21 American Control Conference Marriott Waterfront, Baltimore, MD, USA June 3-July 2, 21 WeC19.5 Modeling and Identification of a Mechatronic Exhaust Gas Recirculation Actuator of an Internal Combustion Engine S. Laghrouche, F. S. Ahmed, M. El Bagdouri, M. Wack, J. Gaber, M. Becherif Laboratoire Systèmes et Transports, Université de Technologie de Belfort-Montbéliard, 9 Belfort, France. Abstract This paper addresses the physical modeling and identification of an EGR Actuator. The EGR actuator has a nonlinear behavior due to its mechanical construction and different friction forces. A nonlinear physical model for an EGR actuator manufactured by Valeo is presented here. Special focus has been given to modeling frictions with the Dahl Model. Different parts of the actuator and friction have been identified. Comparison between simulation and experimental results shows the effectiveness of the proposed model. The model can act as a reference to characterize different designs and future control strategies. Index terms EGR Actuator; Modeling; Automotive Control; Torque Motor; Cam; Friction; Dahl. 1. INTRODUCTION Future regulations regarding NO X and particulate matter emissions would force manufacturers to seek in-cylinder strategies to reduce these emissions along with aftertreatment devices [1]. motor and valve [4, 6]. Friction, present in the mechanical parts of the actuator, plays a significant part in the nonlinear behavior [4, 5]. An accurate and reliable model of a mechatronic EGR actuator for control purposes requires that these non linearities be incorporated [6]. This paper is aimed at providing a complete physical model using a commercial EGR actuator manufactured by Valeo (figure 1) and identifying its parameters. The primary purpose is to understand and simulate actuator dynamics, which are often neglected in global engine control. This model can also serve as a general characterization of mechatronic EGR valves in order to identify new valves and to design control systems around them, using this methodology. Exhaust Gas Recirculation (EGR) is one of the most effective techniques for reducing NO X emissions in internal combustion engines (ICE) [1,2]. This technique is applied using a control actuator that recirculates the exhaust gas given out by the engine, adding it to the fresh fuel-air mixture at the intake. The addition of inert gases to the intake mixture reduces peak burned gas temperatures and hence, reduces NO X formation rates while improving fuel consumption [2]. Precise and accurate modeling and control of the EGR actuator is essential to the system since, while improving fuel consumption, the low temperature reduces combustion rate and makes stable combustion difficult to achieve. EGR percentages in 15 to 3% range are the maximum that an SI engine would tolerate [2], while EGR has to be cut off completely during ignition and idling. An ideal control strategy would be expected to correlate EGR rate with NO X generation [3]. Older vacuum EGR Valves are now losing their popularity in favor of fast and efficient mechatronic actuators that are controlled using DC or Brushless DC (BLDC) motors [2]. These actuators allow faster response times and accuracy in transient conditions. Mechatronic valves pose problems in control because of nonlinearities [4, 5, 6, 7, 9]. These nonlinearities arise from several sources such as temperature transients, external perturbations, and aero-load dynamics. Another possible source is a nonlinear transmission between the actuator Figure 1: Valeo EGR Actuator connected to the experimental setup This paper is organized in the following manner. Section 2 deals with overview of the actuator under study and its modeling. Section 3, is dedicated to dynamic friction modeling. In section 4, the experimental setup is discussed and the parameters of the complete model are identified. Model validation is discussed in section 5 while in section 6, some conclusions are presented. 2. DESCRIPTION OF THE EGR ACTUATOR 2.1 Overview Figure 2 shows that the Valeo EGR actuator splits easily into two parts, the motor assembly, containing the motor, spring and position sensor, and the mechanical assembly containing the valve. 978-1-4244-7425-7/1/$26. 21 AACC 2242
Figure 4: Cam (Rot-Lin Transmission) Figure 2: Valeo EGR Actuator with Motor and Mechanical Assemblies being separated The shaft inside the cavity of the mechanical assembly is installed in a variable height groove, which is carved into the sides of the cavity, and thus moves up or down when rotated about the axis of the casing (figure. 3, 4). The shaft fitted with bearings at the ends, sits in the grooves. This assembly forms the cam. The cam is connected to the valve plate below: In order to model the cam to find a relation between the angle and the linear displacement, the valve position was carefully measured at different angles (using the experimental setup described in section 4.1). The curves shown in figure 5 show the relationships obtained between the angle, the sensor voltage and the cam position. Since the sensor voltage is the only quantity that can be measured directly, the mechanical assembly was modeled as the valve linear position, L with respect to the sensor voltage u. Using classical curve fitting this curve of the cam was found to correspond to the following function: Figure 3: Simplified Mechanical Diagram As the cam rotates, it pushes the valve plate down. The coupling between the cam and the motor holds the shaft between its prongs. (a) The deep grooves of the prongs allow for the vertical movement of the shaft. The actuator is spring-loaded, so that it remains shut when no power is applied to the input. The spring returns the cam to its highest point. 2.2 Mechanical Assembly Modeling The cam converts the angular rotation of the motor into linear displacement of the valve. It allows angular motion of about 62 and linear displacement of 6mm. The linear displacement is not proportional to the rotation. The nonlinear response is evident in the sketch in figure. 4. (b) Figure 5: (a) Angle vs. Position Sensor Voltage, (b) Angle vs. Valve Position 2243
2.3 Motor Assembly Modeling The motor used in this actuator is a torque motor that has a limited rotation of 8, further reduced to 6 due to the limitation of the cam. Since the motor angle has a linear relationship with the position sensor output up to 6, this system is modeled directly in terms of angular position. While the torque of a torque motor is a function of its angular position, the characteristic curve in figure 6 shows that the mechanical limits of the motor ensure its operation in the constant torque region. Hence it can be modeled in the same way as a DC motor. The motor s rotation is countered by a spring, housed inside the motor casing. This motorspring system allows the motor shaft to have the following dynamics [4, 9]: Motor Position (Deg ) EGR Valve Static Characteristics 7 6 5 4 3 2 1 5 1 1 Input PWM (%Duty Cycle) 5 Figure 6: EGR Actuator Characteristic Curve 2 Here, θ is the angular position of the motor; K a and E a are the motor constant and the back EMF respectively, while R a and L a are motor resistance and inductance. J tot represents the total moment of inertia of the system while ω is the angular velocity. The transitory current can be neglected since the mechanical time constant is always much greater than the electrical time constant [4, 6]. T f is the friction force, a dynamic identity in itself. T o is the spring precompression torque working against the motor before it starts to move. K spr is the spring constant. Putting all values in the dynamic model results in the following relationship: 3. FRICTION A characteristic feature of the actuator, prominent in figure 6 is the hysteresis between the opening and closing paths of the actuator. This hysteresis is due to friction [4, 8]. Friction can be divided into two components, the static part which is needs to be overcome to start the relative motion between two surfaces and dynamic part which is parallel to the surfaces and always opposite to the direction of motion [5, 8] Dynamic friction comprises of two parameters, dry friction, also called Coulomb Friction and viscous friction which comes through addition of lubricants [8]. When a body starts from zero velocity, i.e. breaks away from static friction, the transition between static and dynamic friction is called Stribeck effect [8, 9]. This effect can be understood in figure. 7; which shows two friction models, with and without Stribeck effect. The friction force, T f is modeled in the next section, while the pre-compression, T o is constant and must be overcome by the motor before the shaft starts to move. is defined as the voltage required to overcome T o and T f. The remaining would hence result in actuator motion. Therefore the motor and spring dynamics can be modeled completely as Considering initial conditions to be zero, the Laplace transform of the system comes out to be: Figure 7: (a) Static friction + Coulomb friction (b) Viscous Friction added (c) Stribeck Effect added The Dahl friction model considers friction to arise from the asperities or irregularities of surfaces in contact. It hence models the asperities as microscopic springs [8, 9], which hold the surfaces in place until their elastic limit is exceeded. Hence this model allows for coulomb and viscous friction modeling. This is effective for ball bearings since the value of static and coulomb friction are very near. This model has been used here to identify the dynamic friction working in the EGR valve. Dahl s model [8, 9] mimics the stress-strain curve in classic solid mechanics [9]. It is the simplest of all dynamic models, for example, LuGre etc. since it has the minimum parameters of all dynamic friction models. If x is the displacement, F is the friction force F ; the Dahl model has the form [9] 2244
Where, σ is the stiffness coefficient and α is a parameter defining the shape of the stress strain curve. A value higher than 1 results in sharper bends. actuator was tested at no load, it went from closed to full open position by varying the duty-cycle from % to 18%. The armature voltage, V a is the average on-time of the PWM pulse per second. 4.2 Motor-Spring Identification Figure 1 represents the complete block diagram of our model of the EGR motor. Figure 8: Characteristic curve of Dahl Model As seen in figure. 8, the Dahl model relates friction to position. If we consider the Dahl model with respect to time, the model becomes: Figure 1: Block Diagram of EGR Actuator Model The value of armature resistance R a can be measured experimentally at stationary positions through Ohm s Law i.e. by measuring current at different voltages where the rotor is either locked or at a stationary position. Voltage divided by current would give us the armature resistance. Where, v is the velocity. The parameters can be found easily once the curve is known. 4. EXPERIMENTS AND PARAMETER IDENTIFICATION Figure 11: Actuator Characteristic Curve (simplified) Figure 9: Experimental Setup The experiments were conducted using National Instruments CompactRIO system, as shown in figure 9. The actuator motor was powered through PWM. A square wave of 1 khz, with an amplitude of V s = 15V is given to the motor and the average power is varied by varying the duty-cycle. Since the With figure 11 as a reference, we define D PC as the dutycycle leading to countering the spring pre-compression, D s as the amount countering the static friction. The value of static friction and spring pre-compression torque can directly be calculated from the graph. The effective duty-cycle and armature voltage then become: 2245
for all positive values of D a and for the rest. V s is the maximum applied voltage. measured values, θ taken at the same armature voltages same as the estimation. The vector β estimate is then obtained by solving the following least squares problem through a nonlinear minimization algorithm The algorithm was implemented in Matlab and it provided the following results: R a = 3.75Ω K a = 19.6mN.m/A K spr =45.97 mn.m/rad J tot = 1.3e -7 Kg.m 2 Figure 12: EGR ActuatorStep Response The value of T o can be calculated from the characteristic curve graph, since we know that the motor torque T m equals T o at 5% PWM. Using the relationship motor torque relationship, Using the motor-spring dynamics from section 2.3 This transfer function can be compared to the general form of a second order system, 4.3 Dynamic Friction Identification The ease of using the Dahl model is that it considers static friction and coulomb friction to be equal. Hence only two parameters are to be identified, F c and σ. Now the Dahl model would be used to identify the parameters of the dynamic friction. Recalling from section 2.3: Our model parameters can be found out using the generic second order step response form. The experimental step response in figure 12 shows the system response to be overdamped. Hence the generic form would be: All other parameters except T f have been determined. In order to reach the characteristic curve of the Dahl Model, all other components except T f were subtracted. From here, the value of σ and F c was found to be: F c = 12.633mN.m σ =.5x1-3 The values of the unknown parameters (K a, K spr, J tot ) through the standard Least Squares procedure using any non linear minimization function. An estimation vector, β=[ K a, K spr, J tot ] is defined for the estimation algorithm, which evaluates the model on the vector : 5. MODEL VALIDATION While NI LabVIEW was used for experiments and data acquisition, the identification and modeling procedures were performed on Matlab. The model was simulated and the results were compared with data obtained from experiments. The correspondence between measured and calculated angles was considered for verification, since the actuator does not have any direct means for measuring the linear, cam guided movement of the valve plate. In figure 13, the graphs show the experimentally obtained curves with simulated ones. It can be seen that the results corroborate well with the experimental data. Where Va represents the armature voltage values on which the model is evaluated. This model is compared to a set of 2246
(a) (b) Figure 13: Experimental Values vs. Model Estimated Values (a) Static Characteristics (b) Dynamic Characteristics 6. CONCLUSION A commercial EGR actuator has been modeled and its electrical and mechanical parameters have been successfully identified. In addition, friction forces acting on the actuator have also been dynamically modeled. The results of validation have been successful. [3]. M. Zheng, G. T. Reader; J. G. Hawley, Diesel engine exhaust gas recirculation, a review on advanced and novel concepts Energy Conversion and Management 45 883-9 (24). [4]. R. Scattolini, C. Siviero, M. Mazzucco, S. Ricci, L. Poggio and C. Rossi, Modeling and Identification of an Electromechanical Internal Combustion Engine Throttle Body Control Eng. Practice Vol. 5. No.9. pp. 1253-1259 (1997). [5]. F. Contreras, I. P. Quiroz, C. C. dewit, Further Results on Modeling and Identification of an Electronic Throttle Body Proc. 1 th Mediterranean Conf. on Control and Automation-MED (July, 22). [6]. J. B. Song, K. S. Byun, Throttle Actuator Control System for Vehicle Traction Control Mechatronics 9 477-495 (1999). [7]. C. Rossi, A. Tilli, A. Tonielli Robust Control of a Throttle Body for Drive by Wire Operation of Automotive Engines, IEEE Trans. Control Systems Technology Vol. 8 (6 November 2). [8]. D. Pavkovic, J. Deur, M. Jansznn N. Peric, Adaptive Control of Automotive electronic Throttle Control Engineering Practice 14 121-136 (26). [9]. H. Olsson, K.J. Åström, C. Canudas de Wit., M. Gäfvert, P. Lischinsky, Friction Models and Friction Compensation European Journal of Control 4(3) (1998). [1]. T. Tjahjowidodo, F. Al-Bender, H. V. Brussel, Friction Identification and Compensation in a DC Motor IFAC (25). [11]. P. Myszkorowski, F. Altpeter, R. Longchamp, Position Control of Drives with Friction Proc. 38 th Conference on Decision and Control (December 1999). [12]. H. M. Kim, S. H. Park, S. I. Han, Precise friction control for the nonlinear friction system using the friction state observer and sliding mode control with recurrent fuzzy neural networks Mechatronics 19 85-815 (29). [13]. B. Borsotto, E. Godoy, D. Beauvois, E. Devaud, An Identification Method for Static and Coulomb Friction Coefficients Int. Jour.Contro, Automation and Systems 7(2) 35:31 (29). [14]. Melexis. MLX9316 Rotary Position Sensor IC Datasheet(27),http://www.melexis.com/Sensor_ICs_H all_effect/triaxis_hall_ics/mlx9316_566.aspx Future studies would be focused on further improvement in hysteresis and friction modeling. More comprehensive friction models are going to be used (eg. LuGre), to model Stribeck effect and static friction. Actuator tests under load are also in preparation along with tests to observe variations in actuator parameters with temperature. REFERENCES [1]. A. Maiboom, X. Tauzia, J. F. Hétet, Experimental study of various effects of Exhaust Gas Recirculation (EGR) on combustion and emissions of an automotive direct injection diesel engine Energy 33 22-24 (28). [2]. G. H. Abd-Alla, Using Exhaust Gas Recirculation in Internal Combustion Engines: A Review, Energy Conversion and Management 43, 127-142 (22). 2247