized procedure for Monte Carlo simulations is given below:

1. Define a range of possible input variations;

2. Generate inputs randomly from a probability distribution;

3. Perform repeated simulations using the generated inputs;

4. Aggregate and analyse the results - regression analysis.

An important step in defining the Monte Carlo simulations is to identify the parameters for which the sensitivity analysis is to be made. This means defining the input parameters that would be biased (disturbed). There are many inputs to the system that can be possibly biased. However, including all these biases would necessitate a large number of repeated simulations to obtain accurate results. In order to limit the computational time needed, certain important signals are selected based on prior knowledge of the system. Since the main focus in this study is to look at the robustness of the IEM strategy, the main focus in selecting the bias signals has been made on the inputs to the IEM strategy. The signals that are being biased are shown in Figure 11, indicated by the blue arrows. It should be noted that the figure shows the [[lambda].sub.3] parameter with a PI controller. This implementation is discussed later in the paper. For the current Monte Carlo simulations, the [[lambda].sub.3] parameter is a constant and calibrated similar to [[lambda].sub.1] and [[lambda].sub.2]. Details of the applied calibration for [[lambda].sub.1-3] parameters is discussed in [8] and [10].

Biases

The next step in defining the Monte Carlo simulation consists of defining a range of the input variations. Relevant tolerance values for the parameters identified are chosen based on sensor specifications. Table 3 lists the chosen range for the input disturbances.

It should be noted that in selection of actuator biases, BPV actuator is chosen to be biased, while leaving out EGR and VTG actuators. This is done because the EGR and VTG valves are closed-loop controlled by the air management controller and is hence assumed to be robust enough in realizing the provided set-points. Also, SCR ageing has not been used as a bias parameter.

Data Sampling

Next, from this defined range, a number of sample points are randomly chosen at random such that they together represent a probability distribution (a uniform distribution in this case). The number of samples chosen influences the accuracy of the results obtained. Typically, the number of samples should be such that the samples are sufficiently able to represent a uniform distribution.

There are several statistical methods available (e.g., Kolmgorov-Smirnov (KS) test) to quantitatively determine how accurate a given distribution of samples represents a particular probability distribution. The sampling algorithm used for random sampling of data points within the given range, together with the total number of samples contribute towards the quality of the Monte Carlo simulations.

In this paper, a Latin Hypercube Sampling (LHS) algorithm is used (as opposed to a simple random sampling algorithm). The LHS algorithm divides the entire range of bias distribution into several smaller regions and makes sure that each region is equally represented. Figure 12 shows the differences in random sampling of 500 data points in the range {0,1}. The LHS sampling algorithm more accurately represents a uniform distribution compared to the simple random sampling algorithm. The advantage this improved sampling method poses is that the quality of the Monte Carlo simulations can be maintained by reducing the number of simulations. For the current work, 500 Monte Carlo simulations are defined. This means that within the given range of bias distribution for each bias parameter, 500 data points are randomly chosen. Mathematically, the matrix X can be written as

X = X(500,12) and, det(X'X) = 1.04e48, > 0

This satisfies the criterion from Equation (8). Thus for the current set of simulations defined, the matrix containing the disturbances is invertible and has a high degree of accuracy indicated by the fairly large value of the determinant.

RESULTS OF SENSITIVITY ANALYSIS FOR MODEL-BASED CONTROL

The Monte Carlo simulations are carried out for the system and analysed for the baseline as well as IEM control strategies. The key performance indicators of the system in the presence of the various disturbances are shown in Figure 13 and Figure 14. Each plot shows the distribution of the variation in performance indicators simulated for the same drive cycle in the presence of different disturbances. The fuel and Adblue consumption as well as the total fluid costs have been normalized with respect to the baseline value calculated for a system with no disturbance (nominal system). Table 4 lists the performance indicators for both baseline and IEM strategy for a nominal system (also normalized with respect to the baseline nominal value). The IEM strategy reduces fuel consumption for both BSFC and the real world cycle by 0.4% and 0.26% respectively, while the Adblue consumption has increased compared to the baseline strategy. However, the fuel price being significantly larger than the Adblue cost (see Table 1), there is still a saving on fluid costs. In both cases the IEM strategy is compliant with respect to tailpipe emission levels.

From Figure 13 and Figure 14, it can be observed that both the baseline and the IEM tend to show variations in cycle result values for the WHTC as well as the real-world cycle. However, the most interesting result is that of the tailpipe N[O.sub.x] levels. For the WHTC, it can be observed that the baseline control strategy is robust enough to remain within type approval limits in the presence of disturbances. A similar trend can also be observed in other performance indicators for the baseline strategy for the WHTC, wherein, the variance is small in comparison to that of the IEM control strategy. The IEM strategy provides lower fluid costs, however, it is not compliant for all considered disturbances. Finally, it can also be observed that for the WHTC, the distribution of the fuel consumption values shows two peaks. This can be observed for both the IEM and the baseline case. The reason for this can be attributed to the functioning of the AT state monitor which changes the engine mode in discrete steps. It was found that a positive bias in the SCR temperature sensor (meaning the AT state monitor thinks the SCR is more efficient than it actually is) resulted in engine to be operated in a more fuel efficient mode for a longer duration of time over the entire drive cycle. This is an artefact of the applied discrete-mode AT state monitor controller and not of the IEM strategy. This resulted in significant drop in fuel consumption compared to the cases with other biases, resulting in two distribution peaks for the fuel consumption values.

Analysis for the real-world cycle shows both the IEM and the baseline control strategies have a similar variation in performance indicators. It can also be seen that in this case, both the IEM and baseline control strategies have a small set of ISC results above the legislative limit.

The IEM strategy however, shows insufficient robustness in terms of tail-pipe emission levels in the presence of disturbances. The reason for this could be attributed to the inherent "open-loop" control structure present in the IEM optimal control approach. The IEM controller does not get a feedback signal from tailpipe sensors and is thus blind to the actual tailpipe N[O.sub.x] emissions.

FEEDBACK CONTROL OF TAILPIPE N[O.sub.X] EMISSION FOR IN-SERVICE CONFORMITY

The IEM optimal control algorithm selects the lowest cost operating point for the engine and aftertreatment system, given an equivalent cost of fuel, Adblue and NOx-emissions. Because of continuously Figure 13 Monte Carlo simulation results of Baseline and IEM with fixed [[lambda].sub.3] varying ambient conditions, engine operating points and aftertreatment states, the trade-off between the key performance variables is optimized differently each time step, and there is no direct control of the tailpipe emission levels - the tailpipe emission levels are not constant and may exceed legislation limits in certain cases.

By introducing feedback of the tailpipe N[O.sub.x] emission, control of absolute tailpipe emissions levels can be gained and external disturbances can be suppressed. Compliant emission levels can thus be guaranteed. It should be noted, however, that the use of tailpipe N[O.sub.x] emission feedback from a sensor presents difficulties, such as cross sensitivity towards N[H.sub.3] concentration, slow sensor dynamics and sensor errors / disturbances. In this study, cross-sensitivity and sensor dynamics have been neglected, while sensor errors have been added in the Monte Carlo simulations as shown in Table 3. Also in this study, sensor unavailability at low temperature operations is not present since only cold start conditions are not considered.

In the IEM controller, as demonstrated in [10], N[O.sub.x] emissions depend strongly on the magnitude of the [[lambda].sub.3] Lagrangian multiplier (co-state) of the Hamiltonian, which represents the equivalent N[O.sub.x] cost in the cost-minimization formulation. The [[lambda].sub.3] co-state can therefore be a suitable control-input to obtain desired specific tailpipe emission levels (typically given in g/kWh), but should not result in constant emission levels at all times, as this would unnecessarily constrain the engine operating range. Some variation in the instantaneous emission levels in g/kWh is always present, but the controller should ensure that these levels do not exceed compliance levels for extended periods of time. On the other hand, the tailpipe N[O.sub.x] controller can relax the emission constraint of the engine at times when tailpipe emission levels are low. This provides an opportunity to reduce operating costs.

The compliance limits for ISC in Europe have been defined as Work-Based-Window (WBW) emission limits. For a given use-case, the tailpipe emissions are averaged over time-windows corresponding to the engine-work of a WHTC cycle. Of all such windows, at least 90% must have averaged emission levels lower than 1.5 times the type-approval emission limit. This means that 90% of all WBWs must have an average emission level of lower than 0.69 g/kWh [14].

The response time of a feedback-controlled system is typically called by its inverse: control bandwidth [Hz], and corresponds to the timescale [s]=1/[Hz] at which disturbances can be suppressed and setpoints can be tracked. The choice of control bandwidth for the tailpipe emission controller can be seen as a tradeoff between fuel-consumption ('engine operating freedom') and suppression of external disturbances such as unpredictable drive-cycles, ambient conditions and aging. The bandwidth should not be too high (too fast control response) as this unnecessarily constrains the engine operating freedom, but must be fast enough to result in compliant emission levels over a WBW.

The WHTC is a low-power cycle lasting 1800 seconds. Therefore, during high-power operation, a WBW will correspond to a shorter time window, while during low-power operation the WBW spans a longer time. To be compliant at all times, the response time of the feedback controlled system must be faster than the shortest WBW. In this paper, the engine used is rated at 375 kW. Using this engine, the work done to complete the WHTC is 28 kWh. This gives the reference work for all the WBW used for ISC calculations. Thus the smallest possible WBW is around 260 [s] long. The longest WBW is restricted by the minimum power requirements for each WBW as defined in [14] (20% of the rated engine power) and under normal circumstances is around 1344 [s].

In reality, depending on the drive cycle (torque and speed), the WBW length can vary in real-time. In order to be emission compliant over all WBWs, the bandwidth of the controller should also vary in real-time. This would require drive cycle prediction algorithms using preview information from navigation systems. In order to implement a fixed bandwidth controller, while at the same time achieving In Service Conformity limits, a time based window approach is used, wherein, the averaging window length is calculated based on a fixed time basis.

A PI-control strategy is chosen with bounded outputs on [[lambda].sub.3], between zero and a system upper limit (based on [[lambda].sub.3] sweep results presented in [2] and [10]). The error signal used for the controller is obtained by using the specific emissions in [g/kWh] over the last 100 [s]. This means that the length of the averaging window is chosen to be 100 [s].

[mathematical expression not reproducible] (9)

Where [mathematical expression not reproducible] [g/kWh] is the error signal used as the input to the feedback control, [mathematical expression not reproducible] is the normalized tailpipe N[O.sub.x] emission setpoint [g/kWh], and [mathematical expression not reproducible] is the measured tailpipe NO emission in [g/s]. The control law can be given by:

[mathematical expression not reproducible] (10)

Ideally, the setpoint should be the ISC limit of 0.69 [g/kWh]. Since the averaging window length is of 100 [s], the control bandwidth of the system will be much higher (of the order of 500-1000 [s]). This means that the ISC limits cannot be guaranteed for all WBWs as defined by the legislations (especially for very high power cycles). To circumvent this effect, a conservative [mathematical expression not reproducible] of 0.4 [g/kWh] is chosen for the controller, which is very close to the TA cycle limit of 0.46 [g/kWh].

SIMULATION RESULTS

The implementation of the feedback loop with the PI controller is shown in Figure 11. The Monte Carlo simulations are performed again using the new IEM control strategy, using a feedback controller for [[lambda].sub.3], for the WHTC and a real-world cycle. For a fair comparison, the same set of inputs to the Monte Carlo simulations are considered as before. The results of this simulation are presented in Figure 15 and Figure 16.

The WHTC results are shown in Figure 15. It can be seen that the new IEM strategy shows similar performance in terms of BSFC in comparison to the old IEM strategy. However, the Adblue and subsequently, the total fluid costs are lower than the old IEM strategy. The total fluid costs are also lower than the old IEM strategy and the baseline strategy. More importantly, the new IEM control strategy is able to reduce the distribution of the tailpipe N[O.sub.x] emissions in comparison to the old IEM strategy. A vast majority of the simulations have a tailpipe emission level lower than the TA cycle limit. Certain simulations show a tailpipe N[O.sub.x] level higher than the TA limit. The reason for this can be attributed to the fact that the WHTC corresponds to a short duration cycle, with very few time based windows.

For the real-world cycle results shown in Figure 16, the new IEM strategy performs significantly better. Again, in terms of BSFC, Adblue and total fluid costs, the new IEM strategy performs similar to the old IEM strategy. However, in terms of ISC tests, the new IEM strategy manages to control the emission output to below the ISC limit for all simulations. Almost 80% of the simulations have a Conformity Factor in the range of 0.4 to 0.5, which is lower than the baseline as well as the old IEM strategy.

Table 5 lists the nominal cycle result for the new IEM strategy and compares it with the old IEM and the baseline strategies. The new IEM strategy still provides savings in terms of BSFC compared to the baseline strategy. The savings in fuel consumption are comparable to the old IEM strategy, while the tailpipe emission levels for both TA and real world cycles are lesser than the old IEM strategy.

Figure 17 shows the normalized BSFC Vs ISC for and normalised TFC Vs ISC for the real-world cycle. The trade-offs between fuel consumption and emissions become more apparent from this figure. In terms of fuel consumption, the old and new IEM strategies are lower than that of the baseline strategy, while the new IEM strategy is more robust on tailpipe N[O.sub.x] emissions as seen by the very narrow spread on the ISC axis. In terms of TFC, all three control strategies give similar results. The new IEM strategy is thus capable of being robust on the emission levels, while maintaining the same TFC. The nominal point corresponds to the result obtained from running a baseline strategy simulation with no disturbances. Both the BSFC and TFC have been normalised with respect to this point.

CONCLUSIONS AND OUTLOOK

From the study presented above, the following conclusions can be drawn:

1. A model update in terms of using an efficiency state feedback of the SCR from the lower level controller to the IEM controller was necessary to reduce the error in tail pipe emission prediction inside the IEM aftertreatment model.

2. Monte Carlo simulations for the WHTC showed that the baseline control strategy was more robust towards tail pipe emission levels in comparison to the IEM control strategy.

3. For a real-world drive cycle, both the baseline as well the IEM control strategies were not robust enough to handle disturbances such as sensor and actuator errors.

4. A robust method of handling the disturbances has been introduced that uses a feedback signal from the tailpipe N[O.sub.x] sensor signal to adapt the Lagrangian parameter corresponding to the tailpipe NOx emissions. A PI controller using tailpipe N[O.sub.x] emission information has been implemented in order to adapt online the Lagrangian parameter. The controller has been tuned in order to control the tailpipe emissions in each work-based window, such that the In service conformity regulations are met.

5. By using such an approach, it is seen that the IEM strategy is able to handle the simulated disturbances. The improvement (robustness towards emissions) can be seen mostly in real-world cycles, wherein, the PI controlled [[lambda].sub.3] is able to control tailpipe N[O.sub.x] emissions to meet the ISC emission limits.

6. In terms of fuel and Adblue consumption, the proposed IEM strategy performs similar to the original IEM strategy. However, it is still able to control the tailpipe emissions to meet legislation limits. This can be observed more for the real-world cycles than the WHTC, since the controller has been setup for the real-world cycle emission tests (In Service Conformity).From the above study, a few points to consider for the future are derived. A few of them are listed below.

1. The above results are from a simulation study. Although the powertrains models used were validated to represent actual engine and aftertreatment systems, a next step would be to test and prove the proposed control strategy on an engine test bench (or on an actual heavy-duty truck).

2. Future extensions of the IEM control strategy will include the effect of particulate matter emissions and inclusion of a fuelling strategy (injection timing and pressure). Fuelling strategy has a significant control over the engine-out N[O.sub.x] and PM emissions, while also affecting the C[O.sub.2] emission (fuel consumption).

3. Climatic effects such as temperature, humidity and altitude changes have not been included in this study. Studying the effects of these changes on the system is useful in terms of understanding the robustness of the IEM control strategy towards these parameters.

REFERENCES

[1.] DieselNet, "Emission Standards - European Union - Heavy-Duty Truck and Bus Engines," 2015. [Online]. Available: http://www.dieselnet.com/standards/eu/hd.php.

[2.] EPA and NHTSA, "EPA and NHTSA Propose Standards to Reduce Greenhouse Gas Emissions and Improve Fuel Efficiency of Medium-and Heavy-Duty Vehicles for Model Year 2018 and Beyond," EPA-420-F-15-901, June, 2015.

[3.] European Commission, "WHITE PAPER - Roadmap to a Single European Transport Area - Towards a competitive and resource efficient transport system," COM/2011/0144 final, 28 March, 2011.

[4.] IVECO, "Hi-Performance: The High Efficiency SCR system," 01 July 2012. [Online]. Available: http://www.iveco.com/enus/press-room/kit/pages/8-hiperformancethehighefficiencyscrsystem.aspx.

[5.] Scania, "New 450 HP Engine with SCR only," 03 June 2014. [Online]. Available: http://scania.com/media/pressreleases/P14402EN.aspx.

[6.] Cloudt R. and Willems F., "Integrated Emission Management strategy for cost-optimal engine-aftertreatment operation," SAE International Journal of Engines, vol. 4, no. 1, pp. 1784-1797, 2011.

[7.] Mentink P., Willems F., Kupper F., and van den Eijnden E., "Experimental Demonstration of a Model Based Control Design and Calibration Method for Cost Optimal Euro-VI Engine and Aftertreatment Operation," SAE Technical Paper 2013-01-1061, 2013, doi:10.4271/2013-01-1061.

[8.] Mentink P., van den Nieuwenhof R., Kupper F., Willems F. and Kooijman D., "Robust emission management strategy to meet real-world emission requirements for HD diesel engines," SAE International Journal of Engines, vol. 8, no. 3, pp. 1168-1180, 2015.

[9.] Wahlstrom J. and Eriksson L., "Modelling diesel engines with a variable-geometry turbocharger and exhaust gas recirculation by optimization of model parameters for capturing non-linear system dynamics," Proc. Institution of Mechanical Engineers, Part D, Journal of Automobile Engineering, vol. 225, no. 7, pp. 960-986, 2011.

[10.] Willems F., Mentink P., Kupper F. and van den Eijnden E., "Integrated emission management for cost optimal EGR-SCR balancing in diesel engines," in 7th IFAC Symposium on Advances in Automotive Control, Tokyo, Japan, 4-7 September, 2013.

[11.] Transport en Logistiek Nederland, "The average fuel price in the Netherland without VAT over 2013-2014," [Online]. Available: http://www.tln.nl/Dieselprijs.aspx#.VDzYKvmSwus.

[12.] Bulk price of urea, TLN, "Verbruik 1 op 71 - Ondanks lag verbruik verdienen AdBlue-kosten aandacht," nummer 5, pp 22-24, 2009.

[13.] Cloudt, R., Saenen, J., Eijnden, E., and Rojer, C., "Virtual Exhaust Line for Model-based Diesel Aftertreatment Development," SAE Technical Paper 2010-01-0888, 2010, doi:10.4271/2010-01-0888.

[14.] European Directive, "Work-based method calculation," 2055/55/EC-2005/78/EC in Annex III, Appendix 2, Section 5.

CONTACT INFORMATION

Satish Ramachandran

TNO Automotive

Automotive Campus 30

5708 JZ Helmond

P.O. Box 756

The Netherlands

satish.ramachandran@tno.nl

DEFINITIONS/ABBREVIATIONS

ABBREVIATIONS

IEM - Integrated Emission Management

N[O.sub.x] - Nitrogen oxides

C[O.sub.2] - Carbon dioxide

OBD - On-Board DiagnosticsOCE - Off-Cycle Emission

ISC - In-Service Conformity

WHTC - World Harmonised Transient Cycle

DOC - Diesel Oxidation Catalyst

DPF - Diesel Particulate Filter

SCR - Selective Catalytic Reduction

AMOX - AMmonia OXidation catalyst

EGR - Exhaust Gas Recirculation

VTG - Variable Turbo Geometry

SV - Space Velocity

MVEM - Mean Value Engine Model

BPV - Back Pressure Valve

HC - HydroCarbons

PID - Proportional Integral Differential

N[H.sub.3] - Ammonia

WBW - Work Based Window

TA - Type Approval

sp - Setpoint

SYMBOLS

tp - tailpipe

eo - engine-out

c - Specific heat capacity [J/kgK]

[lambda] - Lagrange multipliers

[eta] - Efficiency [%]

T - Temperature [K]

C - Concentration [ppm]

exh - exhaust

[pi] - Price [[euro]]

W - Mass flow rate [kg/s]

[P.sub.d] - Drive power [kW]

Z - TA cycle emission limit [g/kWh]

H - Hamiltonian function

p - Pressure [Pa]

em - Exhaust manifold

[theta] - Ammonia stored on SCR [g/l]

e - Error signal [g/kWh]

Satish Narayanan Ramachandran, Gillis Hommen, Paul Mentink, Xander Seykens, Frank Willems, and Frank Kupper

TNO Automotive

doi:10.4271/2016-01-0961
Table 1. Fluid prices

Fluid                       Price [[euro]/kg]

Fuel ([[pi].sub.fuel])            1.485
Adblue ([[pi].sub.asblue])        0.24

Table 2. Drive cycle specifications

Cycle  Average power on the cycle [kW]  General classification

WHTC                 28                     Type approval
RW-1                 45                         Urban

Table 3. Monte Carlo parameters and chosen bias values

Parameters                            Bias Values     Units

Adblue injector                       [+ or -]8    [%]
Temperature               Low range   [+ or -]5    [[degrees]C]
sensor (post DOC,
pre SCR and post          High range  [+ or -]10   [[degrees]C]
SCR)                      Threshold   280          [[degrees]C]
Exhaust pressure sensor               [+ or -]5    [kPa]
BPV actuator                          [+ or -]10   [%]
                          Low range   [+ or -]10   [ppm]
Tailpipe N[O.sub.x]
sensor                    High range  [+ or -]10   [%]
                          Threshold   100          [ppm]
Exhaust mass flow sensor              [+ or -]10   [%]

Table 4. Cycle results for Baseline and IEM control strategies

                                    WHTC
                       Baseline  IEM (fixed [[lambda].sub.3])

BSFC (%)                100                  99.61
Adblue (%)              100                 199.38
N[O.sub.x,eo] [g/kWh]     4.26                8.21
N[O.sub.x,tp] [g/kWh]     0.39                0.45
CF-ISC                  NA                    NA

                               Rea World - 1
                       Baseline  IEM (fixed [[lambda].sub.3)]

BSFC (%)               100                 99.74
Adblue (%)             100                137.42
N[O.sub.x,eo] [g/kWh]    5.08               6.49
N[O.sub.x,tp] [g/kWh]    0.29               0.16
CF-ISC                   0.87               0.70

Table 5. Cycle results for IEM with variable [lambda]3 compared with
baseline and old IEM strategies

                                 WHTC
                                IEM                IEM
               Baseline       (fixed            (variable
                         [[lambda].sub.3])  [[lambda].sub.3])

    BSFC        100             99.61              99.53
   Adblue       100            199.38             185.96
N[O.sub.x,eo]
   [g/kWh]        4.26           8.21               7.57
N[O.sub.x,tp]     0.39           0.45               0.36
   [g/kWh]
    CF-ISC       NA             NA                 NA

                              Fteal World -1
                         IEM                IEM
               Baseline  (fixed             (variable
                         [[lambda].sub.3])  [[lambda].sub.3])

    BSFC       100        99.74              99.81
   Adblue      100       137.42             140.39
N[O.sub.x,eo]
   [g/kWh]       5.08      6.49               6.65
N[O.sub.x,tp]    0.29      0.16               0.13
   [g/kWh]
   CF-ISC        0.87      0.70               0.43
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Author:Ramachandran, Satish Narayanan; Hommen, Gillis; Mentink, Paul; Seykens, Xander; Willems, Frank; Kupp
Publication:SAE International Journal of Engines
Article Type:Report
Date:Sep 1, 2016
Words:7332
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