ACTIVE VIBRATION CONTROL FOR TORSIONAL OSCILLATIONS IN POWERTRAINS FOR FULLY ELECTRIC VEHICLES

Transcription

1 F24-Special Session Vehicle Dynamics Control for Fully Electric Vehicles Outcomes of the European Project E-VECTOORC ACTIVE VIBRATION CONTROL FOR TORSIONAL OSCILLATIONS IN POWERTRAINS FOR FULLY ELECTRIC VEHICLES Orus, Javier * ; Theunissen, Johan 2 ; Meneses, Ruben ; Rodriguez-Fortun, Jose-Manuel Aragon Institute of Technology (ITA), Zaragoza, Spain 2 Flanders Drive, Lommel, Belgium KEYWORDS: Active Vibration Control, Switch Reluctance Motor, Electric Powertrain, Torsional Oscillations ABSTRACT To fully exploit the potential range of opportunities for vehicle dynamic control in Electric Vehicles (EV), fast reacting powertrains are required. Although, on-board motor powertrain configurations are a more feasible option compared to in-wheel ones, their dynamic behaviour is affected by low natural frequency and low damping. In consequence, torsional oscillations are easily excited leading to driver discomfort and system instabilities during ABS and TC electric actuations. The present paper is aimed at the development of an active vibration control (AVC) for on-board transmission. Given the limitation of pure mechanical approaches for reducing the oscillation at the transmission, normally increasing weight and system cost, the authors propose an AVC implemented in the electric motor which modifies the system dynamics by a damping feedback law proportional to the difference between the wheel and the motor speed. This solution keeps the original vehicle hardware, using the sensors and actuators already available. The nonlinear nature of the problem is solved by the use of gain scheduling for the adaptation of the controller parameters to the different driving situations. Simulation models using IPG and SIMULINK are used for the adjustment and verification of the controllers under different test conditions assuring the system stability and performance. Finally, the controller is experimentally validated under different conditions using a high performance electric car prototype with independent wheel motors, fully sensorized and equipped with the hardware dspace. The results in the paper include the design methodology for assuring a speed independent performance at all driving conditions. This process is based on simulation results using step and sweep actuation signals modifying the driving conditions in terms of road characteristic and vehicle speed. These reference tests are afterwards repeated on a real vehicle for validating the overall performance. The resonance damping in flexible transmissions is not a novel technological problem and some papers for electrical vehicles have been published. Compared to those previous works, the present paper proposes a controller strategy and a design methodology for its implementation assuring velocity independent performance, and robustness in presence of real vehicle limitations, like low cost sensors, long sample times and signal delays. Apart from that, the present implementation succeeds in combined operation with ABS and TC electrical actuations assuring stability and performance. Both simulation and experimental results show that the proposed AVC algorithm damps the resonant response, keeping the system performance independent of the vehicle speed. The damped behaviour of the powertrain allows increasing the gains of the ABS/TC controller, improving the overall vehicle performance.

2 INTRODUCTION Full Electric Vehicles (FEV) with two, three or four motors configurations open a wide potential range of opportunities for the vehicle dynamic control (VDC), as direct yaw control (DYC) and torque modulation for traction control (TC) or antilock brake system (ABS) []. To fully exploit this potential, fast reacting electric powertrains are required. In-wheel motors seem the best option because of the direct action on the wheels, but their use is still limited by packaging issues and the large unsprung mass involved in their implementation. Then, in-board motors are a more feasible option, which require a gearbox and a halfshaft to transmit the power from the motor installed on the chassis to the wheel. However, the dynamic behaviour of this powertrain is normally characterized by a low natural frequency, because of the two relatively large rotary inertias (rotor and wheel) and a relatively low torsional stiffness. Besides, the system is weakly damped in the rotational degree of freedom [2][3]. Thereby, this configuration is prone to suffer from torsional oscillations that can be excited by different sources: - Fast response of the electric motor, can induce oscillations in a wide range of frequencies when fast demand changes are requested by the driver or the VDC [2]. - In the case of Switched Reluctance Motors (SRM) or Permanent Magnet Synchronous Motors (PMSM), as they are controlled using position feedback, the closed loop could encompass unmodeled torsional resonance modes [3]. - Perturbations coming from the road [2]. - Backlash and other nonlinear behaviour in the powertrain [2]. - Friction brake torque, as a variable load applied to the wheel inertia []. The existence of torsional oscillations in the drivetrain can lead to several problems in the vehicle from the point of view of comfort, durability and stability: - Driver comfort can be affected by the vibrations induced by the drivetrain oscillations [2]. - Oscillations in the torque can cause wheel blockage or slip [3]. - If the modulation of the torque in ABS and TC actuations is done by the electric motors, resonant responses in the frequency range close to the expected TC and ABS demands could lead to destabilization of the controllers. - Oscillations in the powertrain torque will result in accelerated fatigue of mechanical components [2][3]. Given its importance, different strategies have been adopted for the Active Vibration Control (AVC) of the electric powertrain of FEVs. In general, the problem can be mitigated by a correct mechanical design and in this connection, increasing the motor inertia or the powertrain stiffness is found to be an effective way to alleviate the resonance [5]. Nevertheless, the mechanical methods are normally accompanied by electronic controllers for improving the performance in a more efficient way using the sensors available in the vehicle. Active vibration control in low damped transmissions is a general technological problem which has been extensively analyzed in the industry, for example in milling machines and lathes. From these applications, many control strategies are defined: state feedback damping, speed feedback [3], speed control with a virtual damper based on the relative velocity feedback [4], acceleration feedback [7][], torsional torque feedback [4]. In some cases, it is necessary to include observers for estimating some variables, like in [5]. Apart from the previous cases, other approaches are model predictive control [2], sliding mode control [9], Hinf control [] or flatness based control (FBC) [6]. In [9], a model free approach based on Grey estimators is used. Before trying to apply the previous techniques to the AVC of a FEV compliant transmission, it is important to pinpoint the special features appearing in the case under analysis: first, the main objective of the vehicle transmission is assuring a traction force, not maintaining a definite wheel speed as it happens in typical tooling applications; second, the force transmission depends on the special characteristics of the contact between tire and ground, which is highly non linear. In consequence, most of the standard AVC techniques should be modified before being applied to FEV transmissions. In this connection, many works are focused on controlling the torque, like in [3] and [6], which defines a closed loop transmission torque control using a Kalman filter and measuring the speed at the electric motor and the wheel; or in [5], which uses the same sensors for estimating the real reaction of the tire and closing the loop applying state feedback for damping the transmission subsystem. A state feedback is also proposed in [4] for mitigating the oscillation and, in this case, an estimator is used for reducing the number of sensors to only one. In [7] the direct feedback of the relative speed between wheel and motor is outlined as part of a bigger braking system. The present paper

3 applies this technique and proposes a design methodology for assuring its performance at all vehicle speeds. The influence of the vehicle velocity appears due to the non linear nature of the problem. For affording it, a gain scheduling strategy based on this variable is proposed. Compared to other approaches, the selected one does not require the inclusion of an estimator, and it has a very low computational cost. Although being a classical approach, its performance and simplicity makes it a very interesting option. The method has been successfully implemented and applied to a real vehicle. SYSTEM DESCRIPTION A fully electric vehicle (FEV) with four independent on-board motors is considered, though results can be easily extended to FEVs with two motors either in front or in rear axle. Power is transmitted from each motor to the corresponding wheel by a gear box and a halfshaft, linked by CV joints. Figure shows a conceptual sketch for one corner. Wheel CV joints Gear box Electric motor Halfshaft Figure.-Powertrain of the on-board FEV. The vehicle control system outputs a torque demand (T dem ) to each motor defined by the driver demand and the Slip and Dynamic Yaw Controls. The torque generated at the motor (T EM ) can be modelled as a first order delay of the T dem : Torsional dynamics of the powertrain is defined by the torque balances in both the electric motor and the wheel: Where r t is the transmission ratio of the gear box, eq is the equivalent transmission efficiency, is the torque in the shaft, is the motor and transmission inertia (equivalent in the motor side), is the wheel inertia, T d is the traction torque that depends on the road friction and wheel slip, T roll is the rolling resistance torque and EM and w are the motor and wheel speeds. Both dynamics are linked by the shaft equation (4): Where k s and d s are the stiffness and the viscous friction of the shaft, respectively. Finally, longitudinal dynamics on a quarter car are considered here: () (2) (3) (4) Where M v is a quarter of the vehicle mass, R w is the wheel radius and T drag are velocity dependant forces on the car. T d refers to the delayed response of the tyre:

4 Where F N is the normal force on the wheel and is a function that can depend on several factors (road conditions, F N, among others). refers to the relaxation length. The main parameters for the model in the table are taken from the available data and specific identification tests (see TEST RESULTS section) for the 4WD prototype developed inside the EU funded project EVECTOORC. Parameter Value Units 2.2 ms r t. -- J eq.32 Kg m 2 k s 65 N m/rad d s.4 N m s/rad J w.9 Kg m 2 M car 25 Kg R w.3696 m Table.- Powertrain parameters ACTIVE VIBRATION CONTROLLER DESIGN The figure 2 shows the main structure of the controller. It uses a feedback law proportional to the difference between the measured speed at motor and wheel, taking into account the transmission effect. From a physical point of view, this solution is equivalent to installing a virtual damper between these two bodies. T dem LPF + - v car Σsystem w EM kd + - r t Figure 2.- Control basic architecture. Although simple, the previous implementation should take into account the nonlinear nature of the tire reaction. This effect is embodied in the term. In order to be able to use the system theory techniques for LTI systems, we will linearize the system by using a first order Taylor approach without considering the tyre torque delay and the motor response time. For clarity reasons, the rolling resistance and vehicle drag force are also neglected in this analysis. Under previous hypotheses, the resulting system is:

5 Where the new linearized variables represent the variation of their value with respect to a reference point. For the analysis, we will focus on the transfer function between and : Where, As observed in the expression above, the system can be understood as a second order behavior. The resonance frequency ( ) and the damping can be related with the parameters of the equation by: It is important to remark: - That the variations due the wheel contact are affected by a low pass filter defined by the tire stiffness, the road conditions and the mass of the car. - The parameters of the second order system are variable with, and. Given the range of variation of these parameters in normal conditions, the gain schedule is focused on. Future activities are intended to experimentally evaluating the sensitivity to the rest of the parameters. Once the behavior of the system is understood, the design procedure is applied for assuring the performance of the system. This last is defined as the combination of: - Response time: the system has to react at a high speed for allowing good performance of TC and ABS electric actuations and avoiding closed loop instability. As design criterion, a maximum variation of gain at resonance peak of 5% with regard to stationary response is allowed (see figure 4). - Damped behavior: oscillations in the torque have to be minimized for increasing the system endurance capability and avoiding annoying oscillations. Initially, a maximum overshoot of 5% is defined as reference for step inputs. The control law is defined as:

6 Phase (deg) Magnitude (db) Half shaft Torque (Nm) Where we have included a low pass filter for avoiding the sensor noise and reducing the frequency content in the electric motor. With this command, the figure 3 shows the root locus obtained in From: AVC To: Fcn K= K= K=2 K=3 K=4 K=5 K= when the controller is included: K= K= K=2 K=3 K=4 K= Real Axis Figure 3.- (left)root locus of the function ; (right) Halfshaft torque (T shaft) response to step input demand. As shown in the figure 3, which represents the zero-pole plot for the transfer function, the increase in the damping of the system, with the movement of two conjugated poles leftwards, is accompanied by the increase in the response time, observed as a third pole moving rightwards on the real axis. As a compromise between these two effects, gains in the range between K= and K=2 are selected, depending on the speed (the final gains appear in the figure 5). Overshoot below 5% and response amplitude approximately equal to the static one at the resonance frequency are obtained. The previous behaviour can also be observed in the Bode plot of T shaft/t dem in the figure 4. Resonance peak is eliminated, while dynamics for lower and higher frequencies can be kept similar From: AVC To: Left Front Half-shaft Torque K= K= K=2 K=3 K=4 K=5 K= Frequency (Hz) Figure 4.- Bode plot of T shaft/t dem with different control gains The previous results are obtained by linearizing the system at 25 m/s under a step signal of 5Nm at the motor. For obtaining the complete controller, the same process was repeated at different speeds.

7 Half shaft Torque (Nm) Half shaft Torque (Nm) Gain (-) Torque (Nm) SIMULATION AND EXPERIMENTAL RESULTS Dynamic performance of the designed AVC is analyzed by both simulation and experiments. The vehicle for the research is a Land Rover Evoque prototype with independent drivetrains in each front corner, powered by switched reluctance motors (SRM). The AVC is implemented in SIMULINK and it is part of the complete vehicle dynamics controller software. For studying the dynamic response of the controlled system, step and sweep sinus torque signals are entered to the SRMs under different conditions of braking/acceleration intensities and car velocities. I SIMULATION RESULTS For the simulation analysis a detailed model of the vehicle is considered, based on the commercial IPG/Carmaker model combined with specific descriptions of powertrain and electrohydraulic brakes (EHB). These models have been experimentally validated and integrated in SIMULINK. Detailed simulation in IPG is used for tuning the gain scheduling as a function of vehicle speed. Figure 5 shows both the gain function and the results in terms of halfshaft torque for an acceleration step of Nm (motor side) at three different speeds, either with constant or with scheduled gain. Gain scheduling generates a damped response almost independent of the vehicle speed..5 Halfshaft Torque Car Velocity (m/s) Figure 5- Gain scheduling function (a) and effect of gain scheduling on the damped response(b). In the implementation of the AVC, the sensor time response can highly affect its real performance. Therefore, before starting the tests on prototype, the effect of different delays and sample times is analyzed by simulation. The results can be seen in the figure 6 for a step of 5 Nm (motor side) at 8 m/s, which shows no stability issue even for relatively long delays and sample times. In those cases, the dampening of the oscillation is slightly reduced V=8 m/s without gain scheduling V=8 m/s with gain scheduling V=25 m/s without gain scheduling V=25 m/s with gain scheduling V=4 m/s without gain scheduling V=4 m/s with gain scheduling Without delay ms delay 2 ms delay ms sample time ms sample time 2 ms sample time Figure 6.- Effect of wheel speed signal delay (a) and sample time (b)on halfshaft torque.

8 Speed (km/h) Slip (-) As previously described, the oscillation of the drivetrain can highly reduce the performance of the vehicle controllers. An example of this effect can be seen in the figure 7, which compares the simulation results for ABS control with or without AVC (step of Nm for the 4 motors, at a speed of 33 m/s). As observed, the AVC improves the tracking of the target slip, avoiding large amplitude oscillations. 2 Only ABS ABS & AVC. Slip reference Without AVC With AVC II TEST RESULTS Figure 7.- Effect of AVC on ABS slip control. Vehicle speed (a) and longitudinal slip (b). Figure 8 shows the architecture of the electric powertrain. It consists of four individual switched reluctance motor units, each attached to a two-stage reduction box. The 6V battery pack with 9 kwh energy capacity provides the power to the motors via the 3-phase inverter unit. The most important sensors are the original (ABS) wheel speed sensors, the motor resolvers (angular position sensors), the throttle pedal sensor, the brake pedal travel sensors, steering wheel sensor and the 6-degrees-of-freedom sensor, including the three-axial accelerations and three modal speeds. The Motor-Generator Unit (MGU), which is basically the chassis controller, incorporates control functions of basic drivability, energy and system management, dynamic yaw control, wheel slip control, control allocation and a brake blending strategy. The battery pack contains as well some safety circuitry and high-voltage connectors, including pre-charge solution and a battery charger connected to the grid. Finally, a DC/DC converter unit provides the charge of the 2 VDC battery. Tw 23V AC ~ Drive shaft (x4) System boundary 6VDC battery pack Battery charger Acc. pedal Reduction Tm box (x4) BMS slaves APPS SC IMD BMS αth INV SR-M (x4) MGU AS FlexRay θ m TCU (x4) (x4) MMI Coolant pump Front radiator Coolant reserv. 6VDC Priv CAN HS-CAN Fan 6DOF Twb Brake calliper (x4) pb SCB SCBU SAS Steering wheel αbr DC/DC conv. 2VDC battery Figure 8.- System architecture of the electric powertrain consisting of four individual switched reluctance motor unit. All software in MG has been implemented by means of Matlab-Simulink into the rapid prototyping platform dspace Autobox. First tests without AVC are performed to validate the simulation model. Results in terms of longitudinal acceleration both for sweep and step tests are included in figure 9. A good agreement is found in terms of response time, overshoot, amplification and natural frequency. WS WS WS WS PTS EPS AUX Wheel speed sensors Brake pedal

9 Motor speed[rpm](signal 32) Ax[m/s2](signal 96) Ax[m/s2](signal 96) Motor speed[rpm](signal 32) Ax[m/s2] Ax[m/s2] test model.5 test model Figure 9.- Validation of system model by comparison to experimental results. Acceleration plots for sweep and step tests(step of 5Nm at 4 m/s; sweep between Hz and 3 Hz at 4 m/s) Step and sweep sinus tests for AVC analysis are performed at different torque levels and different AVC gains (% is the gain adjusted by simulation (see figure 5), both in braking and acceleration. Plots in figure show the system response in terms of longitudinal acceleration and motor speed for step test of 5 Nm (motor side) at 4 m/s, whist figure shows the same variables for sweep tests between and 3 Hz at a speed of 4 m/s Effect of AVC gain (5kph,5Nm) % 5% % 2% Effect of AVC gain (5kph,5Nm) % 5% % 2% Figure.- Experimental results for step test. Motor speed and longitudinal acceleration Effect of AVC gain (5kph,S).5 Effect of AVC gain (5kph,S) % 5% % 2% % 5% % 2% Figure.- Experimental results for sweep sinus test. Motor speed and longitudinal acceleration. In the real car, the system response is effectively damped by using AVC with regard to the original situation. In step tests, acceleration overshoot can be reduced to values around % if the highest gain is selected, without affecting the effective motor acceleration. With the same highest gain in the sweep sinus, the

10 resonance peak is eliminated. However, as previously observed in simulation, too high gains would result in reduction of the system response with regard to static gain at frequencies close to the natural one (7% reduction at natural frequency for 2% gain). Further adjustment of the gain between % and 2% will be done in future research together with ABS/TC tuning, to find the best compromise between overshoot reduction and maximum bandwidth. CONCLUSIONS This paper describes a method for designing an AVC for a compliant powertrain based on a linear relative speed feedback controller. This controller is improved with a gain scheduling to take into account non-linear tyre behaviour as a function of speed. The resulting control effectively dampens the powertrain oscillations, avoiding comfort problems and improving the durability of the powertrain and stability in the torque modulation. The performance of the controller is characterized by: - The application of gain scheduling results in a damped behaviour independent of the vehicle speed, compensating the natural lower damping of the system at low speeds. - The control algorithm is robust to relatively long both sensor delays and sample times in the wheel sensors with a minimum reduction of dampening performance. - AVC improves the performance of other vehicle controllers, like ABS. The AVC has been both virtually and experimentally evaluated. In the first case, a fully vehicle model had been previously validated for matching the real behaviour. The test results in the vehicle prototype show effective and stable damping with the AVC enabled for different gain values. Further activities contemplate the adjustment of the gain in combination with the ABS/TC tuning to find the best compromise between maximum bandwidth and torque oscillation reduction. Apart from that, updated control strategies, like the one proposed by the authors in [5] are planned to be evaluated in the future for improving the performance of the current approach. ACKNOWLEDGEMENT The results described in the present paper are part of the activities developed in the EVECTOORC project, which has received funding from the European Union Seventh Framework Programme FP7/27-23 under grant agreement no REFERENCES [] Hiroo Kanamori. Shaking without Quaking [J]. Science, 988, 279(5359): [2] Peyton Z. Peebles. Probability, Random Variable, and Random Signal Principles [M]. New York: McGrawHill, 2. [3] J.Böcker, N.Amann, B.Schulz, Active Suppression of Torsional Oscillations 3rd IFAC Symposium on Mechatronic Systems, Sydney, Sept.24. [4] G.Götting, R.W.De Doncker, Active Drive Control of Electric Vehicles Using a Modal State Observer, 35th Annual IEEE Power Electronics Specialists Conference (24). [5] J.M.Rodriguez-Fortun, R.Meneses, J.Orus, Active Vibration Control for Electric Vehicle Compliant Drivetrains, 39th Annual Conference of the IEEE Industrial Electronics Society, IECON 23. [6] M.Rosenberger, M.Kirschneck, T.Koch, M.Lienkamp, Hybrid-ABS : Integration der elektrischen Antriebsmotoren in die ABS-Regelung, 2. Automobiltechnisches Kolloquium München, (2). [7] M.Rosenberger, R.A.Uhling, T.Koch, M.Lienkamp, Combining regenerative braking and anti-lock braking for enhanced braking performance and efficiency, SAE International 22.