CONTROL AND OPTIMIZATION OF TURBOCHARGED SPARK IGNITED ENGINES. Lars Eriksson Simon Frei Christopher Onder Lino Guzzella. ETH Zurich, Switzerland

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1 Copyright 00 IFAC 5th Triennial World Congress, Barcelona, Spain CONTROL AND OPTIMIZATION OF TURBOCHARGED SPARK IGNITED ENGINES Lars Eriksson Sion Frei Christopher Onder Lino Guzzella ETH Zurich, Switzerland Abstract: The subject of this study is the trade-off between fuel econoy and transient perforance in turbocharged engines. It quantifies the losses and gains of different engine control strategies. Two extree strategies are analyzed, one for optial fuel econoy and the other for fast transient response. Models for the coponents that influence the fuel econoy are developed and described. An optiization proble for best fuel econoy is solved analytically and a fuel-optial controller is ipleented based on that result. This controller is copared to one which is optiized for fast transient response with respect to the gains in fuel econoy and losses in transient response. Siulations of a highly boosted engine show that a fuel-optial controller can iprove the fuel econoy of a vehicle operated at cruising speed by -3% and at highway speed by %, and that the highest achievable iproveent is above 0%. The losses in transient response are around 0. s for cruising conditions. Furtherore, easureents on a low-boosted engine on a test bench are used to show that the fuel-optial controller reduces fuel consuption by.9% at highway conditions. Keywords: Engine control, turbocharging, response tie, fuel consuption.. INTRODUCTION Custoer deands for vehicles with a low fuel consuption are aong the ain driving forces for the technical developent of engines and vehicles. However, custoers do not sacrifice driveability for a reduced fuel consuption. Downsizing and supercharging concepts are one proising way of reducing the fuel consuption while delivering the sae rated power, as presented in detail in Guzzella et al. (000) and Soltic (000). In turbocharged engines the deands for best fuel econoy and good driveability are conflicting goals for the control syste design. Current industry practice is to optiize the syste for driveability, i.e., for the fastest possible transient response, with a sacrifice in efficiency. The ai here is to quantify the gain in fuel econoy and the loss in response tie if a control strategy for best fuel econoy is used instead.. SYSTEM OVERVIEW AND TC MATCHING In a turbocharged engine, the exhaust enthalpy is used to copress the air in the intake anifold and thus to achieve an increase in ass flow through the engine a. The engine investigated in this paper is highly boosted, i.e., it runs with a axiu intake anifold pressure of p i,ax = bar. An overview of the engine is given in Figure. The syste has two control inputs: the throttle signal u th which affects the intake anifold pressure p i, and the waste gate signal u wg which affects the exhaust back pressure and the boost pressure p c. When the syste has to reach a certain state, e.g., when the torque T q e and engine speed N are fixed, one degree of freedo reains. This degree of freedo can either be used to keep the copressor

2 Air Filter Intercooler p af Air flow p c p ic Exhaust flow Cop. & Turb. Throttle u th p i p t Exhaust Wastegate u wg Exhaust an. Engine Intake an. Fig.. Overview of the engine. The odel consists of six receivers for each of which the pressure variable is shown. speed at its highest possible level, which provides a fast transient response, or to lower the back pressure, which ensures good fuel econoy. This leads to two different control strategies that will be described in section. Matching up a copressor, a turbine, and an engine is a coplex task that involves several steps. The following procedure is a siplification, but it illustrates the key steps: ) Deterine engine displaceent and axiu engine power, which results in data on the boost level and on the axiu air ass flow. ) Deterine the copressors that fulfill those requireents and that reach the desired boost pressure without surging at the lowest flows possible. 3) Deterine the turbines that drive the copressors as closely to the surge line as possible without generating too high a back pressure. Based on this procedure, siulations and experients are done to find the copressor and the turbine that best atch a set of given perforance criteria. Three-way catalytic converters are typically used to reduce eissions by requiring the engine to operate at stoichioetric conditions, i.e., λ =. We thus focus our investigation on engines operating at λ =, thus ignoring the proble that current turbine aterials cannot withstand teperatures above 300 K. Current practice is to protect the turbine at high air ass flows by fuel enrichent, which significantly raises the levels of pollutants and the fuel consuption. 3. OPTIMAL FUEL ECONOMY: FORMULATION OF THE PROBLEM The brake-specific fuel consuption BSFC is defined as the fuel ass flow f divided by the generated power P BSFC f P = f T q π N where N is the engine speed in revolutions per second. One proble with the definition of BSFC is that there is a singularity at zero torque. Therefore it is advantageous to look at BSFC = T q π N/ f which then has to be axiized for best fuel efficiency. Optiizing the cruising scenario with constant speed for the best fuel econoy is thus the sae as axiizing T q/ f. For cruising we now also consider the axiization under liited resources, that is a desired fuel flow f,des, which now becoes ax T q(u th, u wg, f ) subject to f (u th, u wg ) = f,des A constant fuel flow corresponds to a constant air flow, since we are restricting engine operation to stoichioetric conditions. This leads to the following forulation of the proble ax T q(u th, u wg, a ) subject to a (u th, u wg ) = a,des (). MODELING OF A TURBOCHARGED ENGINE The structure incorporates a nuber of control volues which are separated by flow restrictions (see Figure ). As a detailed explanation of the coplete odel would exceed the scope of this paper, only the coponents necessary for studying the proble of fuel optiality are described in the following paragraphs. The forulation of the fuel-optial operation of turbocharged SI engines shows that odels for engine torque and engine air-ass flow are necessary. Since the control inputs affect the intake and exhaust anifold pressures, the odels ust describe how these pressures influence the torque levels and the air flow.. Engine Air Mass Flow The air ass flow to the engine is odeled using the voluetric efficiency η vol which provides the data necessary to calculate the aount of fresh

3 gases in the displaced volue V d. The air ass flow is a (N, p i, T i, ) = η vol V d N p i R T i () with T i representing the intake anifold teperature. Since the intercooler efficiently takes away the teperature increase produced by the copressor, T i is assued to be constant. The voluetric efficiency η vol depends on the valve overlap as well as on the intake and exhaust anifold pressures, see e.g., the odel by Fox et al. (993). Since the engine considered here is highly boosted, the valve overlap can be assued to be very sall, in order to avoid scavenging losses. Therefore the residual gas ass is considered to be a function of the exhaust anifold state and of the clearance volue only. In the ideal Otto cycle, with no valve overlap, the voluetric efficiency is given by ( ) / r c pe p i η vol = C ηvol (3) r c where C ηvol is a constant, is the ratio of specific heats, and r c is the copression ratio.. Engine Torque The engine torque is odeled on the basis of the work produced, where net work W n is deterined fro the gross indicated work W ig, produced by the high-pressure part of the engine cycle, inus the su of puping and friction work W p + W f during one cycle. T q = W n π = W ig W p W f π The gross indicated work is W ig = f q HV η ig () where q HV is the lower heating value of the fuel and f is the injected fuel ass per engine cycle. The gross indicated efficiency η ig depends on the therodynaic cycle and heat transfer. It is assued to be independent of p i and. The puping work is and the friction work is W p = V d ( p i ) W f = V d FMEP(N, f ) where the friction ean effective pressure FMEP depends ainly on the speed. The slight dependence on engine load is captured by the variable f. The FMEP odel used here is based on the ETH odel (Inhelder, 99; Stöckli, 99). With this paraeterization, the friction odel as well is independent of p i and..3 Copressor and Turbine The pressure ratios over the coponents are defined as the pressure after the device divided by the pressure before the device, which for the copressor and turbine pressure ratios ay be expressed as follows: Π c p c p af >, Π t p t < Copressor and turbine perforance is usually available in ters of aps easured in a flow bench by the anufacturer. These aps show the interrelationships aong speed, flow, pressure ratio, and efficiency. The echanical efficiency of the turbocharger is usually included in the efficiency ap for the turbine. Steady-state operation is deterined fro the power balance of the turbine and the copressor. P t = P c (5) The power consued by the copressor is ] a c p,a T bc [Π c P c = () η c where η c is the copressor efficiency. The power delivered by the turbine is ] P t = e c p,e T bt [ Π η t (7) where η t is the turbine efficiency. t 5. OPTIMAL FUEL ECONOMY: THE SOLUTION With the odels at hand we once again turn to the proble of fuel-optial control introduced by eqn. (). Studying the torque odel under the constraints of constant speed and constant fuel ass flow and with the odeling assuptions, we see that the only ter affected by the control inputs is the puping work. Thus, axiizing () for constant fuel ass is identical to iniizing puping work W p. Dividing W p by the constant V d yields the following function to be iniized: U(, p i ) = p i In turbocharged engines it is possible to have a p i that is higher than, which eans that the puping actually produces energy. It is now of great interest to see if the controller can take advantage of this effect to increase the engine output torque and fuel econoy. However, as will be shown below, this is not the case, allowing the following fuel optiality stateent to be ade: The optial controller for proble () always iniizes p i and if the air flow odel (), (3) and the following inequality hold

4 ( pi ) < 7 () At first glance this stateent contradicts coon sense since the puping losses see to be lowered when p i is increased. In the next section, first the stateent and then inequality () will be justified. 5. Justification of fuel optiality stateent First the fuel ass flow constraint is studied. For a given air ass flow through the engine, eqs. () and (3) define the relation between the intake anifold and exhaust anifold pressures. By anipulating () and (3) the following function can be defined f e (p i ) p i = ( r c a p i ) (9) where a = Cη vol V d N (r c ) R T i > 0. This function is always positive, and it is onotonously increasing with p i, since f e(p i ) = (r c ) a p }{{ i a p } > 0 (0) i >0 where r c a p i > 0 follows fro (9) and fro the fact that the air ass flow is positive. This relation says that p i onotonously increases with. The function to be iniized, U(p i, ), can be rewritten as a function with only one variable, V (p i ), using the definition of f e (p i ) V (p i ) p i = p i (f e (p i ) ) Its derivative is: V (p i ) = f e(p i ) p i + f e (p i ) Now we have to prove that V (p i ) > 0 for all possible values of p i. First of all, if f e (p i ) > then (0) shows that V (p i ) > 0 (which is > p i and approxiately naturally aspirating ode of the supercharged engine). Thus the optial strategy is to iniize p i in this region. The case that reains to be investigated is f e (p i ) < () Inserting (0) into V (p i ) and anipulating the resulting equation yields V (p i ) = (r c ) + f e (p i ) a p i a p i = f e (p i ) (r c f e (p i ) ) + fe (p i ) Finally, () together with () can be used to show that since > and r c the derivative is positive. V (p i ) = f e (p i ) } {{ } > 7 }{{} > (r c f e (p i ) ) + f e (p i ) }{{}}{{} < >0 } {{ } >r c > 7 (r c ) > 0 The fact that r c is derived in Soltic (000) where a database of production engines was investigated and the sallest copression ratio for a turbocharged engine was found to be. The fuel optiality stateent is thus justified Justification of () Inequality () defines a bound on the pressure ratio over the engine for which the fuel optial stateent is valid. Evaluating the bound for =. yields pi < 90. This is uch higher than all attainable values of the pressure ratio. Currently the highest pressure ratios delivered by copressors start reaching values of, so there is a very large argin. However, this argin is not satisfactory since it relies upon current copressor liitations. We thus seek a theoretical upper liit on the pressure ratio. Inserting () and (7) into the power balance (5) yields Πc Πt = e c p,e T bt a c p,a T bc η c η t }{{} A Multiplying both sides with Πt ( Πt ) and solving for the following Πt Πc eventually yields = A Πt [ Π t (Π t Π c ) (A + ) A ] + Πt In order to get an upper bound on A, we assue the axiu teperature of the turbine inlet to be 300 K, which is at the liit of what the turbine aterial can tolerate, and the lower liit on the inlet conditions to be 73 K, with the following liits for the fluid properties, c p,e >.3 [ J /g K], c p,a >.00 [ J /g K], and e = + (A/F ) s <.07. a Inserting these nubers, together with the definitions of the pressures, and noting that all turbines and copressors have efficiencies lower than unity leads to the following liit, A <.73 ηc=η t= ( ) pi <.3 This liit of.3, based on the above assued physics, is uch lower than the value of 7 and therefore () holds in any realistic case.

5 . CONTROL DESIGN The fuel optiality stateent says that it is always favorable to lower p i and as uch as possible. The strategy indicated by this stateent is to open the waste gate (or in the case of a variable nozzle turbine to open the nozzles) as uch as possible. The controller to achieve this can be described as follows.. Layout : Fuel-optial controller Starting fro low load the waste gate is fully open and the throttle is used to control the load. Only after the throttle is fully open the waste gate starts to close and controls the intake anifold pressures above abient pressure. BMEP [bar] 0 0 Iproveent in fuel econoy [%] Engine speed [rp] Fig.. Siulated iproveent in brake-specific fuel consuption at steady state when using the fuel-optial controller Layout : Driveability-optiized controller In current series production cars the tie-optial strategy is ipleented. The goal of this strategy is to keep the turbocharger on the highest possible speed. This is due to the fact that the rotational dynaics of the turbocharger are the liiting factor for the tie response. This is achieved by closing the waste gate as uch as possible until an appropriate boost pressure after the copressor p c is reached. This level lies above the axiu of p i, since the intercooler and the open throttle act as flow restrictions. In this strategy the throttle is used for load control and the waste gate is only used to liit the boost pressure. Pressure [bar] Lower back pressure Mean pressures Volue [ 3 ] Open WG Closed WG 7. COMPARISON OF THE TWO CONTROLLER VERSIONS 7. Difference in fuel econoy Figure shows the iproveent in fuel econoy that can be achieved when using the fuel-optial controller. The gains are especially high for low loads and high engine speeds. But the ost interesting points are those below 3500 rp and 0 bar BMEP, as ore than 0% of the operating tie fall into that region. The iproveent in fuel econoy for cruising conditions, approxiately 000 rp and bar BMEP, is around %, whereas for highway driving with higher speeds and loads the iproveent is around % Experiental validation Measureents have been perfored on a ildly-boosted turbocharged SAAB.3 liter engine to validate the predicted gains in fuel econoy. Since the engine only has low boosting, the gain in fuel econoy will be lower than the gains shown in Figure.The Fig. 3. Plot showing easured cylinder pressure averaged over 0 cycles for the two control strategies at the sae air ass flow and engine speed. In the plot the decreased back pressure is clearly shown, which decreases the puping losses. conditions for the test are the sae as for (). Two easureents at the sae engine speed and with the sae air ass flow are ade, one with the wastegate fully closed and one with it fully open. The speed, ass flow, and λ are controlled using three closed-loop controllers. The operating condition was an engine speed of 300 rp and a BMEP of 5. bar. The cylinder pressures fro the two easureents are plotted in Figure 3. Quite obviously, the exhaust back pressure is decreased when the wastegate is open. In the easureents, the torque increased fro to 05.5 N when the wastegate was opened, which reflects an efficiency increase of.9%.

6 BMEP [bar] 0 0 Tie delay standard controller [s] Engine speed [rp] 7.3 Discussion of the strategies As turbocharged engines are known to suffer fro an inherently bad dynaic behavior, the additional deterioration shown in Figure 5 ight not be acceptable. A solution to this proble is to detect the driver s intention. If an upcoing acceleration could be detected one-half of second in advance, 95% of the engine states could be handled (see Figure 5). Another solution would be to connect the choice of the control strategy to an Eco Button, with which the driver could choose between the good fuel econoy and the fast transient response. Fig.. Siulated tie to reach 90% of torque after tip-in with a driveability-optiized controller BMEP [bar] Absolute tie delay [s] Engine speed [rp] Fig. 5. Siulated difference in response tie between the standard and fuel-optial controller. 7. Difference in response tie In order to study the torque developent and torque response ties, a constant engine speed test case was used to isolate the results fro gearbox and vehicle influences. The response tie is easured as the tie delay fro tip-in to the instant when the torque reaches a value of 90% of the axiu that is achievable at that speed. The response tie for the standard controller is shown in Figure. The large delay around 500 rp is due to the low air ass flow and the high torque level achievable. Below this speed the axiu torque decreases and can therefore be attained faster. The engine with the fuel-optial controller has a longer response tie since it starts with a lower speed of the turbocharger. Figure 5 shows the differences in response ties between the fueloptial and standard controllers. The additional tie delay is around one-half of a second for noral cruising conditions.. SUMMARY AND CONCLUSIONS The question of how a fuel-optial controller for a turbocharged spark-ignited engine has to be designed has been investigated. An analytical investigation showed that under the entioned siplifications, it is always advantageous to keep the pressures before and after the engine as low as possible. This leads directly to the proposed fuel-optial controller that opens the waste gate as uch as possible without reducing the desired air ass flow. This new strategy was copared with a standard controller which tries to keep the speed of the turbo charger as high as possible. Siulations show that the fuel-optial controller can iprove the fuel econoy at cruising speed by around -3%, at highway speed by %, and that the highest achievable iproveent is above 0%. This iproveent coes at the expense of longer response ties. In the operating region where the fuel econoy was copared, the response tie for the torque was increased by up to a second. REFERENCES Fox, J., W. Cheng and J. Heywood (993). A Model for Predicting Residual Gas Fraction in Spark-Ignition Engines. SAE Technical Paper Guzzella, L., U. Wenger and R. Martin (000). IC-engine downsizing and pressure-wave supercharging for fuel econoy. SAE Technical Paper Inhelder, J. (99). Verbrauchs- und Schadstoffoptiiertes Ottootor-Aufladekonzept. Dissertation no 9, ETH Zürich Soltic, Patrik (000). Part-Load Optiized SI Engine Systes. Dissertation no 39, ETH Zürich Stöckli, M. (99). Reibleistung von -Takt Verbrennungsotoren. Internal report of the Laboratory of Internal Cobustion Engines, ETH Zürich