Torque Management of Engines
`with Variable Cam Timing
`
`Mrdjan Jankovie, Florian Frischmuth, Anna Stefanopoulou, and Jeffrey A. Cook
`
`into the intake stroke. more exhaust gas is drawn into the cylinder
`providing internal exhaust gas recirculation, In this manner. the
`amount of residual gas trapped in the cylinder at the end of the
`exhaust stroke is controlled by cam timing. suppressing NOX
`formation and reducing the pumping losses [1]. [9]. [14]. Fur-
`thermore. this residual contains some unburned hydrocarbons;
`consequently. retaining it in the cylinder through two combus-
`tion cycles also reduces hydrocarbon emissions [8].
`In addition to the reduction of NOx and HC emissions. vari-
`able eam timing permits the engine designer to optimize cam
`timing over a wide range of engine operating conditions. provid-
`ing both good idle quality (minimal overlap between the intake
`and exhaust events) and improved wide-open throttle perfor-
`mance (maximum inducted charge). In this aniclc. we will as-
`sume that
`the camshaft position is continuously variable to
`
`A:tontotivc powertrain control systems are. subject to diverse
`nd, usually, conflicting requirements. In particular, exhaust
`emissions must meet increasingly stringent Federal and Califor-
`nia standards while fuel economy must meet customer expecta-
`tions and contribute to Federally mandated Corporate Average
`Fuel Economy (CAFE) imperatives. Neither vehicle perfor-
`mance nor reliability may be compromised in attaining these
`goals (emission performance must be guaranteed for 100000
`miles). Of course. all these objectives must be achieved at the
`lowest possible cost and with the minimum number of sensors
`and actuators.
`
`The conventional method of reducing feedgas oxides of nitro-
`gen (NOx) emissions is by the application ofcxhaust gas recircu-
`lation (EGR). Formation of NOx during thc combustion process
`is influenced by air‘fuel ratio (A/F) and temperature. These vari-
`ables are typically adjusted by directing
`exhaust gas from the high pressure ex-
`haust manifold via a pulse-width modu-
`lated valve to the low pressure
`induction system where it serves to re-
`ducc the combustion temperature and
`dilute the airvfuel mixture in the cylin-
`der. A desirable side-effect is that the
`
`
`
`presence of inert exhaust gas raises the
`intake manifold pressure reducing the
`pumping losses and improving fuel
`economy. Although effective, the dy-
`namics associated with this system
`(transport delay, valve and intake mani-
`fold dynamics) ean result
`in vehicle
`performance deterioration.
`The variable cam timing (VCT) sys—
`tem with which this paper is concerned
`addresses both dn’vability and emis—
`sions perfonnance by utilizing an elec-
`tro-hydraulic mechanism to rotate the
`camshaft relative to the crankshaft in
`order to retard the cam timing with re-
`spect to the intake and exhaust strokes
`of the engine. Variable cam timing op-
`eration is illustrated in Fig. 1. By retard-
`ing the exhaust valve closing further
`
`Jankovic, Frischmuth. and Cook are with Ford Research Laboratories. P. 0. Box 2053. MD 2036 SR]. Dearbom, MI 48 I 2 l. Stefurwpoulou is
`with the Dept. ofMechanical and Environmental Engineering, Univarsity of Califomia. Santa Barbara, CA 93106.
`
`34
`
`0272-1708/98/310.00©199XIEEE
`
`IEEE Control Syslems
`
`VW EX1008
`
`US. Patent No. 6,557,540
`
`VW EX1008
`U.S. Patent No. 6,557,540
`
`

`

`g.J
`
`Base Valve Timing
`
`gg F
`
`ig. 1. Valve lift profiles ofconventional and VCT engines. By retarding the camphasing, the exhaust valve stays open during the intake event
`for a longer time period, retaining otherwise unbumed HC and reducing the combustion temperature due to the dilution of the inert gas.
`
`achieve the full benefits in emissions and torque. There are suc»
`cessful examples of simple. two-position VCT systems that ad-
`dress and partially resolve the idle versus wide-open throttle
`performance trade-off. Obviously, variable cam timing has a
`substantial effect on the breathing process of the engine.
`Properly controlled. the variable cam can be used to operate the
`engine at higher intake manifold pressures, reducing pumping
`losses at part throttle conditions and providing a fuel economy
`improvement as well [2]. [4]. [7].
`Four versions of VCT are available for double overhead cam-
`
`shaft (DOHC) engines: phasing only the intake cam (intake
`only), phasing only the exhaust cam (exhaust only). phasing the
`intake and exhaust cams equally (dual equal). and phasing the
`two camshafts independently (dual independent). The dual inde-
`pendent VCT provides the best performance. but it is the most
`complex and expensive to implement. Of the remaining three.
`dual equal VCT, where the intake valve timing and exhaust valve
`timing are advanced or retarded equally. gives the best overall
`performance in terms ofemissions and fuel economy [6]. On the
`other hand, the dual equal VCT causes the greatest disturbance to
`cylinder air—charge and air-fuel ratio which may result
`in
`drivability problems and increased tailpipe emissions above lev-
`els predicted by the steady state analysis [1 1].
`One method of reducing the air-charge variation and improv-
`ing drivability is to “detune the cam“ by slowing down the re-
`
`sponse of the VCT mechanism. However. dettming the cam re-
`sults in engine operation with lower levels of recirculated
`exhausr gas and increased NOx emissions. Drivability can also
`be improved by selecting a less aggressive (steady-state subopti-
`mal) cam timing schedule. but again the price for this is increased
`NOx emissions and reduced fueleconomy. Instead, in this article
`we pursue an active method of compensation for cylinder air-
`charge variation due to VCI‘ which employs either an electronic
`throttle or an air-bypass valve. Electronic control of the throttle
`provides an additional degree of control capability to affect
`emissions and fuel economy while providing the performance
`desired by the driver as interpreted from the accelerator pedal po-
`sition. The air-bypass valve is a conventional actuator of limited
`authority used to admit air flow to the engine under closed throt-
`tle operation, and to effect idle speed regulation [3]. [5].
`From the controller design point of view. several prominent
`characteristics of this problem will dictate our approach:
`0 The model of the plant is low order, nonlinear, with known
`nonlinean'ties available from the dynamometer mapping data.
`
`O The disturbance (cam phasing) is measured.
`
`0 The output (cylinder mass air flow. or cylinder air charge,
`or torque) is n0t measured.
`
`0 Transient response is much more important than steady
`state accuracy.
`
`October I998
`
`35
`
`

`

`T(mqr.A/F.N]
`
`Fig. 2. Engine model with VCT and electronic throttle.
`
`The first three items above suggest that a feedforward com-
`pensation may be the most appropriate, so this is the approach we
`adopt. Our compensator design is based on a low order nonlinear
`model ofa VCTengine derived in [12]. Starting from the nonlin-
`ear model we develop a nonlinear control algorithm that rejects
`the air-charge (torque) disturbance and recovers the drivability
`of the conventional engine. (Note that the "conventional engine”
`in this context is the engine which corresponds to fixed cam at 0°
`(base cam). However. this algorithm requires a degree of control
`authority which is available only if the engine is equipped with
`an electronic throttle (ETC). If the engine is equipped only with
`an air-bypass valve (ABV), the limited control authority of this de-
`vice forces us to change the design objective: rather than to emu-
`late the conventional engine, our compensation tries to achieve the
`dn'vability of an engine with a different characteristic.
`Because the relative degree from the disturbance to the output
`is smaller that the one from the control input to the output (the
`disturbance is closer to the output than the control). our compen-
`sation algorithm uses the derivative of the disturbance (cam
`phasing). We present two different methods of implementing this
`term in order to find a trade-off among the performance of the
`compensator, the sensitivity to measurement noise, and the sen-
`sitivity to parameter variation.
`
`VC’l‘ Engine Model
`The control design engine model described here is a continu-
`ous-time nonlinear, low-frequency phenomenological model de-
`veloped in [10] and modified to incorporate VC’I‘ in [12]. Details
`about the VCT engine model can be found in [l 3]. A block dia-
`gram in Fig. 2 shows the cam timing reference C", scheduled on
`engine speed and driver demanded throttle 60.
`
`
` Notation
`A/F air-fuel ratio
`
`N engine speed
`Pm: manifold pressure
`m M: mass of air into cylinder
`T: torque
`QM: cam phasing command
`Cm: cam phasing
`90: throttle angle due to driver request
`6': additive throttle angle due to compensation
`9: total throttle angle
`(991 mass air flow rate into manifold
`¢nl= mass air flow rate into cylinders
`5: 'opening of the air-bypass valve
`AT: duration of the intake event
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`The engine breathing dynamics describe the filling and emp-
`tying of the manifold. The rate of change is proportional to the
`difference between mass air flow rate into the manifold through
`the throttle (¢,) and the mass air flow rate out of the manifold into
`the cylinders mm)
`
`P. =K.(¢.—o..,)»
`
`(1)
`
`The mass air flow through the throttle body into the manifold
`is a function of the upstream atmospheric pressure P", the mani-
`fold pressure, and the throttle angle:
`
`4% =gI(PnI I Pa)g2(e’Pa)‘
`
`where
`
`(PIP)
`M
`a =
`
`g
`
`'
`
`‘f£"—<—3—fi
`il/2_:__)II'T"|T
`jib—(W, I
`P' 4'“)
`J.
`3
`L"
`5%};((ffl'-(%~ ) ir:—:>(,-3;r-'.
`V
`
`(2)
`
`with y = cp/cy = 1.4. g2(9,Pa) is the throttle dependent mass air
`flow characteristic obtained from static engine data We assume
`that Pa = lbar and suppress the dependence of g, and g2 onfl.
`In this application, the throttle angle is comprised of the throt-
`tle position due to the driver‘s request (09) and an additive term
`due to the compensation (6')
`
`e=eo+e'.
`
`It is important to observe in Fig. 2 that the cam is scheduled
`only on 90. The mass air flow rate into the cylinders can be repre-
`sented as a function of cam phasing Cm. manifold pressure P",
`and engine speed N:
`
`on, =F<N.PM.§...).
`
`(3)
`
`For our design model we approximate F(N.PM.CM) by a
`function linear in P":
`
`on, =a.(N.;m,.)P.. mama“).
`
`(4)
`
`where 0tI and a2 are low order polynomials in N and Cam.
`The generation of torque depends on the cylinder air charge
`"7:va air-fuel ratio A/F, spark retard from MB'I‘ o. and engine
`speed. This relationship is best captured by curve fitting of ex-
`perimental data:
`
`T e T(mq,,A/F.6,N),
`
`<5)
`
`a: spark retard from maximum braking torque (MBT) setting.
`
`
`
`36
`
`IEEE Control Systems
`
`

`

`The basic idea is to find a control law fore'
`
`such that the rate of change of 0..., coincides
`with that of the conventional engine. We start
`with the equations (1) and (3) which describe
`the manifold filling and engine pumping rates.
`By differentiating tp 0.: we obtain
`-
`a
`°m_ F(N PM-C.....
`8N
`8F(N+ Mm
`3PM
`1""
`
`To simplify our presentation we shall assume
`that the N term is approximately equal to the
`conesponding term in the conventional engine;
`that is. we assume thataF(N”Q ) / 3N —
`8F(N.Pm /3N)N= 0. Hence we suppress
`the N -terms in our subsequent derivation If this
`assumption does not hold we can redesign our
`compensator in a straightforward way to account
`for this additional disturbance term. By using the
`linear (in PM) approximation of F and expanding
`PM we obtain
`
`
`
`,2
`
`AEE039
`
`'
`
`Fig. 3. Engine torque response to a change in arm phasing atfired throttle and engine
`speed.
`
`$.71 =a I(N‘§mm)Km(gI(P JgZ(eo+e.)_¢q{)
`
`
`+ [_act.
`9C..-
`
`+2802;]
`3cm “‘""
`
`"
`
`(6)
`
`Now we can use 6' to cancel the disturbance term propor-
`tional to Cm. This. however. will not achieve complete distur-
`bance rejection becauseor| and PM depend on Q”. To achieve our
`objective we have to choose 9' in such a way that (pm behaves as
`if it is a cylinder mass flow rate of the conventional engine:
`
`43“,, =a.(N,0>K.<g.té.)g.(e.,)-om».
`
`(7)
`
`wherePM is a fictitious reference manifold pressure which should
`be equal to the manifold pressure of the conventional engine
`driven with the throttle 60 and engine speed N. This reference
`manifold pressure is generated by
`
`_ =KM(g.(}_’,.)8;(90)-a,(N.OJPM -0t:(N.0)).
`
`(8)
`
`The expression for 8' is simplified ifwe substitutea,(N,CMM) in-
`stead ofa,(N.0) in (3). This is justified by the fact that between the
`maximal and the minimal values ofQM. ,th changes by approximately
`20—25% and thatct I affects mostly the speed of response of pm.
`To achieve (3) with or,(N .CMM) instead of a,( N .0). the fol-
`lowing equality must be satisfied
`
`where m0,, 2» omAT. (AT is the duration of the intake event
`which depends on engine speed).
`In spark ignited (gasoline) engines the air—fuel ratio is main-
`tained at stoichiometry ( l 4.3) in order to ensure that the catalytic
`converter operates at its peak efficiency. Thus. from the expres-
`sions (3) and (5) it is clear that the change in cam timing affects
`the torque through the change in cylinder mass air flow rate. In
`sonic flow. when 8.(Pm) = c (c is a constant), the change in Cm
`does not change the steady state value of the torque. This can be
`verified on the model by noting that, in steady state when PM = 0,
`4)”, = on = cg,(0) independently of Cm. However. cam tran-
`sients do affect the torque as one can see in the dynamometer test
`data in Fig. 3 that show the response of engine torque to a change
`mg", with the other variables held constant. if the throttle flow is
`subsonic. cam changes also affect the steady state values of the
`cylinder mass air flow and torque.
`The cam timing has to change depending on the operating
`conditions. For this reason. QM, is scheduled on engine speed and
`throttle position. Typically, the schedule reaches maximal cam
`retards at part throttle which provides maximal internal EGR.
`While close [0 idle and at wide open throttle the cam phasing is at
`zero or slightly advanced. Scheduling cam timing on throttle
`causes it to change when the pedal is depressed or released. The
`torque variation caused by the cam transient leads to an undesir-
`able engine response and drivability problems. This effect will
`be illustrated in subsequent sections.
`
`Electronic Throttle Based Compensator
`We design a compensator to remove or reduce the effect of the
`cam transients on the cylinder mass air flow which employs 9' as
`a virtual actuator. We assume that the variables available for
`measurement are the manifold pressurePM, engine speed N. and
`the earn position Cm. Our design objectiveis to recover the driv—
`ability of the conventional engine.
`
`October 1998
`
`a (N g )KMg.(PM )g (eu+e')
`
`Ba
`
`[awnaji ‘
`
`30.2
`
`_
`
`a ,(N.€.M)ng.(7’.)g..(9o)-
`
`(9)
`
`37
`
`

`

`Thus, the compensation 9' should be chosen as
`
`-
`an,
`dull,
`-
`P)
`_
`.
`m+
`“summon ~60.
`e =g.‘ 3”
`Kngl(mexl
`gl(Pm)
`
`(10)
`
`smaller sensitivity of (12). The resulting steady state error in the
`cylinder mass air flow rate does not affect the drivability.
`To analyze the stability of the equilibrium at Pu”, we define
`x = P", — Pf. WithCm = 0. the linearization of the manifold pres-
`sure dynamics around the equilibrium P = P: results in
`
`Because the function 3, changes little in the range of manifold
`pressures between 0.2 to 0.8 barLanother possible simplification
`is to use the steady state yalue Pu"(60'~) instead of the dynami-
`cally generated pressure P". In simulations, a slight degradation
`in performance is noticeable only at high reference manifold
`pressures.
`
`Robust stability
`The above compensation method uses the information of the
`engine speed, cam phasing, and manifold pressure to modify the
`throttle and achieve the drivability of the conventional engine.
`Even though it is designed as a feedforward compensator. be-
`cause of its dependence on P", there is a feedback component
`which necessitates stability analysis.
`if. forfixed N and 60. cam retard causes the steady state mani-
`fold pressure to rise into the subsonic region, the compensation
`will create a different set point at a higher value of manifold pres—
`sure. This new set point, denoted by PS, may be sensitive to mod-
`eling uncertainties. Below, we propose a simple modification
`which makes the value ofP: less sensitive tomodcling uncertain-
`ties and guarantees that it is a stable equilibrium point.
`If the functions g, and g2 are known accurately, the implemen-
`tation of the control law (3) leads to
`
`-"°'—P + 3‘“
`———ai=C.M +g.(P.)gzteo>-F(N.P..,t,...)
`
`(11)
`
`In steady state; when PM and gm are zero, on, =
`l-‘tN “,ngggm) = g,(P,‘”)g2(60), that is, in steady state, the cylin-
`der mass air flow rate of the compensated VCT engine is exactly
`equal to that of the conventional engine.
`To analyze the sensitivity of the compensation method we
`note that the functions 3,, g2, or, and 0tz can be relatively accu-
`rately modeled from the static engine data. The only significant
`source of sensitivity arises because the function g., which is
`close to 0 at high manifold pressures, appears in the denominator
`in (10). So we only analyze the effect of modeling errors in g. on
`the steady state pressure P: and the stability of this equilibrium.
`To make it distinct from the “true” value g,, we use g, to denote
`the subsonicflow correction factor employed in the compensator
`(10).
`The steady state pressure P"? can be obtained by solving
`
`= SAP")
`.
`.
`stilt.)
`
`0
`
`é1(finn)g2(em_F(N“‘Rnt 3'1)‘
`
`(12)
`
`x-[§:[ap 8.
`38.31 gl( m )g2( o) (1.x.
`I— __ .a_g_L‘ _.&£
`"
`i5”
`0 _
`
`By our choice of g we have assured not only that g, 2 3l 2 0,
`but also thatl 8g, laPm SIBg,/8PmlSince8g1/8PM and ag, 18PM
`are both negative,
`this
`implies
`that (8g, I an); -
`(3g, / BP,,,)gI S 0. Because g, , 32, and otl are always positive, the
`equilibrium x = 0 is asymptotically stable. Hence, our compen-
`sation creates a single equilibrium P: which is asymptotically
`stable.
`
`Simulation results for ETC compensator
`To demonstrate the effecuveness of the compensation ( 10) we
`have tested it on a model which differs from the one used in the
`
`controller design. We have used a simpler design model in order
`to keep the compensator simple. In addition. this provides some
`indication of the effects of modeling errors on the performance
`of the compensator.
`can
`To implement C
`tiatlon
`
`we have chosen an approximate differen—
`
`
`t...~ ‘t
`._
`‘ts+l
`
`m,
`
`1 = 0.04s.
`
`If the high frequency measurement noise present in the signal
`gm is excessive. one can use a model based approximation of
`CM. We shall discussed this issue in the final section.
`The compensator, which has been developed in continuous
`time, has been discretized for simulations. The sampling rate is
`chosen to be l0ms.
`
`Fig. 4 shows the reduction of the torque fluctuation during
`cam transients achieved by the compensation. For this simula-
`tion run we have varied the reference cam independently from
`the throttle and engine speed (which are held constant). ln this
`and all other simulations the MBT spark is used. that is o = 0.
`Clearly, the compensator achieves a substantial level of distur-
`bance attenuation. ’lhe disturbance rejection is not perfect be-
`cause of the differences between the design and simulation
`models, discretization, and filtering used for the derivative of
`CW. The performance of the compensator appears much better if
`we look at its effect on drivability. Fig. 5 shows the performance
`of the compensated VCT engine compared with the conventional
`engine and uncompensated VCT engine. The input is the throttle
`step with the engine speed held constant and the cam reference
`scheduled on throttle and engine speed. The uncompensated
`VCI‘ engine response is not monotonically increasing, indicat-
`ing a drivability problem. Our compensation 0', which can be
`seen in the top plot in Fig. 5 as the difference between the solid
`and dashed curves. brings the response of the VCT engine close
`to that of the conventional engine, effectively removing this
`problem. We emphasize that the difference between the steady
`state values of the conventional engine and the (uncompensated)
`VCT engine has little effect on drivability. Rather, it is the shape
`
`At higher manifold pressures. the solution of ( l 2) is very sen-
`sitive to changes in [2,. We can reduce this sensitivity by inten-
`tionally skewing g, so that £103") > g,(PM) when P," is high. say
`Pm 2 0.75 bar. This guarantees the existence of a single solution
`of (12) and forces it to assume a lower value, in the direction of
`
`36‘
`
`IEEE Control Systems
`
`

`

`
`
`
`
`Fig. 4. Torque response of the V0 engine (dashed lines) to cam phase steps (0 to 44
`deg.) at fixed engine speed (2000 RPM) and throttle angle (7 deg. ); response with
`active compensation (full lines) shows substantial reduction in torque variation.
`
`To explain this point, we refer to Fig. 6. The
`dashed and dotted curves show the static
`throttle-to-load (load is the normalized cylinder
`air charge) characteristics at a fixed engine speed
`for conventional (Cm = 0°) and fixed cam (
`Cm = 35°) engines. By scheduling the cam on
`the throttle and engine speed, we create a new
`static characteristic for the VCT engine shown by
`the solid curve in Fig. 6. Now our objective is to
`modify the transients of the VCI' engine. using
`the ABV, so that the torque response is the same
`as that of a (fictitious) conventional engine which
`has a static throttle-to-lond characteristic shown
`
`by the solid curve .
`The new objective creates a problem for the
`design because now we do not have simple refer-
`ence manifold pressure dynamics. In fact, as we
`change the throttle, the scheduled QM changes.
`and our reference manifold pressure model
`changes. We emphasize that it is not sufficient to
`introduce F(N.P,,.C,,,) instead of F(N.P,,.0) in
`the manifold pressure dynamics (8). The prob-
`lem is that, at the step change in QM, not only
`must the dynamics for the reference pressure
`change, but also reference pressure value at that
`instant must change (jump). The generation of
`the desired reference manifold pressure can be
`done systematically at the expense of significant
`complexity. Instead. as a reference pressure we
`use the steady state value of the manifold pres-
`sure corresponding to the current values of N .90.
`and CW. Simulation results have confirmed that
`the simplified algorithm performs very well.
`With the air-bypass valve. the ideal gas law
`has to take into account the additional air coming
`through the ABV:
`.
`PM = Kmlg.(P,, )(gz(eo)+ 81(5))- F(N.R,,.§m)l.
`
`(13)
`
`of the transient response which affects it the most. This observa-
`tion will be used to modify our design objective in the next sec-
`tion, because low control authority of the air-bypass valve
`prevents us from recovering the torque response of the conven-
`tional engine.
`
`where 5 = 6,, HT is the opening of the air-bypass valve and g1 is
`its static flow characteristic. We assign 6 = 0 to the completely
`closed and 8 = l to the completely open valve. Following the
`same steps as for the electronic throttle compensation, we obtain
`
`Compensation with the Air-Bypass Valve
`In the previous section we showed an effective way to modu-
`late the electronic throttle to make a VCT engine respond like the
`conventional one. in most cases the engine will be equipped only
`with an air-bypass valve (ABV) which is used to control the idle
`speed by modifying the amount of air entering the intake mani-
`fold. We employ the ABV to affect the transients of the VCT en-
`gine and improve drivability.
`Because an ABV has much smaller control authority than an
`ETC. we have to change our design objective: instead of trying to
`perfectly match the response of the conventional engine. we shall
`only try to modify the torque transient to have the same shape as
`that of a conventional engine. The steady state torque will be dif-
`ferent, equal to that of the uncompensated VCT engine.
`
`6' = g"
`
`.2; P». + fi-
`J:1-....fi..asf:—~ Clam
`'K-g.(P.)a.(N.§...
`
`gal—1.")
`_""" v e
`
`+ 8.03..) [g( a)+g3(
`
`6o
`
`)1]
`
`_80 v
`
`the reference pressure E,” =
`where. as we have said above.
`[7,,“(N.60.50.§,,) is the steady state value of the manifold pres-
`sure corresponding to the present values of the variables N. 60,50,
`and CW. The evaluation of the reference pressure E,“ in real time
`can be done by evaluating two functions of two variables (two
`look-up tables).
`The potential for instability for the compensation with the
`ABV is much smaller than with the ETC. The reasons are (i) at
`
`October 1998
`
`39
`
`

`

`spouses of the compensated and uncompensated engines are the
`same. However, this happens in the region where the VCT does
`not cause drivability problems.
`
`Implementation of in,"
`Our compensation algorithms require that the derivative of
`(mm be available. Two methods to obtain this derivative are ex—
`plored. One method is to use the approximate differential of the
`available measurement as we have done for the simulations. the
`other one is a model based estimator. For the approximate differ-
`ential. we use the a second order, low-pass Butterworth filter.
`The model based estimator usesQM and N as inputs to the model
`of the VCl‘ mechanism (c.f. Fig. 2) which is itself a feedback
`loop consisting of the VCT actuator controlled by a PI'D regula-
`tor.
`
`The VCT actuator system consists of a control valve and the
`actuator itself. This control oriented model captures the domi-
`nant behavior of the VCT actuator system. These dominant dy-
`namics can be reduced to a single integrator. Adding higher
`frequency components does not add much to the accuracy of this
`model. The static control valve behavior is captured in the func-
`tion F(-). It is purely a function of the control input. The gain of
`the VCT actuator depends heavily on the engine speed N and is
`described by the static function K(N ). A block diagram of the
`VCT mechanism model is shown in Fig. 8.
`In Fig. 9, the estimated cam position and the cam position
`measured on the engine are the solid and dotted curve. respec-
`tively. The plot shows that the model captures the VCT mecha-
`
`
`
`30
`20
`Throttle Angle (degrees)
`
`40
`
`Fig. 6. Load vs throttle characteristic for the conventional engine
`(dashed line). an engine with com fixed at 35° retard (dotted line),
`and the VCTengine with cam scheduled on throttle and engine speed
`(fitll line).
`
`Throttledeg 6
`o88888
`
`ivo
`
`l l
`
`TorqueNm
`
`Time (sec)
`
`Fig. 5. Comparison of the throttle step torque response of the
`conventional engine (dotted lines), VCT engine without
`compensation (dashed lines), and VCT engine with compensation
`(fill! lines): engine speed is 2000 RPM, throttle is steppedfrom 4 to
`12 and back to 4 deg.
`
`the high endJ—in“ < P3. and (ii) at the operating regimes with high
`manifold pressure, the ABV has little control authority. Never-
`theless. we have used the skewed value g, in the implementation.
`The simulations are performed with the same simulation and
`design models as in the case of electronic throttle except that
`both models now include the air-bypass valve as an actuator. The
`air-flow characteristic of the valve is modeled as a sigmoidal
`function forthe simulation model and as a straight line for the de-
`sign model.
`Plots in Fig. 7 show the ainbypass valve opening 6 and the
`torque responses to throttle steps with the cam timing scheduled
`on throttle angle and engine speed. The torque of uncompensated
`VCT engine (dashed line) flares at both tip—ins and tip-outs indi—
`cating a drivability problem. Our compensation algorithm re-
`sults in the torque response which closely resembles a scaled
`down response of the conventional engine (full line). The dy-
`namics of the air-bypass valve have been neglected in the simula-
`tion model; the traces of 8 for the uncompensated VCT engine
`show the dash-pot functionality of the air-bypass valve. The dif-
`ference between the steady state values for two torques in Fig. 7
`is due to the difference between the simulation and design mod-
`els. It has no consequence on drivability and can be removed with
`a simple high-pass filter if desired.
`’l11e algorithm has shown very good performance in simula-
`tions The compensator has performed well over a variety of
`speed and load conditions. At high loads (high values of throttle)
`the air-bypass valve loses its control authority and the torque re-
`
`40
`
`IEEE Control Systems
`
`

`

`
`SAF. papct 910445, 1991.
`
`References
`[l] T.W. Asmus. “Perspectives on Applications of Variable Valve Timing."
`
`[2] A. C. Elrod and M. 1‘. Nelson. "Development of 2 Variable Valve Timing
`Engine to Eliminate the Pumping bosses Associated with Throttled Opera-
`tion.“ SAE Paper No. 860537. 1986.
`
`.
`.
`.
`”8- 10- CUMW’I-W" 0] guy" estimate obtained b)‘ appmxrmate
`difl’erentlation (dotted) and the model based one (solid).
`
`October I998
`
`4 I
`
`Fig. 9. Comparison ofthe model basedCM estimate (solid) andCM
`Fig. 7. Normalized arr-bypass valve opening 6 and torque response measured (dotted).
`for the VC‘T engine without compensation (dashed lines) and with
`compensation (fit/l lines): throttle steps 0 to 9 to 0 deg. engine speed
`[250 RPM.
`
`
`
`Fig. 8. Simplified contmls-oriented model ofthe VCTmechanistu.
`
`nism dynamics very well. It also shows high frequency noise
`content in the measured signal which forces us to use a low band-
`width Butterworth filter for approximate differentiation.
`The estimates of Cm obtained by two methods are shown in
`Fig. 10. The one obtained by differentiating the measured cam
`position lags the model-based one because of the low pass filter-
`ing and measurement delay. It appears that the model is suffi-
`ciently accurate to show a clear advantage over an approximate
`dilTerentiation method. One must keep in mind. however. that
`this conclusion applies for the particular hardware implementa-
`tion of the VCT sensor and actuator.
`
`dd!CAM[deg/sec]
`
`

`

`[3} A. I- Emtage. P. A. Lawson. M. A. Passmorc. G. G. Lucas and P. L. Ad-
`cock. "The Development ofnn Automotive Drive—ByJMrc Throttle System
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`
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`
`[5] S. C. Hsieh. A. G. Stefanopoulou, l. S. Freudenberg. and K. R. Butts.
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`
`[6| T.G. Leone. EJ. Christensen. RA. Stein. “Comparison of Variable Carn-
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`
`[7] T. H. Ma, “Effects of Variable Engine Valve Timing on Fuel Economy."
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`
`[81 G.-B. Meacham. “Variable Cam Timing as an Emission Control Tool.”
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`
`[9] Y Moriya. A. Watanabe. ll. Uda. H. Kawamurtt, .Vl. Yoshiuka. “A Newly
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`
`I 10] B.K. Powell. .I.A. Cook. “Nonlinear Low Frequency Phenomenological
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`pp.332—340.
`
`[ l I] A. Stefanopoulou, KR. Butts. IA. Cook. 1.8. Freudenbcrg. 1W. Grizzle.
`“Consequences of Modular Controller Development for Automotive Power-
`trains: A Case Study." Proceedings of CDC. New Orleans LA. 1995. pp.
`768—773.
`
`[[2] A. Stefanopoulou, “Modeling and Control of Advance Technology En-
`gines," Ph.D. Dissertation, University of Michigan. Ann Arbor MI. 1996.
`
`I I3] A.G. Stefanopoulou. J.A. Cook. J.W. Grime. J.S. Freudenberg. “Control-
`Oriented Model of a Dual Equal Variable Cam Timing Spark Ignition En-
`gine. ASME J. ofDynamical Systems. Measurement, and Control. vol. 120.
`June I998.
`
`[I4] R.A. Stein. KM. Galietti, T.G. Leone. “Dual Equal VCT—A Variable
`Camshafi Timing Strategy for Improved Fuel Economy and Emissions."
`SAE Paper 950975. 1995.
`
`[IS] R. A. Stein, K. M. Galietti and'l‘. G. Leone. “Dial Equal VC'F- A Vari-
`able Camshaft liming Strategy for improved Fuel Economy and Emissions.”
`SAE Paper No. 950975, I995.
`
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`
`
`
`Mrdjan Jankovlc received the BS degree in Electrical
`Engineering from the University of Belgrade. Yugosla-
`via. and MS and D.Sc. degrees in Systems Science and
`Math from Washington University. St. Louis. He has
`held postdoctoral positions with Washington Univer-
`sity and University of California. Santa Barbara. In
`[995 he joined Ford Research Laboratories to work on
`development of advanced powertrain control systems.
`Dr. Jankovic’s research interests include nonlinear and
`adaptive control with application to powenrain control systems. He has
`co-authored numerous technical articles and one book: Constructive Nonlin-
`ear Control (Springer-Vcrlag. I997). Currently. Dr. Jankovic serves as an As-
`sociate Editor for IEEE Transactions on Control Systems Te