THIESEL 2006 Conference on Thermo- and Fluid Dynamic Processes in Diesel Engines

Improving the Engine Transient Performance using Model-based Predictive Control

Martin Florián1, Jan Macek1, Miloš Polášek1, Pavel Steinbauer1, Zbyněk Šika1, Michal Takats1, Ondřej Vaculín1, Michael Valášek1, Jiří Vávra1, Oldřich Vítek1 and Vít Doleček1

1Czech Technical University in Prague, Josef Bozek Research Center. Technicka 4, CZ-166 07 Praha 6, Czech republic.

E-mail: polasekm@fsid.cvut.cz Telephone: +(420) 224 352 492 Fax: +(420) 224 352 500

Abstract. The paper deals with a model-based predictive control of a DI diesel engine equipped with Variable Geometry Turbine (VGT). The work is based on an integrated approach combining experiments and simulation tools of different levels. The formulation of a real-time engine model is the essential part of the work. The model and way how to employ experimental data is described in details in the paper. The steady state measurements on a real engine are used to calibrate a detailed engine model and to find optimal engine operating points. The de-tailed engine model is further used to extend the data set and to define dependencies of engine parameters such as indicated efficiency, max firing pressure, etc., in form of regression formulas or look up tables. The parame-ters are used in the simplified engine model which represents a quasi-dimensional one. It is still yet physically detailed enough but it is real-time capable. It allows for an extensive testing of control algorithms and designing new ones. The model in combination with the experimental data represents training data which is used to formu-lation of a black box model. The black box model is fully real-time capable and it has also the predictive func-tion. It can be directly incorporated into the ECU control procedure. The system identification to obtain the black box model has been performed using the LOLIMOT model. The procedure is demonstrated on the DI diesel en-gine for a light truck. Results of different control strategies focused on the VGT turbocharger control are pre-sented.

Notation (optional)

AEPC Injection pump control signal. AVGT, Aref turbine equivalent nozzle diame-ter.

Ik Moment of inertia. K1,2 Constants. LHV Lower heating value. mair mass of air. mfuel mass of fuel. N engine smoke. nM, ERPM engine speed. pboott – boost pressure. pexh exhaust pressure pint intake pressure. pK2 compressor outlet pressure. pT1 turbine inlet pressure t time. Tind Engine indicated torque Tint intake temperature. tK2 compressor downstream temperature. Tloss Torque of mechanical losses. Tq engine effective torque. tRPM Turbo speed. tT1 turbine upstream temperature. tT2 turbine downstream temperature. Ulsk VGT actuator position. α Crank angle. ηind indicated efficiency. ηvol volumetric efficiency. λ air excess.

1. Introduction

Diesel engines have undergone very significant development over past two decades. The development has been driven by demands for a further improvement of engine performance while meeting very stringent emission

2 Martin Florián, Jan Macek, Miloš Polášek, Zbyněk Šika, Michael Valášek at al.

regulations. These targets have been achieved by enhancing diesel engine technology as well as by introducing new engine features and improved combustion systems. Current DI diesel engines are using advanced injection systems, VGT turbochargers, EGR, aftertreatment systems, etc. It is clear that the whole system is very complex and it requires sophisticated engine control to fully utilize its potential. The engine control strategy has to be op-timized for both steady state and transient operations. Especially the transient operation is very demanding in terms of the engine control. The optimization of the engine control strategy could contribute to further improve-ment of the engine transient performance.

Current engine control is usually based on quasi-static maps with dynamic corrections. The advantage of the system is that it is possible to obtain basic inputs to the control algorithm using engine full characteristics. It is possible to optimize the system for the engine steady operation by means of standard approaches. However, the procedure has limitations when it comes to the engine transient operation. Therefore the recent attention has been paid to the engine and complete powertrain control using the knowledge of their models (Pischingeret al. 2004), (Winsel et al. 2004).

The main aim of the work is to propose a procedure for designing an engine model-based predictive control. An implementation of the procedure is the next aim of the work.

Fig. 1, Scheme of the used model hierarchy

The implementation of the model-based predictive control requires reliable and fast models with a predictive capability. The models have to be able to run in real time and faster to allow for predicting engine states for sev-eral future cycles, i.e., injection events. Such models are usually based on input and output models (black-box models). Defining the model, it is necessary to identify behavior of a dynamic system to be described on a very large set of data. It would be very expensive to base this analysis on experimental data only. Therefore, the paper describes an integrated procedure combining experiments with models of three levels - Fig. 1. Experimental data is used to the calibration of the detailed model of engine cycle. The model has been created in the GT-Power – (Morel at al. 2004) in the presented case. The GT-Power models of full engine cycle are very accurate but they are not real-time capable. The computational time is at several orders of magnitude longer than real time. How-ever, the model is very useful because of its accuracy and it can be used to extent data set and generate input data for a simplified model. A model called TRANSIENT proposed by the authors – (Macek at al. 2006) - has been incorporated in the next stage. The model is briefly described in section 2.2. The TRANSIENT model is simpli-fied but based on physical sub-models describing the engine cycle. The model is real-time capable. It bridges the gap between the detailed model and the black-box one. It is very important to have such a model in the chain as it considerably speed up the simulation procedure and it can be directly incorporated in designing and optimizing the control strategy. The black-box model is the last model in the hierarchy. It has to have the predictive capabil-ity if it is used in the model-based predictive control.

The implementation of the algorithm gas been tested on a diesel engine for a light truck. Basic parameters of the engine are summarized in Table 1. The engine control is a complex task. The involvement of the model based predictive control further extends the problem complexity. Therefore, the work has been focused on an op-timization of the turbocharger control (VGT) only to reduce the problem complexity. The target has been to op-

Improving the Engine Transient Performance using Model-based Predictive Control 3

timize transient performance (load response, smoke) while keeping prescribed limiting parameters. Following constrains have been assumed: air excess, turbo speed, turbine inlet temperature and engine smoke limit.

Table 1, Parameters of the target engine

Bore 102 mm Stroke 120 mm Compression ratio 17.5 Turbocharger CZ Strakonice, VGT Nominal power 100kW/2400 min-1 Injection pump Bosch VE

2 Description of the integrated procedure for control algorithm design

2.1 Detailed simulations of the target engine

The detailed simulations of the target engine have been performed by means of the GT-Power code – (Morel at al. 2004). The GT-Power code represents typical engine simulation tool which is capable of simulating whole engine at steady and transient operation. The code is 1-D capable. It enables a simulation of wave phenomena and transport delays in pipes. The model describes both low frequency and high frequency phenomena. The fre-quency is defined relatively with respect to the engine cycle duration or frequency of the transient. Pressure waves in exhaust and intake exhaust manifold represents a typical example of the high frequency phenomena. The capability of describing the high frequency phenomena is an advantage of the model but it slows the model down significantly. The model run is approximately at 3 orders of magnitude longer compared to real time (de-pending on model complexity and computer power). Despite the longer computational time especially for engine transients, the model is very useful in the proposed procedure. It is necessary to obtain data for simplified mod-els, e.g., indicated efficiency, volumetric efficiency, influence of pressure pulses in exhaust manifold, etc. The model represents the engine very well and can be regarded as a virtual engine. It can be used to the verification of proposed control algorithms at the final stage before they are implemented in real engine.

2.2 Model TRANSIENT

The model TRANSIENT is a simplified model of internal combustion engine. Only main features of the model are described in the paper. A detailed description can be found in (Macek at al. 2006). The model code has been realized in the MATLAB/Simulink environment.

The main purpose of the TRANSIENT model is to describe transient behavior of the engine. The model is simplified but, unlike the black-box model, yet detailed enough in terms of involved physics. Basic modules of the model include cylinder, manifolds, turbocharger, etc. The engine element dynamics is involved. The demand for the simplified model definition arose from the need to have a “virtual engine” which correctly simulates real engine behavior and it is fast enough to be used for designing and testing of engine control algorithms. The con-trol strategy optimization and evaluation require an excessive amount of explored cases and the fast and reliable model is necessary. Furthermore, the code can be used to extend the range of data to be used for the dynamic system (engine) identification and definition of fast black-box models.

The proposed model represents typical 0-D model of the IC engine combined with algebraic sub-models. All low-frequency phenomena influencing engine instantaneous torque and engine dynamics are described by differ-ential equations. Pipes are treated as volumes with homogeneous state inside them. Engine crank and turbo-charger dynamics have to be involved. High-frequency phenomena are not neglected but they are involved into the algorithm through correction coefficients obtained from the detailed model. The modules of the model have to correctly describe all engine parts, which have the strongest influence on engine transient performance. Pipe systems are divided into sections and mass and energy conservation equations are applied to them.

The basic equation of the model is engine crank movement equation – (1). Integrating eq. (1), instantaneous engine speed is obtained. Correct solutions of the indicated engine torque (Tind) and toque of mechanical losses (Tloss) are the crucial parts of the model.

( )M

kredk

MlossindM ndt

d

I

nTT

dt

dn6;

,...30

,

=−

=∑

απ

(1)

4 Martin Florián, Jan Macek, Miloš Polášek, Zbyněk Šika, Michael Valášek at al.

There are two possibilities how to determine the engine torque in the model. The first is based on cylinder pres-sure reconstruction using parametrized p-V diagram. Then forces in the crank gear are known and direct solution of the engine torque is possible – (Macek at al. 2006). The second model is further simplified. The way how the engine torque is solved is illustrated by eq. (2). The form of the equation (2) does not fully correspond to the pro-cedure implemented in the model. It is presented here to show parameters required to close the model module solving the engine torque.

int

int2,1

11

T

pLHVKmLHVKT volindcylairindind ⋅⋅⋅⋅⋅=⋅⋅⋅⋅= ηη

λη

λ (2)

Provided that fuel properties, in-cylinder air mass, air excess and engine indicated efficiency are known, the de-termination of the indicated torque is possible. However, the simplified model does not solve details of the hi-pressure part of the engine cycle. Just states in pipes at the cylinder are known. Thus, the model is not able to re-solve engine indicated efficiency and in-cylinder air mass. It calls for a definition of other modules solving en-gine efficiencies. In the torque module, it is necessary to know indicated efficiency and engine volumetric effi-ciency (in-cylinder air mass) to close the model.

The needed parameters which are not directly resolved by the model have been taken from the detailed simu-lations. A procedure for defining the data based on steady state and transient simulations have been proposed. It is necessary to cover whole engine operating range. It is important to include regimes which are far from steady state in terms of boost pressure and exhaust backpressure. Parameters such as indicated efficiency are pa-rametrized in form of regression formulas – (3).

= exh

cyl

cylfuelcylMind pp

V

mnf ,,,, int

,λη

(3)

Engine torque and some other engine parameters such as in-cylinder mass and mass of injected fuels are updated with discrete delays.

The TRANSIENT model incorporates other unique features. A compressor map extrapolation to pressure ra-tios bellow 1 is one of it. The description of other model features is beyond the scope of the paper.

2.3 Nonlinear predictive models of ICE - LOLIMOT models

The considered predictive model is based on general (black-box) input-output models. A local linear neuro-fuzzy modelling approach has been used. It is an adaptive combination of linear models that approximates the nonlinear behaviour of an identified system by linear models valid in particular sub-regions of the whole region. The identification algorithm is called LOLIMOT and was developed in (Nelles 1999). A new implementation was done at Czech Technical University in Prague (CTU) (Stefan 2002). The mathematical models of a system identified with the LOLIMOT are called LOLI-models. They are created with multiple inputs but single output. For systems with multiple outputs the LOLI-models are determined for each output exclusively.

The main idea is to approximate the generally non-linear multivariable function of a system output with the scalar product of the vector of linear functions and the vector of so-called validity functions. In general, each linear function approximates the system output in sub-region determined by a relevant validity function. The complexity of the resulting model is given by the number of the members of these vectors. The output y~ of the model can be then written as

( ) ( ) ( )(( ) ( )

( ) ( )

( ) ( )( )( ) ( )( )) ( )Liypnnnni

pnnnipnnni

pppnnni

ppnnnippnnni

nnini

nini

M

iiii

M

iLii

nkyw

kywkyw

nkuw

kuwkuw

nkuwkuw

kuwnkuw

kuwkuwwyy

yp

pp

p

pp

u

u

Φ−+

+−+−+

+−+

+−++

+−++−+

++−+

+−++=Φ=

+++++

++++++++++

++++

+++++++++

+++

++

==

−−

∑∑

...,

2...,1...,

...,

1...,...,

222,23,

22,111,

112,11,0,

1

21

2121

21

121121

211

11

...

21...

...

1

...

......1

...

1~~

(4)

where iy~ is the output of the i-th local linear model (LLM),

( ) ( ) ( ) ( ) ( ) ( ) ( ) TyppL nkykynkukunkukuku ],...,1,,...,,,...,1,[ 21111 −−−−−=u is the vector of inputs, ( )Li uΦ is the

validity function for the i-th LLM,

[ ]Tpnnnniii yp

www +++++= ...,1,0, 21,...,,w is the vector of the parameters of the i-th LLM, and M is the number of

Improving the Engine Transient Performance using Model-based Predictive Control 5

LLMs. The vector uL of the inputs contains generally not only the actual dynamic system inputs uj(k), j=1..p, but also their previous values uj(k-rj), rj=1..nj and also the previous values y(k-s), s=1..ny of the output to reflect the dynamic order of the system. Normalized orthogonal Gaussian functions are chosen as the validity func-

tions ( )Li uΦ .

Fig. 2 General structure of LOLIMOT models inputs and outputs

It was necessary to develop a multi-step prediction model, to be able to apply the predictive control - Chyba! Nenalezen zdroj odkazů.. Two variants of the model have been developed. The first one directly uses the LOLIMOT formulation. The multi-step model is trained directly. The second variant applies the LOLIMOT training procedure to one step models and these models are put together in order to create a multi-step model (Pelikan 2004). Thus, the first model is trained globally using the complete data set meanwhile the second model is trained step-wise. These two variants of LOLIMOT application has been proposed and tested in (Pelikan 2004). The reason for that is to find an optimal strategy. The results presented in (Pelikan 2004) show that nei-ther of the variants is optimal in all the examined cases. Both versions of the LOLIMOT model have been com-bined to find a compromise. The difference of two training methods can be explained by illustrative scheme in 2. The values within the light grey area are used as LOLIMOT models inputs. The first two rows contain the values of proper control inputs, whereas the values in other rows correspond to measured system outputs. The future control inputs (in 2 from column k-5 to column k) are computed based on control law in the course of LOLI-models application in predictive controller.

Consequently, the LOLIMOT models must be able to predict values of measured quantities in point k. The first variant (A) directly trains the models of the target length of prediction horizon, whereas the second method trains partial models of shorter (e.g. one step) horizon (B). Then the target prediction outputs are com-puted by repetitive application of models B. Both variants have been tested, the example of comparison is in Fig 3. The variant A has been used in further application, seeing that it gives slightly better results.

Fig. 3 Prediction of lambda by methods A and B

The system inputs considered for training of predictive models were the VGT position and the mass of injected fuel. The engine speed, the turbocharger speed, the intake manifold pressure and the exhaust manifold pressure

6 Martin Florián, Jan Macek, Miloš Polášek, Zbyněk Šika, Michael Valášek at al.

have been used as the system outputs. The training and testing data sets have been generated by different random signals of inputs. The created model was subsequently tested using different input and output signals, as shown in Fig.4.

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5x 10

5

n TD [m

in-1

]

0 10 20 30 40 50 60 70 80 90 100-2

-1

0

1

2x 10

4

time [s]

erro

r of

nT

D [m

in-1

]

Fig. 4 Turbocharger speed process and testing error

2.4 Model and experiment integration

Described models are fully integrated both with experiments and amongst themselves. It is big advantage of the procedure. A common interface between the engine and the control system has been formulated. The control sys-tem has been realized in Simulink. The engine is equipped with sensors and actuators. The communication be-tween the control system and the engine is limited to the control signals only. The same layout has been used for both the real and the virtual engine. It enables us to switch between the real and virtual engine at any stage of the control algorithm development.

Fig. 5 The illustration of the engine model and the control system model integration.

3. The procedure implementation on a real engine

This section describes the procedure application on a real engine. The engine control has been implemented in 2 steps. In the first step basic engine control algorithms have been applied to verify the procedure. The algorithms have been tested on the virtual engines as well as experimentally. In the next stage, the predictive model-based control has been implemented. This approach has been tested on the virtual engine only up to know.

Improving the Engine Transient Performance using Model-based Predictive Control 7

3.1 Implementation of basic engine control algorithms

The work is focused on turbocharger and engine fuelling control. The engine has been equipped with new VGT turbocharger produced by CZ Strakonice. Limited number of parameters has been sensed and used as an input to the control procedure:

• Engine speed ERPM • Boost pressure pboost • Intake temperature Tint • Air mass flow mair • VGT position AVGT • Turbocharger speed tRPM • Mass of injected fuel mfuel (Accelerator pedal position)

The parameter set has been sufficient at this development stage but the system is not limited to it only. Real im-plementation allow for further extension up to the level typically used in practical engine control systems.

Following parameters have been actuated: • Mass of injected fuel mfuel (Accelerator pedal position) • VGT position AVGT

The limited number of actuated parameters have been determined by quite old-fashioned hardware used (no common rail, EGR, etc.)

The goal of the control strategy has been to achieve a prescribed engine transient performance while keeping limiting parameters. The engine transient performance has been compared with the engine equipped with waste-gate turbocharger.

Several control algorithms have been tested. The simplest algorithm has limited maximum boost pressure (turbo speed) only. In fact the VGT turbine has been used in place of the waste-gate turbocharger The control kept the VGT turbine closed in regimes in which maximum boost pressure has not been reached. The width of the regulation band and regulator gains have been tuned on this simple setup. This simple algorithm does not al-low for the full utilization of the VGT technology.

The control system has been extended for a dynamic 3-D map defining optimal setting of the VGT position. The VGT position is often defined by dimensionless number called the turbine rack position. The same approach is used in the presented work. The rack position 0 corresponds to the fully closed turbine. The rack position 1 represents the fully open turbine. The map respects advantages of open turbine at low loads which reduces ex-haust backpressure and leads to an improvement in fuel consumption. This algorithm is further enhanced to im-prove engine transient performance. The map defining the turbine rack position is dynamically scaled at engine transients to ensure the fast engine response and keeping relatively low engine smoke (air excess constraint). The dynamic scaling tries to reflect rate of the load change. The real air excess, which is computed by the control system, is compared with optimal one possible at corresponding steady state. When the difference is very high the control system dynamically changes the turbine rack position to increase boost pressure and ensure faster re-sponse of the turbocharger. This algorithm incorporates some predictive functionality to the regulator. The en-gine fuelling is controlled in very simple way to fulfill the air excess constraints prescribed as simple engine speed dependence.

The control strategy, 3-D maps and dynamic corrections have been proposed using engine steady state tests and consequently optimized using the TRANSIENT code. An example of results is shown in Fig. 6. Engine torque (Tq), smoke emission (N), turbo speed (tRPM), control voltage of the VGT actuator (Ulsk), intake tem-perature (tK2), exhaust temperature (tT1), boost pressure (pK2) and level of the injection pump control signal (AEPC) are plotted as a function of time. Three variants are compared – waste-gated turbocharger (WG) and two variants of the VGT turbocharger with different air excess constraints (VGT-Alg.A and VGT2-Alg.A). The VGT2 variant has more stringent requirements on minimum air excess. Engine speed has been kept constant in this work (1200 min-1). Engine fuelling has been varied in the considered cases because of different air excess constraints and slightly changed control procedure. All the variants had the same engine full load curve and comparable air excess at corresponding regimes. The purpose of the Fig. 6 is to show possibility to achieve the same engine transient performance while reducing smoke. The engine smoke can be further reduced by stricter air excess constraints. As it has been expected, the more stringent constraints imposed on lead to the smoke re-duction – compare VGT and VGT2 variants. The problem is that it deteriorates engine transient performance and engine hits the top torque with delay.

The VGT turbine with advanced engine control allows for significant reduction of engine smoke while the re-quired engine response to the load change is achieved. It is necessary to stress at this point that it is not possible to compare just maximum values but their integrals over a time period.

8 Martin Florián, Jan Macek, Miloš Polášek, Zbyněk Šika, Michael Valášek at al.

Fig. 6 Comparison of different engine layouts and different control strategies. Constant engine speed of 1200 rpm.

3.2 Predictive model-based control

The considered predictive control is based on locally linearized model. Without the local linearization, the con-trol law cannot be solved easily and becomes a computationally very difficult task. The method B described in

Improving the Engine Transient Performance using Model-based Predictive Control 9

chapter 2.3 has been used for training of basic two steps nonlinear predictive models. These models for consid-ered output quantities (engine speed, turbocharger speed, intake manifold pressure and exhaust manifold pres-sure) are locally (for actual values of quantities) linearized. The considered inputs were the VGT position and the mass of injected fuel.

The nonlinear predictive LOLI-models are incorporated into the controller. The outputs of the main LOLI-models (measurable quantities) are considered as states of a substitutional linear model used for predictive con-trol. That means, the LOLI-models are locally (for the measured actual values of the states) linearized and in-serted into the matrix form (6). This procedure enables to compute the linear system matrixes A, B, C by direct way. The following formula (5) is used for computation of discrete transfer function instead of the predicted output

∑ ∑

∑ ∑∑Φ−Φ−

ΦΦΦ=

i iLyniLyi

i iLmiLi

iLi

ww

www

u

y

))(,),(,1(

))(,),(),((

,,,1,

,1,0,

uu

uuu

K

K

(5)

Then the transfer function is transformed into the classical discrete state description with locally constant state matrices A, B and C (Valasek et al. 2005)

kk

kkk

xCy

BuxAx

∆=+∆=∆ +1

(6)

where ∆x are system states and y are investigated outputs. The predictive control can be applied to the model created using the above described procedure. The prediction horizon used for predictive control simulations was 16 and alternatively 32 steps.

Writing the relation (6) for N subsequent steps as follows,

11

11

1

1

++−

+

++−

+

+

+

+++∆=

+++∆=∆

+∆=+∆=∆

∆=

NkkN

kN

Nk

NkkN

kN

Nk

kkk

kkk

kk

CBuBuCAxCAy

BuBuAxAx

CBuxCAy

BuxAx

xCy

K)

K)

M

)

)

(7)

and rewriting these equations into the matrix form, the prediction of the outputs is obtained Gufy +=)

(8)

Where

kN

x

CA

CA

f

= M

,

=− CBBCA

0CB

G

K

MOM

K

1N

.

(9)

The control is derived from the optimization of a quadratic performance index (Camacho and Bordons 1999).

The performance index Jk is optimized in the step k using the prediction [ ]TNkk ++= yyy)

K))

1 for y.

{ }{ }puufGuQfGuε

puuyQyε

TT

TTk

zz

zzJ

+−+−+=

=+−−=

)()(

)()())

(10)

where εεεε is a mean value operator, N is the prediction horizon, y is the output vector, z is the desired output vec-

tor, Q is a penalization matrix of the outputs, p is a penalization of the inputs, and [ ]T1,..., ++= Nkk uuu is

the input vector. From the requirement of the minimization of the performance index )(min u

ukk JJ =

(11)

the control law is derived:

)()( 1 fQGpQGGu −+= − zTT . (12)

However, only the first element of the vector u is used for the nearest control action. The control problem very often includes the constraints of the values of different variables. In case of

the ICE, the constrained values may involve operation constraints (e.g. of turbocharger revolutions) and envi-ronment pollution limitations. In order to incorporate these constraints, the direct computation procedure (12) must be generalized. Quadratic programming appears to be a good tool for this purpose. The unconstrained op-timization problem (11) is reformulated as a quadratic optimization problem

10 Martin Florián, Jan Macek, Miloš Polášek, Zbyněk Šika, Michael Valášek at al.

+ ufuHuu

TQPQP2

1min T

.

(13)

with a constraint condition

QPQP buA ≤.

(14)

This optimization problem is solved in every sampling instant. Again, only the first element of vector u is

used for the nearest control action. The algorithm of model predictive control based on identified LOLI-models and quadratic programming can be briefly summarized as follows:

The nonlinear predictive LOLI-models (4) of engine (and/or complex simulation model of engine) are iden-tified, assembled and tested by the LOLIMOT program. The measurable quantities of the system are chosen as the outputs of individual LOLI-models (y). Additional LOLI-models are assembled and tested for controlled and constrained quantities (for example lambda subjected to constraints during control).

The locally linearized additional LOLI-models are assembled into equality and non-equality constraints (14) (Valasek at al 2005). Examples of the simulation results of the model predictive control are shown in the figures 7 and 8 (Macek at al. 2006). Fig. 7 depicts the engine speed control with and without consideration of lambda constraints. The Q matrix used for this example introduce the linearly decreasing weight for requested engine speed values depending on their positions within the horizon. The left part of the figure depicts the results ob-tained by the direct computation of the control inputs (12), i.e. without any constraints, whereas the two plots on the right show the application of the lower air excess limit of 1.35. For the prediction of lambda, the physical formula for lambda was combined with the trained LOLI-model of the air mass in a cylinder. It is evident from the picture, that the application of the lambda constraints affects the attainable values of the controlled output. The influence of the VGT position is shown in Fig. 8. Engine load is varied in the same way as in the previous case. It is clear that engine is not able to follow desired engine speed curve when turbine is widely open. It is possible to achieve the target with closing the turbine. Fully closed turbine provides the higher boost pressure, i.e., air excess. It could be good for the smoke reduction but it is not favorable for the engine efficiency. The sys-tem has to be carefully optimized. The synchronous fulfillment of basic control target (engine speed) and fulfill-ment of air excess limit eventuate in requirement for VGT position.

Conclusions

Integrated procedure for designing engine control algorithms have been proposed and tested. Three levels of models have been combined. The real-time capable model TRANSIENT has been created. It is accurate when calibrated with experimental data and detailed simulations. The calibration is quite easy as the model incorpo-rates transparent physical sub-models. The TRANSIENT code can be used to design and optimization of engine control strategies.

The methodology of very fast black-box model definition with the predictive capability has been proposed and tested. It is based on the identification algorithm called LOLIMOT. The locally-linear identification of com-plex dynamic system provides very efficient tool for the formulation of reasonably accurate and very fast in-put/output models of the internal combustion engine. The model represents the base for the model-based predic-tive control. The model based predictive control could be a promising procedure to enhance engine transient performance. There are still some problems to be discussed, e.g., it is necessary to define global targets to be op-timized considering engine emissions. The question is still open as the main purpose of the predictive control should not be just to improve engine performance in required emission tests but to decrease engine impact on the environment globally.

Basic control strategies focused on the VGT turbine control have been tested on real engine. The results show that it is possible to reduce engine smoke using the VGT technology in combination with advanced control algo-rithms having some sort of the predictive capability.

Improving the Engine Transient Performance using Model-based Predictive Control 11

0 5 10 15 20800

1000

1200

1400

1600

1800

time [s]

n M

[rpm]

Lambda without constraint

0 5 10 15 200.8

1 1.2 1.4 1.6 1.8

2 2.2

time [s]

lambda

0 5 10 15 20 800

1000

1200

1400

1600

1800 Lambda limited by 1.35 from bellow

time [s]

n M

[rpm]

0 5 10 15 20 0.8

1 1.2 1.4 1.6 1.8

2

time [s]

lambda

realizedrequested

realizedrequested

Fig. 7 Model predictive control of engine rpm – simulation results. Comparison of predictive control with and without con-strained air excess.

0 5 10 15 201000

1200

1400

1600

1800

Aref

=4*10-4[m2]

0 5 10 15 201

1.5

2

2.5

0 5 10 15 201

1.5

2

2.5x 10

5

time [s]

0 5 10 15 201000

1200

1400

1600

1800

Aref

=5*10-4[m2]

0 5 10 15 201

1.5

2

2.5

0 5 10 15 201

1.5

2

2.5x 10

5

time [s]

0 5 10 15 201000

1200

1400

1600

1800

n M [r

pm]

Aref

=6*10-4[m2]

0 5 10 15 201

1.5

2

2.5

lam

bda

0 5 10 15 201

1.5

2

2.5x 10

5

time [s]

p SP [P

a]

realized

desired

realized

desired

realized

desired

Fig. 8 Engine predictive control – constrained air excess. Different turbine rack position (Aref = var).

Acknowledgement

The current research has been supported by the project # 1M 6840770002 granted by the Ministry of Education of the Czech Republic and by the project of the Ministry of Industry and Trade of the Czech Republic. These supports are gratefully appreciated. Authors would like to further acknowledge the cooperation of engineers from the CZ Strakonice.

12 Martin Florián, Jan Macek, Miloš Polášek, Zbyněk Šika, Michael Valášek at al.

References

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