MODEL-BASED CONTROL DESIGN FOR IC-ENGINES ON DYNAMOMETERS: THE TOOLBOX OPTIMOT. M. Hafner, M. Weber, R. Isermann

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1 Copyright 2002 IFAC 15th Triennial World Congress, Barcelona, Spain MODEL-BASED CONTROL DESIGN FOR IC-ENGINES ON DYNAMOMETERS: THE TOOLBOX OPTIMOT M. Hafner, M. Weber, R. Isermann Darmstadt University of Technology, Institute of Automatic Control Landgraf-Georg-Str. 4, D Darmstadt, Germany MHafner, MWeber, phone: fax: Abstract: : A new approach towards a model-based optimization of IC engine control on dynamometers is presented in this paper. The proposed methodology comprises advanced measurement strategies for a fast dynamic measurement of engine characteristics on dynamometers (DYNMET), a model-based offline optimization of feedforward control maps (STATOPT), and the optimization of dynamic transitions of turbocharged engines with exhaust gas recirculation (DYNOPT). The respective program packages are being integrated into a MATLAB-Toolbox called OptiMot: optimization of IC motors. This paper shortly reviews the underlying algorithms of the package, such as the design of measurements, the identification of the engine, and the optimization of the static and dynamic engine behavior. Then, the OptiMot toolbox is described in detail in order to give the reader a vivid image of how to use the algorithms by means of a graphical user interface. Keywords: engine control, emissions, identification model-based optimization, OptiMot toolbox 1. INTRODUCTION The calibration of ECU functions has become one of the main bottlenecks in cutting the time-to-market of new cars. This is due to the fact that a lot of new electronically controlled technologies have been introduced in order to fulfill upcoming emission laws, [1]. Figure 1 displays a simplified structure of a state-ofthe-art Diesel engine control system where the engine inputs injected fuel m inj, injection angle Θ inj, injection pressure p inj, induced air mass m air, and charge pressure p 2 are feedforward- or feedback controlled, respectively. All these inputs are coupled and influence the outputs of the engine (consumption, emissions, driveability etc.) in a nonlinear way. This results in the problem of finding an optimal control for a coupled nonlinear multiple input multiple output system. More specific, Fig. 1. Simplified structure of Diesel ECU a set of optimized control settings has to be determined for each operating point of the engine. Due to the coupling of the system it is not favorable to sequentially optimize one setting variable after the other. It is rather necessary to parallelly optimize all inputs which can hardly be done manually any longer, [2].

2 Model-based approaches allow the implementation of mathematical routines in order to optimize the electronic engine control on dynamometers. At the Institute of Automatic Control at the Darmstadt University of Technology, a program toolbox called OptiMot (optimization of IC Motors) has been developed which addresses the respective steps for a model-based optimization of IC engines according to Figure DESIGN OF MEASUREMENTS The time required for conventional static measurements rises exponentially with the number of inputs to be varied, [6]. Furthermore the collected data can not be used for dynamic modeling which becomes more and more important for sophisticated engine controls. Therefore, a new dynamic measuring technique (DYN- MET) has been applied in order to measure the transient behavior of the engine in short times. The idea is to modulate an amplitude-modulated binary random signal (APRBS) on all engine inputs. Prior knowledge concerning standard values can be used in order Fig. 2. Model-based optimization of IC engine control In this paper, the functionality of the OptiMot toolbox and the underlying algorithms are described. The toolbox (and also this paper) can be structured as follows: design of fast measurement strategies dynamic modeling of engine emissions and torque optimization of feedforward control maps for the static engine behavior calibration of dynamic control functions to minimize transient soot emissions Fig. 3. Conventional static measurement (STATMET) and fast dynamic measuring technique (DYN- MET) with APRBS to avoid measuring in areas where the engine would never run. Figure 3 compares the static and dynamic approaches and gives an example on how the injection angle Θ inj varies over time during a DYNMET measurement. 2. THE OPTIMOT TOOLBOX The toolbox comprises the complete functionality for the proposed model based optimization of the static and dynamic engine behavior on dynamometers. The basic concept of the graphical user interface was to guide the user through the whole procedure from designing the experiment, deriving neural engine models, running the static and dynamic optimizations, and visualize the resulting control maps and functions. Default values always give the user an indication on reasonable settings to choose. The toolbox was programmed in MATLAB and will be introduced concerning both, the basic functionality and the graphical user interface, in the following sections. For a more detailed description of the underlying functions refer to [3,4,5]. The OptiMot toolbox allows the user to design the DYNMET-measurement according to his individual specifications, Figure 4. The first thing to do is to determine the relevant input variables which have to be excited. Usually these are the electronic engine settings (or controlled variables) as well as the engine speed. When choosing the inputs, the user also has to set the lower and upper bounds of the setting variables (i.e. their physical range). Concerning the APRBSfrequency, a minimal static time between two APRBSsteps has to be given for the individual inputs. Finally, the user has to set the desired measurement time, the maximal amplitude of the APRBS (e.g. some 30 % of the physical range when measuring around settings from a given engine control), and an arbitrary number of static points where the process settles during the measurement (these static points are equally distributed over the measurement).

3 The design of the measurement is then automatically calculated, plotted and stored in an ASCII-table (one column per varied input over time). This table can directly be imported and evaluated by the test stand computer system. Fig. 5. OptiMot toolbox: Training and generalizing neural engine models Fig. 4. OptiMot toolbox: Designing the DYNMET measurement 4. ENGINE MODELING The model based optimization in the next section bases on adequate static and dynamic models of engine emissions and -torque. Physical modeling of emissions still requires by far too much calculation time, [7]. Neural networks, especially some new fast derivatives, allow a very fast and compact emission modeling based on experimental data derived from the DYNMET measurements. An introduction to the basics of the used LOLIMOT neural network can be found in [8,9]. Before training the network, however, the user should thoroughly prepare the measured data, i.e. correct outliers, eliminate crank-angle synchronous effects, resample the data at an appropriate sampling time and compensate known sensor dynamics. For details refer to [4]. This process of data postprocessing is of fundamental importance, especially when dealing with dynamic processes. On the one hand, too fast sampling results in little dynamic information from one data point to the other. On the other hand, sampling too slowly will not be sufficient to extract the dynamic behavior of the process. [10] suggests to place 5-8 sampling points on the system s step response rise time. The next step after analyzing and preparing the data is training the neural network. One specific of the LOLIMOT algorithm is that there are very few fiddle parameters to be set. It will mostly be sufficient to rely on the default settings proposed by the OptiMot graphical user interface, Figure 5. The user basically has to choose the training data file, determine the model inputs and outputs, and set a maximal number of neurons for the models. The ideal number of neurons always has to be found iteratively as a compromise between accuracy and overfitting. This is done based on the convergence curve of the model error and by means of the generalization of the model when it is applied to a new, unknown data set, [8]. The dynamics of the model, i.e. the dynamic delays q ij (i = number of input, j = number of regressor of input i) in y(k) = b 11 u 1 (k q 11 ) + b 12 u 1 (k q 12 ) +b 1j u 1 (k q 1j ) + b 21 u 2 (k q 21 )... +b ij u i (k q ij ) + a 1 y(k q 01 ) +a j y(k q 0j ) can be chosen individually for each input. Again, default values for specific engine configurations (e.g. turbocharged Diesel engine with exhaust gas recirculation) are proposed in order to help the user with a reasonable first guess. Figure 6 shows the performance of dynamic emission models and the respective input variables taken from a DYNMET measurement covering the whole operating regime of the engine. The training data consisted of some data points with a sample rate of 10 Hz. The dynamics were chosen to y(k) = b 1 egr(k 1) + b 2 egr(k 3) +b 3 m inj (k 1) + b 4 n eng (k 1) +b 5 Θ inj (k 1) + b 6 tc(k 1) +b 7 tc(k 3) + a 1 y(k 1) and the training of the neural net with 25 neurons took less than 10 minutes on a Pentium-III PC.

4 different ranges of the outputs. Often, the respective output y 0 due to the production car engine control setting can be used. The best solution for the loss function is constrained by a minimal torque to be produced by the engine. The weights k i are iteratively adapted to a given dynamic legal test cycle (MVEG or FTP) according to [5]. The procedure bases on static and dynamic emission models and is illustrated in Figure 7. Fig. 6. Dynamic neural emission models (LOLIMOT) derived from dynamic DYNMET data, Opel 2.0L DTI Diesel engine 5. MODEL BASED ENGINE OPTIMIZATION The optimization of the electronic engine control towards low consumption, low emissions and good driveability is divided into a static and a dynamic part. Both approaches base on neural engine models and find an optimal calibration by minimizing specific loss-functions. 5.1 Static optimization The goal of the static optimization is to calibrate engine control maps in a way that the legal emission limits are met, the fuel consumption is minimized and the torque characteristic (driveability) is not negatively affected. In the following example the inputs exhaust gas recirculation (egr), injected fuel (minj), injection angle (qinj), and the turbocharger s wastegate position (wg) are to be optimized in a way that the engine s specific fuel consumption (sfc) is minimized and the emission limits for NOX and opacity (op) are fulfilled. This leads to the loss-function with J α,n (u) = k sfc sfc(u) sfc 0 +k op op(u) op 0 + k NOx NO x(u) NO x0 min u = [egr, m inj, n eng, Θ inj, tc] that has to be evaluated in each (n,α) = (speed,pedal)- operating point of the engine. The terms in the loss function have to be normalized in order to consider the Fig. 7. Scheme of the static optimization of engine control map settings The basic idea is to calculate a set of complete optimized control maps with initial weighting factors (e.g. ones) and simulate the resulting engine performance in the cycle based on dynamic emission models. Then the weights are adapted in each following iteration proportionally to the under/overfulfillment of the limits. The grid density of the control maps is arbitrary and can be defined in the graphical user interface, Figure 8. For finding the optimal weights, the user can choose the test cycle and a maximal number of iterations. Alternatively, fixed weights for NO X, Op and sfc can be read in. Fig. 8. OptiMot toolbox: Calibration of engine control maps with optimized settings The used mathematical algorithm for determining the optimized settings in each engine operating point is the sequential quadratic programming - state-of-theart algorithm for multivariable, multicriterion, nonlinear optimization problems with constraints, [11]. As

5 this algorithm might stick to a local optimum the user can check a box in order to choose multiple starting points for the optimization at the cost of a longer calculation time. The time required for the optimization of a set of optimized engine control maps mainly depends on the grid density and the use of multiple initialization. Typical values vary from minutes. 5.2 Dynamic optimization Transient soot emissions during acceleration of Diesel engines are still significant and often visible, even for modern cars. This is especially true for turbocharged Diesel engines with exhaust gas recirculation where dynamic effects influence the air/fuel ratio in the cylinder. A static control like shown in Figure 9 does not consider these dynamics and results in high transient soot emissions. Fig. 9. Dynamic effects due to exhaust gas recirculation and turbocharger setting This soot peak can be substantially be lowered by the dynamic control strategy on the right hand side of the Figure. The idea is to dynamically under- or oversteer the feedforward control of the exhaust gas recirculation valve and the turbocharger position in order to improve the controlled variables (air flow and boost pressure) and consequently the air-fuel ratio. This dynamic control from one static setting (y10) to another (y20) can be realized by the control function Fig. 10. Main window of OptiMot toolbox comprising design of measurement, modeling, static optimization and dynamic optimization The detection of a dynamic situation is done by evaluating the gas pedal signal and its derivative. Generally, the dynamic optimization is limited to some 3-5 seconds. Figure 10 displays the main window of the toolbox with the dynamic optimization in the lower right corner. Two different approaches are possible for the dynamics: Either the dynamic optimization is performed online during the cycle or ideal pedal steps are optimized offline with the T V,opt saved in maps. For the online optimization the user can activate a reinitialization of the algorithm after 2 seconds in order to consider changes of the driver behavior during the dynamics. Also, the incorporation of the injected fuel into optimization (better results are possible, mostly at cost a slightly lower torque production) could be activated. For the offline approach, basically the grid density has to be determined. Generally, the name and type of the neural network models has to be chosen from listboxes and an adequate weighting vector has to be set. Typical weighting factors for lowering the soot peak are [k NOx /k Op /k sfc ] = [0/1/0] or [1/9/1]. y dyn (t) = y 10 + (y 20 y 10 ) [1 (1 T V T 1 ) e t T 1 ] where the time constant T 1 is set to constant values (e.g s) and lag times T V,i (= T V,egr,T V,tc and T V,Θinj ) remain the only parameters to be optimized. This is done model-based by means of dynamic neural networks. The loss function considers the integral behavior of consumption and emissions. If the predominant goal is to minimize the soot peak, the loss function becomes J loss (T V,egr, T V,Θinj, T V,tc ) = Op(egr, m inj, Θ inj, tc)dt. dyn 6. RESULTS Experimental results of the dynamic optimization are depicted in Figure 11. On the left handside, the statically optimized engine settings ([k NOx /k Op /k sfc ] = [0.75/0.70/4.20] due to the iterative adaptation of the weights to the FTP cycle) were applied to the process and compared to the series ECU settings. The static optimization led to a reduction of 5% in fuel consumption for the extracted part of the FTP cycle. At the same time, the NO X emissions could be lowered by some 6% whereas the opacity and the torque did not change in average. In an additional measurement, the dynamic control function approach was applied at the marked acceleration in

6 Fig. 11. Experimental validation results for the static and dynamic optimization at an Opel 2.0L DTI Diesel engine Figure 11. The zoomed plots on the right show the dynamic control settings compared to the statically optimized ones. Also, the measured NO X and opacity emissions are plotted and prove the intended goal of significantly lowering the emitted soot (opacity) over the transient. Further verification results can be found in [4,5,12,13]. 7. CONCLUSIONS The OptiMot toolbox was presented in this sequel which was designed to handle the functionality and the complex underlying algorithms of the developed program package for a model based optimization of IC engine control settings. The static and dynamic optimization use mathematical optimization routines and base on adequate static and dynamic emission models. These are realized by modern neural networks which are trained with data collected from engine measurements on dynamometers. Suitable dynamic measurement strategies are fundamental for a good model quality and consequently for good optimization results. The OptiMot toolbox is meant to guide the user through all these procedures. An intense use of default values allows also non-experts to quickly come up with satisfying results which can then be iteratively improved. [2] Guzzella, L.; Amstutz, A.: Control of Diesel Engines. In IEEE Control Systems Magazine, Vol 18(5), 1998 [3] Hafner, M.; Schüler, M.; Nelles, O.; Isermann, R.: Fast Neural Networks for Diesel Engine Control Design. In Control Engineering Practice (CEP), Vol 8(11), 2000 [4] Hafner, M.: Model Based Determination of Dynamic Engine Control Function Parameters. In SAE Spring Fuels & Lubricants Meeting, Orlando, USA, 2001 [5] Hafner, M.; Isermann, R.: The Use of Stationary and Dynamic Emission Models for an Improved Engine Performance in Legal Test Cycles. In International Workshop on Modeling, Emissions and Control in Automotive Engines, Salerno, Italy, 2001 [6] Edwards, S.; Grove, D.; Wynn, H.: Statistics for Engine Optimization. Professional Engineering Publishing Limited, London, 2000 [7] Pitsch, H.; Barths, H.; Peters, N.: Threedimensional Modeling of NOx and Soot Formation in DI-Diesel Engine Using Detailed Chemistry Based on a Flamelet Approach. SAE International Congress, Detroit, USA, No , 1996 [8] Nelles, O.: Nonlinear System Identification with Local Linear Neuro-Fuzzy Models. Darmstadt, Technische Universität, Dissertation, 1999 [9] Takagi, T.; Sugeno, M.: Fuzzy Identification of Systems and its Applications to Modeling and Control. In IEEE Transactions on Systems, Man and Cybernetics, Vol 15, 1985 [10] Ljung, L..: Modeling of dynamic systems. Prentice Hall, 1994 [11] Vanderplaats, G.: Numerical Optimization Techniques for Engineering Design, McGraw-Hill, New York, 1984 [12] Isermann, R.; Hafner, M., Mechatronic Combustion Engines - From Modeling to Optimal Control. In European Control Conference, Porto, Portugal, 2001 [13] Schüler, M.; Hafner, M.; Isermann, R.: Modelbased Optimization of IC Engines by Means of Fast neural Networks. In MTZ Worldwide, Vol 61(10/11), REFERENCES [1] Bauder, R.: Die Zukunft der Dieselmotoren- Technologie. In MTZ-Supplement, Vol 59(7/8), 2000