A Systematic Approach Towards Automated Control Design for Heavy-Duty EGR Diesel Engines

Transcription

1 AVEC 1 A Systematic Approach Towards Automated Control Design for Heavy-Duty EGR Diesel s Chris Criens, Frank Willems,, Maarten Steinbuch Eindhoven University of Technology, TNO Automotive Den Dolech 2, P.O. Box 513, WH MB, Eindhoven, The Netherlands Phone: c.h.a.criens@tue.nl This paper presents a model-based design method for a robust air path controller of a diesel engine with Exhaust Gas Recirculation (EGR). Following the µ synthesis framework, a MIMO controller is developed, which guarantees robustness and optimal performance. This controller simultaneously controls EGR flow and air-fuel ratio. Due to the systematic design approach, this controller can be automatically generated, which dramatically reduces calibration time. Performance improvements are shown using simulations. Topics / Powertrain & Drive Train Control, Truck & Heavy Duty Vehicle Model & Simulation 1. INTRODUCTION To meet the upcoming Euro-VI and US21 targets for nitrogen oxides (NO x ) and Particulate Matter (PM) emissions, truck manufacturers will apply heavy-duty diesel engines with Exhaust Gas Recirculation (EGR) and common rail fuel injection equipment. These engine measures will be combined with exhaust gas aftertreatment technology: SCR-deNO x catalyst and a Diesel Particulate Filter (DPF). In this paper, we focus on the air path control of a heavy-duty EGR diesel engine. Typically, these engines are equipped with a variable geometry turbocharger and an EGR system, as shown in Figure 1. The compressor is driven by the variable turbine geometry (VTG), which is mounted on the same mechanical shaft. By moving the inlet guide vanes, the delivered turbine power can be adjusted and flow conditions can be matched in the most efficient way. The EGR system diverts part of the exhaust gas flow back to the intake system. With this EGR flow, the combustion mixture is diluted. This results in reduced in-cylinder combustion temperature and oxygen concentration (O 2 %), and hence reduced NO x formation. For low PM emissions, on the other hand, it is important that the air-fuel ratio is sufficiently high. The objective of the air path controller is to realize the desired air-fuel ratio and EGR flow by manipulating the VTG and EGR valve. This controller has to meet the following requirements: Optimal performance: specified NO x and PM emissions have to be realized in combination with minimal fuel consumption. For emission legislation, focus is on performance over both steady-state and transient test cycles. Furthermore, the driver s torque Compressor Variable Turbine Geometry Fresh air Exhaust EGR Intake manifold, O 2% Cylinders Exhaust manifold Fig. 1: Scheme of the studied EGR engine Torque demand has to be met without unacceptable PM levels during fast transients; Robustness: with the introduction of In-Service Conformity (ISC) legislation, additional targets for real-world vehicle emissions are defined. This sets new requirements for the robustness of emission control systems. Specified emissions have to be achieved despite system uncertainties (production tolerances, wear, aging) or external disturbances (ambient conditions; Calibration effort: for current control systems, a large number of engine maps has to be calibrated. With growing complexity of engine and powertrain systems, this effort will dramatically increase in the coming years. In order to reduce time-to-market and costs, there is an ongoing interest in efficient control design and calibration methods. During the past decade, the air path control problem for diesel engines has been extensively examined. However, the vast majority of research focused on the coordination of VTG and EGR valve to simultane- 165

2 AVEC 1 ously control air-fuel ratio and EGR flow (or related performance variables) and to improve transient response, see e.g. [1, 2, 3, 4, 5, 6, 7]. Only a few studies dealt with robustness issues. Those included the constructive Lyapunov design approach in [8], the gain-scheduled H control approach in [9, 1], and the model-based quantitative feedback approach in [6]. In these studies, the (equivalent) gain and phase margins are determined. Note that this does not a priori guarantee controller robustness for model uncertainties. In order to guarantee robustness properties, we apply the µ synthesis framework to the studied air path control problem. This model-based approach can deal with the multivariable control problem and can also guarantee optimal performance. Furthermore, it opens the route to a systematic control design procedure, and thus potential for reduced calibration time. A similar approach can be found in [11]. However, there are differences in the way of obtaining the uncertainty model. Jung et al followed a more physical approach, whereas our approach is more suited to be automated. Also, in our study the selection of the optimization criterion is more based on real life conditions. This paper is organized as follows. First, the studied heavy-duty diesel engine is briefly described. Then, the main system characteristics are studied in Section 3. Section 4 discusses the control problem and design. To demonstrate the potential of the designed controller, simulation results are presented in Section 5. Finally, conclusions are drawn and directions for future research are given. 2. SYSTEM DESCRIPTION This study focuses on the control of a six cylinder heavy-duty diesel engine. This 12 liter, 375 kw engine is equipped with an unit pump fuel injection system, a variable geometry turbocharger, and a highpressure EGR system. This engine was calibrated to meet US27 emission standards. For the studied engine, a sixth order mean value model is developed [12]: ẋ = f(x, u, w) z = g(x, u, w) (1) with states x, control inputs u, external inputs w, and controlled outputs z: x = [p im, m air,fresh, m inert, p em, T em, ω t ] u = [u EGR, u V T G ] w = [ω e, W f ] z = [, O 2 %] (2) From model fit and validation, it is seen that this model can accurately describe the dynamic responses of the air and exhaust flows in the engine. Figure 2 illustrates the selection of the controlled outputs. Emission legislation limits are converted to targets for NO x and PM emissions in the different engine operating points. This is realized indirectly, by EGR VTG Model speed Fuel O 2 % Emission Model NO x Fig. 2: Scheme illustrating the selection of the control outputs O2% EGR PM VTG Fig. 3: The equilibrium values of and O 2 % resulting from sweeping the VTG and EGR valve at 15 rpm and 1 mg/inj. Steps in the EGR valve are 2.5% and in the VTG angle 5%. specifying the corresponding air-fuel ratio and EGR flow rates, including transients. Also, related quantities such as intake and exhaust pressure, fresh air flow, or burned gas fraction are applied [1, 2]. However, in this study air-fuel ratio and oxygen concentration O 2 % in the intake manifold are applied. This selection is mainly driven by the strong correlation between these quantities and the emissions to be controlled. The formation of PM is strongly linked with. Especially low values of lead to excessive PM formation. The formation of NO x is strongly linked to the O 2 %. A lower O 2 % lowers the combustion temperature and also less oxygen is present near the flame front. Both effects are beneficial for lowered NO x formation. 3. SYSTEM ANALYSIS In this section we investigate the properties of the diesel engine airpath that are of interest for the design of the control system using the mean value engine model. More precisely: effects like dynamic coupling, the feasible range of the outputs and uncertainty are studied. 3.1 Static analysis Figure 3 shows the output values resulting from a sweep of the input values. This graph shows that the range of and O 2 % that can be obtained is limited. Opening the EGR valve will result in a lower O 2 % and lower. Opening the VTG vanes results in an increased O 2 %. The effect on depends on the conditions. The range of obtainable and O 2 % is clearly limited by the selected hardware. 166

3 AVEC 1 O 2 % EGR step VTG step Legislation & Road usage model specifications Control model Optimization criterion synthesis Fig. 5: Diagram showing the main steps followed in control design process Time Time we want to apply a feedback control that adapts the VTG and EGR to counteract these disturbances and uncertainties. The uncertain dynamic response will cause robustness problems when standard feedback strategies are used. Fig. 4: EGR (left) and VTG (right) step responses. In black: nominal; colored: disturbed. Setpoint selection The goal of the controller will be to make sure that desired values for and O 2 % are obtained in practise. It remains to choose these setpoint values. Given the range of feasible points in Figure 3, the best point has to be chosen. The point that is chosen determines the tradeoff that is made between the different emissions and engine efficiency. Generally a high O 2 % gives a high efficiency, low PM, but high NO x. A reasonable tradeoff setpoint value that we will use in this study is O 2 % = 16%. The setpoint for is the result of a tradeoff between PM emissions, BMEP and pumping losses. In this paper we will use = 2 as a setpoint. 3.2 Dynamic analysis Important for the design of a feedback controller will be how the system responds to a change in the control inputs. The black line in Figure 4 shows the response of the outputs to a unit step change in the inputs starting from nominal conditions. This response clearly shows the coupling between all inputs and outputs that is present in the system. This means that any single-input single-output SISO control strategy will not be able to get optimal performance from this system. A multi-input multi output (MIMO) control approach is required to obtain the best performance. The time scales needed for reaching a value close to the equilibrium are between one and three seconds for all responses. The effect of VTG on, is the slowest. Furthermore, non-minimum phase behavior is observed in the VTG- response. This complicates the design of a high performance feedback controller. 3.3 Effect of uncertainties Model uncertainties and changing ambient conditions will have an effect on both the dynamic response of the system and the resulting equilibrium values for and O 2 %. We want to maintain the setpoint values of and O 2 %. This is the reason We implicitly study the sensitivity to changing conditions by choosing an operating point that deviates from nominal. Due to the nonlinearity of the system, this generates a different response. This way we can study the sensitivity to changing conditions without having to change the model. For the design of the control model, in section 4.2, 81 different operating points are included. A selection of 5 responses that deviate ±5% from nominal in engine speed, fueling, EGR valve position and/or VTG vane angle is shown in Figure 4. The differences between the step responses are of the same order of magnitude as the individual step responses themselves. This makes it very important to take robustness into account for control design. 4. CONTROL DESIGN The purpose of the controller is to adapt the VTG and EGR valve in such a way that the desired intake conditions for both and O 2 % are maintained, regardless of disturbances or uncertainties in the behavior of the engine. To achieve this, feedback control is indispensable. For the feedback controller, we assume and O 2 % are both directly measurable. As seen in the previous section, we are faced with a system that exhibits strong coupling between inputs and outputs. Also, nonlinearity plays an important role, which results in a large uncertainty to the local dynamic response. Robust performance in the face of this uncertain response is a main requirement for the controller. To be able to take this into account in a systematic way, we propose to use the µ-synthesis framework [13] for the design of the controller. Using the µ-synthesis framework presents possibilities for a robust control design which optimizes the worst case performance for an uncertain system. In Figure 5, the followed steps for this design are depicted schematically. Following this scheme results in a framework that can be fully automated. The engine design and modeling have been completed already. Also, the emission legislation, road usage and control specifications are not the subject of this study. This leaves three topics for this section: making a control model, formulating the optimization criterion and finally controller synthesis. 167

4 AVEC 1 Reference, O2% + EGR, VTG We Wu Model: P ze zu, O2% Fig. 6: A schematic representation of the placement of the performance weights. Magnitude Frequency in Hz Fig. 7: In blue, green and red the weights on respectively O 2 %, and both control inputs. 4.1 Optimization criterion The optimization criterion will determine how the tradeoff between robustness, maintaining the desired outputs and use of the system inputs is made. Robustness of the controller will be taken into account by including model uncertainty in the control model. This will be covered in section 4.2. The µ-framework makes it possible to design frequency dependent weights on the signals in the systems. Using DK-iteration we then design a controller that gives the best weighted performance. We will use weights on the setpoint error, W e, and control input, W u. In Figure 6 this is schematically depicted. A higher weight on a signal means that more effort will be used to make sure that the performance target for that signal is reached. Four individual targets can be identified. The first two are to maintain the desired and O 2 % during real world driving. The second two targets are to limit the use of the two input signals. Especially, highly fluctuating input signals should be penalized, because they would decrease the lifetime of the actuators. To make a meaningful weight on the tracking performance of and O 2 %, it is important to first consider the conditions of operation. Two different sources of disturbances are expected. The first source is slowly varying disturbances caused by e.g. changing ambient conditions, heat up of the engine or ageing. As these disturbances are typically much slower than the dynamics of our system, integral control will be a suitable solution. The second source of disturbance is the changing torque request by the driver. This disturbance is measured and hence can be counteracted using feedforward techniques. However, due to the uncertain response of the system, this feedforward will be imperfect and an error still remains. The error will likely have about the same frequencie distribution as the original disturbance. The European Transient Cycle (ETC) is a typical example of real world driving. It represents urban, suburban, and highway driving. Moreover, it is used as part of the European emission legislation tests. By studying the frequency contents of the ETC, we have a representative and objective way to quantify the expected disturbances due to the driver input. The ETC frequency distribution can be described fairly accurate by a first order transfer function. This first order estimate of the ETC will be combined with an integrator that penalized the low frequency disturbances. The integrator zero is placed a factor 3 lower in frequency than the pole of the ETC part. True integral weights would cause numerical problems when used during synthesis. Therefore, to facilitate control synthesis using the Matlab dksyn algorithm, a pole is added to the integral weight at a frequency a factor 1. before the integrator zero. Now, to make the final weight W e on tracking error of and O 2 %, we add a scaling gain to make the tradeoff in allowed setpoint errors between these two outputs. For this, we look at the expected errors without feedback control and we end up choosing the gain on three times higher than on O 2 %. The weight W u on the input signal is employed to prevent large control actions and highly fluctuating control actions. This weight helps to prevent saturation of the input signal, though no guarantees can be given. It is important to keep in mind that control actions that are within the required performance region, i.e. up to the dropoff of W e are needed for accurately keeping the setpoint. Penalizing these frequencies will decrease the performance. We use a first order weight on both system inputs that increases after the dropoff of W e. Different scalings are not needed this time, because the inputs are both normalized. In Figure 7 the frequency response of the weights is shown. 4.2 Control model The applied mean value engine model is not suitable for controller synthesis. To make controller synthesis practical, we are much better off with a linear time invariant (LTI) model. For each operating point there is an LTI model that is equivalent to the general simulation model. These LTI models are only accurate in a small neighborhood around the nominal point. Disturbances will cause the system to leave the nominal point and the response of the system to a change in the input parameters will change as well as shown in Figure 4. To take this into account, we will not describe the system by a normal LTI model, but by an uncertain LTI model. By identifying the behavior of the system in a set of operating points located around the nominal point, we investigate the changes in the behavior of the system. An uncertain LTI model will then be made that represents the pos- 168

5 AVEC 1 sible responses of the system. We will use an additive uncertainty model of the form: [ ] δ1,1 w P (z) = P nom (z)+t 1,1 (z) δ 1,2 w 1,2 (z) δ 2,1 w 2,1 (z) δ 2,2 w 2,2 (z) (3) With P nom the nominal system behavior, T a transformation matrix and δ i,j an uncertain complex value such that δ i,j < 1 and w i,j a transfer function to describing the maximum uncertainty. It is worth noting here that P nom will not be equal to the system behavior at nominal conditions. To make the uncertain system model P, a series of steps is needed. The first step is to generate a set of possible system behaviors. For this a nominal point of operation needs to be chosen. We will use 15 rpm, 1 mg/inj, VTG 7%, EGR 6%, resulting in = 2 and O 2 % = 16% (see section 3.1.1). Next a range of operating points is defined. For all four parameters of the operating point (engine speed, fueling, VTG and EGR) we will use low, high and nominal values. The difference between low, high and nominal is ±1%. Combining the three possible values of the four parameters gives 3 4 = 81 different variations of the system. To identify the local behavior at the 81 operating points the engine model is used. Small steps are applied at the control inputs. Next a method called approximate realization [14] is applied to identify an LTI system that gives the same dynamic response. This method will yield very accurate approximations, because we use simulation data free of measurement errors or noise. The difference between the LTI approximation and the simulation data is negligibly small. A convex combination of these 81 LTI systems is expected to represent all possible behaviors of the system. The uncertain model should accurately describe the identified set of of behaviors. For this we need to choose a P nom, four w i,j and a matrix T. The nominal model P nom that is calculated is designed to make the required uncertainty as small as possible. A general optimization algorithm is applied to calculate on a logarithmically distributed set of frequencies which nominal response will give the smallest required uncertainty radius. Next, output error optimization is used to calculate a low order fit on the calculated optimal response. For each of the four elements of the response, a fourth order fit is made. Combining the models for all individual input-output elements into a single LTI system gives the nominal system model. A transformation matrix T is calculated to take into account some of the structure that is present in the uncertainty. An optimization algorithm is applied to calculate a transformation that puts as much of the low frequent uncertainty in the diagonal blocks. This should reduce the conservatism that is introduced by using the elementwise uncertainty model. Using the just made P nom, the largest difference Magnitude Magnitude EGR input Frequency in Hz 1 1 VTG input Frequency in Hz Fig. 8: The magnitude frequency response of T 1 P. Nominal model (line) and the uncertainty range (dashed). between the nominal LTI model and the set of identified system behaviors is calculated at the same logarithmic set of frequencies for each of the four elements of the transfer function. This results in an uncertainty radius at each of the frequencies. When the fit of the nominal system is close to the optimal data, this uncertainty radius will be close to the smallest uncertainty radius that was calculated before. Now an overbound on the uncertainty radii is made by calculating four SISO transfer functions w i,j. Only the magnitude of these functions are of importance, because complex uncertainties are used. Hence the phase of the uncertainty is completely undetermined. The combination of the nominal model with the uncertainty model gives the final uncertain system model P. In Figure 8 T 1 P is depicted. The reverse transformation is used to better show the uncertainty model. The model P will be augmented with the weights on the setpoint error W e and control input W u, as shown in figure Figure synthesis Given the uncertain system model and performance specifications, we want to find the controller that optimizes the worst scenario. For this a µ- synthesis procedure is applied [13]. In the modeling of the uncertain system it was already taken into account that DK-iteration will be used for the controller synthesis. DK-iteration means that by repeated calculation of D-scales and controllers (K), an optimal controller is synthesized. The performance weights are scaled such that the resulting controller gives a peak value of µ that is close to one. Having µ = 1 can be interpreted as robust performance for all possible variations of the uncertain system. 5. RESULTS To test the performance of the controlled system, 169

6 AVEC 1 O 2 % speed in rpm EGR% Time in seconds VTG% Fuel in mg/ing Time in seconds Fig. 9: In blue, a simulation without feedback control of an engine undergoing disturbances in engine speed and fueling. The nominal operating point is 15 rpm and 1 mg/inj. In green, the same simulation, but now with the feedback controller switched on. we simulate its performance using step disturbances. These disturbances are particularly challenging for the controller and show the transient performance of the feedback controlled system. In Figure 9 the results are shown. The feedback controlled simulation, depicted in green is able to keep the setpoint error small by adapting the input signal. The time needed for the feedback controlled system to adapt to the disturbance is about two seconds. This is indeed fast compared to the real life disturbances, which makes the controller suitable for accurate control in real life conditions. 6. CONCLUSION & FUTURE RESEARCH A method for controller design for EGR-VTG control of a heavy duty diesel engine is presented. The design is fully model-based and suitable to be automated. It features optimal performance and robustness against model uncertainties. Future research is needed to make the controller suitable for the complete engine operating range. A real life test on a heavy-duty diesel engine can show the practical benefits. The ultimate goal of my research is to formulate a control strategy for obtaining optimal fuel consumption and low emissions from a diesel engine. REFERENCES [1] M. van Nieuwstadt et al., Egr-vgt control schemes: experimental comparison for a highspeed diesel engine, IEEE Control Systems Magazine, 2. [2] A. Stefanopoulou, I. Kolmanovsky, and J. Freudenberg, Control of variable geometry turbocharged diesel engines for reduced emissions, IEEE Transactions on Control Systems Technology, vol. 8, no. 4, pp , 2. [3] M. Amman et al., Model-based Control of the VGT and EGR in a Turbocharged Common- Rail Diesel : Theory and Passenger Car Implementation, SAE paper , Jan. 23. [4] H. Ferreau et al., Predictive control of a realworld diesel engine using an extended online active set strategy, Annual Reviews in Control, vol. 31, 27. [5] G. Stewart and F. Borrelli, A model predictive control framework for industrial turbodiesel engine control, in Proc. of IEEE Conference on Decision and Control, 28. [6] Y. Wang, I. Haskara, and O. Yaniv, Modelbased quantitative feedback control of egr rate and boost pressure for turbocharged diesel engines, in Proc. of American Control Conference, 28. [7] J. Wahlström, L. Eriksson, and L. Nielsen, Egr-vgt control and tuning for pumping work minimization and emission control, IEEE Transactions on Control Systems Technology, Accepted for publication. [8] M. Jankovic, M. Jankovic, and I. Kolmanovsky, Constructive lyapunov control design for turboharged diesel engines, IEEE Transactions on Control Systems Technology, vol. 8, no. 2, pp , 2. [9] E. Alfieri, A. Amstutz, and L. Guzzella, Gainscheduled model-based feedback control of the air/fuel ratio in diesel engines, Control ering Practice, vol. 17, 29. [1] X. Wei, Gain scheduled H control for air path systems of diesel engines using lpv techniques, IEEE Transactions on Control Systems Technology, vol. 15, no. 3, pp , 27. [11] M. Jung, K. Glover, and U. Christen, Comparison of uncertainty parameterisations for H robust control of turbocharged diesel engines, Control ering Practice, vol. 13, 25. [12] TNO, simulation tool DYNAMO. TNO Sciency & Industry. [13] S. Skogestad and I. Postlethwaite, Multivariable Feedback Control Analysis and Design, [14] L. Silverman and M. Bettayeb, Optimal approximation of linear systems, Joint Automatic Control Conference, San Francisco, CA,