Improved Cylinder Air Charge Estimation for Transient Air Fuel. Ratio Control. the feedback, or closed-loop portion of the A/F

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1 Improve Cyliner Air Charge Estimation for Transient Air Fuel Ratio Control J.W. Grizzle, J.A. Cook y an W.P. Milam y Abstract Moern automobile engines require precise regulation of air-fuel ratio (A/F) to attain high catalytic converter eciency an minimize tailpipe emissions. During engine transients, goo A/F control requires, in turn, accurate estimation of the air charge entering the cyliners uring each inuction event. This paper escribes the evelopment an valiation of a nonlinear, open-loop air charge estimator. A key feature is the inclusion of the ynamics of the mass air ow meter. The estimator was implemente on a V engine in a ynamometer test cell. Experimental results conrm the improve A/F control preicte by simulation. The prototype implementation was accomplishe using an automatically generate highlevel language control coe executing in a eicate PC an communicating via a share memory boar with the prouction microprocessor-base controller. 1 Introuction Precise control of air-fuel ratio (A/F) to the stoichiometric value is necessary to minimize exhaust emissions in vehicles employing a three-way catalytic converter (TWC). A/F control has two principal components: a close-loop portion in which a signal relate to A/F from an exhaust gas oxygen (EGO) sensor locate in the exhaust stream of the engine is fe back through a igital PI controller to regulate the fuel injection pulse with, an an open-loop, or feeforwar portion in which injector fuel ow is controlle in response to a signal from an air ow meter. Due to the relatively long elay inherent in the inuction-compression-power-exhaust cycle of the en- Department of EECS, Control Systems Laboratory, University ofmichigan, Ann Arbor, MI 19-; work supporte in part by the National Science Founation uner contract NSF ECS ; matching funs to this grant were provie by FORD MO. CO y For Motor Company, Research Laboratory, Control Systems Department, Mailrop 117 SRL, Dearborn, MI 1-53 gine, plus the transport elay in the exhaust manifol, the feeback, or close-loop portion of the A/F control system is fully eective only uner steaystate operating conitions. Equally important, a reliable EGO sensor signal is available only after the sensor has attaine a stabilize operating temperature, an thus close-loop A/F control is not possible immeiately upon starting the engine. Hence, uner transient an col start conitions, the feeforwar portion of the A/F controller is particularly important. In this paper, we escribe the evelopment an implementation of an air charge estimator for an eight cyliner engine. The estimator is require to preict the air charge entering the cyliners ownstream of the intake manifol plenum from available measurements of air mass ow rate upstream of the throttle. A schematic iagram of the system is shown in Figure 1. One of the main motivations for this stuy was the practical problem pose by the fact that the hot-wire anemometer use to measure mass air ow rate has fairly slow ynamics. Inee, the time constant of this sensor is on the orer of an inuction event for an engine spee of 15 revolutions per minute, an is only about four to ve times faster than the ynamcis of the intake manifol. We will show that taking these ynamics into account in the air charge estimation algorithm can signicantly improve the accuracy of the algorithm; it will also be seen to have substantial benets for reucing emissions. In the following sections, a phenomenological moel incorporating the ynamics for the air meter an intake manifol is assemble, an an on-line estimator for cyliner air charge is evelope. Simulation evience is rst presente showing the importance of incluing the ynamic characteristics of the air meter in the estimator. An experimental implementation is iscusse an corroborating engine ata are presente.

2 Manifol Filling an Cyliner Air Charge Moel Mathematical moels of the air path in an n- cyliner combustion engine have been stuie for many years. The moels can be roughly categorize as two types: PDE moels for engine component esign or o-line simulation [1, 3, 9] an lumpe moels for control law esign an real-time simulations [5, 7, ]. In the following, we will assemble a lumpe moel suitable for eveloping an on-line cyliner air charge estimator 1. Let P, V, T an m be the pressure in the intake manifol (psi), volume of the intake manifol an runners (liters), temperature ( R) an mass (lb m )of the air in the intake manifol, respectively. By the ieal gas law, P = mrt=v ; (.1) where R is a gas constant. Dierentiating (.1) with the assumption that the manifol air temperature is constant gives t P =(RT=V ) m: (.) t The last term in (.) represents the net mass ow rate of air into the intake manifol, an thus is the ifference of the mass air ow metere in by the throttle, MAF a, an the air pumpe out of the intake manifol by the cyliners; the latter can be represente by a function of engine spee, N, an manifol pressure esignate Cyl(N;P); it is assume that both MAF a an Cyl(N;P) have units of lbm/sec. Equation (.) can thus be expresse as t P =(RT=V )[MAF a, Cyl(N;P)] (.3) which is a nonlinear ierential equation for manifol pressure in terms of engine spee an mass air ow rate metere by the throttle. The cyliner pumping or inuction function Cyl(N;P) is usually etermine by regressing the coecients of a polynomial against engine ynamometer ata [7]. For the V engine use in Section 5, this was etermine to be Cyl(N; P)=3 h,:5+:9 P The moel will not capture the iniviual cyliner malistribution eects which are the focus of [5]. Amittely, this is not a totally accurate assumption; however, manifol temperature is slowly varying enough relative to the uration of an inuction event that substituting the current estimate value (base on inlet air temperature an water coolant temperature) or an actual measure value for the manifol temperature into (.3) is aequate to represent variations in manifol pressure ue to temperature uctuations. P 3:9, P 3 1:9 +11:1 N :3 N P : N P, N 5: N P N +: :9 lbm/sec. (.) 1 where N is engine spee in revolutions per minute (RPM) an P is manifol pressure in psi. The mass air ow rate through the throttle is moele as a function of the throttle position, (egrees), throttle boy inlet pressure, P TB (psi), an manifol pressure [, ]. Cyliner air charge per inuction event, CAC, is the critical quantity require for the feeforwar computation of the fuel injector pulse with. It can be etermine irectly from (.3). In steay state, the integral of the mass ow rate of air pumpe out of the intake manifol over two engine revolutions, ivie by the number of cyliners, is the air charge per cyliner. Assuming that engine spee (RPM) is constant over a single inuction event leas to a ynamic approximation of the inucte air charge on a per cyliner basis: CAC = Cyl(N;P) lbm: (.5) nn Remark: Assuming ry air, the gas constant R is 53.3 ft-lb f / lbm m R. Further assuming that the manifol volume is approximately 7 liters an manifol air temperature is 5 R (1 F) gives that R T/Visequal to lb f / lbm-in. 3 Cyliner Air Charge Estimator For simulation stuies, it is usual to inclue the throttle in the air path moel. However, air ow through the throttle is a sensitive function of P TB, the throttle boy inlet pressure, an in most vehicles, this is not measure. Ambient air pressure is normally not measure, an in any event, is not easily relate to P TB ue to the pressure rop across the air lter an also ue to air ram charging eects associate with vehicle motion. Seconly, in prouction vehicles, the throttle position sensor is typically not very accurate. For these reasons, the estimator will be base on the measurement of mass air ow rate provie by the mass air ow meter. The ynamics of the mass air ow meter can be approximately moele as a rst orer lag with a time constant on the orer of msec. That is, t MAF m + MAF m = MAF a ; (3.1) where MAF m is the measure mass air ow, MAF a is the actual mass air ow through the throttle an,

3 the time constant of the air meter, is approximately msec. Substituting the left han sie of (3.1) for MAF a in (.3) yiels t P =(RT=V ) t MAF m + MAF m, Cyl(N;P) (3.) To eliminate the erivative ofmaf m in the above equation, let x = P, (RT=V )MAF m. This yiels t x =(RT=V )[MAF m, Cyl(N;x +(RT=V )MAF m )] : (3.3) Cyliner air charge is then compute from (.5) as CAC = nn Cyl(N;x +(RT=V )MAF m) : (3.) Note that the eect of incluing the mass air ow meter's ynamics is to a a feeforwar term involving the mass air ow rate to the cyliner air charge computation. When =, (3.3) an (3.) reuce to an estimator which ignores the air meter's ynamics, or equivalently, treats the sensor as being innitely fast. The set of equations (3.3) an (3.) provies an estimate of cyliner air charge base upon measure mass air ow through the throttle. This is not a stanar \observer" where one assumes that the inputs to a system are ireclty measurable with no sensor ynamics; it is more an inverse of the air meter propagate through the manifol an cyliner inuction ynamics. However, if a manifol pressure sensor were available, then a better estimator coul still be erive by applying the extene Kalman lter or recent results in nonlinear observer theory. This woul allow one to essentially apply an \error correction term" (that is, output injection) to the estimator (3.3)-(3.). If a moel of the throttle boy coul be use, then a \true" asymptotic observer coul be esigne, but this woul require an accurate throttle position sensor an a throttle inlet pressure sensor (unless only correction uring sonic ow is esire). The estimator (3.3) an (3.) must be iscretize for implementation. As is often one in engine moels [], an event base sampling scheme will be use. Let k be the recursion inex an let t k be the current time in secons per 5 crankangle egrees or 1 revolution; that is, t k = N 7:5 k sec., where N k is the current engine spee in RPM. Then (3.3) can be Euler integrate as x k = x k+1 +t k (RT k =V )[MAF m;k,cyl(n k ;x k,1 +(RT k =V )MAF m;k )] : (3.5) The cyliner air charge is calculate by CAC k = 1t k n Cyl(N k;x+(rt k =V )MAF m;k ) : (3.) Remark: An (analog) anti-aliasing lter is use on the mass air ow meter signal. It was etermine that, with the above sampling scheme, a lter time constant of 33 Hz appears to be a goo value for noise rejection an anti-aliasing purposes over a wie range of engine spees. Simulation Evience for the Eectiveness of the Estimator A Matrix X -base simulation moel of a V engine was constructe to investigate the eectiveness of the propose metho of estimating cyliner air charge on the basis of measure mass air ow rate. Equation (.3) was use to represent the \true" engine, with Cyl(N,P) given by (.); the moel contains (3.1) plus a 33 Hz analog lter to represent the relation between the measure mass air ow an the actual air ow; noise was ae to assess its eleterious effects as well. Equations (3.5) an (3.) with = were use in the case that the air meter's ynamics were ignore; this is terme the \uncompensate metho"; the same set of equations with =: is terme the \compensate metho". The uncompensate metho is actually a goo representation of the air charge algorithm use in the on-boar controller of the V engine of Section 5. A throttle square wave of twenty egrees amplitue an.5 Hz was applie to the engine moel an the engine spee was set at 15 RPM. The resulting manifol pressure varie between 5 an 13 psi. A zero mean uniform white noise signal (/1 SNR) was ae to the measure mass air ow rate before sening it through the two estimators: neglecting air meter ynamics an incluing the ynamics. This was one to assess the sensitivity of the inversion process. Figure shows the relative errors in the estimate cyliner air charge for the compensate an uncompensate methos. It can be seen that neglecting the air meter ynamics results in maximum relative errors exceeing % uring transient operation. Incorporating the air meter ynamics reuces the peak error to less than 7%. Even more importantly, the integrate error of the compensate metho is also greatly reuce, which shoul correlate with reuce emissions. On an engine, it is icult to measure irectly the actual cyliner air charge 3, so it is important to n another way of experimentally assessing the eectiveness of incluing the air meter's ynamics in the cylinr air charge estimator. It turns out that the manifol pressure response presents another way to 3 The experimental set-up use in Section 5 was not equippe with in-cyliner pressure sensors.

4 juge the performance of the estimators. The key observation is that the cyliner air charge an manifol pressure responses are ynamically similar. This is illustrate in Figure 3 where cyliner air charge is scale to manifol pressure, an the compensate an uncompensate methos are compare. It is evient that the true air charge follows manifol pressure very closely, the uncompensate air charge lags the manifol pressure substantially, an the compensate air charge is quite close to the true value. This comparison of estimate CAC to measure manifol pressure will be use to experimentally evaluate the performance of the estimator in Section 5. 5 Experimental Verication on a Dynamometer In actual operation on the engine, the air charge estimator must take into account computation an scheuling elays between air measurement an fuel injection. Typically, a elay equal to 1 egrees of crankshaft rotation occurs between the computation of cyliner air charge an the time this value is use to generate a fuel pulse with. To account for this computation elay, a simple preiction algorithm was incorporate. The anticipation feature oes a least squares t of a line through the current an past two values of the air charge computation to preict forwar two engine events (1 egrees). For the purpose of ientifying the function Cyl(N,P) from steay state engine mapping ata, a SenSym TM absolute pressure transucer was installe in the intake manifol. The mass air ow was recore as a function of spee an manifol pressure on a warme up engine (19 F engine coolant temperature) over a range of spee from to 5 RPM an pressure from to 1 psi. Exhaust gas recirculation was isable. The expression use for Cyl(N,P) was given in (.). The cyliner air charge calculations escribe by equations (3.5) an (3.) plus the anticipation algorithm base on a simple linear extrapolation of the previous three air charge calculations were implemente in block iagram form using the Matrix X System Buil simulation language an converte to real-time language control coe using the Autocoe facility. This coe was execute in an INTEL base PC, synchronous with the embee controller. A ual port share memory interface between the embee system an the PC allowe rapi implementation of the estimator without the necessity of moifying the prouction microprocessor control al- This is because Cyl(N;P) N pressure. is fairly ane in manifol gorithms. For purposes of comparison, the nal value of cyliner air charge was selectable: either the value calculate by the prouction embee microprocessor, which is uncompensate for the ynamics of the air meter, or the air meter compensate value (3.5) an (3.), coul be use for fuel pulse with calculation []. The engine was equippe with an electronically controlle, stepper motor riven throttle with a close-to-wot (wie open throttle) time response of about.1 sec. The estimation algorithm was exercise over a range of engine operating conitions from to 3 rpm. Since all of the results are quite similar, only the ata from 15 RPM are reporte here. Figure shows the ynamic engine conitions at the nominal 15 rpm operating point. The throttle was steppe as rapily as possible from close to nearly wie open throttle, resulting in a manifol pressure excursion from about 5 psi to 13 psi. This is illustrate in Figure 5, where the manifol pressure compute from (3.5) is compare to the actual manifol pressure using the high banwith absolute pressure sensor referre to above. It can be seen that this excursion is accomplishe in fewer than ve 9-egree engine events (where four engine events comprise the complete engine cycle consisting of intake, compression, power an exhaust strokes. Engine events occur at intervals of 9 egrees of crankshaft rotation in an cyliner engine). Figures an 7 compare the cyliner air charge neglecting air meter ynamics (but incluing a preiction algorithm) an the compensate air charge calculation with the manifol pressure ynamics. It is clear that the uncompensate value, even with anticipation, barely keeps up with the manifol pressure. The compensate value, on the other han, leas the manifol pressure by the require two engine events. Note that the compensate signal is \noisier" than the uncompensate air charge signal. Part of this is associate with the feeforwar nature of the compensation as escribe previously. Some of it, however, is ue to the fact that sampling is engine event base using a signal erive from a Hall-eect sensor locate on the camshaft. Errors in the computation of t k are ue in large part to camshaft inertial eects. Since the preicte value of the compensate air charge for fueling purposes is calculate base on the past three values, an then preicte forwar, the sample time variations are fe through to the anticipate value causing \noise". The above ynamometer results provie inirect evience that the estimator (3.5)-(3.) yiels a signicantly improve estimate of cyliner air charge in comparison to the existing on-boar algorithm use

5 in the engine uner stuy. This shoul translate into improve transient A/F control, which in turn, shoul lea to reuce emissions. An attempt was mae to evaluate the transient A/F improvement associate with the the estimator (3.5)-(3.). To this en, an NTK UEGO sensor was installe in the engine very close to the prouction location an the 15 rpm step response tests were repeate. This is a linear-type, exhaust gas oxygen sensor with a time constant of about 5 msec. No attempt was mae to ajust the fuel portion of the transient A/F strategy. The A/F trace for the two estimation schemes is shown in Figure. Bearing in min that the time constant of the A/F sensor is much larger than the time constant of the mass airow meter which is being compensate, it is nonetheless gratifying to note that the measure A/F exhibits improve performance on both tip in an tip out. More importantly, engine ynamometer ata inicate an improvement of greater than 1% in HC mass emissions over the Feeral Test Proceure (FTP) riving cycle; recent vehicle ata have conrme the estimate. [] B. K. Powell an J. A. Cook, \Nonlinear Low Frequency Phenomenological Engine Moeling an Analysis, Proc. 197 Amer. Contr. Conf., vol. 1, pp. 33-3, June 197. [7] B. K. Powell, A ynamic Moel for Automotive Engine Control Analysis, Proc. 1th IEEE Conf. Decision an Control, pp. -, [] R. Prabhakar, \Optimal an Suboptimal Control of Automotive Engine Eciency an Emissions," PhD Thesis, Mechanical Engineering, Purue University, West Lafayette, IN, [9] M.P. Thompson an H.W. Engelman, \The two types of resonance in intake tuning", ASME 9- DGP-11, Figures Throttle Hot Wire Probe Electronic Circuit Acknowlegement The authors are grateful to Dan Colvin an Dave Trumpy for their very helpful comments on manifol lling, mass air ow meter ynamics an transient air fuel ratio compensation. Lou Sherry, Dennis Ree an Kip Mercer are sincerely thanke for their contributions to the experiments. Runner Intake Manifol Exhaust Valve Intake Valve References [1] D. Broome, \Inuction ram", Automobile Engineer, Part I, April, pp ; Part II, May, pp. 1-1; Part III, June, 199 pp. -7. [] P.A. Hazell an O.J. Flower, \Sample ata theory applie to the moelling an control analysis of compression ignition engines", Int. J. Control, Vol. 13, No. 3, [3] J. Heywoo, Internal combustion engine funamentals, McGraw Hill, 19. [] W.P. Milam, \A Distribute Computing Approach to Rapi Prototyping for Embee Controllers," Proc. of the IEEE Miwest Symposium on Circuits an Systems, Detroit, MI, [5] P.E. Moraal, J.W. Grizzle an J.A. Cook, \An Observer Design for Single-Sensor Iniviual Cyliner Pressure Control", Proceeings of the IEEE Conference on Decision an Control, San Antonio, December, 1993, pp % Relative Errors in Cyliner Air Charge Esitmation Figure 1: Schematic of air path in engine. Compensate Uncompensate Time in Figure : Percent relative errors in air charge estimation.

6 1 Scale Cyl_Air_Chg Scale Estimate Cyl_Air_Chg Man. Pressure True CAC Time in 1 Man. Pressure Comp. CAC Uncomp. CAC Time in Manifol Pressure in PSI 1 CAC_Pro Scale -- MAP Measure Figure 3: Inirect metho to assess elity of air charge estimation. Figure : Cyliner air charge which ignores air meter ynamics. 1 Throttle Position 1 CAC++ Scale -- MAP Measure MAF in LBm per Sec Manifol Pressure in PSI Figure : Engine operating conitions at nominal 15 RPM. Figure 7: Cyliner air charge which accounts for air meter ynamics. 1 MAP Compute -- MAP Measure A/F Using compensate CAC -- A/F Using prouction CAC Manifol Pressure in PSI 1 Air Fuel Ratio Figure 5: Comparison of measure an compute manifol pressure. Figure : Air fuel ratio traces.