Engine Management Systems

Transcription

1 Engine Management Systems John Lahti John Deere Power Systems, Waterloo, IA, USA 1 Introduction 1 2 Engine Management System Components 1 3 Engine Control Strategies 3 4 Individual Cylinder Models 13 5 Conclusion 15 Nomenclature 15 References 16 Further Reading 16 1 INTRODUCTION This chapter provides an overview of the engine control strategies that are commonly used for diesel and spark ignition engines. Models are now routinely used within the electronic control unit (ECU) to predict parameters that are not measured. The models may also be used for calculating the required actuator positions. These models and their use in the control structure are described. Strategies are explained for modeling and controlling the airflow, exhaust gas recirculation (EGR), variable geometry turbocharger (VGT) vane position, fuel injection, and spark advance. Model fidelity is discussed and a new individual cylinder engine model is introduced. Engine control strategies for diesel and spark ignition engines are slightly different because of the different combustion strategies, but for the most part the engine models that are used for controlling the engine are the Also published in the Encyclopedia of Automotive Engineering (print edition) ISBN: same. The main control differences are in the way the fuel is delivered, how combustion is initiated, and the strategy for regulating the air to fuel ratio. With spark ignition engines, the torque is regulated primarily with the air throttle, while the fuel is normally delivered at a rate that results in a stoichiometric mixture in the cylinder for combustion. Diesel engines regulate torque by directly controlling the fuel injection mass, with the engine running lean most of the time. The fuel injection mass may be limited to prevent smoke when there is insufficient air for complete combustion. Engine models may be used in the controller to predict some of the control parameters. The models of engine flow, throttle flow, EGR, as well as the turbocharger models are the same for both engine types. In both applications, EGR is used to reduce emissions of nitrogen oxides (NO x ). The same models can be used with each engine type to predict the concentration of air in the manifolds and in the cylinder. 2 ENGINE MANAGEMENT SYSTEM COMPONENTS Engine controls were originally implemented using mechanical devices such as the carburetor, mechanical diesel fuel injector, distributor with centrifugal or vacuum advance, and thermal bimetal actuators. Although these devices provided acceptable performance in many applications and were relatively inexpensive, they could not provide the level of control needed to meet the emission regulations of today. Many of the control functions performed by these devices are now done electronically using sensors and actuators. The sensors provide information about the operating condition of the engine while the actuators are used to regulate its operation. The ECU

2 2 Engines Design Mass airflow sensor Intake air Temperature sensor Compressor Turbocharger speed sensor Turbine u vgt VGT vane postion sensor m cmp T cmp Charge air cooler m fuel ECU Barometric pressure sensor u ecam u at m cac T cac P cac u icam Intake camshaft position sensors Crankshaft position sensor Exhaust camshaft position sensors m trb χ aem T em Air throttle position sensor m at Intake manifold pressure sensor Intake manifold T at m iv χ aim T im m ev χ aevo T ev Exhaust manifold Exhaust manifold pressure sensor Intake manifold temperature sensor m im T im χ aim P im m em χ aem T em P em Oxygen sensor m egr u egr EGR valve position sensor χ aegr T egr m egrcin χ aem T em EGR cooler m egrc χ aegr T egrc P egrc Figure 1. Engine components and model parameters. processes information from the sensors and determines the desired position for each actuator. Some of the components that make up the engine control system are shown in Figure 1. Also shown are model parameters described later. 2.1 Sensors Some sensors interpret inputs from the driver of the vehicle. Examples of these include the accelerator pedal position, transmission range selector, and brake pedal switch. Other sensors provide information about the operating condition of the engine. These include the coolant temperature sensor, intake air temperature sensor, and barometric pressure sensor. These signals change at a slow rate, allowing the sampling to occur at a slower rate than other sensors. Some sensors provide information about the current state of the engine and may be used for feed forward and feedback control. These include the crankshaft position sensor, which is used for ignition and fuel injection timing as well as for calculating the engine speed. The camshaft position sensor along with the crankshaft position sensor determines where each cylinder is within the engine cycle. It may also be used to control camshaft phasing if the engine is equipped with variable valve actuation. The manifold air pressure sensor and mass airflow (MAF) sensor are used in the airflow calculations that determine the amount of fuel to inject and what spark advance is required. Oxygen sensors in the exhaust system provide feedback to the engine controller indicating whether the engine is running rich or lean. 2.2 Actuators Actuators are devices that regulate operation of the engine. Examples of actuators include the fuel injector, air throttle,

3 Engine Management Systems 3 EGR valve, VGT turbine vanes, and ignition system. Actuators that have position control normally have a position sensor that is used with a feedback controller to maintain the desired position. 2.3 Controller One of the factors contributing to widespread use of electronic engine controls has been emission regulations. Electronic controls make it possible to more accurately control the air to fuel ratio, spark advance, fuel injection timing, and EGR flow rate. Electronic controls can also improve performance, drivability, fuel economy, and integration with other vehicle systems. Figure 1 shows some of the common sensors and actuators on an engine. The air throttle, EGR valve, and VGT vane are controlled using actuator commands: u at,u egr,and u vgt, respectively. The intake and exhaust camshaft phasing are controlled using commands u icam and u ecam. Engines with electronic fuel injection regulate the fuel rate by controlling the duration of the fuel injector for each cylinder. 3 ENGINE CONTROL STRATEGIES The block diagram for a typical engine control system is shown in Figure 2. The actuator controls are shown as just one block in this figure but the actuator control may have its own sensor and feedback controller. Proportionalintegral-derivative (PID) controllers are commonly used for actuator position control. The actuator controller is within the control loop of the setpoint controller, which requires special consideration when selecting the controller gains. The actuator controls need to be fast enough during transient conditions to prevent the setpoint controller from making adjustments to the actuator setpoint because the actuator position and the corresponding engine response have not yet been achieved. To prevent dynamic interactions between these control loops the actuator control should ideally be more than 10 times faster than the setpoint control. A factor as low as 5 may be acceptable in certain cases. The feed forward calculation shown in Figure 2 is a calculation of the required actuator position using the given setpoint command and known system parameters. Feed forward control allows the system to respond quicker under transient conditions because the required actuator position is calculated at each time step with essentially no lag. The feedback controller is different in that it is designed to remove control system error over a period with a certain time constant. Using the combination of feed forward and feedback control allows the system to respond quickly to changes in the setpoint command while still having the ability to correct for system changes or errors in the feed forward calculation. When the feed forward calculation is done correctly, the output of the feedback controller will be small. The feed forward term can be obtained from tables, empirical models, or physics-based models. In some cases, the steady state position for the actuator is determined for each operating condition and those values are then placed in tables that are used to determine the feed forward term. This approach gets the actuator close to the required steady state position fast but it does not provide compensation for the system dynamic so the control under transient conditions is not as good as it could be. Empirical and physicsbased models that more accurately account for the system dynamics can provide better transient response. The main difference between empirical models and physics-based models is that empirical models generally require engine data for calibration whereas physics-based models are based mostly on first principles, allowing them to be calibrated with parameters such as component sizes and fluid properties. An example of a physics-based model is the compressible gas flow equation for an orifice (Equation 1). This equation is commonly used for modeling airflow through the throttle. The parameter ψ is a function of the pressure ratio across Feed forward calculation Setpoint command Error Feedback controller Measured state Actuator setpoint Actuator (& control) Sensor Actuator position Engine Engine state Figure 2. Engine control using sensor feedback.

4 4 Engines Design ψ P out Figure 3. Parameter ψ for air throttle compressible gas flow equation. the throttle and the ratio of specific heats for the fluid (Guzzella & Onder, 2010). Within the ECU, the parameter ψ is typically stored in a table covering a range of pressure ratios. The table lookup in this case is more efficient in terms of ECU throughput than the equation for ψ. A plot of ψ versus pressure ratio is shown for air in Figure 3. This model considers the throttle opening area, upstream air properties, and pressure ratio across the throttle. The effective area (C d A) is typically calibrated using data from a flow bench and a table in the ECU with throttle position as the input. ( ) P ṁ = C d A in ψ (1) Rin T in ( 2 ψ = k k 1 ( ) 1 Pout k ψ = P cr = P in for P out P cr ( 2 k 1 ) k1 k1, P in 2k k 1 ) k k1 Pin for Pout < P cr ( 1 ( Pout P in 0.9 ) k1 ) k, 1 combustion cycle. The model does account for changes in manifold pressure, manifold temperature, and engine speed, making it a reasonably good method for predicting flow to the engine cylinders. This model is discussed in more detail in Section Models such as these can be used in a feed forward calculation to determine what manifold pressure is required to achieve the desired airflow to the cylinders or what throttle position is required to achieve a given airflow through the throttle. In some cases, the desired control parameter does not have a sensor to provide a feedback signal. It may be impractical to have certain sensors because of cost or reliability. For example, it is not practical to measure the flow at the intake valve or to measure the mass fraction of air within the cylinder. If such parameters are important for controlling the engine, a model may be used to estimate these parameters so that the feedback controller can use them. Such a model is called an observer (Figure 4). The observer receives the same inputs as the real engine so dynamically it responds similar to the engine. The states of the model are compared to the measured states on the real engine allowing corrections to be made to the model, reducing the parameter estimation error. In addition to providing state information to the feedback controller, information from the observer model and the model parameters may also be used in the feed forward calculation. The following discussion describes how an observer model can be used to improve the engine airflow estimate that is used for controlling the air to fuel ratio and setting the spark advance. 3.1 Engine airflow A mean value engine model is a model of the engine that does not consider the effects of individual cylinders. It assumes the flow through the engine is continuous as it would be in a gas turbine. When such a model is used for control purposes, the mass of air, fuel, or exhaust gas within each cylinder is calculated by evaluating the total mass going through the engine in one cycle and dividing by the number of cylinders Speed density flow An example of an empirical model is the speed density calculation for engine airflow using volumetric efficiency (VE) tables (Equation 2). This is a mean value model of the engine that does not account for the discrete events of each cylinder or the delays associated with the The speed density model calculates flow to the engine cylinders using engine speed, the density of the fluid in the intake manifold, the displacement of the engine, and the VE (Equation 2). VE is the ratio of the actual flow to the theoretical flow that would be achieved if flow

5 Engine Management Systems 5 Feed forward calculation Setpoint command Error Feedback controller Actuator setpoint Actuator (& control) Actuator position Engine Engine state Sensor Measured state Model correction Observer controller Model error Engine state estimate Actuator model Actuator position estimate Engine model Engine state estimate Sensor model Measured state estimate Engine observer Figure 4. Observer-based engine control. equivalent to the displaced volume of the engine at the intake manifold fluid density were achieved during each engine cycle. Sometimes, VE is specified with respect to the density of air at atmospheric conditions but this method is seldom used for control purposes. By setting Equation 2 equal to the measured mass flow from an engine test, it is possible to solve for the VE. The VE is sometimes calibrated using a table with axes of engine speed and intake manifold pressure. Turbocharged applications may require a more complex empirical model to accurately predict the VE. ṁ iv = ( Ne 120 ) ρ im V disp VE (2) This flow estimate includes both air and EGR entering the cylinder. During operation of the engine, the ECU calculates the mass entering each cylinder using the intake manifold fluid density, cylinder displacement, and VE as shown by Equation 3. ( ) Vdisp m cyl,in = ρ i VE (3) n cyl The total mass in the cylinder at the time when the intake valve closes is equal to the mass that entered through the intake valve plus the residual mass that remained in the cylinder from the previous engine cycle (Equation 4). m cyl,ivc = m cyl,in m cyl,res (4) A separate model provides the estimate of m cyc,res.the residual mass will be affected by engine speed, manifold pressures, fuel rate, and valve timing. The speed density method provides reasonably good estimates of flow to the cylinder under steady state operation but there are several sources of error under transient conditions: 1. The mass of residual exhaust gas retained within the cylinder may change from one cycle to the next, making the VE under transient conditions different than the steady state value. When the intake manifold pressure is increasing the speed density flow estimate will be too low because the residual mass has not yet increased to the steady state value, which may cause the spark advance to be set too high resulting in engine knock. 2. The wave dynamics within the intake manifold will be changing under transient conditions and the pressure near the intake valve at the time when the valve closes may be different than it was during the steady state condition, resulting in a different VE. 3. On a port fuel injected engine, the fuel has to be injected before the intake stroke. The manifold pressure may change between the time at which the fuel was injected to the time when the intake valve closes, causing an error in the air to fuel ratio. The flow estimate will be too low when the intake manifold pressure is increasing and it will be too high when the intake manifold pressure is decreasing. The speed density flow estimate will cause the engine to run lean on tip-ins and rich on

6 6 Engines Design tip-outs. This flow estimate tends to lag behind the true flow to the cylinders. Some of the limitations listed here can be addressed by adding ad hoc features to the control software that make corrections under certain conditions. For example, when a tip-in is detected the spark advance can be reduced by several degrees to prevent knock. Alternately, to improve fuel control extra fuel can be added with a tip-in, or removed with a tip-out. Calibration of these corrections for all operating conditions can be very time consuming. The speed density flow estimation can be improved by using predicted manifold pressure instead of a measured value that may have to be filtered. The method of using predicted manifold pressure is discussed more in Section Measured mass airflow A MAF sensor measures flow in the air intake duct between the air cleaner and the throttle, or before the compressor on turbocharged engines. Under steady state conditions, this flow (plus the EGR flow rate) should match the speed density flow estimate. Under conditions where the intake manifold pressure is changing, the mass contained within the intake manifold will also be changing. For the case with no EGR flow, when the intake manifold pressure is increasing the measured MAF will be higher than the actual airflow into the cylinders. Likewise, when the intake manifold pressure is decreasing the measured MAF will be lower than the actual airflow into the cylinders. These characteristics are opposite to those of the speed density calculation. The measured MAF tends to lead the true cylinder airflow. The measured MAF would not provide very good fuel control under transient conditions if used directly. The real benefit to using a MAF sensor is that corrections can be made to the VE, improving the airflow estimate under steady state conditions. The speed density model provides an estimate of flow to the cylinder while the VE is corrected with the MAF reading. This model-based approach to cylinder air charge estimation is described more in the following section Model-based cylinder air charge estimation One way to improve the estimate of air entering the cylinder is to use a model-based approach. By constructing an observer model of the engine, it is possible to predict the rate of change in intake manifold pressure. The rate of change in manifold pressure can then be used to predict the pressure in the manifold at the time when the intake valve closes. The modeled version of the intake manifold pressure will have less variation than the measured value and will not require filtering. This approach can overcome the lag associated with the speed density flow estimate and provide a much more accurate estimate of cylinder air charge for the fuel injection calculations. The observer model can also estimate the concentration of air and exhaust gas within the cylinder, allowing spark advance and other control parameters to be set for the expected state of the cylinder. This approach improves control under transient conditions. 3.2 Exhaust gas recirculation EGR significantly increases the complexity of the models needed to predict the mass of air entering the cylinder and the composition of the mixture within the cylinder. Modeling airflow, EGR flow, and residual exhaust gas within the cylinder allows the air per cylinder and exhaust gas concentration to be calculated. This information can then be used to deliver the correct amount of fuel and to set the spark advance. Diesel engines regulate the exhaust gas concentration for controlling NO x. Since diesel engines commonly run lean, the calculation of residual and recirculated exhaust gas must consider the concentration of excess air retained in the exhaust gas. In order to control the mass of air per cylinder and exhaust gas concentration, an estimate of these parameters is needed. The next section describes an engine model that can be used as an observer within the ECU to provide this information Exhaust gas recirculation model The model described in this section includes airflow, exhaust flow, and EGR flow. This is a mean value engine model with lumped parameter manifold models. Lumped parameter means that the concentration of air and exhaust gas is assumed to be evenly distributed within each manifold. The pressure and temperature within the manifold is also assumed to be uniform. Manifold models are based on the principal of conservation of mass. Manifold pressure can be calculated using the ideal gas law with manifold fluid mass and estimated or measured manifold temperature as inputs. The equations that follow are for an engine with direct fuel injection. The equations will be slightly different for an engine with port fuel injection. The rate of change in intake manifold mass is equal to the MAF through the throttle, plus the EGR mass flow,

7 Engine Management Systems 7 minus the mass flow entering the engine through the intake valves (Equation 5). dm im = ṁ dt at ṁ egr ṁ iv (5) The rate of change in air mass within the intake manifold is equal to the MAF through the throttle, plus the EGR mass flow times the mass fraction of air contained in the EGR, minus the mass flow entering the engine through the intake valves times the mass fraction of air in the intake manifold (Equation 6). dm aim = ṁ dt at ṁ egr χ aegr ṁ iv χ aim (6) The mass fraction of air contained in the intake manifold is equal to the mass of air in the intake manifold divided by the total mass of air and exhaust gas in the intake manifold (Equation 7). χ aim = m aim m im (7) The rate of change in exhaust manifold mass is equal to the mass flow leaving the engine through the exhaust valves, minus the EGR mass flow, minus the mass flow through the turbine (Equation 8). dm em = ṁ dt ev ṁ egr ṁ trb (8) The rate of change in air mass within the exhaust manifold is equal to the mass flow leaving the engine through the exhaust valves times the mass fraction of air in the exhaust gas when the exhaust valve opens, minus the mass flow to the EGR cooler times the mass fraction of air in exhaust manifold, minus the mass flow through the turbine times the mass fraction of air in the exhaust manifold (Equation 9). dm aem = ṁ dt ev χ aevo ṁ egrcin χ aem ṁ trb χ aem (9) The mass fraction of air contained in the exhaust manifold is equal to the mass of air in the exhaust manifold divided by the total mass of air and exhaust gas in the exhaust manifold (Equation 7). χ aem = m aem m em (10) The mass flow in the cylinder at the time when the intake valve closes is equal to the mass flow that enters the cylinder through the intake valve plus the residual mass (Equation 11). Mass flow rates are used here because this is a mean value model. In a real engine, these would be discrete masses for each cylinder event. ṁ ivc = ṁ iv ṁ res (11) The exhaust gas residual mass fraction is defined as the mass of residual exhaust gas divided by the total mass in the cylinder at the time when the intake valve closes (Equation 12). Engine speed, manifold pressures, fuel rate, and valve timing all affect the residual mass fraction. x r = m res m iv m res (12) Equation 12 can be rearranged and the residual mass can be expressed as a flow rate as shown in Equation 13. Expressing the residual mass as a mass flow allows it to be used in the mean value model. ( ) xr ṁ res = ṁ iv (13) 1 x r The mass flow in the cylinder at the time when the exhaust valve opens is equal to the mass flow in the cylinder at the time when the intake valve closes plus the fuel mass flow rate (Equation 14). Mass flow rates are used here because this is a mean value model. In a real engine, these would be discrete masses. ṁ evo = ṁ ivc ṁ fuel (14) The mass flow through the exhaust valve is equal to the mass flow in the cylinder at the time when the exhaust valve opens minus the residual flow (Equation 15). ṁ ev = ṁ evo ṁ res (15) The MAF in the cylinder at the time when the intake valve closes is equal to the mass flow through the intake valve times the mass fraction of air within the intake manifold, plus the residual mass flow rate times the mass fraction of air in the cylinder at the time when the exhaust valve opens (Equation 16). ṁ aivc = ṁ iv χ aim ṁ res χ aevo (16) The mass fraction of air in the cylinder at the time when the intake valve closes is equal to the mass of air in the cylinder at the time when the intake valve closes divided by the total mass in the cylinder when the intake valve closes (Equation 17). χ aivc = ṁaivc ṁ ivc (17)

8 8 Engines Design The MAF in the cylinder at the time when the exhaust valve opens is equal to the MAF in the cylinder at the time when the intake valve closes minus the fuel mass flow times the stoichiometric air to fuel ratio (Equation 18). For modeling purposes, the fuel is assumed to react with a stoichiometric amount of air in the cylinder. This assumption only applies when the engine is running lean. If the engine is running rich, there will be no remaining air in the exhaust gas. ṁ aevo = ṁ aivc ṁ fuel AFR stoich (18) The mass fraction of air in the cylinder at the time when the exhaust valve opens is equal to the mass of air in the cylinder at the time when the exhaust valve opens divided by the total mass in the cylinder when the exhaust valve opens (Equation 19). χ aevo = ṁaevo ṁ evo (19) The equations presented up to this point can be shown in block diagram form as illustrated in Figures 5 and 6. Figure 5 is a model of the total mass flow through the engine. Figure 6 is a model of airflow and air concentration. The orifice equation for throttle airflow was shown in Equation 1. The speed density calculation was shown in Equation 2. The EGR valve and cooler could be modeled as an orifice and a volume, or with an empirical model in a different form. The mass fraction of air in the recirculated exhaust gas could be modeled using a transport delay instead of a volume with uniform mixture distribution. The hardware configuration and desired level of model fidelity will determine which model is the best for the application. The mass of air and exhaust gas entering the cylinder from the intake manifold depends on the pressure in the manifold and the composition of the mixture within the intake manifold. Cross coupling exists between the pressure and concentration terms. To achieve the same mass of u at m at Air throttle u icam u ecam 1 s Camshaft phasing m im R im T im V im P im x r 1 x r VE Speed density m iv X m res m evo m ivc m ev 1 s m em R em T em V em P em m at u vgt Turbo & charge air cooler m trb P cac P im m egr m iv m fuel P im m trb u egr m egrcin m egr EGR valve & cooler P em P cac Figure 5. Engine mass flow model. m fuel AFR stoich m iv X m at 1 m aim χ aim m aiv m aivc m aevo s X m im m evo m ev χ aevo 1 m aem X s m em χ aem m aegr m aiv m egr m egrcin m ares X m ivc χ aivc m aegrcin X X m trb m atrb X χ aegr EGR valve & cooler χ aem m res m egrcin m egr Figure 6. Engine air mass concentration model.

9 Engine Management Systems 9 air in the cylinder with a higher concentration of exhaust gas requires higher intake manifold pressure. In general, opening the EGR valve, closing the turbocharger vanes (higher back pressure), or closing the air throttle (lower intake manifold pressure) will provide more recirculated exhaust gas to the intake manifold, whereas closing the EGR valve or opening the air throttle will provide more air to the intake manifold. Depending on the operating range of the turbocharger, closing the vanes may increase both fresh airflow and EGR flow. Certain actuators are better at providing fast response under transient conditions while others may be used to guide the system to an efficient operating point. For example, the air throttle provides the fastest air response but in many cases it is desirable to have the throttle opened all the way to minimize pumping losses. Likewise, the EGR valve can provide fast response for controlling the EGR rate but adjusting the VGT vanes also affects the EGR rate and there will be an optimum setpoint for each actuator under steady state conditions. Different manufacturers have different strategies for controlling these actuators and the details are mostly proprietary. Some research papers have been published on this topic while additional work is still ongoing to determine the best approach. PID controls may provide acceptable performance in certain applications where the control response does not have to be very fast. The controls for these actuators are cross-coupled and very nonlinear, which can limit the gains used in a PID controller. Some researchers have proposed methods for decoupling the system, and others have proposed the use of sliding mode control to better handle the nonlinear characteristic of the system. Multivariable control is an option that could provide very good control but is more difficult to implement. It uses optimization cost functions to provide a response that uses all the actuators in a way that can be calibrated to provide a response that is considered ideal or optimal. The cost functions penalize factors such as excessive actuator movement, slow response, or control overshoot. Multivariable control works best with linear systems and the engine system is very nonlinear. One of the steps to implementing multivariable control is to create a model in state variable form, which may require the creation of several linear operating point models of the system. Another challenge is the proper handling of system constraints such as actuator limits, limits on manifold pressure, or turbocharger speed. 3.3 Fuel injection On diesel engines, the driver demand torque (or governor torque) is primarily controlled with fuel. The other engine actuators respond as needed to provide the correct amount of air and EGR for the mass of fuel that is to be injected into the cylinder. Diesel engines typically run lean so the mass of air in the cylinder is not of much concern until operating at high loads where there may not be sufficient air in the cylinder to prevent smoke. Under a transient smoke-limited operating condition, the fuel injection mass may be limited until the other actuators can make adjustments to provide sufficient air to the cylinder. With spark ignition engines, the driver demand torque is primarily controlled with the air throttle. The fuel injection quantity depends on the mass of air that is expected to be in the cylinder. A stoichiometric air to fuel ratio is normally maintained so that low levels of both hydrocarbons and NOx can be achieved. In addition, a stoichiometric air to fuel ratio allows the three-way catalytic converter to be most efficient at reducing emissions. The rest of this section focuses on fuel injection controls for spark ignition engines Port fuel injection Switching from carburetors to throttle body fuel injection offered the ability to accurately control the amount of fuel delivered to the engine. The real challenge was calculating how much fuel was required under transient conditions. A speed density type model could predict the airflow to the engine cylinders with reasonably good accuracy but the changing intake manifold pressure affected the evaporation rate of the fuel and the resulting air to fuel ratio for the mixture entering the cylinders. One solution was to inject extra fuel with a throttle tip-in similar to the accelerator pump on a carburetor. Likewise, less than the normal amount of fuel could be injected when a throttle tipout was detected. This ad hoc solution was difficult to calibrate for all operating conditions and did not provide very accurate control. Aquino (Aquino, 1981) proposed a wall-wetting model of the intake manifold that accounted for the mass of liquid fuel within the manifold and the rate at which that fuel evaporated (Figure 7). By inverting this model, the fuel injection quantity can be adjusted to compensate for the liquid fuel accumulation and evaporation that occurs within the manifold. The wall-wetting model was initially developed for throttle body fuel injection systems and then later applied to engines with port fuel injection. Although each port had independent fuel films that could be modeled separately it was common to continue using a single mean value wallwetting model. The following equations are used to model the wallwetting process. The mass flow of injected fuel entering the

10 10 Engines Design Fuel injector m inj Intake port m if Fuel film m f m ic m fc Mass flow rates m inj : from injector to cylinder & fuel film m if : from injector to fuel film m ic : from injector to cylinder m fc : from fuel film to cylinder m cyl_fuel : from injector & fuel film to cylinder m cyl_fuel Intake valve Calibration parameters x f : fraction of injected fuel entering fuel film τ : fuel film time constant Figure 7. Port fuel injection wall-wetting model. fuel film is equal to the mass flow of injected fuel times a factor x f called the impact factor (Equation 20). The impact factor is the fraction of injected fuel entering the fuel film. ṁ if = x f ṁ inj (20) The mass flow of injected fuel not entering the fuel film is equal to the mass flow of injected fuel times one minus the impact factor (Equation 21). ṁ ic = (1 x f ) ṁ inj (21) The fuel film is assumed to evaporate with a time constant of τ (Equation 22). Fuel evaporating from the fuel film is assumed to enter the cylinder. ṁ fc = m f (22) τ The change in mass of the fuel film is equal to the mass flow entering the film from the injector minus the mass flow that is evaporating and entering the cylinder (Equation 23). dm f = ṁ dt if ṁ fc (23) Figure 8 shows these equations in block diagram form. This model has the fuel injection mass flow as the input and the fuel mass flow entering the cylinder as the output. This model can be inverted as shown in Figure 9 to have the mass flow entering the cylinder as the input and the mass of injected fuel as the output. The model in this form m inj 1 x f m ic m cyl_fuel dm f m if dt m 1 f m 1 fc x f s τ Figure 8. Wall-wetting model block diagram. m cyl_fuel m ic 1 1 x f m inj dm f m fc 1 m f 1 dt m if τ s x f Figure 9. Inverted form of wall-wetting model.

11 Engine Management Systems 11 can be used in the feed forward calculation to determine the amount of fuel to inject. This model will cause more fuel to be injected during a tip-in, when less fuel is evaporating from the fuel film, and less fuel to be injected during a tip-out, when more fuel is evaporating from the film Gasoline direct injection The wall-wetting model is not required for engines with direct fuel injection because all the fuel stays in the cylinder until combustion. Gasoline direct injection normally occurs early in the engine cycle before the intake valve closes. This provides more time for fuel atomization before combustion, reducing hydrocarbon emissions. In addition, the cooling effect of the injected fuel allows more air to enter the cylinder, which allows higher peak torque and power to be achieved Closed loop air to fuel ratio control To achieve a high level of conversion efficiency with the catalytic converter the air to fuel ratio has to be controlled very close to the stoichiometric ratio. Engine to engine variation, variation in fuels, and purging of the evaporative emission canister can cause the engine to run rich or lean of stoichiometry. Closed loop control can be used to correct for these fueling errors. The closed loop fuel controller uses an oxygen sensor for feedback (Figure 10). The oxygen sensor is installed in the exhaust manifold or exhaust pipe and provides a signal that is related to the oxygen concentration in the exhaust. The oxygen sensor is constructed from a ceramic material called zirconium oxide. The sensor is in the shape of a thimble that protrudes into the exhaust stream. The inner and outer surfaces of the sensor are coated with porous layers of platinum, which act as the electrodes. When there is a difference in oxygen concentration between the inner and outer surfaces of the sensor, oxygen ions pass through the ceramic material with reactions occurring at the platinum electrodes generating an electric potential that can be measured as a voltage. V o ZrO 2 e Air side reaction: O 2 4e 2O 2 Figure 10. Oxygen sensor. Porous platinum electrodes Exhaust side reaction: 2O 2 O 2 4e V o (mv) Rich 1 Lean Air to fuel equivalence ratio (λ) Figure 11. Oxygen sensor response curve. The sensor voltage is related to the oxygen partial pressure at each electrode. The voltage can be approximated using the Nernst equation: V o = R F 4F ln ( PO2 ref P O2 exh ) (24) where R is the gas constant, T is the temperature, P is the partial pressure, and F is the Faraday constant. A typical response curve is shown in Figure 11. As the engine switches from running lean to rich, the oxygen sensor voltage increases significantly. The sensor operates as a switch, indicating whether the engine is currently operating rich or lean. The sensor temperature has to be above a certain value for the reactions to occur at the platinum electrodes, generating the sensor output voltage. The minimum operating temperature for the sensor is about 300 C. Some sensors use an electric heating element to warm up the sensor so that it can be used for control sooner after a cold start. The sensor is normally used with a proportion integral (PI) controller to adjust the mass of fuel that is injected. Figure 12 shows two examples: control with just integral control and control with a PI controller. With integral control, the fuel injection mass is adjusted up or down at each fuel injection event depending on the output of the sensor. When the oxygen sensor indicates that the engine is running lean, the integrator will increase the fuel injection mass until the oxygen sensor indicates that the engine is running rich; then, the fuel injection mass will start decreasing. There is a delay between the time when fuel is injected and the time its effect is detected at the sensor. Part of this delay is associated with the engine cycle time and part is due to the transport delay for the exhaust gas to travel from the exhaust valve to the location of the sensor. The transport delay causes the air to fuel ratio at the engine to overshoot the setpoint and affects the period of the rich lean cycling. The cycle time can be reduced by using a PI controller. Since a certain amount of overshoot is expected because

12 12 Engines Design Integral control Period Fuel to air equivalence ratio (1/λ) Rich Equivalence ratio at engine Transport delay Equivalence ratio at sensor Oxygen sensor voltage V o (mv) Lean 200 Time Proportional plus integral control Period Fuel to air equivalence ratio (1/λ) Equivalence ratio at engine Transport delay Equivalence ratio at sensor Oxygen sensor voltage V o (mv) Rich Lean 200 Time Figure 12. Air to fuel ratio control. of the transport delay, the proportional term can be used to quickly change the fuel injection mass when a rich-to-lean or lean-to-rich transition occurs at the sensor. Figure 12 shows a reduction in the period of the rich lean cycling with the PI controller. 3.4 Spark advance Spark advance is normally set to a value that provides the maximum torque with the minimum amount of spark advance. This is called the minimum spark advance for best torque (MBT). Under some conditions with regular grade fuel the spark advance may have to be set lower to prevent engine knock. Knock occurs when the combustion mixture auto-ignites, making a knocking sound rather than burning as a flame front that propagates from the spark plug to the edge of the piston. Combustion may start off as a flame front and then auto-ignite once a certain temperature and pressure is achieved. Reducing the spark advance lowers the pressure during combustion, reducing the tendency to knock. The spark advance for the engine is normally calibrated using tables that are sometimes called maps. The base spark advance is normally set to the minimum of the MBT spark advance and the knock-limited spark advance. The base spark advance table normally has engine speed as one axis and some indication of engine load on the

13 Engine Management Systems 13 Exhaust gas mass fraction in-cylinder Engine speed implemented as an observer in the ECU. There are still some sources of error that may need to be addressed if more accurate control is required for advanced combustion strategies such as homogeneous charge compression ignition (HCCI). These limitations are as follows: Air mass in-cylinder Figure 13. In-cylinder parameter-based spark advance table. other axis. If only measured parameters are available the throttle position or intake manifold pressure are sometimes used as the second axis. If an engine airflow observer is implemented in the ECU, then the mass of air per cylinder could be used for the second axis. The combustion burn rate is affected by the mass fraction of exhaust gas contained in the cylinder. If an estimate of exhaust gas mass fraction is available it could be used as a third table axis as shown in Figure 13. The use of in-cylinder parameters for setting the spark advance provides good control under transient conditions because the advance is set using factors that ultimately affect the combustion process. The spark advance may also be adjusted for non-standard operating conditions such as when the engine is colder or hotter than normal. These adjustments can be made using additional tables that adjust the spark advance based on coolant temperature or the estimated in-cylinder temperature. Using only actuator positions or sensor measurements as inputs to spark advance tables would require many tables to cover all operating conditions and would not provide the level of transient control that is possible with in-cylinder estimated parameters. 4 INDIVIDUAL CYLINDER MODELS As can be seen from what has been described up to this point, the mean value engine model can provide a lot of useful information for controlling the engine when 1. The real engine operates in discrete cylinder events with delays associated with the engine cycle that are not properly captured by the mean value model. This can cause errors in the residual cylinder mass and composition calculations. 2. The model does not account for the wave dynamics in the intake manifold that can significantly change the flow entering the cylinder under transient conditions from that of the flow predicted by the speed density method using VE tables. 3. Engines with variable valvetrain systems offer a wide range of valve-opening strategies, making it difficult to accurately model all possible operating conditions with VE tables. These limitations can be overcome by using a higher fidelity model that includes individual cylinders and by modeling the wave dynamics of the intake and exhaust manifolds. Such a model provides more information but requires more processing capacity from the ECU. This approach eliminates the need for VE tables. A project at the University of Wisconsin Madison created a real-time combustion and compressible gas flow model that could be used in an ECU as an observer (Lahti, 2004). The following discussion provides an overview of that model. The wave dynamics were modeled using a process called the method of characteristics. The governing equations are the continuity equation and the momentum equation. Through a process or variable transformations the state of the fluid in the manifold runners can be defined using parameters called Riemann variables. One Riemann variable defines the right moving characteristic and the other defines the left moving characteristic. For isentropic flow, the Riemann variables remain constant as they propagate through the manifold runner. This modeling technique makes it possible to predict the state of the fluid at the valve and to predict the flow through the valve when the cylinder pressure is known. The reader is referred to Benson (Benson, 1982) for more details on the wave modeling techniques. The method of characteristics was originally developed for solving wave problems on a drafting board. Later it was implemented as a computer program. Other wave analysis methods may provide more accuracy but the software code may not run fast enough to be used in a real-time

14 14 Engines Design application. This method was found to work well when the isentropic flow assumption was not violated. If the valve timing was such that hot cylinder gases entered the intake runner during part of the intake event, the model would not accurately represent the wave dynamics at that point. If such a valve-opening strategy were required, a slightly more complex model could be implemented to more accurately model those effects. An individual cylinder model was developed to calculate the temperature and pressure in the cylinder throughout the engine cycle. This information was used with the wave dynamics model to determine the flow through the valves. The states of the cylinder were modeled using the first law of thermodynamics, conservation of mass, and the ideal gas law. The first law equation for the cylinder is Q cv Ẇ cv ṁ iv h Si ṁ ev h Se = d(mu S)cv dt This right side of the equation can be rewritten as d(mu S )cv dt = (ṁ iv ṁ ev ) u S m cyl C v dt cyl dt (25) (26) It is now possible to solve for the rate of temperature change: dt cyl dt = Q comb Q wall Ẇ cv ṁ iv h Si ṁ ev h Se (ṁ iv ṁ ev ) u S m cyl C v (27) The temperature at each time step is calculated as T cyl (t t) = T cyl (t) dt cyl(t) t (28) dt The cylinder mass is updated using the mass flow rates at the valves m cyl (t t) = m cyl (t) (ṁ iv ṁ ev ) t (29) The pressure at the new time step is calculated using the ideal gas law: P cyl (t t) = m cyl(t t) R cyl (t t) T cyl (t t) V cyl (t t) (30) This model was evaluated using a single cylinder spark ignition research engine. Figure 14 shows the measured and estimated cylinder pressures through one engine cycle. During this test, the model was running in real time using a dspace rapid prototype control system. The measured and estimated cylinder pressures were nearly the same throughout the cycle. Similar results were obtained for different combinations of valve timing, valve lift, airflow, and engine speed. The combustion heat release was modeled using a mathematical function called a Weibe function. Weibe functions are commonly used to model the mass fraction of fuel that has burned as a function of crank angle. The calibration parameters for the Weibe function were stored in tables log 10 [cylinder pressure (kpa)] Measured Estimated Figure 14. Real-time individual cylinder model data Normalized volume displaced

15 Engine Management Systems 15 of the form shown in Figure 13 to be consistent with the strategy used for the spark timing. More complex models could be implemented to define the heat release for applications using premixed, partially premixed, or multiple direct inject combustion strategies. With the individual cylinder models, each cylinder event is a transient event. The cylinder pressures and temperatures are continually changing. There is intermittent flow through the valves, and the mass within the cylinder keeps changing. This is much different than the mean value model where the flow is continuous and the engine cycles are assumed to occur with no delay. One of the challenges to implementing HCCI in a production application is controlling the process under transient conditions. Current engine control strategies using mean value models are not able to provide information about the state of the engine with sufficient accuracy to control the process. The individual cylinder models offer an alternative that accurately represents many of the factors that affect when combustion begins. Information from the models could be used for controlling the trapped residual mass and EGR flow as a way of regulating the HCCI process. A patent for the engine control technology described in this section is held by the University of Wisconsin Alumni Research Foundation (WARF) at the University of Wisconsin Madison (Lahti & Moskwa, 2006). 5 CONCLUSION In many cases, the engine parameters that need to be controlled are difficult or impractical to measure. It may be possible to model the important parameters using the actuator and sensor information that is available. Such a model is called an observer. There are several advantages to using observers: they provide the desired state feedback information without adding sensors, the modeled response does not require filtering like a sensed parameter, the model information can be used for feed forward calculations to provide better control response, and the observer can be used for diagnostics to detect changes in engine operation. The mean value engine model may provide sufficient information for controlling the engine in some applications. As with any model, assumptions are made and those assumptions can be a source of error under certain conditions. The mean value model assumes continuous flow through the engine with no delays. This assumption may be acceptable for some applications but not for others. The level of model fidelity for an application may vary depending on the requirements. Increasing model fidelity has many control advantages but the model must be capable of running in real time within the ECU, which has limited processing capacity. As processor capacity increases, in the future it may be possible to implement higher fidelity models such as the individual cylinder model, and models of the manifold wave dynamics. These higher fidelity models allow better control under transient conditions, which may resolve some of the implementation problems associated with alternative combustion strategies. NOMENCLATURE The variables listed below are used in the equations that follow. t ρ im τ χ aegr χ aem χ aevo χ aim χ aivc ψ A AFR stoich C d C p C v ECU EGR H H s k m aem m aim m cac m cyc m cyl,in m cyl,ivc m cyl,res m egrc m em m f m im ṁ ṁ aevo ṁ aivc controller time step intake manifold fluid density wall wetting time constant mass fraction of air in EGR mass fraction of air in exhaust manifold mass fraction of air when exhaust valve opens mass fraction of air in intake manifold mass fraction of air when intake valve closes compressible gas flow parameter orifice area stoichiometric air to fuel ratio discharge coefficient specific heat at constant pressure specific heat at constant volume engine control unit exhaust gas recirculation enthalpy sensible enthalpy ratio of specific heats mass of air in exhaust manifold mass of air in intake manifold mass in charge air cooler mass in cylinder mass that entered the cylinder from intake valve mass in cylinder when intake valve closes residual mass in cylinder mass in EGR cooler mass in exhaust manifold wall-wetting model fuel film mass mass in intake manifold mass flow through orifice mass flow of air (mean value model) when exhaust valve opens mass flow of air (mean value model) when intake valve closes