Controlling GCAI (Gasoline Controlled Auto Ignition) in an Extended Operating Map

2012 Workshop on Engine and Powertrain Control, Simulation and Modeling The International Federation of Automatic Control Rueil-Malmaison, France, October 23-25, 2012

Controlling GCAI (Gasoline Controlled Auto Ignition) in an Extended Operating Map Thivaharan Albin ∗ Ren´ e Zweigel ∗ Frank Heßeler ∗ ∗∗ Bastian Morcinkowski Adrien Brassat ∗∗ Dirk Abel ∗ ∗ Institute of Automatic Control, Department of Mechanical Engineering, RWTH Aachen University, 52074 Aachen, Germany (corresponding e-mail: [email protected]). ∗∗ Institute for Combustion Engines, Department of Mechanical Engineering, RWTH Aachen University, 52062 Aachen, Germany (corresponding e-mail: [email protected]).

Abstract: The gasoline controlled autoignition (GCAI) is a modern combustion method with which the fuel consumption and the pollutant emissions can be reduced. The major drawback of the combustion method is the limited operating map. In this contribution it is shown how the operating map can be extended towards lower loads by the use of a spark plug for a spark-assisted GCAI combustion. Compared to the GCAI combustion, the spark plug is used additionally and the controller has to be adapted, such that the spark-assisted GCAI combustion is also considered. As controller a model-based predictive controller (MPC) is developed. In this contribution a special focus is set on the investigation of the underlying model for the MPC. Keywords: Controlled Auto Ignition, Internal Combustion Engine, System Identification, Rapid Control Prototyping, Model-Based Predictive Control 1. INTRODUCTION The main goal of the current development of powertrains with gasoline engines is set on the reduction of CO2 emissions while minimizing other pollutant emissions at the same time. A promising way for achieving these goals is the research on the combustion process. Especially combustion methods, characterized by a highly homogenized combustion and the absence of temperature peaks, which is achieved by Exhaust Gas Recirculation (EGR) show a high potential. Combustion methods with these characteristics are known under different equivalent acronyms, among these are Homogenous Charge Compression Ignition (HCCI) and Gasoline Controlled Auto Ignition (GCAI), which is the acronym used in the present contribution. Compared to the conventional stochiometric throttled operation, GCAI combustion allows a minimization of CO2 emissions by up to 30 % in part load operation (see Karrelmeyer (2009)). The advantages result from substantially less gas exchange losses (dethrottling due to the open throttle valve), optimized gas properties caused by the lean relative air-fuel ratio as well as the thermodynamic effective and quick fuel combustion. The combustion is initiated by the trapped residual gas of the previous cycle and ⋆ The authors gratefully acknowledge the contribution of the Collaborative Research Center 686 ’Model-based control of homogenized low-temperature combustion’ supported by the German Research Foundation (DFG) at RWTH Aachen University, Germany, and Bielefeld University, Germany, see www.sfb686.rwth-aachen.de for details.

978-3-902823-16-8/12/$20.00 © 2012 IFAC

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starts simultaneously at different spots in the combustion chamber. The NOX emissions can be lowered to the detection limit due to the resulting low-temperature combustion in the low part load. By using the GCAI combustion method, a possibility is given to achieve the consumption potential of stratified combustion methods available on the market without separate NOX aftertreatment. However, GCAI combustion requires a more complex process control than conventional gasoline combustion. In a conventional gasoline engine, the ignition is initiated by a spark plug which acts as a trigger to start the combustion. As for GCAI the combustion is started by autoignition, there is no direct trigger for start of combustion present anymore. The timing of autoignition depends on the thermodynamic state in the combustion chamber (Westbrook (2000)). Among others the thermodynamic state is defined by the global pressure and temperature level in the combustion chamber and the local stratification of the residual gas, local temperature and air-fuel ratio (Adomeit (2009)). Thus, the autoignition depends on the combustion in the previous cycle and is also very sensitive to factors like the engine speed or the cooling water temperature. Moreover, the combustion process is characterized by a strong nonlinear and unstable behavior: at the same load, higher rates of trapped exhaust gas result in larger maximum pressure rise gradients (DPMAX), which correlate with noise and higher stress on the components. In contrast to that, low residual gas rates can delay the combustion and lead to large standard deviations for the indicated mean effective pressure (IMEP) or it is even possible that no auto-ignition 10.3182/20121023-3-FR-4025.00050

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

Table 1. Characteristics of the Engine Cylinder Pressure (bar) Valve Lift (mm)

Data Bore Stroke Displacement volume Compression ratio Valves per cylinder Valve lift Injector

Combustion Chamber Recirculation

Value 84 mm 90 mm 0,499 dm3 12 4 8 mm Continental Piezo

is initiated. This is the reason why process control plays a vital role for the GCAI combustion: the task of the controller is to stabilize the process by influencing the fuelmixture generation and injection. Different control conepts have been published for the GCAI process, see e.g. Ravi (2012). The major drawback of the GCAI combustion process is that the applicable load range of the combustion process is limited. The limitations occur for low loads by means of the decreasing combustion stability due to the low enthalpy of the trapped exhaust gas (lower temperature of the residual gas under usually higher residual gas rates). For high loads, the operating map is either limited by an air efficiency which is too low or by the increasing pressure rise gradients and NOX emissions. In consequence, a special research challenge is the question how to extend this limited operating map. This contribution deals with the extension of the operating map in which the GCAI combustion can be operated by the process controller concerning the lower loads. The extension is realised by the use of a spark plug for a spark-assisted GCAI combustion (SAC). On top of the additional use of the spark plug, the controller has to be capable of handling the SAC and the GCAI combustion at the same time. As this control problem is a nonlinear multiple input multiple output (MIMO) control problem a model-based predictive controller (MPC) was chosen (see Bemporad (2006)). In this contribution, the emphasis lies on the investigation of the underlying control model for the MPC controller. The validation of the control algorithms is performed on a single-cylinder test engine. The test engine is a direct injecting single-cylinder gasoline engine with a fully variable electromechanical valve train (EMVT). The injector and the spark plug are located in the center of the roof of the combustion chamber. The applied piezo injector opens outwards; its high flow rate and a very short actuating time provide a wide span concerning the amount of injected fuel. Table 1 summarizes the essential technical features of the test engine. 2. MULTIVARIABLE CONTROL PROBLEM FOR EXTENSION OF THE OPERATING MAP As stated earlier, the problem with lower loads in the GCAI combustion is that the enthalpy of the trapped residual gas is lower than in higher loads as the exhaust gas has a lower temperature at usually higher residual gas rates. Through the lowered enthalpy, the combustion stability decreases and it is likely to happen, that no autoignition occurs. As the next combustion cycle depends on the hot residual gas of the previous cycle, in case of an ignition failure, it is no longer possible to run following cycles in the GCAI combustion. In consequence,

467

50 40 30 20 10

EVC

IVO

0 90

180

270

360

450

540

630

0

90

Crank Angle (°CA aTDC) Cylinder Pressure Valve Lift IV Valve Lift EV

Pre-injection Main-injection

Fig. 1. Actuated Signals for Combustion Chamber Recirculation a combustion has to be ensured for every cycle. In Zigler (2010), it is shown experimentally that an additional spark ignition leads to improved stability, especially in lower loads. This spark-assisted combustion (SAC) mode still shows good efficiency and low emissions. In Dahms (2010), the effect of spark-assist on the GCAI combustion is also simulated. With the SAC, a flame front is initiated by the spark plug, resulting in a heat release which increases the pressure and the temperature in the unburnt gas region, which initiates the auto-ignition process. In the following a control approach is shown for enlarging the operating map based on the idea of using the spark plug. The actuated and controlled variables are described along with the control structure. 2.1 Actuated Variables For enabling lower loads, the spark plug is used as an actuated variable. The influence of the spark timing on the crank angle of 50% released heat (the center of combustion) is not as high as the influence of the exhaust gas. Thus, the spark timing is set constant and only the choice ’on’ / ’off’ is actuated. The test engine is equipped with an EMVT, which offers a wide variability of valve control timing. The large amount of residual gas required for autoignition are supplied using the valve control strategy called combustion chamber recirculation (CCR). According to this strategy, the exhaust valve closes early and the trapped residual gas is compressed during the gas exchange TDC (top dead center). The valve control timings ’Exhaust Valve Opens’ (EVO) and ’Intake Valve Closes’ (IVC) are set constant. The valve control edges ’Exhaust Valve Closes’ (EVC) and ’Intake Valve Opens’ (IVO) are adjusted symmetrically to the gas exchange TDC (360◦ CA aT DC) (see Fig. 1). Due to this adjustment one degree of freedom UEV C results in terms of the actuated variables (see Hoffmann (2009)). This degree of freedom varies the negative valve overlap and, consequently, also the internal exhaust gas recirculation rate (EGR). If the EVC edge has been shifted late, the negative valve overlap is reduced and thus also the EGR is reduced. In addition to the valve control timing, also the injection is used for actuation in the control strategy. The early closing of the exhaust valve offers substantial degrees of

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

freedom for the calibration of various injection strategies. In the selected approach, the combustion is calibrated by a double injection. A small amount of fuel is injected into the hot residual gas before the gas exchange TDC, which has a significant effect on the combustion phasing. The amount of pre-injection UDOI1 acts as an additional actuating variable for the controller. The amount of the main-injection UDOI2 is used as the fourth actuating variable. The crank angle at which the pre-injection and main injection are started are kept constant independently of load and speed. 2.2 Controlled Variables The main task of the controller is to provide the torque desired by the driver, which is taken into account as a controlled variable in terms of the indicated mean effective pressure (YIM EP ). Besides the value for IMEP, also the center of combustion (YCA50 ) is controlled. An optimal center of combustion is necessary to obtain a good efficiency and thus low CO2 emissions. The optimal CA50 value for the GCAI combustion is defined by the engine load and speed. The desired CA50 value moves from the higher engine part load (8◦ CA aT DC) to earlier center of combustions (1◦ CA aT DC) with decreasing engine load and increasing engine speed. The third controlled variable is the maximum pressure rise gradient (YDP M AX ) which correlates with noise emissions and mechanical stress on the components. For YDP M AX , an upper limit value of 5 bar/◦ CA is defined which corresponds to an acceptable amount of noise emissions. During operation YDP M AX should not exceed this limit and thus has to be considered as a constraint in the controller. To determine the three controlled variables, online analysis of the cylinder pressure signal is performed cycle-resolved. Fig. 2 gives an overview of the employed actuating and controlled variables. For the GCAI combustion three actuating variables influence three controlled variables which causes a coupled multivariable control problem. In the case of SAC this structure is even extended towards four actuated variables.

combustion parameters increases substantially, even with the use of a feedback controller. The increase in the standard deviation goes along with a decrease concerning the stability margins, which poses a problem especially for transient operation. Thus, it makes sense to use the spark plug below this threshold in order to gain more combustion stability. It has to be mentioned that above the threshold (which is equal to the GCAI operating map) the spark plug has no advantage and thus it is shut off. In order to prevent chattering between the control signal ’on’ and ’off’, a hysteresis has been added around the threshold. In both cases, the SAC and the GCAI, the remaining three actuated variables have to track the reference values for YIM EP and YCA50 and try to keep YDP M AX below a certain threshold. For this task, a model-based predictive controller (MPC) along with a Kalman-Filter (see Grewal (2008)) is used. The MPC is based on a model of the process to be controlled. This process model predicts the process outputs over a finite prediction horizon of length Hp . This prediction is used as a basis for the solution of a finite horizon open-loop optimization problem. By minimizing a cost function subject to constraints, the MPC algorithm computes an optimal control step sequence at discrete time instants k with k ∈ 0, 1, 2, ...: ∆U∗(k|k) ....∆U∗(k+Hu −1|k) . Here Hu denotes the length of the control horizon and (·)(k+j|k) the prediction of the variable (·) for time k + j at time k. Now, the task of the controller is to minimize the cost function in each timestep. After optimization, only the first control signals are applied to the system: U(k) = U(k − 1) + ∆U∗(k|k) . The optimization problem is solved in each sampling step. In the given control problem one sampling step correlates to one combustion cycle. In the following sampling step a new optimization problem is calculated over a receding prediction horizon. Hence for realising real-time capability the optimization problem has to be solved within one sampling step respectively one combustion cycle. The described strategy implements a feedback control law which enables setpoint tracking and the rejection of disturbances (see Rawlings (2009)).

2.3 The Control Structure Engine Speed

To control the GCAI process, the structure presented in Fig. 3 is employed, which is explained in the following more in detail. In experiments it was evaluated that below a threshold of YIM EP = 2.3 bar the standard deviation for characteristic

UDOI1 UDOI2 UEVC

(Spark-Assisted) GCAI-Combustion

Reference Value

SI

IMEP

SI

SI Kalman-Filter & MPC Optimization

YIMEP YCA50 YDPMAX

(USI)

Fig. 2. In- and Outputs for the GCAI Combustion Process and for the Spark-Assisted GCAI Combustion Process

468

Fig. 3. Control Structure

DOI1 DOI2 EVC

GCAI Combustion

IMEP

IMEP CA50 DPMAX

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

u1 U1,op2 U1,limit Up1

1

2

main static and dynamic behavior of the process. On the one hand, a simpler model usually also results in a simpler optimization program which has to be solved online during operation. On the other hand, as the controller relies very much on the used process model, it is crucial that the model is as general as possible, which correlates with the simplicity of the model. Thus in the following nonlinear models with reasonably low complexity are compared to linear models. First of all the effect of the SAC and GCAI is investigated for constant speed. Afterwards the effect of the SAC and GCAI is investigated for varying engine speed.

3

U1,op1 U1,limit Lo1

t u2 U2,op2 U2,limit Up1 U2,op1

3.1 Model for Constant Engine Speed

U2,limit Lo1

t Fig. 4. Measurement Program for System Identification, Example for two Actuated Variables The cost function takes the following into account: deviations of the controlled variables Y from the setpoints Yref and the change of actuator signals U against the predicted steady state values USS (see Rawlings (2009)). This optimization task for the MPC algorithm is subject to constraints. By using the contraints the actuation limits can be considered, which arise from the physical limits of the actuators. One example is the minimal and maximal possible fuel injection applicable by the injector. Moreover, the maximum pressure rise gradient YDP M AX is also considered in the constraints. The controller tries to keep YDP M AX below a definable limit value YDP M AX,limit . 3. PROCESS MODELLING An essential element of a MPC controller is the process model. Within the approach followed in this contribution, a dynamic data driven model is used, which is generated by means of process identification. The process identification is based on measurements of the input to output behavior of the process. Multiple measurements were taken at different speeds and loads at the engine test bench described in section 1. A scheme of the measuring program is depicted in Fig. 4. The measuring program is divided into three parts, where the related outputs are always measured synchronously to the inputs for every cycle. In the first part, based on the operating point, for one speed and load the actuated variables in the measuring program are adjusted quasistatic. This gives insight about the static behavior of the process. In the second part, based on the operating point Uop , the actuated variables are adjusted stepwise to the limits, where a stable operation is still possible. This gives inside about the dynamic behavior of the process. In the third part, the actuated variables are adjusted from one operating point (Uop,1 ) to another (Uop,2 ), which also gives inside about the dynamic behavior of the process. In the first and second part just one single actuated variable is modified at a time, while the others are kept constant. The sequence is repeated for every actuated variable independently. In the third part all actuating variables are changed at the same time. It is desirable that the model used in the MPC is as simple as possible, while still being able to capture the

469

The MPC controller relies on a model which captures the relation between UDOI1 , UDOI2 , UEV C and the outputs YIM EP , YCA50 , YDP M AX for the GCAI and the SAC combustion. In Albin (2011) the modelling for the GCAI operating map is described. It is stated that for constant engine speed an affine model is sufficient. In the following it is investigated how the model has to look like for the SAC combustion. For reproducing the process behavior two different models are compared to each other. The parameters of the described models were estimated with the System Identification Toolbox from Matlab. The models are built up, such that the matrices A and B represent the dynamic behavior of the model. In steady state the state equals the input: XSS = U . The matrix C and the affine term f represent the static behavior of the model. The first model is an affine state space model in the form of (1)-(2). In the following it is called affine model. In this case, one affine model is used for reproducing the SAC and the GCAI operating map at the same time. Thus, the measurement data of the SAC and the GCAI operating map are both used to identify one model, where the parameters are constant over the whole operating map. X(k + 1) = A · X(k) + B · U(k) Y(k) = C · X(k) + f

(1) (2)

As second model a linear model is investigated, where the parameters are varied depending on the recent operating map (SAC vs. GCAI). The difference in the operating maps correlate with the use of the spark plug (USI ) and respectively the load. In the following it is called load dependent model. In this case one affine state space model is built for the SAC and respectively one for the GCAI operating map. In consequence, for the SAC model the measurement data of the SAC operating map is used and analog the same holds for the GCAI model. The measurement data has shown, that the dynamics can be assumed to be constant over the GCAI and the SAC operating map. Thus, the matrix A and B are not varied in dependence of USI . For consideration of the different static behavior a separate Matrix C and affine term f are used. X(k + 1) = A · X(k) + B · U(k) Y(k) =



CGCAI · X(k) + fGCAI , CSAC · X(k) + fSAC ,

USI = 0 USI = 1

(3) (4)

In Fig. 5 measurement data is depicted along with the simulated data of the load dependent model and the

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

3.2 Model for Varying Engine Speed

Table 2. RMSE of YIM EP (bar) of the Affine and Load Dependent Model Actuated Variable

Affine Model

Load Dependent Model

UDOI1 UDOI2 UEV C

0.109 0.070 0.051

0.045 0.050 0.017

Load Dependent Model Measurement Data

In the following, the reproduction of the process behavior for varying engine speeds is investigated. Two different models are compared to each other. The first model is constant with respect to a change in the engine speed, it is called speedconstant model. The same equations as in (3) to (4) are used. The difference is that now the model is built out of measurement data taken for the engine speeds n1 = 1500 1/min, n2 = 2000 1/min and n3 = 2500 1/min. Thus, one set of parameters is used over the whole operating map concerning the engine speed.

Affine Model

IMEP (bar)

1.4

As second model a model is used in which the parameters now also depend on the engine speed. Concerning the engine speed, it is linear parameter varying with an affine term, it is called parameter varying model in the following. In this case, the matrix C and the affine term f now also depend on the engine speed (5)-(6). Examinations have shown that the matrices A and B, which are responsible for the dynamic behaviour can be viewed as constant in a good approximation, since the measurement data does not show strong variations of dynamics over the characteristic map.

1.3 1.2 1.1 1 95

100

105

110

DOI 1 (μs) 1.8

IMEP (bar)

1.6 1.4

X(k + 1) = A · X(k) + B · U(k)

1.2 1 185

Y(k) = 190

195

200

205

210

215

220

225



CGCAI (n) · X(k) + fGCAI (n), CSAC (n) · X(k) + fSAC (n),

USI = 0 USI = 1

(5) (6)

DOI 2 (μs)

To define the engine speed dependent parameters of the matrix C and the affine term f , single affine state space models were identified respectively for the engine speeds n1 = 1500 1/min, n2 = 2000 1/min and n3 = 2500 1/min. For engine speeds between these three points, the model parameters are interpolated linearly. The engine speeds n1 and n3 mark the outer limits of the applicable operating map of the GCAI and SAC combustion process and thus no extrapolation is necessary. In (7) the equations for calculating C(n) are given.

1.35

IMEP (bar)

1.3 1.25 1.2 1.15 255

260

265

EVC (°CA aTDC)

Fig. 5. YIM EP Measurements Along With Model Outputs for the Affine and the Load Dependent Model C(n) =

affine model. In the figure three different cases are shown: influence of DOI1, DOI2 and EVC on IMEP. In each case, the other actuated variables are kept constant. The different measurement points are determined by averaging a larger data set with same actuated variables. The affine model does not seem appropriate as control model: It predicts a decrease of IMEP with increasing DOI 1 but the measurement data shows an increase of IMEP while DOI 1 increases. In the case of EVC the simulated IMEP for the affine model shows an offset compared to the measurement data. In contrast to that the load dependent model reproduces the measurement data better. In all three cases a good quantitative and qualitative accordance is given. The Root-Mean-Square Error (RMSE) can be used as a benchmark for comparison, it is given in Table 2. All in all the load dependent model is better suited for the purpose of control modelling. Thus, the following models build up on the load dependent model and the affine model is neglected.

470

 n − 1500 2000 − n  · C(2000) + · C(1500),   500  500 n ∈ [1500, 2000]

n − 2000 2500 − n  · C(2500) + · C(2000),   500  500

(7)

n ∈]2000, 2500]

The affine term f (n) is calculated in an analog manner as follows:  n − 1500 2000 − n  · f (2000) + · f (1500),   500 500  f (n) =

n ∈ [1500, 2000]

n − 2000 2500 − n  · f (2500) + · f (2000),   500  500

(8)

n ∈]2000, 2500]

Fig. 6 shows the difference in reproduction of measurement data from the speedconstant model and the parameter varying model at the engine speed n3 = 2500 1/min. Once again, in the figure three different cases are shown: the influence of DOI1, DOI2 and EVC on IMEP. In each case, the other actuated variables are kept constant. For reproducing the measurement data, the parameter varying

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

Table 3. RMSE of YIM EP (bar) of the Speedconstant and Parameter Varying Model Speedconstant

Parameter Var. Model

UDOI1 UDOI2 UEV C

0.0820 0.139 0.049

0.0153 0.0607 0.012

2.5

IMEP (bar)

Actuated Variable

2 1.5

Parameter Varying Model Measurement Data Speedconstant Model CA50 (°CA aTDC)

10

1.45

IMEP (bar)

Parameter Varying Model

Measurement Data

1.4 1.35

5

0

1.3 1.25 92

4

94

96

98

100

102

104

DPMAX (bar/°CA)

DOI 1 (μs) 1.7

1.5

265

1.4

EVC (°CA aTDC)

IMEP (bar)

1.6

1.3 195

2

200

205

210

215

220

225

230

260

Actuated Signal

255

DOI 2 (μs) 250

1.4

100

1.3

DOI 1 (μs)

IMEP (bar)

1.35

1.25

80

1.2 1.15 254

256

258

260

262

264

EVC (°CA aTDC)

Fig. 6. YIM EP Measurements Along With Model Outputs for the Speedconstant and the Parameter Varying Model model is more suitable than the speedconstant model. Especially the effect of the actuating variables on the output in terms of the gradient is captured much better with the parameter varying model than with the speedconstant model, as for the influence of EVC on IMEP. For the example shown in Fig. 6 the RMSE are given in Table 3. The effect of the two different models on the closed loop behavior is investigated in section 4 through experiments at the engine test bench. The parameter varying model is not only capable of reproducing the process behavior at the engine speeds n1 = 1500 1/min, n2 = 2000 1/min and n3 = 2500 1/min, where measurements were taken for the reason of identification. Measurement data has shown, that the model can also reproduce the process behavior at engine speeds, at which no measurement data was used for the identification. Thus, the linear interpolation is justifiable. In Fig. 7 the time response on the actuated signal is depicted along with the simulated data from the parameter varying model. All three actuated variables are varied in

471

DOI 2 (μs)

350

300

250 0

100

200

300

400

500

600

time (s)

Fig. 7. Measurement Data Along With the Parameter Varying Model Output for n = 1500 1/min a quasi-static and in a stepwise manner, starting from the operating point at t = 0s. The process behavior of the SAC can be reproduced well by the parameter varying model. Nevertheless the validity of the model is only given close to the operating points. In the figure it can be seen that the model validity decreases by distancing from the operating point (given at t = 0s). 4. CONTROL RESULT FOR SPARK-ASSISTED GCAI COMBUSTION The control concept introduced in this article was implemented in Matlab/Simulink. As QP solver, qpdantz was used, which is part of Matlab/Simulink. The controller was validated on the single-cylinder engine test bench, de-

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

5 4

IMEP (bar)

Fig. 8 presents the experimental results of the controller from the engine test bench at the constant speed n = 2500 1/min. In this case the speedconstant model is used, where the parameters do not depend on the engine speed but on the load. In Fig. 8, the setpoint and measured values for YIM EP and YCA50 are depicted. The closed loop system is not stable. At time t = 95.1s the engine shuts down. There exists one cycle where the controller is not able to ensure a combustion. In the following cycle the hot residual gas of the previous cycle is missing for initiating the auto ignition process and thus the engine process can not be maintained anymore. Moreover at time t = 31.5s and t = 37.8s there also exist cycles with poor combustion, in consequence the controller can track the reference signal only with high tracking errors. The instability arises already in the case of constant engine speed. For varying engine the speed the control performance is even worse.

Reference Value

Measurement Data

Engine Off

3 2 1

CA50 (°CA aTDC)

0 20 15 10 5 0 -5

Engine Speed (1/min)

DPMAX (bar/°CA)

8

DPMAXlimit

6 4

0 3000 2000 1000 1

SI (-)

Fig. 9 presents the experimental results of the controller from the engine test bench for varying engine speed. In this case the parameter varying model is used, where the parameters depend on the engine speed and on the load. In the figure, the setpoint and measured values for YIM EP and YCA50 are depicted. The experimental results show that the engine is running during the whole test and no ignition failure occurs. Thus, the controller is capable of stabilizing the process during the given load and speed transients. On top the controller is able to track the setpoints offset free and with fast dynamics. Even if the setpoints change with fast dynamics, the controller can still track the setpoints for both controlled variables at the same time with high control performance. Special attention should be paid to the fact that the tracking is possible although the engine speed varies continously during the test. The engine speed acts as a disturbance on the controller. By adapting the recent model in dependence of the engine speed and the spark plug actuation, it is nevertheless possible to track the reference values. The switching between the GCAI and SAC operating map happens without any noticable effect on the controlled variables. Moreover, it can be seen in the experimental results that taking into account YDP M AX in the cost function helps to minimize the exceeding of the limit value of YDP M AX which was set to YDP M AX = 5 bar/◦ CA in this case. In Fig. 9, also the three acuated variables UEV C , UDOI1 and UDOI2 are shown.

2

Actuated Signal

0.5 0

EVC (°CA aTDC)

300 290 280 270 260

DOI 1 (μs)

120 100 80 60 40 20

DOI 2 (μs)

600 500 400 300 200 100

0

10

20

30

40

50

60

70

80

90

100

time (s)

Fig. 8. Closed Loop Control Result Based on the Speedconstant Model scribed in section 1. A dSpace MicroAutoBox was used as Rapid Control Prototyping hardware for controller tests. The C-code for the target platform was generated automatically with the Realtime-Workshop. A second dSpace MicroAutoBox is used for the calculation of IMEP, CA50, and DPMAX from the pressure trace signal in every cycle, along with a RapidPro Unit it also serves as a tailor-made ECU for actuating the injection, valve timing and spark plug. In the following, the control results gained at the engine test bench for the load extension using the spark plug are presented.

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It can be concluded that a single affine model or the speedconstant model are not appropriate for extending the GCAI process towards lower loads with the additional spark plug. If a parameter varying model is used for a model-based control approach, the experiments show a stable closed loop behavior. In consequence, the operating map of the GCAI combustion can be extended towards lower limits. In Fig. 10 the operating map for the GCAI and the SAC operating map are shown. It can be seen that the operating map can be substantially extended by the additional use of the spark plug. 5. CONCLUSION In this paper, a control approach for the Gasoline Controlled Auto Ignition process was presented. A special focus was set on extending the operating map towards

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

Measurement Data

IMEP (bar)

Reference Value

5

GCAI Spark-Assisted GCAI

IMEP (bar)

4 3

4.6 4.0

2 1

CA50 (°CA aTDC)

0

2.3

20 15 10

0.7

5 0

Engine Speed (1/min)

DPMAX (bar/°CA)

8

Fig. 10. Operating Map of the GCAI and the SparkAssisted GCAI Combustion Mode control performance, even when the speed varies. Thus it is possible to enlarge the operating map towards lower loads.

DPMAXlimit

6 4 2 0 3000

REFERENCES

2000 1000

SI (-)

1

Actuated Signal

0.5 0

EVC (°CA aTDC)

300 290 280 270 260 250

DOI 1 (μs)

120 100 80 60 600

DOI 2 (μs)

500 400 300 200 100

2500

1500

-5

Speed (1/min)

0

50

100

150

200

250

time (s)

Fig. 9. Closed Loop Control Result Based on the Parameter Varying Model lower loads. A spark plug is used in lower loads to initiate a spark-assisted GCAI combustion. In order to control the process, a model-based predictive controller is developed. Different models were compared to each other for the purpose of the underlying control model of the MPC. A linear parameter varying model has shown to capture the nonlinear behavior of the process very well while still being relatively simple. Experimental results, gained at an engine test bench, show that the MPC controller based on the parameter varying model is able to stabilize the process and track the desired combustion values with good

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P. Adomeit et al. Operation Strategies for Controlled Auto Ignition Gasoline Engines. SAE, 2009-01-0300, 2009. T. Albin et al. Modellbasierte Optimalregelung der ottomotorischen kontrollierten Selbstzuendung (GCAI) mit variablem Ventiltrieb und Mehrfacheinspritzung VDI AutoREG, 2011. A. Bemporad. Model Predictive Control Design: New Trends and Tools Proceedings of the 45th IEEE CDC, pp. 6678 - 6683, 2006. R. Dahms et al. Detailed chemistry flamelet modeling of mixed-mode combustion in spark-assisted HCCI engines. Proceedings of the Combustion Institute, Vol. 33, pp. 3023 - 3030, 2011. M. S. Grewal and A. P. Andrews. Kalman Filtering: Theory and Practice using Matlab. John Wiley & Sons, 2008. K. Hoffmann and D. Abel. Non-linear Model-based Predictive Control with Constraints for Controlled AutoIgnition. E-COSM09 IFAC Workshop on Engine and Powertrain Control, Simulation and Modeling, 2009. R. Karrelmeyer et al. Strategien zur Regelung von HCCIBrennverfahren. AT - Automatisierungstechnik, Vol. 57, 2009. N. Ravi Model predictive control of HCCI using variable valve actuation and fuel injection. Control Engineering Practice, Vol. 20, pp. 421 - 430, 2012. J. B. Rawlings and D. Q. Mayne Model Predictive Control: Theory and Design. Nob Hill Publishing, 2009. C. K. Westbrook. Chemical kinetics of hydrocarbon ignition in practical combustion systems. Proceedings of the Combustion Institute, Vol. 28, pp. 1563 - 1577, 2000. B. T. Zigler et al. An experimental investigation of the sensitivity of the ignition and combustion properties of a single-cylinder research engine to spark-assisted HCCI. International Journal of Engine Research, Vol. 12, pp. 353 - 375, 2010.