Torque Observers Design for Spark Ignition Engines ... - IEEE Xplore

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 19, NO. 1, JANUARY 2011

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Torque Observers Design for Spark Ignition Engines With Different Intake Air Measurement Sensors Munan Hong, Tielong Shen, Member, IEEE, Minggao Ouyang, and Junichi Kako

Abstract—This paper presents a design approach and an experimental evaluation of torque observers for Spark Ignition (SI) engines. An engine model simplified from the generally used mean value model is proposed. Based on the developed model, torque observers are designed for engine systems with different intake air measurement sensors. The torque production model is introduced first to give a nominal value of torque estimation. Then, using the rotational dynamic equation of the crankshaft, an online adjusting term is added to modify the nominal estimation. The intake pressure, as an input of the torque production model, is directly measured if a pressure sensor is used. When an air mass flow sensor is adopted instead, an additional intake pressure observer is included in the torque observer. Simulation and experimental results are shown finally to demonstrate the proposed observers. Index Terms—Engine, mean value model, stability, torque observer.

I. INTRODUCTION

T

HE INCREASE of complexity and interaction of formerly autonomous systems gives a new challenge in modern vehicle control. In order to manage the resulting network of more and more integrated systems, a new standard interface between vehicle coordination and engine management system (EMS) is required. The engine torque is a key variable in this new interface [1]. In a laboratory, the indicated torque is usually calculated by in-cylinder pressure obtained from pressure transducers. The effective torque can be also obtained by subtracting torque losses. However, such in-cylinder pressure sensors are too expensive and not technically available for commercial production engines. Thus, indirect methods to measure engine torque are required. Indeed, torque estimation is not a novel topic but has attracted a great deal of attention. Earlier publications about torque estimation can be classified into several groups. The most common torque estimation method involved lookup tables where the signals used to generate the tables included mean engine speed, intake pressure, exhaust pressure, spark advance, and fuel injection quantity [2]. The second group paid attention to modeling the system from throttle angle to torque output, Manuscript received January 22, 2009; revised October 22, 2009. Manuscript received in final form January 08, 2010. First published February 17, 2010; current version published December 22, 2010. Recommended by Associate Editor F. Vasca. M. Hong and M. Ouyang are with the Sate Key Laboratory of Automotive Safety and Energy, Department of Automotive Engineering, Tsinghua University, Beijing 100084, China (e-mail: [email protected]; [email protected]). T. Shen is with the Department of Engineering and Applied Sciences, Sophia University, Tokyo 102-8554, Japan (e-mail: [email protected]). J. Kako is with the Power Train Development Center, Toyota Motor Corporation, Shizuoka 410-1193, Japan (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCST.2010.2040620

which includes intake manifold dynamics, fuel dynamics, and combustion process. In [3], an empirical formula was used to model the torque production. In [4], a linear model was proposed by introducing a new index defined as ratio of air charge and engine speed. The third group explored the relationship between engine torque and speed. For the mean torque estimation, the difference between the maximum and minimum engine speed during a combustion event was abstracted as an index which could be easily correlated to the mean torque in [5] and [6]. Using the difference between estimated and measured engine speeds, a proportional integral (PI) observer [7] and a sliding mode observer [7], [8] were designed, respectively. For the instantaneous torque estimation, the engine speed fluctuations were used for torque determination based upon an elastic model [9] and an electrical circuit model [10] of the rotational dynamics of the crankshaft, respectively. Two different torque estimation schemes were presented in [11] entitled “Stochastic Analysis” and “Frequency Analysis” by the measurement of crankshaft speed variation. A real-time combustion torque estimator on a diesel engine test bench using time-varying Kalman filtering was proposed in [12]. The last group considered the whole system from throttle angle to engine speed. In [13], an extend Kalman filter was used to modify the output of a gray box engine model. Two cases with known and unknown load torque were considered and for load estimation a simplified power train model was introduced. In [14], by reducing the nonlinear engine model to a second order Taylor approximation around a generic engine operating point, an linear quadratic (LQ) controller had been applied to solve the estimation problem as a tracking problem. In this paper, an engine model simplified from the generally used mean value model is proposed. With the developed model, a nominal value of the engine torque is provided first, and an online modification based on the difference between the measured and the estimated engine speeds is applied. The estimated engine speed is determined by exciting the estimated torque on the crankshaft rotational model. In the constructed observer, the intake pressure is required to give a nominal torque value. If a pressure sensor is used, the intake pressure is directly measured. If an air mass flow sensor is adopted instead, an additional intake pressure observer, which can be obtained from the developed model, is included in the torque observer. The theoretical analysis of the convergence of the proposed observers is also presented. The organization of this paper is as follows. In Section II, a simplified engine model to be used in the observer is proposed. In Section III, torque observers for different intake air measurement sensors are presented and the stability is analyzed. Sections IV and V give the simulation and experimental validation results, respectively. The conclusion and future works are summarized in Section VI finally.

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II. ENGINE DYNAMICS MODELING Engine system modeling is difficult due to its nonlinear and time varying dynamic characteristics. Many publications have been presented in this field from different viewpoints [3], [15]–[21]. A general approach is to create a physics-based model from fundamental thermodynamic, fluid mechanics and rigid body mechanics. A nonlinear three state dynamic model for SI engines is given in [17]. Since it is relatively simple as a mean value model, and can still describe the major dynamical behaviors of the engine, it is adopted here to derive a more compact engine model.

is the theoretical air fuel mass ratio for gasoline and where is equal to about 14.7. The indicated power , which forces the crankshaft via the fuel flow, is given as follows [17]: (6) is the fuel low heating value and is the indicated where efficiency. Substitute (4) and (5) to (6), let the resultant equation be di, the mean indicated torque vided by . Notice that can be derived

A. Air Path Model In the air path model, the manifold is regarded as a rigid volume with an input air mass flow at the throttle . The intake manifold filling dynamic equation can be derived with the law of mass conservation and the ideal gas law [17]

(7) If the loss in the rotational movement of the crankshaft such as friction dissipation is denoted by , the mean effective torque can also be obtained

(1) where is the intake pressure, is the gas constant, is the air temperature in the intake manifold, which is assumed to be is the displacement of the engine, is the engine constant, is the volumetric efficiency speed in radians per second and based on intake conditions. The volumetric efficiency in (1) is the most difficult parameter to be identified. An approximate relation between this parameter and the intake pressure was found in [21] (2) , are related to many facwhere the coefficients tors such as the compression ratio, the air temperature and the engine speed. It was also found that they depend mainly on the engine speed and can be even dealt with as constants in a large engine operating range. A complete proof and validation have been given in [21]. Substituting (2) to (1), yields

(8) The indicated efficiency depends on many physical factors, such as engine speed, intake pressure, spark advance, and air fuel ratio. It is approximately an exponential function of the engine speed, as other factors only give a slight perturbation [17]. The loss in the rotational movement of the crankshaft mainly depends on the engine speed. With being approximately constant and taking (2) into account, (8) can be rewritten as

(9)

B. Torque Production Model

are related to engine speed. where It should be pointed out that the torque production model is derived neglecting the effects of some factors such as air-fuel ratio and spark advance. It may not be valid over a large engine operating region and under transient conditions. The resultant errors can be dealt with as the uncertainty of the model paramand . Nevertheless, we believe that a more aceters curate torque production model should be a future development direction. For instance, should not be dealt with as constant but a function of ; should not only be a function of engine are speed but also spark advance; the model parameters , functions of engine speed, air fuel ratio and spark advance.

Using the speed density formula, the air mass flow into the can be obtained by [17] cylinder

C. Rotational Dynamic Model

(3) where , ,

can be dealt with as constants because are approximately constants.

,

(4) where is the engine speed in rotations per minute. for a desired air Then the fuel mass flow into the cylinder fuel equivalence ratio (usually is equal to 1) is

(5)

The crankshaft can be simply regarded as rigid for mean value modeling and the engine rotational dynamic model can be derived directly from Newton’s second law as following: (10) where is the equivalent inertia of crankshaft including pistons and flywheel of the engine, is the load torque.

HONG et al.: TORQUE OBSERVERS DESIGN FOR SPARK IGNITION ENGINES

III. OBSERVER DESIGN A. Problem Statement A natural motivation of Section II is to use the torque production model to estimate the engine torque. Indeed, the en, are gine torque can be directly calculated by (9) if known. However, they cannot be exactly known in practical applications. Simply using the torque production model will lead to estimation error all along without any modification. To deal with the problem of parameters uncertainty of the torque production model, an appropriate modification should be added, namely, a closed-loop observer is required. Since the engine torque excites and rotates the crankshaft, the resultant speed contains torque information. Actually, this has led to a great many publications trying to find the relationship between torque and speed [5]–[11]. Furthermore, engine speed is easily obtained on commercial engines. Thus, we can construct a torque observer in such a way that the nominal torque calculated with the torque production model is adjusted based on the online error between the measured speed and the output speed of the rotational model which is excited by the torque estimation. If the output speed of the crankshaft model forced by the estimated torque is exactly equivalent to the measured one, then we can accept the estimated torque as the true value. It should be noticed from the crankshaft rotational dynamic (10) that the engine load should be known. A possible way is to estimate the load torque using the vehicle model [13], [22]. For the sake of simplicity in presentation of the basic idea, this issue is out of target with this paper. We suppose the load torque is known in the observer design. Generally, the objective of this paper is to design a torque observer which is insensitive to torque production model uncertainty. Both engine systems with intake pressure sensor and air mass flow sensor are considered: these are the most common systems currently in use.

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load torque is known. For the adjusting law, PI is used for its simple structure and practicality; a switching term is also introduced to guarantee the stability. Basic idea of this approach is to use the feedforward model to provide a primary estimation at an operation point, and to use the feedback adjusting term to compensate the perturbations from the feedforward estimation. Generally, the feed-forward term should provide basic estimation so that the range of the error dynamics is small. The torque observer is finally created and represented by (12) (12)

where respectively. Let

,

,

are the proportional and integral gains,

, the error system of (12) is represented by (13)

In the following, the conditions to guarantee the stability of the proposed observer (12) are established. Theorem 1: Suppose that Assumption H1 holds. Then, for any positive constants and , the error system (13) is Lyaas . Furthermore, as punov stable, and . Proof: Let , the error dynamics (13) becomes (14) Consider the candidate of Lyapunov function (15) Then, along any trajectory of the error system

B. Design With Measured

(16)

When the intake pressure sensor is used, can be measured directly. The observer is designed with the following assumption. is measurable, the parameters and Assumption H1: in (9) are not exactly known, however, can be represented as

Note that

, we have (17)

This follows Lyapunov stability of the error system. Moreover, from (17) and (14), we can conclude

(11) , , unknown conwith known nominal mappings stant and unknown function which is bounded by a , i.e., . known function The torque observer is constructed as Fig. 1(a), where denotes the throttle position, and are the estimated mean effective torque and engine speed, respectively. denotes the amount of modification added on the nominal mapping torque . It is introduced to compensate the estimation error caused and . is a given estimaby the modeling error between tion of load torque, it is equal to with the assumption that the

(18) By LaSalle’s invariant set principle, and converge to the set where as . From (11) and (12), it is , , the estimated torque obvious that in the set

(19) This implies that in the invariant set

as

.

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Remark 1: The stability analysis does not consider the chattering caused by the sign function. A modified sign function is adopted to attenuate the chattering in the following simulations and experiments: (20) where is a predefined bound. Remark 2: When the observer is digitally implemented, the estimation error may not tend to zero due to the limited sampling rate and quantization. Remark 3: If the load torque can not be exactly known, e.g., (21) is an unknown constant and is an unknown where function which is bounded by , i.e., , we and let can choose the switching gain , then the error system is changed to

Fig. 1. Architecture of torque observer. (a) Torque observer with p able. (b) Torque observer with p unmeasurable.

measur-

We modify the observer to involve the estimation of intake as follows with the structure shown in Fig. 1(b): pressure

(24)

(22) Select the candidate of Lyapunov function (23) The same conclusion as (17) is obtained. That means the observer is still convergent. But unfortunately, in this case, we can only guarantee that as under the condition that as . That is because the modification term of the observer is based on the crankshaft model, which is driven by both the engine and the load torque. It is difficult in the presented framework to provide separately the estimations of the engine and the load torque from the engine side only. We believe that to incorporate load estimation and load uncertainty in the observer, further information from the vehicle side, for example, the rotational motion of power train, is required. Actually, this idea has attracted some researchers [13], [22].

C. Design With Estimated Modern vehicles especially luxurious cars are usually equipped with air mass flow sensor. The air mass flow passing through the throttle then is used to estimate air charge which provides the torque production indirectly. However, this approach is only effective in steady operation conditions. During the transient conditions, the information from the air mass follow is not sufficient, since between the air charge and the mass follow there exists a dynamics of the intake manifold which is dominated by the pressure. So in this case, the observer is still based on the dynamical observation of the pressure. is measurable, and satisfy Assumption H2: the condition in Assumption H1.

where is the estimated intake pressure and justing gain function to be designed later. Then, the error system of (24) is represented by

is the ad-

(25) . where Theorem 2: Suppose that Assumption H2 holds and let the intake pressure observer adjusting law be given by (26) where stants

is a positive number. Then, for any positive con, the error system (25) is Lyapunov stable, and as . Furthermore, as . Proof: Note that the error dynamics becomes and

(27) Choose the candidate of Lyapunov function as (28) Then, along any trajectory of the error system, we have

(29)


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Under the bounded condition described in Assumption H2, it is obtained that by setting the intake pressure observer adjusting as (26) law (30) Thus, with this inequality, it is concluded that the error system is Lyapunov stable. Moreover, from (30), (26) and (27), we can conclude

(31) By LaSalle’s invariant set principle, , and converge to as . From (24), it the set where is obvious that in this set, the estimated torque

(32) This implies that in the invariant set as . Remark 4: The same as the first observer, the chattering caused by the sign function is not considered. The modified is used in the simulations and experisign function ments. Also, the estimation error may not tend to zero when the observer is implemented in a discrete system. If the load torque is not exactly known, we have the similar conclusion with Remark 3. IV. SIMULATION RESULTS This section shows the simulation results to demonstrate the validity of the proposed observers. Simulation is conducted on a V6 engine model provided by SICE (the Society of Instrument and Control Engineers) Research Committee on Advanced Engine Control [23]. The simulator consists of the intake air dynamics, the combustion process where the cylinder pressure with respect to the crank angle is calculated, and the mechanical portion of the crankshaft system. The engine torque directly given by the simulator is the instantaneous torque which fluctuates due to the reciprocation movement of the pistons. We apply a eight-order butter-worth low-pass filter to get the mean value torque (used as benchmark) from the instantaneous one. The cutoff frequency is set to 50 Hz in order not to cause much time delay in phase. An offset square wave signal of throttle angle is given to the 12-17 s), the speed is kept around simulator. At the first part ( 2000 r/min by adjusting the engine load which is directly acted on the simulator and as the input of the observer. At the second 17-22 s), the engine load is kept around 30 N m. The part ( effective torques from the simulator and the observer are compared in Fig. 2(a). This is the result with the intake pressure measurable. The black solid line is the signal from the simulator, the red dashed line and the blue dotted line are the estimated values using closed loop observer (with a legend “CO” in the figures) and open-loop observer (with a legend “OO” in the figures), respectively. Here the closed-loop observer denotes

Fig. 2. Observer validation by simulation: p

is measurable.

the observer proposed in this paper and the open-loop observer means torque estimation using (9) directly with the identified , . parameters It should be noted here that we identify the torque model parameters with the ideal air-fuel ratio control and the minimum spark advance for the best torque (MBT). Therefore, the actual control performance of the air-fuel ratio and the deviation of the spark advance from MBT will cause modeling errors. Fig. 3

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Fig. 5. Robustness of the observer to load.

Fig. 3. Effects of other factors to the torque model.

Fig. 6. Test bench.

TABLE I ENGINE SPECIFICATIONS Fig. 4. Estimation errors by simulation: p

is unmeasurable.

shows the effective torque versus the intake pressure with different air-fuel ratios and spark advances. These errors can be dealt with as parameters uncertainty, as it is mentioned previ, from their pracously, namely, the deviation of tical values. To verify that the proposed observer is insensitive to torque model uncertainty, 10% deviation (5% offset and 5% sine disturbance) from their nominal values is added on the parame, and the result is shown in Fig. 2(b). Due to ters the deviation, the accuracy of estimated torque using open-loop observer in Fig. 2(b) is much worse than the one in Fig. 2(a) while the closed-loop observer is not badly affected, which can be seen clearer from error plots in Fig. 2(c). Fig. 4 shows the is unestimation errors in the case that the intake pressure measurable. In all cases, different initial values from the measurements are used in order to demonstrate the convergence of the observers. It is found that the observers are capable of following the real value and do not have any tendency to diverge. Moreover, results regarding robustness of the observer with respect to the uncertainty of load are given in Fig. 5. In the simulation, a sine disturbance (5% amplitude) is imposed on the parameters to account for the inaccurate feedforward model. 0%,

10%, and 20% load deviation is tested. The result of open-loop observer (only using feedforward model) is also illustrated. V. EXPERIMENTAL RESULTS A. Test Bench The test engine is provided by Toyota Motor Corporation and the specifications are shown in Table I. The engine was installed in a test cell and connected to a dynamometer, as it is shown in Fig. 6. Pressure sensors are installed in Cylinder 2, 4, 6, respectively. The electronic control unit (ECU) runs as a standard commercial controller and accepts throttle position command from dSPACE (DS1103) by CAN interface. dSPACE also collects variables from ECU by CAN and signals from sensors by IO interface. The measurements include engine speed, intake pressure, air mass flow, etc.


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Fig. 7. Parameters identification for torque production model.

The “measured” torque is calculated from cylinder pressure, using the following equations:

(33) (34) , denote cylinder pressure and volume, which where are functions of crank angle , is the cylinder number of the engine and , are the mean indicated and effective torques in a cycle, respectively. In the following, all “measured” torque is obtained by this way. The friction torque can be determined by subtracting the load torque from the indicated torque, which is calculated by cylinder pressure. The load torque used for the observer is directly measured from the dynamometer. B. Parameters Identification in (3), , in (9) The model parameters , , in (10) should be identified by experiments first. and The parameters of the air path model , and are obin (3) be equal tained by the following procedures: make to 0, and get (35) without considering dynamics, where , are identified; (3) then is changed to (36) and the parameter is obtained by dynamic identification (35) (36) For torque production model, the relation between and is shown in Fig. 7. It can be seen that the function is approx, then are obtained imately linear. The parameters by linear fitting methods. Moreover, from the figure we can find that in a speed range of 1600–2600 r/min, the parameters are almost the same. It should be pointed out that the linear relation is obtained under steady engine operations. The equivalent inertia of crankshaft is obtained by least square fitting method.

Fig. 8. Torque observer validation: p

is measurable.

C. Torque Observer Validation Due to the restriction in the experimental setup, the experiments are limited in the range of 1600–2600 r/min for speed and 0–100 N m for load. The observer validation experiments

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VI. CONCLUSION

Fig. 9. Estimation errors: p

is unmeasurable.

A simple torque model is presented in this paper. The air charge is first calculated from the speed density formula, where the volumetric efficiency is obtained by an equation related it to the intake pressure. Then the fuel mass flow into the cylinder is known with a theoretical air fuel equivalence ratio. The complex combustion process of the gas mixture is simply described by the indicated efficiency. Finally, it is found that the engine torque is linear with the intake pressure, and the linear coefficients are functions of engine speed. The proposed torque model may be not very accurate during transient conditions but will be helpful when applied to algorithm design with regard to model uncertainty. Based on this model, an observer approach targeting the torque estimation problem is also proposed. The proposed observers in this brief paper are expected valid in a large engine operating range, although the experimental validation tests are over a predefined range due to the restriction in the experimental setup. Different intake air sensors are also taken into account for the first time in the field of torque estimation. Nominal and deviated model parameters are both used in the simulations and experiments. The results demonstrate that the proposed observers are valid and insensitive to model parameters. Nevertheless, there are still problems to be solved from this observer approach to practical application. Load estimation should be further incorporated in the observer using vehicle or power train model. The possible errors of the observer when implemented in a discrete system and the influence of inaccurate measurements by the sensors should be further investigated. Online PI parameters selection according to engine operation should be developed to get better performance although any positive set of parameters can ensure the stability. ACKNOWLEDGMENT

Fig. 10. Different selections of PI parameters.

The authors would sincerely like to thank Y. Oguri and P. Li for their valuable assistance in the experimental setup. REFERENCES

in a real engine are conducted like this: change the throttle position and adjust the load torque to keep the engine speed in the range of 1600–2600 r/min. The results are presented in Figs. 8 and 9. Fig. 8(b) verifies again that the proposed torque observer is insensitive to torque model uncertainty by using the parameters , with 20% deviation (10% offset and 10% sine disturbance) from the identified nominal values. The error plots Figs. 8(c) and 9 show the improvement of the estimation by adding an online modification term. It is also found that the deviation caused by using different initial values does not lead to any divergence and hence demonstrates the proposed observers do converge. It should be noted that the PI feedback parameters depend on the engine operating conditions for proper response. The PI gains should be chosen correctly even though any positive set can ensure the stability. Fig. 10 presents the estimation errors using different PI parameters in the case that the intake pressure is unmeasurable. It is easy to find that the observer goes into chattering if the parameters are not chosen properly.

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