DESIGN AND EXPERIMENTAL VALIDATION OF A VIRTUAL VEHICLE CONTROL CONCEPT FOR TESTING HYBRID VEHICLES USING A HYDROSTATIC DYNAMOMETER

Transcription

1 Proceedings of 2014 ASME Dynamic Systems and Control Conference ASME DSCC 2014 October 22-October 24, 2014, San Antonio, USA DSCC DESIGN AND EXPERIMENTAL VALIDATION OF A VIRTUAL VEHICLE CONTROL CONCEPT FOR TESTING HYBRID VEHICLES USING A HYDROSTATIC DYNAMOMETER Zhekang Du, Perry Y. Li, Kai Loon Cheong and Thomas R. Chase Center of Compact and Efficient Fluid Power Department of Mechanical Engineering University of Minnesota, Minneapolis, MN duxxx139@umn.edu, lixxx099@umn.edu*, cheo0013@umn.edu, trchase@umn.edu ABSTRACT An approach to control a hydrostatic dynamometer for the Hardware-In-the-Loop (HIL) testing of hybrid vehicles has been developed and experimentally tested. The hydrostatic dynamometer used, which is capable of regeneration, was specifically designed and built in-house to evaluate the fuel economy and control strategy of a hydraulic hybrid vehicle. The control challenge comes from the inertia of the dynamometer being only 3% of that of the actual vehicle so that the dynamometer must apply, in addition to any drag torques, acceleration/deceleration torques related to the difference in inertias. To avoid estimating the acceleration which would be a non-causal operation, a virtual vehicle concept is introduced. The virtual vehicle model generates a reference speed profile which represents the behavior of the actual vehicle if driven on the road. The dynamometer control problem becomes one of enabling the actual vehicle-dyno shaft to track the speed of the virtual vehicle, instead of directly applying a desired torque. A feedback/feedforward controller was designed based upon an experimentally validated dynamic model of the dynamometer. The approach was successfully tested on a power-split hydraulic hybrid vehicle with acceptable speed and torque tracking performance. 1 Introduction Hardware-In-the-Loop (HIL) simulation is an effective technique to develop and test complex real-time embedded systems. A HIL system reduces testing complexity by using only part of the hardware which needs to be tested, while interacting with the computer simulation of the remaining hardware. HIL is widely used in the automotive industry to verify performance of production powertrain controller modules (PCM) [1]. A prototype hydraulic hybrid passenger vehicle testbed is being developed within the Center for Compact and Efficient Fluid Power (CCEFP) to advance hydraulic hybrid technologies. While simulations can predict fuel economy and performance of the vehicle, experimental validation is still necessary. Outdoor road testing requires a test track and results are not very repeatable due to environmental conditions. A reliable HIL system, such as a dynamometer (or dyno in short), can enable reliable and consistent measurements without the environmental influence such as wind, weather, tire pressure, and traffic. Furthermore, a dynamometer allows the comparison, development, and tuning of various control strategies for different vehicle and driving conditions. To this end, a hydrostatic dynamometer with motoring capability, necessary for hybrid vehicles, has been developed in our group recently [2]. Commercial chassis dynamometers usually have heavy roller drums to simulate the vehicle inertia. The rolling mass is designed to be close to the vehicle inertia so that when the vehicle is accelerating/decelerating, most of the inertia effect is automatically taken care of by the rolling mass. The dynamometer needs only compensate for the road/aerodynamic drag which can be calculated directly from the wheel speed. On the other hand,

2 hydrostatic dynamometers which use hydraulic pump/motors to provide the braking or regeneration torque on the vehicle, have superior power-to-weight ratio, small inertias for flexibility, are therefore more compact and low cost. For example, the inertia of the dynamometer in [2] is around 3% of the intended vehicle inertia even with the addition of a small flywheel. A unique challenge for dynomometer control is the requirement to emulate the acceleration/deceleration loads related to the large difference in inertia. One approach is to apply the torque according to the acceleration estimate from a Kalman filter [3]. However, this is an inherently non-causal process since acceleration is dependent on the torque applied by the powertrain and the dynamometer. Since the applied dyno torque should be a function of the acceleration, any delay in estimation inevitably leads to inaccurate emulation when acceleration/deceleration is high. To accurately control a low inertia dynamometer to emulate the dynamic load on a vehicle, a virtual vehicle control concept is proposed here. The main idea is to introduce a virtual vehicle dynamic model with information on the intended vehicle inertia and road and aerodynamic drag characteristics. For a given applied vehicle torque, this model generates, in real time, a reference vehicle speed which represents the behavior of the vehicle with the intended vehicle inertia and environmental drag conditions. The control objective for the dynamometer becomes one of exerting the correct torque so that the actual speed of the common vehicledyno shaft follows that of the reference generated by the virtual vehicle model. The need for the non-causal acceleration estimation can thus be avoided. When the actual speed tracks the virtual reference speed, the hypothesis is that the torque applied by the dyno on the vehicle will be exactly the same load as if the vehicle is driving on the ground with full effect of the intended vehicle inertia and road resistance. A variety of control algorithms can be designed to ensure that the vehicle-dyno shaft speed tracks the virtual vehicle speed. In this paper, we use a combination of feedforward control of the required dyno torque for tracking the virtual vehicle reference model, and a feedback stabilization designed based upon affine parameterization and sensitivity shaping. The controller has been implemented on the dynamometer and the virtual vehicle control concept has been experimentally validated. In the literature, development and use of hydraulic dynamometers have focused on testing engine performances [4 9]. One of the earliest report of dynamometer for testing a complete power-train, with simulated load and engine, is found in [10]. Control studies of hydraulic dynamometer in the literature are few. In [11], a generalized framework to analyze and design controllers for a class of dynamic emulation systems using an indirect control input is presented. A feedforward control is used to avoid limitations imposed by stability considerations in feedback designs to improve performance. The controller in [9] is designed based on direct estimation of engine speed and acceleration. FIGURE 1. Schematic of Hydrostatic Dynamometer The rest of the paper is organized as follows: Section 2 illustrates the configuration of the hydrostatic dynamometer. Section 3 explains the virtual vehicle control concept. Section 4 describes the modeling and system identification of the dyno system. Section 5 discusses the controller design. Section 6 presents the experimental results. Section 7 contains concluding remarks of this study with future work. 2 System Description The hydrostatic dynamometer system consists of a hydraulic power supply unit, an accumulator, a proportional directional valve and two tandem swash plate pump/motors (Fig. 1). The displacements of the pump/motor are used as the primary control input to control the load on the vehicle. By operating them in pumping or motoring modes, both load absorbing and regenerating events can be emulated. The proportional valve is normally fully opened to allow unobstructed fluid flow, but it can also be used as the secondary high bandwidth control in case the pump/motor displacement actuation is deemed too slow. They are not used this way in the current study. During load absorbing events, energy from the vehicle is used to charge the hydraulic accumulator. During regenerating events, energy in the hydraulic accumulator is discharged and returned to the vehicle. The hydraulic power unit is used to ensure that the accumulator maintains a sufficiently high pressure in all events. The shaft of the dyno pump/motors is mechanically connected to the output shaft of the vehicle transmission through a torque cell which provides speed and torque measurements (Fig 2). The dynamics of the common vehicle - dyno shaft are: J Sha ft ω = T veh + T Dyno (1) where J Sha ft = J Trans + J Dyno is the combined inertias of the vehicle transmission (also referred to as the vehicle output shaft),

3 J Trans, and of the dyno, J Dyno. T veh is the applied vehicle torque on the transmission output shaft, T Dyno is the applied dyno torque and T meas is the torque cell measurement. Because the vehicle is stationary in dynomometer testing, J Trans is only a small fraction of the equilvalent intended vehicle inertia. In our system, which incorporates a small flywheel, J Sha ft represents 3% of the intended vehicle inertia. By considering the individual dynamics of the dyno inertia and the vehicle output shaft inertia (e.g. via the two free bodies obtained by cutting the transmission output shaft at the torque cell in Fig. 2), the torque cell measurement can be shown to be a combination of the vehicle applied torque and dyno applied torque: T meas = J Dyno J Sha ft T veh + J Trans J Sha ft T Dyno (2) Only when J Dyno J Trans can one assume that the measured torque is the vehicle applied torque T veh. This is true in our case, since the dynamometer has been augmented with a small flywheel so that J Dyno = Kgm 2 and J Trans = Kgm 2. 3 Virtual Vehicle dynamometer control concept 3.1 Virtual Vehicle dynamics The virtual vehicle dynamics mimic the behavior of the intended vehicle to be tested given the applied vehicle torque. This includes the inertial dynamics as well as any aerodynamics and road drag. In terms of longitudinal vehicle speed v, they are: M veh v = F veh F drag (v) (3) where M veh is the vehicle inertia and F drag (v) is the road and wind drag, F veh is the applied traction force. Eq.(3) is converted to the rotational domain in terms of the rotation speed of the transmission output shaft ω veh = R di f f /R w v (where R di f f and R w are the ratio of the output differential gear and the wheel radius): where J veh = M veh J veh ω veh = R 2 w R 2 di f f T }{{} veh T drag (ω veh ) }{{} Rw R F veh di f f Rw R F drag (v) di f f (4) is the equivalent vehicle inertia with respect to the transmission output port. In order for the dynamometer to emulate on-the-road driving, from Eqs.(4) and (1), the dynamometer shoud apply on the vehicle output shaft the load of: T Dyno = (J veh J Sha ft ) ω veh T drag (ω veh ) (5) where the first term corresponds to the difference in inertia, and the second term corresponds to aerodynamic and road drag. Note that direct implementation of (5) is not strictly possible since the measurement or estimation of the acceleration ω veh is noncausal. Specifically, the acceleration is dependent on the control T Dyno applied to it in (1). However, given a measurement or estimate of the applied vehicle torque ˆT veh, the expected transmission output shaft speed profile ω veh (t) can be computed in real time: J veh ω veh = ˆT veh T drag (ω veh ) (6) Eq.(6) is referred to as the virtual vehicle model, and ω veh as the virtual vehicle (shaft) speed. 3.2 Control Concept To avoid the non-causal estimation of acceleration as in [3], instead of implementing Eq.(5) directly, the dynamometer will control the actual combined dyno-vehicle shaft dynamics (ω in Eq.(1)) to rotate according to the virtual vehicle speed (ω veh ) (computed in real time based on the measurement or an estimate of the applied vehicle torque T veh and the virtual vehicle dynamics in Eq.(6)). Suppose that the estimate of the vehicle torque ˆT veh is accurate, and indeed we are successul in making ω(t) ω veh (t), then comparing Eqs.(1) and (4), the dynamometer torque would be: T Dyno = J sha ft J veh T drag (ω) J veh J Sha ft J veh T veh (7) With substitution of T veh using Eq.(1) gives: FIGURE 2. Free body diagram of vehicle - dyno shaft T Dyno = (J veh J Sha ft ) ω T drag (ω) (8)

4 which is exactly the desired dynamometer torque in Eq.(5) that could not be implemented directly. The advantage of this approach is that the original task of a torque control problem becomes a speed control problem. which respects system causality. Moreover, it allows one to test different vehicles under different road conditions by simply tuning the parameters for the virtual vehicle dynamics (6). 4 Modeling and Identification of the Dynamometer Dynamics The hydrostatic dyno torque is modeled as a first order system: FIGURE 4. Frequency response of the closed loop transfer function G p (s) using a proportional control gain of K p = 0.001: a) from physical parameter based open loop model (green: white-box model), b) model from system identification (red: black box model), c) experiments. closed loop transfer function was identified to be: T Dyno = bω + η P 2π D(t) D(s) = ad max s + a U(s) (9) G p (s) = K pg OL (s) 1 + K p G OL (s) = s s = (s + 0.9)(s + 5) (11) where P = P H P L is the difference in pressures in the high and low pressure accumulators, D(t) is the actual displacement of the pump/motor, D max is the maximum displacement of the pump/motor, a is the bandwidth of the swashplate dynamics, b is the damping coefficient in the dyno and U [0,1] is the normalized displacement command input, and η( P, D) is the pump/motor s mechanical efficiency map. P = 2100psi is designed to be constant in this system. The parameters in (9) have been estimated. Damping coefficient b is obtained from experimental testing and from the manufacturers data sheets, it is estimated that the efficiency η 0.8 during operation, and the displacement actuation time constant 1/a 0.18sec. In addition, the combined inertia of the dyno/transmission shaft was estimated to be J sha ft = 0.25kgm 2. From these physical parameters, combining Eq.(1) and (9), the open loop transfer function from pump/motor command U(s) to the shaft speed ω(s) (see Fig.3) is predicted to be: G phy ω(s) OL (s) = U(s) = a K (s + a)(js + b) 2595 = (s )(s ). (10) where K = η PD max /(2π). System identification experiments have also been performed in closed loop where a proportional feedback gain of K p = and a series of sinusoidal reference speeds were applied. The The unwraped open loop system from G p (s) is: G id OL (s) = 2835 (s )(s ) (12) The predicted transfer function Eq.(10) and the experimentally identified model Eq.(12) are quite close. Fig. 4 shows that the closed loop frequency responses from both these two open loop models compare well with the experimentally obtained frequency responses. 5 Hydrostatic Dynamometer Reference speed tracking control In this section, we design a controller that enables the combined dyno/transmission shaft ω in (1) to track the virtual vehicle speed ω veh as given in (6). The control scheme (Fig. 3) consists of a feedforward and a feedback component. The majority of the control effort is provided by the feedforward controller to provide drag torques and to compensate for effects due to difference in inertia between the intended vehicle and the dyno/transmission. The feedback controller is designed to account for model uncertainty and disturbances. 5.1 Estimation of vehicle torque T veh (t) The estimate of the vehicle applied torque ˆT veh (t) is used to drive the virtual vehicle dynamics in Eq. (6) and in the design of the feedforward control term. It is obtained as follows. Consider

5 FIGURE 3. Controller scheme of the hydrostatic dynamometer the torque measurement equation Eq. (2) and the transmission shaft dynamics: J trans ω = T veh T meas (13) and assume that T veh is slowly time varying. Then, T veh is estimated from a Luenberger observer: ( ) d JTrans ˆω = dt ˆT veh ( )( 0 1 ˆω 0 0 ˆT veh ) ( L1 L 2 ( ) 1 T 0 meas ) (ω ˆω) (14) where T meas is the torque cell measurement. L 1 and L 2 are the observer gains chosen so that the poles for the observer are set to be 500rad/sec. Thus, modestly fast variation in T veh (t) can be estimated. 5.3 Feedback control The feedback controller is designed directly around the identified closed loop system with the proportional gain G p (s) in Eq.(11) (see Fig. 3). The design approach taken is based upon the affine parameterization of all stabilizing control in order to shape the complementary sensitity function [13]. Since G p (s) is stable, the set of all controllers C(s) that stabilizes G p (s) is given by: C(s) = Q(s) 1 Q(s)G p (s) (17) where Q(s) is any stable transfer function to be designed. The complementary sensitivity function is given by: T o (s) = Q(s)G p (s) (18) 5.2 Feedforward Control The feedforward controller is designed based on Eq (7) to provide the desired feedforward torque: T f f = J Sha ft J veh T drag (ω veh ) J veh J Sha ft J veh ˆT veh (15) where ˆT veh is the estimated vehicle applied torque in Eq.(14). The feedforward displacement control input U f f (s) in Fig. 3 is then generated by a causal approximate inversion of the open loop dyno plan model: U f f (s) = λ s + a a K s + λ where λ is large compared to the desired bandwidth. (16) Thus, Q(s) can be chosen to shape T 0 (s). By choosing T o (s) to be (Fig. 5), To 100 = s s the controller C(s) is designed to be: C(s) = Q(s) 1 Q(s)G p (s) = s s2 s(s + 20) (19) which can be thought of as a generalized form of PID control where the D term is implemented with a differentiation and a low pass filter.

6 FIGURE 7. Dynamometer testing of hydraulic hybrid vehicle involves three independent controllers: dynamometer controller, hydraulic hybrid powertrain controller and virtual driver controller FIGURE 5. To Nominal closed loop complementary sensitivity function FIGURE 8. drive cycle FIGURE 6. in CCEFP 6 Hydrostatic dyanmometer and hybrid vehicle developed Experimental Results Experimental demonstration of the dynamometer control is performed using the hydraulic hybrid passenger vehicle in Fig. 6) developed in our lab. The vehicle has a diesel engine and hydraulic input-coupled power-split or hydromechanical tranmission, hybridized by a pair of hydraulic accumulators for energy storage. The hydraulic hybrid vehicle is controlled by a 3-level control scheme described in [14, 15] that aims to achieve the driver demanded vehicle torque in a most energy efficient manner. In order to have repeatable testing results, the driver is simulated by a proportional-integral speed controller virtual driver controller. The virtual driver controller, the hydrid powertrain controller, and the dynamometer controller do not com- Experimental speed tracking results using modified urban municate except through the physical variables shown in Fig. 7. A drive-cycle modified from the Environmental Protection Agency s (EPA) Urban Dynamometer Driving Schedule (UDDS) 1 is used as the reference speed profile to test the fuel economy of the vehicle. Figure 8 shows the actual vehicle - dyno shaft speed ω and the virtual vehicle speed ωveh. Note that ω tracks ωveh demonstrating the effectiveness of the dyno-speed controller design in section 5. In order to verify that the dynamometer is applying the correct load, the actual dyno torque and the desired dyno torque needs to be compared. The actual dyno torque is estimated based on the torque measurement on the vehicle - dyno shaft from the observer in Eq. (14). The desired dyno torque is post-calculated based on Eq. (5). The speed profile ωveh is the measured speed of the vehicle - dyno shaft (ω). And the acceleration profile ω veh is calculated by differentiating ω since the entire speed profile is known. As shown in Fig. 9, the calculated desired torque stays within the noise bounds of actual dyno torque. The noise bounds is induced by the resolution on the torque measurement unit. Difference between the experimental torque and the calculated desired torque and between the actual vehicle - dyno shaft speed and the desired UDDS are plotted in Fig. 10. Note that the speed error reflects the performance of the virtual driver con- 1 The speed has been slightly scaled down and the minimum speed capped at positive value due to some limitations of the current hydraulic circuit setups.

7 FIGURE 9. Experimental torque vs. simulated torque results using modified urban drive cycle FIGURE 11. Feedforward vs feedback control effort and variation of dynamometer system pressure 7 Conclusion This paper presents a novel dynamometer control concept together with the modeling and controller design of a hydrostatic dynamometer. The virtual vehicle concept eliminates the noncausal estimation of the acceleration and also enables testing vehicles with different parameters and road conditions. The dynamometer setup also serves as rapid control testing device for the hydraulic hybrid passenger vehicle test-bed. The control parameters in the dynamometer control in section 5 have not been tuned. In particular, the poles of the current inner control (G p (s)) which are cancelled in the design of the affine parameterization control are quite slow. A better tuning of the inner loop control can be performed before designing the affine parametermization controller. Furthermore, incorporating the proportional directional valve in the control will further increase the control bandwidth of the dyno system. FIGURE 10. Experimental speed and torque tracking error using modified urban drive cycle troller rather than the dynamometer controller. The speed error standard deviation is 17RPM. And the torque error standard deviation is 2Nm. Figure 11 shows the feedforward and feedback control efforts in terms of pump/motor displacements. The feedback control effort is small compared to the feedforward control effort. As intended from the controller design, and feedback is only used to recover the tracking error due to uncertainty in models and measurement noise. The dynamometer system pressure P also remains relatively constant between 2000psi and 2200psi, which validates the assumption in previous sections. Acknowledgments This material is based upon work performed within the Center for Compact and Efficient Fluid Power (CCEFP) which is supported by the National Science Foundation under grant number EEC REFERENCES [1] S. Raman, N. Sivashankar, W. Milam, W. Stuart, and S. Nabi, Design and Implementation of HIL Simulators for Powertrain Control System Software Development, Proceedings of the American Control Conference, San Diego, CA, 1999 [2] H. J. Kohring, Design and Construction of a Hydrostatic Dynamometer for Testing a Hydraulic Hybrid Vehicle,

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