Control of Charge Dilution in Turbocharged CIDI Engines via Exhaust Valve Timing

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1 Control of Charge Dilution in Turbocharged CIDI Engines via Exhaust Valve Timing Anna Stefanopoulou, Hakan Yilmaz, David Rausen University of Michigan, Ann Arbor Extended Summary ABSTRACT Stringent NOx and particulate emission constraints require high levels of exhaust gas recirculation. In this paper we model and analyze a Variable Valve Timing methodology that in steady-state achieves large levels of internal Exhaust Gas Recirculation (iegr) or residual charge in Compression Ignition Direct Injection (CIDI) engines. Current external Exhaust Gas Recirculation (eegr) techniques rely on a positive pressure drop between the exhaust and the intake manifold, thus compromising fuel economy by degrading turbocharger and engine matching. In contrast, internal exhaust gas recirculation through early exhaust valve closing allows better control of residual charge with potential benefits in turbolag reduction. The analysis employs a crank-angle based dynamic nonlinear model of a six-cylinder turbocharged CIDI engine. This model captures the transient interactions between VVT actuation, the turbocharger dynamics, and the cylinder-to-cylinder breathing characteristics. A low order linear multi-input multi-output (MIMO) model is identified using sampled data from the higher order non-linear model. A model-based controller is designed that varies Exhaust Valve Closing (EVC) to maximize the internal exhaust gas recirculation under air-to-fuel ratio (AFR) constraints during transient fueling demands. The closed-loop controller is based on tracking optimal and achievable set-points of burned gas fraction using conventional flow and pressure sensors. Simulation results are shown on the full order model. MOTIVATION CIDI engines face increasingly stringent emission regulations. One type of these regulated pollutants is associated with oxides of nitrogen (NO x ). NO x emissions correlate with peak cylinder temperature [2, 3]. Diluting the combustion mixture with recirculated exhaust gas (burned gas) increases the trapped cylinder gas mass for a given AFR. The larger mass from this dilution yields larger heat capacity and lower peak combustion temperature. Exhaust gas recirculation (EGR) can therefore be used to reduce the NOx emissions. With proper control, reduced NOx levels can be achieved without significant power and particulate emissions penalties. Thus, EGR is considered by most heavy duty diesel engine manufacturers. Moreover, in Homogeneous Charge Compression Ignition (HCCI) engines high level of EGR can be used to indirectly control combustion initiation. Consequently, achieving fast and accurate control of EGR is an important objective for conventional diesel and HCCI engines. Conventional external EGR (eegr), relies on a pressure drop from exhaust manifold to intake manifold. The flow of eegr is typically regulated by the EGR valve. Well-tuned and highly efficient CIDI engines often operate under conditions where intake manifold pressure is higher than the exhaust manifold pressure. Such engines require additional hardware for achieving external EGR, such as a venturi system, intake EGR throttle, Variable Geometry Turbocharger (VGT), or exhaust back-pressure valve (see Figure 1). All these mechanisms, have either limited range of operation, or achieve the required EGR level by throttling the intake or exhaust flow, and therefore, reducing the efficiency of turbocharged CIDI engines. Moreover, these mechanisms do not allow fast control of in-cylinder AFR excursions during fueling transients because cylinder charge is controlled indirectly through the turbocharger and the intake manifold [1, 2]. The system dynamics is, thus, limited by the intake and exhaust manifold filling dynamics. Figure 1: Current External EGR Applications: Venturi Mixer, Intake EGR Throttle, Variable Geometry Turbocharger, Exhaust Back-Pressure Valve 1

2 Internal Exhaust Gas Recirculation (iegr), is an alternative method for achieving EGR, can avoid losses that are associated with pumping exhaust gas from the exhaust manifold to the intake manifold through an eegr valve. By employing Variable Valve Timing (VVT), an iegr approach can achieve to the dilution level by Early Exhaust Valve Closing (eevc), Late Exhaust Valve Closing (levc) or re-opening on the induction stroke [1]. In this work, due to piston geometry limitations, eevc is selected as the VVT degree of freedom to achieve EGR control. Using a crank angle based, non-linear, dynamic model of a direct-injection, turbocharged diesel engine, we examine the potential of VVT-regulated iegr for future engine applications. Transient and steady-state response of the engine with VVT is analyzed using the high order non-linear model, and these results are used to create lower order linear models and feedforward control laws. Feedback controllers are then designed to regulate EGR subject to AFR performance constraints. CRANKANGLE-BASED MODEL DEVELOPMENT In a multi-cylinder application, VVT will produce effects that are dependent on interactions between the various cylinders and the manifolds that connect them (see Fig. 2). Although purely thermodynamic models are often sufficient for modeling the compression phase, understanding the dynamic response of the engine to a VVT approach requires an accurate model of combustion and cylinderto-cylinder gas exchange processes. We initially employ a non-linear crank angle-based dynamic model of mass and heat flows in which cylinder volumes are considered individually and intake and exhaust manifolds are lumped into volumes that are coupled to the cylinders and to each other. Each component includes three state variables representing the mass, the pressure, and the burned gas fraction of the respective component. The differential equations for the state variables are derived from the ideal gas law, conservation of energy, conservation of mass, and an assumption that each component is a plenum with homogeneous temperature, pressure and density. The resulting model has 29 crank-angle resolved states. A summary of relevant notation follows: Notations: Definitions: Subscripts: Mass (kg) m Compressor c Pressure (kpa) p Turbine t Temperature (K) T Intake Manifold i Flows (kg/s) W x,y Front Exhaust Manifold e f (from x to y) Efficiencies η Rear Exhaust Manifold e r Volumes (m 3 ) V Collector Exhaust Manifold e c Powers P j th Cylinder cyl j Figure 2. Notations of Control Volumes and Gas Flows Mass flows are calculated from standard orifice equations. Fuel burn rate during combustion is calculated using a Wiebe function for the apparent rate of fuel burned. Parameters for these equations are determined by regression analysis of data collected from an experimental engine. The inputs to the crank angle-based model are fuel rate, and exhaust valve closing timing in terms crank angle. The crankangle speed is a parameter that is considered constant or slowly time-varying. Figure 3 shows simulation results with three values of EVC timing resulting in three different values for iegr. The direction of the arrows indicates the progression of intake and exhaust flows over the range of changing EVC. The first curve in each progression (as indicated by the direction of each arrow) corresponds to the original exhaust valve profile, with EVC at 44 degrees after TDC. EVC is then advanced about 25 degrees and then 5 degrees. Early EVC closing decreases the amount of combustion gas extracted into the exhaust manifold, yielding a higher amount of exhaust gas trapped in the cylinder and compressed through the end of the exhaust stroke. The resultant higher in-cylinder creates a pressure gradient from cylinder 2

3 to intake manifold which causes some amount of residual flow into the intake manifold. When cylinder pressure drops below intake manifold pressure, induction begins, starting with the recently expelled residuals, thereby achieving iegr that can be regulated with a single actuator, EVC. x 1 5 Cylinder Pressure, Scaled Valve Profiles, Gas Flows Through Valves vs. Crankangle In-cylinder Pressure Exhaust Valve Profile Intake Valve Profile Pressure[Pa], Scaled Valve Lift, Scaled Gas Flows 1 5 Gas flow through exhaust valve Gas flow through intake valve Crank Angle (θ) [deg] Figure 3 Quasi-static Response of In-Cylinder Pressure, Valve Profiles, and Gas Flows Through Valves (scaled) vs. Crank Angle ( ) CYCLE SAMPLED BEHAVIOR The high order nonlinear crankangle-based dynamical model captures relevant dynamics, but with a level of detail and operating point-dependent variability that complicates the control design task. Moreover, the controlled variable, EVC, is a cycle-resolved variable and thus a cycle-averaged model-based controller is required. The performance variables are torque (Tq), AFR, and burned gas fraction (Fcyl). Conventional production sensors provide the intake manifold pressure and compressor flow (pi and Wc, respectively). To create a series of linear, time averaged, models, we process the crankangle-resolved data to obtain the input-output cyclesampled behavior. The output data from the simulation is sampled for each 2 crank angle degrees. For torque (Tq) output, all the engine cycle data, 36 data points, are averaged and this arithmetic average value is assigned to the whole cycle period. The in-cylinder burned gas fraction (Fcyl) is sampled for every cylinder and every cycle just before the combustion initiation. The value of the burned gas fraction before combustion corresponds to the charge dilution which affects the combustion characteristics, and thus, the generated emissions. In-cylinder AFR cycle-resolved sampling is similarly performed; the sampling scheme captures the AFR just before the combustion starts and uses this as the relevant value until the next cycle combustion. The cycle-averaged intake manifold pressure and compressor flow are obtained as arithmetic averages of the crankangle resolved data. 3

4 Simulation results for different speeds and loads show a consistent correlation between advanced EVC and increased burned gas fraction.. For most operating conditions it is possible to increase the burned gas fraction in the cylinder beyond 14 % (Figure 4). This increase of the burned gas fraction is followed by relatively low penalties in AFR and mean torque (Figures 5). For extreme values of advanced EVC (5 ) during medium speed - medium load conditions, AFR drops below the acceptable limits. During these operating conditions, effective iegr can be achieved with lower value of advanced EVC, typically around In-Cylinder B urnt Gas Percent (F-cylinder) vs. E VC 16 rpm 82 lb/hr 16 rpm 67 lb/hr 16 rpm 57 lb/hr 11 rpm 82 lb/hr 11 rpm 67 lb/hr 11 rpm 57 lb/hr rpm 82 lb/hr 16 rpm 67 lb/hr 16 rpm 57 lb/hr 11 rpm 82 lb/hr 11 rpm 67 lb/hr 11 rpm 57 lb/hr Air To Fuel Ratio vs. EVC 14 F-cylinder Air to Fuel Ratio EVC ( ) EVC ( ) Figure 4: Steady State maps for In-Cylinder Burned Gas Fraction vs. EVC ( ) Figure 5: Steady State maps for Air to Fuel Ratio vs. EVC SYSTEM IDENTIFICATION In order to design a cycle-based feedback controller we perform multivariable linear system identification around a series of operating points corresponding to various torque and speed combinations. To select the operating points we first identify the fuel level that satisfies the torque demand for each speed, and then select from operating points corresponding to that fueling level the EVC which maximizes the burned gas fraction under AFR constraints [5]. For 16 rpm engine speed, the optimal set points are shown below. Fuel Rate: Optimum Exhaust Valve Closing Time (EVC) Optimum Inlet Manifold Pressure (P1) Compressor Mass Flow rate (Wc) % Torque Loss Compared to Zero EGR Burned Gas Fraction in Cylinder (Fcyl) 82 lb/hr kpa 34 g/sec 9 % 14 % 67 lb/hr kpa 238 g/sec 6 % 9 % 57 lb/hr kpa 197 g/sec 2 % 3 % Table 1: Optimal Set Points The input/output behavior includes all the system inputs, namely, Wf as the disturbance and EVC as the control variable. The identification also includes all the system outputs, namely, [Tq,AFR,Fcyl] as the performance variables, [pi,pe,wc] as the measured outputs. Note here that we include the exhaust manifold pressure as a potential measured output to explore the performance improvements associated with this extra sensor. To identify the linear system, we use step changes in Wf and EVC and sample the cycle-resolved dynamic response. The cycle-resolved data is then imported into the Matlab System Identification 4

5 Toolbox, and the multi input multi output linear system parameters are identified using state space parametric model estimation technique N4SID. System linearization is performed around the operating points corresponding to 16rpm, 57lb/hr with EVC set to the original value of 44 degrees ATDC and the two advanced values, 35 degrees and 395 degrees. These points cover the dynamic range of the EVC as an actuator, thereby providing information necessary to evaluate the suitability of the actuator approach and design a controller that accounts for the varying dynamics. A third order system captures the dynamical behavior of all the operating points allowing controller gain scheduling. Note here that the identified system might not be valid for frequencies higher than 1 rad/sec that corresponds to the cycle sampling frequency at 16 rpm..1 Simulated and Linearized Model AFR output (scaled) vs..2 Simulated and Linearized Model Fcyl Output (scaled) vs..3 Simulated and Linearized Model Torque Output (scaled) vs..15 Simulated and Linearized Model Torque Output Simulated and Linearized Model AFR Output Simulated and Linearized Model Fcyl Output Simulated and Linearized Model P e xhaust (scaled) vs. Simulated and Linearized Model P i nlet (scaled) vs Simulated and Linearized Model Wcomp Output (scaled) vs Simulated and Linearized Model Wcomp Output Simulated and Linearized Model P e xhaust Simulated and Linearized Model P i nlet Input Fuel Rate (Wf) (scaled) vs..7.7 Inputs EVC Timing (scaled) vs Wf.3.3 EVC Figure 6: Comparison of Linear and Nonlinear Model Outputs 5

6 CONTROLLER ARCHITECTURE The goal of the controller design is to maximize the burned gas fraction in the cylinder just before the combustion, while satisfying the driver s torque demand and the smoke-limited AFR range. The system steady-state behavior is used to derive a feedforward map for the EVC command that achieves the Fcyl and AFR steady state objectives for each fuel level and engine speed. We first design a feedback controller for EVC assuming we can measure accurately the performance objectives Fcyl and AFR. A theoretical controller that cancels completely the AFR excursions during fueling step changes is derived. This controller gives us insight to the fundamental limitations of the AFR closed loop response [4]. Realizability and EVC actuator constraints are then considered. A linear multivariable feedback controller using LQG methodology shows good AFR response even during high charge dilution. We then analyze the closed loop performance limitations when conventional engine measurements, such pressure (pi) and flow (Wc), are used. We design the two Degrees of Freedom (2DOF) controller and compare the AFR response during fueling step changes with equivalent torque step changes for the CIDI engine with the conventional EVC (EVC=) and the controlled EVC. Improvements in the transient response are demonstrated in the linear reduced order model and the nonlinear full order model. Figure 7: Control Architecture REFERENCES: 1. H. Dekker, W. Sturm, Simulation and Control of a HD Diesel Engine Equipped with new EGR technology, SAE paper L. Guzzella, and A. Amstutz, Control of diesel engines, IEEE Control Systems Magazine, vol.18, No. 2, pp.53-71, Heywood, J.B., Internal Combustion Engine Fundamentals, McGraw-Hill, Inc., S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis, Design, Wiley, A.G. Stefanopoulou, I.V. Kolmanovsky, and J.S. Freudenberg, Control of Variable Geometry Turbocharged Diesel Engines for Reduced Emissions, IEEE Transactions on Control System Technology, vol.8, No 4, July 2. 6

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