A dynamic PCCI combustion model for Diesel engine control design 1* 2 1 2 2 2 1 C. Felsch , K. Hoffmann , A. Vanegas , P. Drews , T. Albin , D. Abel , N. Peters 1 Institut für Technische Verbrennung RWTH Aachen University, Aachen, Germany 2 Institut für Regelungstechnik RWTH Aachen University, Aachen, Germany Subject of this work is a dynamic simulation model for PCCI combustion that can be used in closed-loop control de- velopment. A detailed multi-zone chemistry model for the high-pressure part of the engine cycle is extended by a mean value model accounting for the gas exchange losses. The resulting model is capable of describing PCCI com- bustion with stationary exactness. It is at the same time very economic with respect to computational costs. The model is further extended by identified system dynamics influencing the stationary inputs. For this, a Wiener model is set up that uses the stationary model as a nonlinear system representation. In this way, a dynamic nonlinear model for the representation of the controlled plant Diesel engine is created. This paper summarizes the work already de- scribed in [Hoffmann et al., A Cycle-Based Multi-Zone Simulation Approach Including Cycle-to-Cycle Dynamics for the Development of a Controller for PCCI Combustion, SAE paper 2009-01-0671, 2009] and [Felsch et al., Combus- tion model reduction for Diesel engine control design, Int. Journal of Engine Research, 2009, submitted]. Introduction testing completely new controlled process va- In the recent past, several efforts have been re- riables. ported in the literature that aim at controlling en- gine combustion. The standard procedure for Combustion Model Formulation creating a controller includes the modeling part as Crucial for reacting turbulent flows is the model- the first step. Often this model differs in several ing of the chemistry. Here, a multi-zone chemistry aspects from models widely used for gathering a model is employed. It covers the nonlinear depen- deeper understanding of combustion details, like dencies within the high-pressure part of the engine three-dimensional computational fluid dynamics cycle with stationary exactness. (CFD) models. From the viewpoint of automatic The multi-zone model employed in the current control, the dynamics describing the dependency study is X0D, a zero-dimensional chemistry solver of the system’s outputs/controlled variables (IMEP, based on multiple zero-dimensional reactors. X0D CA50) on the actors (SOI, external EGR rate, and was developed internally at General Motors R&D total fuel mass injected) is of highest priority. Nev- by Hardo Barths, Tom Sloane, and Christian ertheless, stationary exactness of the model is Hasse, and was first described in Hergart et al. [1]. important, too. Another requirement is an accepta- The governing equations account for species mass ble calculation speed, as it is often applied in dy- fraction conservation, temperature, and pressure namic closed-loop simulations. change in each zone. The multi-zone model also This paper presents a new approach to the de- includes mass exchange between zones, wall heat velopment of a simulation model for the use in transfer, as well as fuel injection and vaporization. closed-loop control development. The model is The underlying chemical mechanism comprises 59 based on a recently introduced multi-zone model elementary reactions among 38 chemical species. for PCCI combustion that was derived from a de- This mechanism mainly describes low-temperature tailed CFD approach. It covers the nonlinear de- auto-ignition and combustion of n-heptane, which pendencies within the high-pressure part of the serves as a surrogate fuel for Diesel in this work. engine cycle with stationary exactness. This model Further details are given in [2]. is extended by a physically inspired description of the gas exchange part of the engine cycle. For the Stationary Validation use in closed-loop simulations, the system’s dy- At the Institut für Technische Verbrennung at namics have to be covered. For this reason, the RWTH Aachen University, Germany, experiments stationary model is further extended by identified were carried out with a 1.9l GM Fiat Diesel engine. system dynamics influencing the stationary inputs. This engine is equipped with a second-generation In this manner, a stationary exact model is ex- Bosch Common-Rail injection system and an tended to a Wiener-type model with a static part EDC16 electronic control unit. A more detailed describing the nonlinearities and an upstream part description regarding the engine, the test cell describing the system’s dynamics. This novel pro- equipment, and injection rate measurements can ceeding integrates the detailed knowledge from be found in Vanegas et al. [3]. combustion simulation tools into closed-loop con- The engine was operated at part-load condi- trol and establishes a broad field of possibilities for tions with a speed of 2000 rpm. For this study, 50 different stationary experiments were carried out * Corresponding author: c.felsch@itv.rwth-aachen.de Towards Clean Diesel Engines, TCDE2009 with variations in external EGR rate, start of injec- model within a closed-loop controller for PCCI tion (SOI), and total fuel mass injected (FMI). combustion requires that it is capable of predicting Figure 1 shows the achieved modeling results the dependency of the controlled variables on the in terms of pressure curve, indicated mean effec- actuators. As mentioned in the “Introduction”, the tive pressure of the high-pressure cycle (IMEPHP), actuators are SOI, external EGR rate, and FMI. and crank angle of 50% burnt fuel mass (CA50) in The controlled variables are the IMEP and CA50. comparison to test bench measurements for five The latter is directly obtained from a simulation selected operating conditions TS-1 through TS-5. with the multi-zone model. The former, however, There is a very good qualitative and quantitative can only be predicted for the time frame from clos- agreement. ing of the intake until opening of the exhaust valves. For this reason, the calculation of the IMEPHP is extended to the gas exchange part of the engine cycle. The calculation of the indicated mean effective pressure throughout the gas exchange (IMEPGE) is physically inspired by pumping losses. This ap- proach is further explained in [4]. After an appro- priate fitting, the approach is capable of predicting the IMEPGE within 5% accuracy for most of the 50 operating conditions mentioned above (see Fig. 2). Fig. 2: IMEPGE of the gas exchange for all 50 experi- ments mentioned above. Comparison between mean value model calculation and experiment Combining the multi-zone model X0D with this gas exchange model therefore leads to a static model, which can be used to determine the static dependency of the controlled variables IMEP and CA50 on the actuated variables SOI, external EGR rate, and FMI. System Identification The combination of multi-zone model and mean value model for the IMEPGE does so far not include any dynamics of the controlled variables. Hence, a structure was chosen, which is suitable for adding Fig. 1: Average cylinder pressure (top), IMEPHP (center), the dynamic aspect to the static accurate model. and CA50 (bottom) for five selected operating conditions As the dynamic physical behaviour of the real en- TS-1 through TS-5. Comparison between simulation and gine shall be enforced on the whole static model, a experiment Wiener-type dynamics was implemented. With this choice, the inputs to the static model are overlaid Gas Exchange Modeling with time attributes, which enforces the dynamic The stationary validation described in the pre- behaviour on the combustion simulation. Thus, vious section is restricted to the high-pressure part of the engine cycle. The usage of the multi-zone IMEP and CA50 are consequently affected by the model parts was validated against transient expe- identified dynamics. rimental data. For identifying the system’s dynamics or the system’s dynamic transfer functions, respectively, various step response experiments were carried out. These are described in detail in [4]. Integrated Model For application within a closed-loop control simulation, the multi-zone model was transferred to an environment suitable for the conception and testing of controllers. The multi-zone model X0D written in FORTRAN 77 was embedded into a Matlab/Simulink FORTRAN s-function enabling the simulation of the multi-zone model from within Matlab/Simulink. Moreover, the gas exchange model was implemented into this s-function. The three identified dynamic transfer functions were added by means of time-discrete PT1-dynamics within appropriate function blocks. Figure 3 shows IMEP and CA50 obtained from the step response experiment, the system identifi- cation with the corresponding identified discrete transfer function, and the transient simulation with the integrated model for an SOI step from -20.7 to -30.7 °CA aTDC and back with an external EGR rate of 30% and an injected fuel mass of 10.2 mg/cycle. The simulation results are in very good Fig. 3: IMEP (top) and CA50 (bottom) for an SOI step from -20.7 to -30.7 °CA aTDC and back with an external agreement with the measurements. In particular, EGR rate of 30% and an injected fuel mass of 10.2 the dynamic step responses are reproduced well. mg/cycle. Comparison between experiment, system Additional results may be found in [2]. This vali- identification, and integrated model dates the integrated model composed of the multi- zone model, the gas exchange model, and the Acknowledgment identified system dynamics. This work was funded within the collaborative research center ”SFB 686 - Modellbasierte Rege- Summary and Conclusions lung der homogenisierten Niedertemperatur- Closed-loop simulations are a necessary and Verbrennung” at RWTH Aachen University, Ger- common tool in the development process of con- many, and Bielefeld University, Germany [5]. trollers. A computationally efficient multi-zone model was employed that is capable of describing References the combustion characteristics for the high- [1] C.-A. Hergart, H. Barths, R.M. Siewert, Modeling Approaches for Partially Premixed Compression pressure part of the engine cycle. The controller to Ignition Combustion, SAE paper 2005-01-0218, be developed shall actuate SOI, external EGR rate, (2005). and total fuel mass injected to control the IMEP of [2] C. Felsch, K. Hoffmann, A.Vanegas, P. Drews, H. the whole engine cycle and the CA50. The IMEPHP Barths, D. Abel, N. Peters, Combustion model re- of the high-pressure engine cycle and the CA50 duction for Diesel engine control design, Int. Jour- can be extracted from simulations with the multi- nal of Engine Research, (2009), submitted. zone model. The former was combined with a [3] A. Vanegas, H. Won, C. Felsch, M. Gauding, N. mean value model for the losses of the gas ex- Peters, Experimental Investigation of the Effect of change to calculate the IMEP of the whole engine Multiple Injections on Pollutant Formation in a Common-Rail DI Diesel Engine, SAE paper 2008- cycle. The combination of these models leads to 01-1191, (2008). an accurate static model, which was further ex- [4] K. Hoffmann, P. Drews, D. Abel, C. Felsch, A. tended to a Wiener model for capturing temporal Vanegas, N. Peters, A Cycle-Based Multi-Zone cycle-to-cycle dependencies. For every input of the Simulation Approach Including Cycle-to-Cycle Dy- model, a transfer function was determined, forcing namics for the Development of a Controller for the whole model to follow the engine’s dynamics. PCCI Combustion, SAE paper 2009-01-0671, All model parts (multi-zone model, mean value (2009). model for the gas exchange, and dynamic time [5] RWTH Aachen University and Bielefeld University, response) were each validated separately. After- SFB 686 - Modellbasierte Regelung der homogeni- sierten Niedertemperatur-Verbrennung, wards, the integrated model composed of all three http://www.sfb686.rwth-aachen.de.