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`Engine Air-Fuel Ratio and Torque Control using Secondary Throttles
`
`A. G. Stefan0poulou: J. W. Grizzle‘ and J . S. Freudenberg‘
`
`Abstract
`
`A control scheme is designed to limit air-fuel ratio
`excursions and track driver—demanded torque for a 4-
`cylinder engine during rapid changes in throttle position.
`The new control scheme is based on joint management
`of air and fuel flow into the cylinders using secondary
`throttles placed before the intake ports of the cylinders,
`in combination with standard fuel injectors.
`
`1
`
`Introduction
`
`Environmental regulations continue to drive research
`on improved vehicle emissions and fuel economy. The goal
`is to achieve cleaner burning and more efficient automo-
`biles, without compromising driveability. This requires
`precise air-fuel ratio (A/F) control, both in steady state
`and in transient engine operation. A challenging prob
`[em for the Control Automotive Engineer is to keep the
`A/F close to stoichiometry during rapid changes in throt—
`tle position. Rapid changes in throttle position strongly
`influence the cylinder air charging process, mixture for-
`mation and transient performance of the engine. These
`rapid throttle movements reflect the driver’s demand for
`changes in torque and vehicle acceleration.
`The goal of the current work is to keep the A [F close to
`stoichiornetry so that the Three Way Catalyst (TWC) op-
`erates with high efficiency, and to track the driver’s torque
`demand during rapid changes in throttle position. The
`torque set point to be achieved is a function of throttle
`position and engine speed. This function, when evaluated
`for all possible throttle positions and engine speeds, forms
`a nonlinear map, called the “demand map”.
`The control of the A/F around stoichiometry is usually
`based on regulating the fuel flow to follow the air flow
`changes imposed by the driver. The associated feedback
`control system does not have high enough bandwidth to
`accommodate fast transients seen in normal driving due
`primarily to the long delay in the induction-compression-
`combustion—exhaust cycle, plus the transport delay in the
`“Control Systems Laboratory, Department of Electrical En-
`gineering and Computer Science, University of Michigan. Ann
`Arbor, Ml48109—2122; work supported in part by the National
`Science Foundation under contract NSF 805-92-13551; match-
`ing funds to this grant were provided by FORD MO. CO.
`
`0-7803-1 968034340001 994 IEEE
`
`exhaust manifold. The addition of a feedforward term for
`the fuel set-point does not completely alleviate this prob—
`lem. DeveIOpments in the area of drive-by-wire (DBW)
`throttle systems [5] have indicated the need for an air con-
`trol scheme in addition to the fuel control, but have also
`originated questions on safety issues In [2], a DBW throt-
`tle system has been used as a way of regulating (in the
`sense of predictability) the changes in air flow into the
`manifold caused by movements of the primary throttle.
`The present work moves a step beyond the DBW scheme
`by developing a joint air-fuel management system.
`The control scheme presented here is based on the in-
`troduction of secondary throttles before the intake ports
`of the cylinders (Fig. 1). The new control surfaces (0c)
`regulate the air flow into the cylinders. These control sur-
`faces in combination with the fuel injectors (Fe) achieve
`low A/F excursions and good tracking of torque demand
`by adjusting the air flow and the fuel flow into the cylin-
`ders. The control surfaces 0: smooth out rapid changa of
`the charging process during throttle movements so that
`the fuel control path is able to maintain stoichiometry.
`
`
`
`Figure 1: Schematic representation of 4-cylinder engine
`with secondary throttles.
`
`The torque and A/F errors used by the controller are
`calculated by measuring the difference between actual and
`desired values. For now we are assuming direct measure'
`ment of the achieved torque; we have also used a lin-
`ear EGO sensor for the estimation of the A/F from the
`exhaust gas. The engine model used in this study is a
`continuous~time nonlinear, low-frequency, phenomenolog-
`ical model with uniform pulse homogeneous charge and
`a lumped parameter approximation of the breathing and
`
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`rotational dynamics [3].
`Definition of the variables and their units is provided
`in the next section. An overview of the model is given
`in Section 3. Section 4 discusses the dynamics of the
`nonlinear breathing process after the introduction of the
`secondary throttles; the nonlinear feedforward design of
`the set points for the secondary throttles is discussed in
`Section 5. The relationship between the primary throttle
`position and the torque set-point for the control scheme is
`described in Section 6. The linear feedback design, results
`and comparisons are given in Section 7. Conclusions and
`future work are discussed in Section 8.
`
`2 Nomenclature
`
`A/F air-fuel ratio, unitless
`in
`mass flow, g/sec
`N
`flywheel speed, rad/sec
`P
`pressure. bar
`T.
`torque, Nm
`0
`primary throttle position, degrees
`9c
`secondary throttle position, unitless (0 + l)
`
`3 Engine Model
`
`This section gives a brief overview of the nonlinear
`mathematical representation of the engine model used in
`our study (see Fig 2). For the complete dynamic equations
`describing the primary throttle body, the engine pump-
`ing and the torque generation, the reader is referred to
`the original paper [3]. A full description of the rotational
`dynamics as a function of the total inertia and the load
`torque is given in [6].
`
`
`
`Figure 2: Engine model with secondary throttles.
`
`The discrete nature of the combustion process causes
`delays in the signal paths: between the mass diarge for-
`mation and the torque generation there exists a delay
`equal to the compression stroke duration, and between
`the exhaust manifold and the EGO sensor there exists a
`delay which equals 3 times the intake event duration. The
`dynamics of the exhaust manifold and the linear EGO sen-
`sor are modeled by first order differential equations with
`time‘constants equal to 0.15 sec and 0.20 sec respectively.
`The model of the fuel puddling dynamics is given in [1]
`
`by
`
`M! = 03%Mii
`where M].-
`:
`injected fuel flow (g/sec)
`My : cylinder port fuel mass flow (g/sec)
`(3.1)
`Precise transient air-fuel ratio control during rapid
`changes in the throttle position by the driver, requires
`feed-forward computation of the fuel injector pulse width
`since the inherent delay in the air-fuel ratio feedback loop
`prohibits rapid corrections. The fuel injector pulse width
`is regulated on the basis of the estimated cylinder air
`charge. The cylinder air charge is calculated by the esti-
`mated air flow rate out of the intake manifold multiplied
`by the duration of the intake event [7]. The dynamics of
`the air flow meter are included in the model by a first
`order lag with a time constant of 0.13 sec. Finally, fuel
`injection is often timed to occur on a closed-valve prior to
`the induction event [7]; this inherent delay has not been
`included in the model at this time.
`
`4 Nonlinear Breathing Process
`
`This section concentrates on the nonlinear dynamics of
`the engine breathing process. The study of the breath-
`ing process behavior is used to investigate and determine
`the operating regions where the secondary throttles (9..)
`have control authority in regulating the air charge into
`the cylinders. The air charge for every intake event is a
`function of the mass air flow rate into the cylinders and
`the engine speed, and it is directly related to the torque
`produced throughout the power stroke. Control over the
`transient and the steady state value of the mass air flow
`is necessary to meet the objectives of good torque track-
`ing and maintaining the A/F at stoichiometry. The signal
`6. must influence the static and dynamic behavior of the
`manifold pressure, the air flow into the manifold through
`the primary throttle position, and the air flow into the
`cylinders through the secondary throttles.
`The manifold acts as a plenum, where the rate of change
`of the manifold pressure (P...) is proportional to the mass
`air flow rate into the manifold (mo) minus the pumping
`mass air flow rate (#1,) into the cylinders. The manifold
`dynamics are described by the following first order difier-
`ential equation (see [12]) that relates the rate of change
`of the manifold pressure (P...) to the flow rates into and
`out of the manifold (mo and 7h, respectively)
`41
`R - T
`—P... = K...(rha —rh,), where K... = —V...
`.1:
`
`(4.1)
`
`The mass air flow rate into the manifold (ins) through the
`primary throttle body is a function of throttle angle (0),
`the upstream pressure (P.), which we assume to be stan-
`dard atmospheric, i.e. P. = 1 bar, and the downstream
`pressure, which is the manifold pressure (P...). When the
`manifold pressure is less than half of atmospheric pres-
`sure, i.e. I’m/Po < 0.5, the flow rho through the throttle
`body is described as sonic flow and depends only on the
`
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`primary throttle position. The function describing mo in
`the two flow regimes is given in [11], and [13] by
`
`me = f(9)y(Pm)
`{(9) = 2.821 — 0.052310 + 0.10299492 — 0.0005393
`
`P _
`5“ "‘) ‘
`
`1
`{Ex/Pmpo — PM?
`
`if P... _<_ Po/2
`if P... > Po/2
`
`(4-2)
`The engine pumping mass air flow rate (in!) is a function
`of manifold pressure (P...) and engine speed (N) and is
`given in [3] by
`
`in; = —0.366+0.008979NPm -0.0337NP.3. +0.0001N’ P...
`(4.3)
`For the basic model (without the mondary throttles)
`the steady state operating point occurs at the intersection
`of the two trajectories of the mass air flow rates. This
`point is the nominal point shown in Figure 3. With the
`introduction of the secondary throttles it is possible to
`scale the engine pumping rate (#1,) by different values
`depending upon the effective area of the passage that is
`regulated by opening and closing these new valves:
`
`7h”: = 9.,- - 1h].
`
`(4.4)
`
`Figure 3 shows the new trajectories of the air flow rate
`into the cylinders and the resulting new equilibriums (set
`points in Fig.
`3) for the breathing process. For suffi-
`ciently large 9.: < l, the steady state value of the mass
`air flow into the cylinder mm is adjusted by causing the
`new equilibrium to shift from the sonic flow regime to the
`subsonic region. A closer investigation of the two regimes
`illuminates their significance in the new control scheme.
`
`“M“W
`
`Hum-n
`
`Figure 3: Trajectories of rho and 'hc‘l for several values
`of 9;.
`
`When the flow through the primary throttle body is
`sonic and therefore does not depend on the manifold pres-
`sure, we operate in the flat region of rh. in Figure 3. Small
`changes in 0: cause no change in the steady state value of
`
`the mass air flow in and out of the manifold. For this rea—
`
`son, when the model of the breathing process is linearized,
`the secondary throttles have zero control authority on reg-
`ulating the steady state mass air flow into the cylinders.
`This can be shown by the following transfer function be
`tween the control signal A9, and the mass air flow into
`the cylinder Am...:
`
`AT’Zm = +5 = 4 (4.5)
`c
`l + 43;"-
`8 + kmkl
`
`The DC gain of the above transfer function is clearly zero.
`The usual technique of incorporating an integrator to reg-
`ulate the steady state mass air flow into the cylinders can-
`not be used here, since the transfer function has a zero
`at the origin that cancels the integrator pole. It is also
`instructive to see this on a block diagram level. Figure
`4 shows the linear dynamics of the breathing process for
`sonic flow after the introduction of the secondary throttle.
`Note that the integrator loop, which is an intrinsic part of
`the manifold dynamics in sonic flow, rejects the signal 0‘
`in steady state. Thus the control signal A0; cannot ad-
`just the air charge into the cylinder by “smoothing" the
`efl'ect of rapid throttle changes. Consequently, the control
`command A9c has zero control authority on the A/F and
`the steady state value of the engine torque.
`
`
`
`Figure 4: Block diagram of the linearized breathing
`process.
`
`In the case where the flow is subsonic, i.e. Pm [P" > 0.5,
`the air flow into the manifold depends on the primary
`throttle position and on the manifold pressure; thus the
`linear model of the engine breathing process is different
`from the above and the application of linear techniques is
`possible. The slope of the function that describes in. (see
`Fig. 3) indicates the control authority of its opearting
`point. It is clear now that the control authority of the
`secondary throttles around the set-point 2 in Figure 3
`is preferable to that around the set-point 1. Around set-
`point 2, the secondary throttles can be used to “smooth"
`any abrupt changes in air flow by regulating the air flow
`into the cylinders at a slower rate.
`In conclusion, a nonlinear feedforward design of the
`9c set-points that allows operation in the subsonic flow
`regime, where the secondary throttle have maximal con-
`trol authority, is necasary. This map will provide the
`steady state position of the new control surfaces.
`
`5 Feedforward Control Design
`
`The natural nominal position of the secondary throttles
`is wide open, i.e. 0,; = 1. However, recall from Section
`
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`4 that under these conditions the secondary throttles of-
`ten have zero control authority in adjusting the steady
`state value of the mass air flow into the cylinders. This
`paper proposes a. solution that uses a control signal (9c),
`which consists of a nonlinear feedforward term (997w) plus
`a feedback term (9c,.,)- The feedforward design ensures
`maximal control authority and smooth engine operation.
`The feedback design is based on an LQG/LTR compen—
`sator.
`
`The nonlinear feedforward term (9c,.) is designed to
`satisfy the following three conditions: 1) it is a smooth
`and non-decreasing function of the primary throttle posi-
`tion (9) and the engine speed (N), La. 9c,“ = 0¢,w(9, N);
`2) the engine should deliver its maximum power output
`when operated at or close to wide open throttle (WOT),
`and 3) maximal control authority should be available
`without sacrificing combustion stability and performance.
`To achieve these objectives over a wide range of engine op-
`erating conditions we should consider the effects of com-
`bustion stability, thermodynamic performance indices and
`idle operating conditions. Presently we have not com-
`pleted such an extended analysis, which we hope the re-
`sults of this paper will initiate. Based only on a controlla-
`bility analysis, we have developed the following map (see
`Fig. 5):
`
`9‘”:
`
`if 0° < 9 < 12°
`
`0.55
`0.6445 — 0.0126 - o
`+1.3125.10“.a2
`+2.1875-10'5-93 u12°go<20°
`14%)”
`if20°50<60°
`1
`if60°50<90°
`
`
`
`Figure 5: Static feedforward nonlinear term of the
`control signal 9c
`
`The reasoning behind this map is briefly explained.
`First of all, usual driving conditions in urban areas cor-
`respond to partly open primary throttle (9) interrupted
`by rapid requests for acceleration and deceleration (which
`are the main causes of A/F excursion). At partly open
`throttle, the maximum power of the engine is not required
`and hence 0c,” < 1 is acceptable.
`In addition, 9c" has
`
`been adjusted to ensure that the breathing process is op-
`erating near set-point 2 in Fig. 3. When the primary
`throttle is at or near WOT, the secondary throttles must
`smoothly operate close to the wide open position to en-
`sure that maximum engine output can be achieved. Under
`WOT conditions, Pm/Po :5 1. Therefore the seconde
`throttles are operating in the maximal control authority
`region. However, they have freedom of movement only
`towards one direction. They can reduce the passage of
`the inlet runners and regulate the transient air flow rate
`into the cylinders during acceleration to cause lower A / F
`excursions. On the other hand, not much can be done
`when the driver closes the primary throttle: the secondary
`throttles cannot open further (0 < 0.: S 1) to “smooth"
`the abrupt decrease of the air flow into the manifold by
`providing additional air. Finally, when the primary throt-
`tle is nearly closed, there is a minimum position for the
`secondary throttles below which idle stability issues have
`to be addressed.
`
`In the present work, we use the above map to investi-
`gate the contribution of the new control actuator to drive-
`ability improvement and emissions reduction. Thermody—
`namic evaluation is needed to determine the interaction
`
`of the new control surfaces with the various engine per-
`formance indices. An initial assessment of the influence
`
`of the suggested feedforward scheme shows that the feed-
`forward term is beneficial to the manifold dynamics. The
`engine operates at I’m/Po z 0.9, i.e. manifold almost
`fully charged, which causes considerably faster manifold
`filling dynamics during part throttle driving. Achieving
`fast quasi-steady conditions close to atmospheric pressure
`in the intake manifold can eliminate wide variation in the
`
`time constant of the fuel puddling dynamics. This might
`reduce the uncertainty inherent in the fuel flow transient
`behavior. We also expect a reduction of the pumping
`losses due to low manifold vacuum . However, the ad-
`ditional complication in the intake system of the engine
`might decrease the volumetric efficiency. Further investi-
`gation of all the above issues will determine the effect of
`the new control scheme on fuel economy.
`Usage of the feedforward term shown in Fig. 5 makes
`linearization fruitful. The Section 7 describes the linear
`
`feedback design for the secondary throttles and the fuel
`injectors.
`
`6 Demand Map
`
`In the proposed control scheme, the primary throttle
`position is the input. It is measured but not controlled.
`The torque set-point is calculated from the primary throt~
`tle position and the engine speed measurements. This re-
`quires a demand map, similar to the one used in DBW
`schemes [5],
`to determine the torque set-point for any
`throttle position and engine speed. The engine model,
`after the introduction of the feedforward term of the sec-
`
`ondary throttles was used to create the nonlinear static
`map. The torque from the demand map will be used as
`
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`
`
`
`
`Figure 6: Simulation of the Oc-scheme and Fc-scheme.
`
`DBW-scheme. Though both responsm are well within
`the high-efficiency window of the catalyst, the absence
`of the lean spike in the A/F in tip-in conditions in the
`DEW-scheme is immediately noticable. In DBW throttle
`systems, the engine is decoupled from the disturbances
`caused by the rapid throttle movements which are im-
`posed by the driver. The closed loop system has the fea-
`ture of isolating the high bandwidth torque demands by
`breaking the linkage between the driver and the primary
`throttles, facilitating smooth A[F control during transient
`engine operation. To achieve the same good A/F results
`we will need to form a smoother torque response in the
`engine.
`In the future we will incorporate the trade-off
`between the fast torque response and the small A/F ex-
`cursion in the control design for the secondary throttles.
`
`i— Q’c-Iehernh
`i
`.... ’...N“§______{L:T:Tn.5;m;..r.._.
`
`.
`
`__
`
`I
`
`.
`
`Ive-m
`
`itfifittu-
`
`the desired torque when the torque error is calculated to
`adjust the control signals.
`
`7 Simulation Example
`
`The purpose of this example is to illustrate some of the
`properties of the closed loop system using the secondary
`throttles The operating point about which we chose to
`linearize the engine model lies in the acceleration curve
`of the engine and third gear was used in the power-train
`rotational dynamics. The nominal primary throttle posi-
`tion used was 9 = 20°, and the nominal set-point for the
`secondary throttles was 61% open, resulting in a manifold
`pressure of Pm = 0.96 bar. The air flow into the cylinders
`was 15.4 g/sec at 3000 RPM producing 31.5 Nm of torque.
`The same amount of torque is produced by the conven-
`tional engine at a primary throttle position of 0 = 11.8".
`with a manifold pressure of 0.51 bar. Note that this op-
`erating point falls into the low oontrol authority region
`explained in Section 4. The resulting linear model has 10
`states and is augmented with the two integrated states of
`the A/F and torque error.
`The closed loop performance of the engine with the sec-
`ondary throttles (oc-scheme) is compared with the con-
`ventional A/F control scheme (Fe-scheme) and with a.
`DBW throttle scheme (DEW-scheme). The conventional
`A/F control scheme regulates the fuel pulse-width dura-
`tion usually with a PI controller. Seeking a fair compari—
`son between the conventional and the proposed controllerI
`the conventional fuel pulsewidth duration regulation is de-
`signed based on an LQG/LTR controller. Both A/F and
`torque measurements are used to improve the estimation
`process. The DBW throttle system is designed to track
`the demanded torque and regulate A/F to stoichiometry.
`The multivariable control law used is based on LQG/LTR
`design methodology.
`Figure 6 is a simulation of the nominal response of the
`Oc-scheme and the Fc-acheme for a 10% step change in
`primary throttle position, which corresponds to 16% step
`change in torque demand. The Oe-scheme has 10.14%
`A/F excursion and essentially zero A/F and torque er-
`ror after 50 intake events. The integrated error of A/F
`during a rapid throttle movement can be used as a mea-
`surement of engine emissions during that period. The
`integrated error of A/F for the Fc-scheme is 0.0402 and
`for the Be-scheme is 0.0051, which indicates a possible
`reduction of engine emissions. Also, the engine reaches
`the specified torque faster than in the Fc-scheme, improv-
`ing driveahility significantly. Note that the conventional
`fuel pulsewidth duration control does not affect the torque
`performance of the engine.
`The simulation in Fig. 7 demonstrates the torque trnk-
`ing performance of the proposed scheme in comparison
`with the DEW-scheme. The emissions performance is
`equivalent in the two systems. The integrated A/F er—
`ror (during one of the throttle step changes pictured in
`Fig 7) in the Gradients is 60% less than that in the
`
`Figure 7: Closed loop response of the 0c-scheme and
`DEW-scheme for a square wave in the demanded torque.
`
`The performance of the 0c-scheme was also tested on-
`
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`der uncertainty in the fuel puddling dynamics due to their
`importance in accurate transient A/F control. Figure 8
`shows the torque and A/F response of the above control
`schemes using a time constant of 0.2 sec in the puddling
`dynamics (see Section 8). The simulation results shcw
`a limited performance degradation of the closed loops.
`however the oc—scheme maintains the improvement of the
`torque response better than the other two methods: inte-
`garted A/F error in the Fc-scheme is 0.0547, and in the
`9c—scherne it is 0.0084; the A/F response of the DBW—
`scheme also slightly degrades and the A/F integrated er-
`ror is 0.0085. Therefore the ac-scheme maintains emis-
`sions results comparable to the DEW-scheme.
`
`
`
`Figure 8: Closed loop performance under uncertainty
`in the fuel puddling dynamics.
`
`8 Conclusions and Future Work
`
`In this paper we investigated a control scheme for tran-
`sient A/F and torque control during rapid changes in the
`primary throttle position. The air and fuel management
`scheme based on the secondary throttles seems promising.
`The modelling and control scheme developed is closely re-
`lated to variable cam timing engines (VCT). This will be
`pursued in future work.
`An important feature that we have to account for in
`the design is the discrete nature of the A/F system. A
`discrete nonlinear engine model with sample rate syn-
`chronous with crank-angle (event-based), as opposed to
`the conventional time synchronous sampling rate, can
`more accurately represent the combustion process, its de-
`lays and the availability of measurements. On the other
`hand, the continuous processes of the manifold breathing
`characteristics and the rotational dynamics of the vehicle
`enclose the discrete combustion process and result in a hy-
`brid system. Designing an associated nonlinear compen-
`sator which functions over the entire operating envelope
`of the engine is our next task.
`
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`
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`
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`
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