Non-Linear Net Engine Torque Estimator for Internal Combustion Engine

ELSEVIER

Copyright © IFAC Advances in Automotive Control Salemo. Italy. 2004

IFAC PUBLICATIONS www.elsevier.comflocatelifac

NON-LINEAR NET ENGINE TORQUE ESTIMATOR FOR INTERNAL COMBUSTION ENGINE PaoIo Falcone, Giovanni Fiengo and Luigi Glielmo.

Dipartimento d'Ingegneria, UniversitiL degli Studi del Sannio, corso Garibaldi 107, 82100 Benevento, Italy. E-mail: {falcone, gifiengo, glielmo}@unisannio.it.

Abstract: An engine torque estimator, based on sliding mode technique, is proposed in this paper: a switching term, function of the error between the estimated and measured instantaneous engine speed is used to ensure the convergence of the estimation error. This approach provides robustness against the uncertainties of the model and the variations of the parameters during the life of the vehicle. The estimator is then tested with a DI Diesel engine simulator, calibrated with experimental data and realized by the authors. The estimator does not include the combustion process , and this feature make it suitable for any kind of internal combustion engine after a short calibration procedure. Copyright © 2004 IFAC Keywords: Internal Combustion Engine, Engine Torque Estimation, Non-linear Observer.

1. INTRODUCTION

to this problem are presented. As an example, it is possible to treat the estimation problem as a tracking one, see (Drakunov et al. , 1995) and (Rizwni and Zhang, 1994) or to compute the engine torque by inverting the model, see (S rinivasan , 1992) and (Ferenbach, 1990) . This last technique is based on a derivative of the engine speed and, although some robust differentiators can be de1>igned, see (Levant, 1998) , this approach introduces an additional computational load. Another possible solution is the estimation of the cylinder pressure using nonlinear sliding observers and a single wne combustion model, see (Shiao and Moskwa, 1995): the indicated torque can then be calculated from cylinder pressure through a crank-slider mechanism model. Unfortunately, this approach could be too complex, from a computational point of view, for real time applications.

The engine torque is one of the most important performance variables of an internal combustion engine and , for this reason, a torque control system can improve substantially the performance of the overall vehicle: but a measurement of the torque is necessary in order to close a control loop. This is the key issue in the problem of the torque control: no cheap and durable sensors are available to be embedded on the crankshaft, see (Schagerberg and McKelvey, 2002) . For this reason, actual torque control systems are simply based on static maps, that cannot provide good performances during transient; moreover they have to be adapted to the parameters changes during the life of the engine. An observer, that reconstructs the torque from the engine 1>-peed can replace expensive sensors. To this aim, a rigid body crankshaft model is chosen for the estimator design. Hence , the goal of the paper is to estimate the input of the model, that is the engine torque. In literature several solutions

In this work, the engine torque is e1>'timated solving a tracking problem by means of a sliding-mode technique: a switching term, based on the speed error, ensures the convergence of the estimation

125

error. The selection of the gain of this switching term is based on the sliding-mode theory, e.g. see (Ut kin and Drakunov, 1995) and (Young et al. , 1999) and this feature awards robustness to the estimator. In (Y-Y- Wang and Rizzoni, 1997) , on the basis of a black box friction model, an indicated torque estimator was designed using the sliding mode technique. The observer effectively reaches good performances but it strongly depends on the reliability of the friction modeL In the present paper, the net engine torque is estimated (Le. for driveability ~ues, gear shift control, traction control, and so on) using a similar technique but based only on the knowledge of the shaft speed. This ensures high robustness to the uncertainties related to, as an example, the friction model.

Fig. 2. Crank-slider mechanism in a two lumped masses connecting rod model. All forces acting on piston and connecting roo are shown.

Nielsen, 2000), (Shiao and Moskwa, 1993) and (Schagerberg and McKelvey, 2002), it is computed as follows:

In the next section the crankshaft model, used in the estimator design, is described; then the technique used for the torque estimate is discussed and the structure of the estimator is presented. Finally some simulation results are shown.

Ne

T m(B, iJ, 8)

= '2)h(8-8j ) +mnr2]B+ j=1

(2)

2. PLANT MODEL.

where

In order to design the engine torque estimator, only the crankshaft model has been considered. Moreover , due to the low resolution of the engine speed sensors available on commercial vehicles and the consequent impossibility to observe the torsional effects, a single body system will be adopted to model the crankshaft dynamics.

(3) is the variable inertia of oscillating masses relative to one cylinder, with mA the sum of all oscillating masses (piston mass plus oscillating mass of the connecting rod) , mn the rotating mass, 81 , .. . , 8N e are the phasing angles, r the crank radius and ,<;(8) is the piston displacement. This is computed, (see figure 2), as

i:..'-"I~

,<;(8) = r(1-cos8)+l

r

Sin

2

8) , (4)

where l is the length of the connecting rod. Friction and pumping losses are very hard to model exactly (Taraza D., Renein N.A. and Bryzik W. , 1996) and, usually, black-box models are more suitable for control applicn.tions instead of complex physical models. Sub~-tituting the equation (2) in equation (1) the dynamic equation of the crankshaft becomes

1;

Fig. 1. Torques acting on the crankshaft: To is the indicated torque, T rn is the mass torque, Tr is the friction torque, 11 is the load torque.

The block diagram of the model is depicted in figure 1 where it is possible to see the different torque components acting on the crankshaft. The dynamic equation of the crankshaft is

Jcra.nJij = Ti (8) - Tm(8 , B, 8) - Tf(B) - T},

(1- V1- ~;

Jwt (e)8 = Ti(8) - T:"(B , iJ) - Tr(B) - T 1,

(5)

where J tot (e ) is the total inertia including the crankshaft inertia JcranJr., the inertia of all rotating parts Ncmnr2 of the connecting rods and the inertia of the oscillating masses (see equation (3)) of all cylinders , i.e.

(1)

where: 8 is the crank-angle; Ti is the combustion torque; Tl is the load torque; Tf models the friction and pumping losses. T m is the mass torque and, for a two lumped masses connecting rod model for a Nc-cylinder engine, see (Kiencke and

Ne

J wt (8) = Jc..T
+ N c m n r2 + L

j= 1

126

JA (e - 8j ), (6)

Hence, using equations (10) and (5) , the condition (11) can be rewritten as follows:

and T:r, (B , 0) is the component of the mass torque depending on the engine speed

sign(S) . . Ssign(S) = - - . - [-kSlgn(S)+

Jtot(B)

, . :

-Tm (8 , 8)

•]

sign(S)

-11 - J (8) [Ti(8)+

(12)

tot

-T:r,(8,0) - Tr(O ) - Tl ] < O. 3. ESTIMATOR DESIGN obtaining a lower bound for the gain k: As discussed in the Introduction, the engine torque estimation is cast as a tracking problem. The goal is to compute the control input of the model described in the previous section, Le. the total torque available to the shaft

Ttot(B ,O) = li(8) - T:r,(8, O) - Tr(iJ) - TJ,

k> - [Tr:,(B,B) + Tl] sign (S )+ - J tot (8) [T; (8) _ T' (8 9) J tot (8) 1 m'

Now, assuming J tot (8) ~ Jtot(8) , when S > 0 the condition (13) is verified for every positive values of the parameter k, because the terms between brackets are always greater than zero. Conversely, when S < 0, an upper bound for those terms terms in parenthesis has to be found in order to ensure an approp~ate choice of the parameter k.

The tracking problem will be solved by means of the sliding-mode control theory. Hence, the first step is the selection of a sliding manifold, S = o. Here S has been .chosen as the difference between the computed, 8, and the measured, 0, engine speed:

= (B -

8).

(13)

-Tr(iJ) - Tl] sign(S) .

(8)

in order to track the desiderated engine speed, i.e. the measured engine speed.

S

+

The term T:r,(B,B)

+ Tl

mainly depends on t~e

load torque ii because the mass torque T:r, (B , B) has zero mean as shown in figure 3; for this reason it is possible to choose

(9)

Then, the estimator has been designed as follows:

max [T:r,(B,B)

+ Tl]

= (h

(14)

_T_ !Cl

where the switching term, function of the engine speed error, estimates the difference between combustion and friction torque (li - Tr) . As regard the mass torque, it depends on engine geometric features (bore, stroke, connecting-rod length) and has not been included in the switching term since it is possible compute it exactly. Moreover, it has been supposed that the load torque is the output of a vehicle model, which computes it with an error of 50% respect to the exact load torque. Uncertainties on the last two terms are compensated by the switching function that, as described in details in the following, ensures the convergence to zero of the engine speed error. It is to be pointed out that this approach does not need models of combustion process and friction and pumping losses, often characterized by many parameters to be identified. Further it can be used both for Cl and for SI engines, and both for cold and for warmed-up engines.

Fig. 3. Mass torque for a 4-cylinder engine. As regards the second bracketed term in the relationship (13), the term Ti(8) - T:r,(8 , 9) - Tr(9) represents the torque that an engine is able to deliver. For a specific engine the maximum value, Tm """ is known, such that it is possible to write

The second step is the determination of the gain k of the switching term, in order to force the estimated state onto sliding manifold (9). This is ensured by the following condition:

S sign(S) < O.

max [Ti(8) - T:r,(8 ,B) - Tr(B) - Tl] =

(15)

= Tmax = rp2· In conclusion, the gain k has to satisfy the inequality

(11)

127

k

>
condition for the calculation of a lower bound for the parameter k is given by the inequality;

(16)

The resulting estimator scheme is depicted in figure 4: the torque Tf is estimated by means of the switching term -k sign(S), while the

t -

torque

t. - Tf -

(1 7)

r:n (0,0) represents t~ estimated

where T~ax is the maximum engine torque in an experiment and T{oad is the load torque calculated by a vehicle model. Since C{)I ~ 7j~ the condition (17) becomes

net engine torque. Its mean value, Tnet, has to be computed in order to be used in a torque control strategy based on mean value models. Therefore a moving average filter, or a crank-angle synchronous one, could be used for this purpose like in figure 10.

k> r:nax'

It is to be pointed out that high values of the gain k can cause high frequency chattering on the estimated torque. This means that the sliding gain has to be selected to obtain a trade-off between the estimation error and the chattering of the torque signal.

-

1:'

e.

s

In Table 2 are reported the simulations results at several operating points, described by different engine and load torque. In particular, in the third and fourth column are respectively the values of the the load torque and maximum engine torque, corresponding to the parameters C{) I and T:"ax' The gain k, first column of the table. should be selected greater then the value T~8X' Finally, in columns fifth and sixth, the absolute error between the total torque obtained from the simulator and the estimator, in terms of the average and maximum value is reported. From these ~-ults it is possible to note that a large error occurs if condition (18) is not satisfied (see rows one, six and ten) , otherwise there is a remarkable reduction; in the aforementioned rows, it has to be taken into account the difference between T\oad and T(oa,d' This proves the validity of the approximation made to compute the sliding gain.

Fig. 4. Slidlng-mode torque estimator scheme.

4. SllvIULATION RESULTS

In this section the simulation results of the estimator, described in the previous section, are presented. To this aim, a simulator, see (Falcone et al. , 2003), has been used as the real system. The simulator, and consequently the estimator parameters, are relative to a. BMW MD47 DI Diesel engine whose main features are illustrated in Table 1. Power 100 kW Bore 84=

(18)

No.

N. Cylinder Max. Torque 280 Nm at 1750 rpm 4 - 1900cc Compression ratio Stroke 19 88= Table 1. Engine data.

k

Torque [Nml Error [Nml Engine Average Max 2.59 8.08 10 5 15 15 1.65 5.53 15 5 1.10 4.09 35 15 5 100 15 1.05 3.45 5 287.5 1.09 5 15 0.30 19.15 6.86 60 35 60 80 35 1.22 6.79 60 100 6.67 35 60 1.10 0.73 332.5 35 3.45 60 115 85 112 16.24 40.41 150 112 2.76 9.09 85 1.72 7.76 200 85 112 407.5 112 1.61 4.81 85 Table 2. Sunulation results. Load

1 2 3 4 5 6 7 8 9

In an implementation on a commercial vehicle, the gain k has to be selected according to the relationship (16) , where the value of C{)2 is the maximum torque delivered by the engine (280Nm for the considered engine) , and
10

11 12 13

In Figures 5 and 6 the simulation results relative to the seventh row of the Table 2 are presented. In particular, the Figure 5 compares the total torque obtained from the simulator, solid line, and from the estimator, dashed line. The Figure 6 reports the real engine speed, solid line, and the estimated, dashed line.

128

6. REFERENCES

~,"I

JO

I

Drakunov, S., G. Rizwni and Y. Y. Wang (1995). On-line Estimation ofIndicated Torque in IC Engine using Nonlinear Observers. Paper no . SP-1086, SAE International Congress and Exposition, Detroit. Falcone, P., M. C. De Gennaro, G . Fiengo, S. Santini, L. Glielmo and P. Langthaler (2003). Torque Generation Modeling for Diesel Engine. Accepted for presentation at Conference on Decision and Control 2009 Maui, Hawaii, USA. Ferenbach, H. (1990). Model Based Combustion Pressure Computation Through Crankshaft Angular Acceleration Analysis. Paper no. 900021 , Proc XXII Int., Symposium on Automotive Techonology and Automation, Florence, Italy. Kiencke, U. and L. Nielsen (2000) . Automotive Control Systems. Springer, SAE International. Levant, A. (1998) . Robust Exact Differentiation via Sliding Mode Control. Automotica 34(3) , 379-384. Rizwni, G. and Y. X. Zhang (1994) . Identification of a Nonlinear Internal Combustion Engine Model for On-line Indicated Torque Estimation. Mechanical Systems and Signal Processing 8(3), 274-287. Schagerberg, S. and T. McKelvey (2002) . lru;tantaneous Crankshaft Torque Measurements. Modeling and Validation. SAE paper (03P167). Shiao, Y. and J. J. Moskwa (1993). An Investigation of Load Force and Dynamic Error Magnitude Using the Lumped Mas.<; Connecting Rod Model. SAE Tech. paper (930617). Shiao, Y . and J . J . Moskwa (1995) . Cylinder Pressure and Combill;tion Heat Release Estimation for SI Diagnostics Using Nonlinear Sliding Observers. IEEE Tmnsactions on Control Systems Technology. Srinivasan, K. (1992). On-line Estimation of Net Engine Torque from Crankshaft Velocity Mesurements U!>i.ng Repetitive Eb'timators. Procedings of American Control Conference. Taraza D., Henein :-;.A. and Bryzik W . (1 996 ). Experimental Determination of the Iru;tantaneous Frictional Torque in Multicylinder Engines . SAE Technical Papers (962006). Utkin, V. I. and S. Drakunov (1995). Sliding Mode Observers. Tutorial. Procedings of the 34th Conference on Decision and Control, New Orlearu;, LA . Young, D . K. , V. I. Utkin and t. Ozgiiner (1999). A Control Engineer's Guide to Sliding Mode Control. IEEE 1hmsactions On Control Systems Technology .

2.5

e:.m.d a..n er..,. T~ '

i

Fig. 5. Simulation a.t load torque of 35Nm, maximum torque of 60Nm a.nd k = 80. The firs t plot shows the simulated mean net torque. The second plot shows the estima.ted one.

'~·~'--~~--~'5~--~--~2.5~--~--~'~'--~ ~,.,

Fig. 6. Simula.tion a.t load torque of 35Nm, maximum torque of 60Nm a.nd k = 80. The figure shows the simulated, solid line, a.nd t he estima.ted, da.shed line, engine speed.

5. CONCLUSION AND FUTURE ACTIVITIES An engine torque estimator has been presented in this paper. The results reported in the previous section show a good performance of the estimator and validate the design criteria. This feature makes it suitable for applicatioru; in which a good estimation of engine torque is required. The main drawback of this approach is the presence of chattering in the calculated torque. Although it is possible to eliminate this chattering by means of a simple crank-angle synchronous moving average filter , the finite time or angle resolution can increase the estimate error. Future works will aim to improve the estimator, so as to make possible the implementation on a real-time systems with a finite angle resolution.

1?Q

Y.Y. Wang, V. Krishnaswami and G. Rizzoni (1997). Event-Based Estimation of Indicated. Torque for le Engines using SlidingMode Observers. Control Engineering Practice 5(8), 1123-1129.

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