FA-4 911 0
`
`Proceedings of the 33rd
`Conference cm Decision and Control
`Me Buena Vista, FL - December 1994
`
`Engine Air-Fuel Ratio and Torque Control using Secondary Throttles
`
`A. G. Stefanopoulou: 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 autome
`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-
`lem 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
`stoichiometry 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, MI 48109-2122; work supported in part by the National
`Science Foundation under contract NSF ECS-92-13551; match-
`ing funds to this grant were provided by FORD MO. CO.
`
`exhaust manifold. The addition of a feedforward term for
`the fuel set-point does not completely alleviate this prob-
`lem. Developments 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 (e,)
`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 8, smooth out rapid changes of
`the charging process during throttle movements so that
`the fuel control path is able to maintain stoichiometry.
`
`Primary Throttle
`
`RUMW
`
`Intake
`ValW
`
`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
`
`0-7803-1 968-0/94$4.00@1994 JEEE
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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
`air-fuel ratio, unitless
`mass flow, g/sec
`flywheel speed, rad/sec
`pressure, bar
`torque, Nm
`primary throttle position, degrees
`secondary throttle position, unitless (0 + 1)
`
`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 p u m p
`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].
`
`me
`
`Figure 2: Engine model with secondary throttles.
`
`The discrete nature of the combustion process causes
`delays in the signal paths: between the mass charge 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
`timeconstants equal to 0.15 sec and 0.20 sec respectively.
`The model of the fuel puddling dynamics is given in [I]
`
`fi
`
`o.l.s+l
`
`by uf - 0 . 6 2 . s + l ~
`where r;ir; : injected fuel flow (g/sec)
`lkf : 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 (e,)
`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
`Oc 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 ( h e ) minus the pumping
`mass air flow rate (hf) into the cylinders. The manifold
`dynamics are described by the following first order differ-
`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 ( h e and hf respectively)
`
`The mass air flow rate into the manifold ( h e ) through the
`primary throttle body is a function of throttle angle (e),
`the upstream pressure (Po), which we assume to be stan-
`dard atmospheric, i.e. Po = 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. Pm/Po < 0.5, the flow m e through the throttle
`body is described as sonic flow and depends only on the
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`primary throttle position. The function describing h e in
`the two flow regimes is given in [ll], and [13] by
`h e = f(o)g(Pm)
`f(e) = 2.821 - 0.052318 + 0.102998~ - 0.000638~
`if P, 5 Pol2
`dPmP0 - PA
`if Pm > P o l 2
`
`(4.2)
`The engine pumping mass air flow rate (hf) is a function
`of manifold pressure (Pm) and engine speed (N) and is
`given in (31 by
`
`hf = -0.366+0.008979NPm -0.0337NP; +0.0001N2 Pm
`(4.3)
`For the basic model (without the secondary 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 (hf) by different values
`depending upon the effective area of the passage that is
`regulated by opening and closing these new valves:
`
`rhcyl = 8,
`
`. +.
`
`(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 & < 1, the steady state value of the mass
`air %ow into the cylinder hCyl 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.
`
`a
`
`.I
`
`1
`
`1
`
` A
`
`1
`
`1
`
` .7
`
`J
`
`1
`
`Figure 3: Trajectories of ke and hcyl for several values
`of e,.
`
`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 h e 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 A& and the mass air flow into
`the cylinder Arhcyl:
`
`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 A& cannot ad-
`just the air charge into the cylinder by %moothing” the
`effect of rapid throttle changes. Consequently, the control
`command A0, 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. PmlP, > 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 h e (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
`0, set-points that allows operation in the subsonic flow
`regime, where the secondary throttle have maximal con-
`trol authority, is necessary. 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 (ec),
`which consists of a nonlinear feedforward term (ecf ) plus
`a feedback term (ecf,). 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 (ecfw) is designed to
`satisfy the following three conditions: 1) it is a smooth
`and non-decreasing function of the primary throttle posi-
`tion (e) and the engine speed ( N ) , i.e. eCfw = eCfw(O, 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):
`
`ecfw =
`
`' 0.55
`0.6445 - 0.0126. e
`e2
`+i.3125.
`. e3
`+2.1875
`1 - ( F ) 2
`1
`
`if 0" < 0 < 12"
`
`if 120 5 e < 20"
`if 20" 5 0 < 60"
`if 60" 5 0 < 90"
`
`Rly-
`
`0
`
`Figure 5: Static feedforward nonlinear term of the
`control signal 0,
`
`The reasoning behind this map is briefly explained.
`First of all, usual driving conditions in urban areas cor-
`respond to partly open primary throttle (e) 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 Ocfw < 1 is acceptable. In addition, Ocfw has
`
`been adjusted to ensure that the breathing process is o p
`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, P,,,/P, % 1. Therefore the secondary
`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, 5 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 P,/P, s 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 DemandMap
`
`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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`

`
`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 f? = 20°, and the nominal set-point for the
`secondary throttles was 61% open, resulting in a manifold
`pressure of P,,, = 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 = 11.801
`with a manifold pressure of 0.51 bar. Note that this op-
`erating point falls into the low control 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 (&-scheme) is compared with the con-
`ventional A/F control scheme (&scheme) and with a
`DBW throttle scheme (DBW-scheme). The conventional
`A/F control scheme regulates the fuel pulsewidth dura-
`tion usually with a PI controller. Seeking a fair compari-
`son between the conventional and the proposed controller,
`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.
`Fijpre 6 is a simulation of the nominal response of the
`&-scheme and the Fc-scheme for a 10% step change in
`primary throttle position, which corresponds to 16% step
`change in torque demand. The C-scheme has f0.14%
`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 &-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 driveability 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 trak-
`ing performance of the proposed scheme in comparison
`with the DBW-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 &-scheme is 60% Iess than that in the
`
`f
`
`e
`
`
`
`f "r-
`
`I
`
`Figure 6: Simulation of the &-scheme and &scheme.
`
`DBW-scheme. Though both responses 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
`DBW-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.
`
`-kponr
`
`I " " '
`
`
`
`" " " " ~ " " ' ~ ~ *
`
`~
`
`~
`
`'
`
`'
`
`'
`
`. '
`'
`
`
`'
`
`. .
`
`o
`
`5
`
`n
`
`it
`
`m
`t.onb
`Figure 7: Closed loop response of the &-scheme and
`DBW-scheme for a square wave in the demanded torque.
`
`U
`
`n
`
`n
`
`a
`
`The performance of the &-scheme was also tested un-
`
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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 3). The simulation results show
`a limited performance degradation of the closed loops,
`however the &-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
`&-scheme 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 &-scheme maintains emis-
`sions results comparable to the DBW-scheme.
`
`Figure 8: Closed loop performance under uncertainty
`in the fuel puddling dynamics.
`
`8 Conclusions and fiture 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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