FUZZY CONTROLLER OF THE AIR SYSTEM OF A DIESEL ENGINE

FUZZY CONTROLLER OF THE AIR SYSTEM OF A DIESEL ENGINE Jean-Fran¸ cois ARNOLD ∗ Nicolas LANGLOIS ∗∗ Houcine CHAFOUK ∗∗ G´ erard TREMOULIERE ∗ ∗

Le Moteur Moderne, 5-9 rue Benoit Frachon 91127 Palaiseau, France ∗∗ IRSEEM-ESIGELEC, Technˆ opole du Madrillet 76801 St-Etienne du Rouvray, France

Abstract: A new strategy based on a fuzzy multi-variable controller is proposed to regulate both the fresh airflow and the intake manifold pressure. The air system controller requires neither an internal model nor certain feed-forward maps. Taking only into account standard engine measurements, it is intrinsically robust and very easy to tune with respect to the PID strategy embedded in the electronic control unit of standard cars. A part of speed trajectory defined by the Euro 5 standard c has been simulated to compare the both strategies. Copyright °2006 IFAC Keywords: Diesel engine, EGR, VGT, fuzzy controller, multi-variable controller.

1. INTRODUCTION The reduction of polluting exhaust emissions imposed by legislation such as Euro V (Transport and Federation, 2004) (Umweltbundesamt, 2003), the improvement of engine performance and the complexity of present automotive applications du to the introduction of certain components made more and more necessary the use of high performance control systems. Techniques such as exhaust gas recirculation and turbocharging have been devised to face the stringent requirements. They give a great deal of freedom to control the behavior of the engine. On the one hand conventional strategies often resort to treating these devices independently as Single-Input, Single-Output systems, thereby ignoring the coupled nature of these two devices (Guzzella and Amstutz, 1998). On the other hand the multi-variable strategies in the literature often resort to treating these devices incompletely, without considering all actuators, or using modelbased controllers (Shirawaka et al., 2001) (Watson

and Bnaisoleiman, 1988) (Ammann et al., 2003) (Bai and Yang, 2002). Since a complete modelbased controller calibration is unrealistic with the present state of the art, and on-vehicle tuning cannot be bypassed, these multi-variable strategies come at the cost of a larger number of controller gains to tune. Starting from these assumptions, a new strategy based on a multi-variable fuzzy controller is proposed. The section 2 presents the considered air system. Then, the standard embedded controller and the strategies in the literature are presented respectively in sections 3 and 4. In the section 5, the proposed fuzzy multi-variable controller is presented and its results compared to the current embedded strategy results.

2. AIR SYSTEM OF A DIESEL ENGINE In this paper, a diesel engine equipped with a variable geometry turbine (VGT) and an external exhaust gas recirculation system is considered.

Fig. 2. Standard control strategy Fig. 1. Diesel engine air system The engine is shown schematically in figure 1. The turbine converts the energy of the exhaust gas into the mechanical energy of the rotating turboshaft, which, in turn, drives the compressor. The compressor increases the density of air supplied to the engine. This larger mass of fresh air can be burned with a larger quantity of fuel thereby resulting in a larger output torque. By varying the stagger angle of the turbine stator blades, it is possible to act on the mass flow rate of the exhaust gas through the turbine (acting indirectly on exhaust manifold pressure) thereby acting on the power generated by the turbine (Moody, 1986). To reduce the emissions of harmful nitrogen oxides (NOx) a portion of the exhaust gas can be diverted back to the intake manifold to dilute the air supplied by the compressor. This process is referred to as exhaust gas recirculation (EGR). It is accomplished with an EGR valve that connects the intake manifold to the exhaust manifold. In the cylinders the recirculated exhaust gas act as inert gas thus lowering the flame temperature and, hence decreasing the formation of NOx. Our diesel engine air system includes an EGR throttle between the compressor and the intake manifold to create a variable pressure drop through the EGR valve, thereby increasing the EGR rates (Stefanopoulou et al., 2000). In this paper, the simultaneous control of the EGR valve, the EGR throttle and the VGT is investigated.

3. STANDARD CONTROL STRATEGY The standard control strategy for VGT and EGR systems uses the Proportional + Integral + Derivative control structure with a feed-forward term as illustrated in figure 2. Although the EGR-VGT plant is highly coupled, it is regulated by two Single-Input, Single-Output

loops. The pressure in intake manifold (MAP) is used as a feedback for the VGT vane control. The fresh airflow is measured upstream of the compressor and is used to close the loop on the EGR system. The output of the EGR’s PID is divided into the EGR valve demand and the EGR throttle demand. The setpoints for these two controllers are derived from extensive engine mapping, involving the sweeping of VGT vane and EGR system positions at fixed engine speed and fuelling inputs to determine the optimum settings with respect to emissions, fuel consumption, driveability, etc. From pre-positioning values, the controller drives the actuators as close as possible to the positions required to attain the desired fresh airflow and boost pressure. The open-loop term can never guarantee accurate setpoint tracking due to the engine variability, aging and driving environment. The closed-loop is used to ensure that the position converges upon the setpoint. The response of boost pressure and airflow to the VGT and EGR system varies with engine operating points, therefore gain scheduling is employed extensively.

4. LITERATURE OVERVIEW To improve the tracking of the two setpoints, new strategies have been presented in recent years.

4.1 Strategies based on a GPC controller The Generalized Predictive Controller (GPC) has attracted attention from both industry and academia alike. In fact the GPC permits us to obtain great precision in steady state and in transient mode. The GPC consists in computing the optimal control signal from a cost function taking the predicted tracking error and other auxiliary performance measurements into account. The cost function used by the GPC is shown below:

JGP C (k) =

N2 X

(wk+i − yˆk+i )2 + λ

i=N1

NX u −1

∆u2i+1 (1)

i=0

where w are the future setpoint values. yˆ are the predicted process outputs, ∆u the future control change. λ is the weighting on control moves. N1 and N2 define the horizon of prediction. Nu is the control horizon. The GPC algorithm provides good results but lacks robustness. The natural evolution of the engine (burn-in, abrasive wear, deposit, failure, etc.) changes the parameters of model equations. These changes are not always supported by the GPC algorithm generating most of the time undesired oscillations.

Such parameter identification cannot be applied to standard engines. Another way to estimate parameter values consists in using embedded identification algorithms (Zito and Landau, 2005) (OuenouGame et al., 1998). In regards to the current high occupation rate of embedded electronics control unit, these algorithms cannot be supported in terms of calculation power (Arnold et al., 2005). To solve both problems, a strategy computed without a model and with a very low calculation need should be provided. To meet these requirements, a fuzzy multi-variable controller is proposed in this paper.

5. THE FUZZY MULTI-VARIABLE CONTROLLER

4.2 Strategies based on a robust controller The problem of high actuator variability and low sensor precision can be solved by using a robust controller. Lots of strategies exist but only a few have been tested on a diesel engine (Jung, 2003). The way to deal with robust stability and performance in the framework of H∞ robust control is to minimize the H∞ norm of certain transfer functions. The plant H(s) can be written as: µ ¶ µ ¶ · ¸µ ¶ e w H11 (s) H12 (s) w = H(s) = (2) y u H21 (s) H22 (s) u where e is the error. The optimal H∞ standard problem is for a given H(s) to find K(p) that stabilizes the system and to minimize kG(P, K)k∞ . For the suboptimal problem, this condition is written as follows: kG(P, K)k∞ < γ

(3)

where kG(P, K)k = kH11 + H12 K(I − H22 K)−1 H21 k(4) Despite improved robustness, strategies based on this controller provide lower performance than strategies based on GPC.

4.3 Strategy Applicability Because these two controllers are model-based, they require engine modelling and parameter identification. Both steps are complex and timeconsuming (about 3 months on a test bed). Unfortunately, the high value variability of engine parameters makes necessary, in the ideal case, an individual identification for each produced engine.

The study of predictive controllers and robust controllers shows behavioral similarities in their control signals even if these signals differ in their amplitude (Wijetunge et al., 2000): • At low engine speed, when the fresh airflow is insufficient, it is necessary to increase the intake manifold pressure (by closing the VGT) and to open the throttle. • At high engine speed, the fresh airflow is regulated only by the EGR valve. • At high engine speed, the intake manifold pressure is regulated by acting on the VGT. The goal of the proposed fuzzy controller is to bring about such behavior. The inputs of this controller are: • • • •

the the the the

error in intake manifold pressure error in fresh airflow engine speed injected fuel quantity

This choice is made using the available measurements on a standard engine. To these inputs, it is proposed to take into account the integral of fresh airflow error as well.

5.1 Input classes Cumulative correction on the throttle and on the EGR valve makes the fresh airflow oscillate. To prevent these oscillations, the integral of fresh airflow error is used to determine two operating areas as in split range strategies (figure 3.3): In the first area, corrections are made only on the throttle and the EGR valve is totally open. The corresponding class is called ”EGR-open” In the second area, corrections are made only on the EGR valve. The throttle is totally open. The corresponding class is called ’EGR-variable’.

• if integral MAF is EGR-variable then throttle positive • if integral MAF is EGR-open then EGR positive • if MAF is null and integral MAF is EGRvariable then EGR null • if MAF is positive and integral MAF is EGRvariable then EGR negative • if MAF is negative and integral MAF is EGRvariable then EGR positive • if MAF is null and integral MAF is EGRopen then throttle null • if MAF is negative and integral MAF is EGRopen then throttle positive • if MAF is positive and integral MAF is EGRopen then throttle negative • if MAF is positive and engine speed is low and fuelling is low then VGT positive • if MAF is negative and engine speed is low and fuelling is high then VGT negative • if MAF is null and engine speed is low and fuelling is low then VGT null • if MAP is negative and fuelling is high or if MAP is negative and engine speed is high then VGT positive • if MAP is positive and fuelling is high or if MAP is negative and engine speed is high then VGT negative • if MAP is null and fuelling is high or if MAP is negative and engine speed is high then VGT null

Fig. 3. Input class of controller inputs

5.4 Eliminating feed-forward maps

The fuzzification of engine speed and fuelling is done according to two classes: high and low. The error in fresh airflow and intake manifold pressure is done conventionally with three classes: negative, null and positive. 5.2 Output values The different output values characterize the correction given on the pre-positioning values. To cover a large range of operating points, the maximum values and thereby the output values are -100%, 0, and +100% named negative, null and positive respectively. The outputs of the fuzzy controller are the control signals of the EGR valve, of the throttle and of the VGT, named EGR, throttle and VGT respectively. 5.3 Rules The rules determine the controller behavior . The chosen rules are:

Fig. 4. New input integral classes As shown in figure 2, PID-based strategies require feed forward maps to control the air system: these maps set an actuator pre-position. Up to now, their tuning has been carried out by testing a set of values for each operating point. Such a method takes time. In fact interferences between the EGR system and the VGT imply numerous tests to obtain the best map values. So, to improve the presented fuzzy controller, it is proposed to by-pass the EGR system feed-forward maps. The idea is to obtain a primary actuator position based exclusively on the airflow error integral values and to correct this position thanks to the instantaneous error values.

1800

1600

1400

1200

1000

800

600

11

12

13

14

15

16

17

Fig. 5. Engine shaft speed versus time (s)

Fig. 8. Zoom on pressure evolution for different parametric modifications

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• if integral is throttle-position then throttle is closed • if integral is EGR-position then EGR is closed

0

6. RESULTS

−100

11

12

13

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Fig. 6. Mass airflow error versus time (s)

• the engine shaft speed (figure 5) • the error between the desired fresh air setpoint and the flow Wc1 calculated by the model (figure 7). A 100% value corresponds to a relative error of 100% between the setpoint and the measurement • the error between the desired intake manifold pressure and the pressure calculated by the model (figure 6)

150

100

50

0

−50

−100

−150

11

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Simulations have been done on a validated engine model (Arnold et al., 2005). The used trajectories is the first part of the standard trajectory defined for the Euro norm. For the proposed strategy and the PID-based strategy, the following are plotted:

17

Fig. 7. Intake manifold pressure versus time (s)

More precisely, when the integral is low, the correction is made by acting on the throttle and the EGR valve is fully open. It is proposed to use the integral values not only to determine on which actuator the correction is made, but also to determine the position of this actuator. To do this, two new classes are considered to characterize the integral values (figure 4). Moreover, two new values for the EGR and the throttle output classes are considered. The default value is open (or 100%) whereas the closed position is 0%. Finally, the supplementary rules are:

In these figures, the dot curve is the response obtained with the PID controller. The set of PID parameters used has been experimentally optimized on a test bed to ensure the best controller stability and robustness achieved up to now. As shown in these figures, the time response of fresh airflow has been considerably reduced and higher accuracy is obtained thanks to the proposed strategy. Moreover, overshoots are reduced in a significant way. The error in intake manifold pressure decreases compared to PID-based strategy results. In transient mode, the reduction of the time response should consequently decrease the polluting emissions (Guzzella and Amstutz, 1998). The observed oscillations at idle speed have the same order of magnitude as the measurement noise observed on these values. This point should be solved in further work.

Because of the lack of theoretical methods suited to such complex system (Cuesta et al., 1999), the controller robustness has been observed in simulation by introducing some parametric variations into the engine model. The parameter modifications considered correspond to the variabilities generally encountered on the engine. They deal with: • • • •

VGT winglet position Engine volumetric efficiency throttle clogging EGR valve clogging

In figure 8, the intake manifold pressure is plotted taking into account the worse variability values encountered in a full engine series. According to these simulation results, the desired robustness has been reached.

7. CONCLUSION In this article, a fuzzy multi-variable controller is presented. This controller allows the simultaneous regulation of both fresh airflow and intake manifold pressure without using an internal model of the air system. Its structural simplicity distinguishes it from predictive and robust controller strategies, currently inapplicable in standard cars. The use of the integral makes it possible to remove the feed-forward maps of the EGR system. In comparison to the current PID-based embedded strategy, a significant improvement in desired setpoint tracking and in time response is obtained when simulating the European urban cycle. This controller will now be implemented in an ECU and tested on an engine test bed in order to validate its performance.

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