Advanced Stability Control for Electric Vehicles via a novel Hybrid Actuator System

7th IFAC Symposium on Advances in Automotive Control The International Federation of Automatic Control September 4-7, 2013. Tokyo, Japan

Advanced Stability Control for Electric Vehicles via a novel Hybrid Actuator System Martin Ringdorfer ∗ Martin Horn ∗∗ Magna Powertrain AG & Co KG, Industriestrasse 35, A-8502 Lannach (e-mail: [email protected]). ∗∗ Alpen-Adria Universtit¨ at Klagenfurt, Universit¨ atsstrasse 65-67, A-9020 Klagenfurt am W¨ orthersee (e-mail: [email protected]). ∗

Abstract: The paper introduces a novel vehicle dynamics control concept based on a hybrid actuator system consisting of friction brake and traction machine. This configuration offers new degrees of freedom in the control of electric vehicles. The proposed approach is based on a cascaded control structure with an inner yaw rate loop and an outer sideslip angle feedback loop. The use of sliding mode algorithms accounts for plant uncertainties and reduces the effort for controller tuning to a minimum without neglecting the aspect of energy efficiency. With the help of selected driving maneuvers it is shown that the performance of a car equipped with the advanced stability control system is superior to a car with conventional electronic stability algorithms. Keywords: Sliding-mode control, vehicle dynamics, hybrid electric vehicles. 2. VEHICLE TOPOLOGY AND HYBRID ACTUATOR SYSTEM

1. INTRODUCTION Future trends and environmental requirements necessitate the introduction of clean and energy saving means of transportation. Driven by customer demands and governmental regulations for electric vehicles (EV) develop car manufacturers new drivetrain topologies. Beside this challenge, car manufacturers also aim to improve the vehicle/passenger safety steadily. Especially electric vehicles bear the potential to use built-in actuator systems for safety functions. From conventional vehicles a deep knowledge on electronic stability control algorithms (ESC) evolved in the last decades, as shown in Jurgen (1999). These algorithms are based on classical friction braking systems, where short brake interventions on single wheels are used to suppress unintended vehicle yaw motion. State-of-the-art EVs apply propulsion torques according to the energy managements demands. In case of unstable driving behavior, the stability program forces the energy management to reduce recuperation due to safety reasons, i.e. the aspect of driving efficiency is of lower priority for a short period of time. This paper describes a new approach, where a hybrid actuator system, consisting of single wheel traction drives and conventional friction brakes, is used for vehicle motion control without neglecting the aspect of energy efficiency. The paper is structured as follows: In section 2 the vehicle topology and the actuator system are described. Section 3 focuses on the design of a cascaded sliding mode feedback structure. The achievable performance of the proposed control system is demonstrated for a number of standardized test maneuvers in section 4. Section 5 concludes the paper and outlines future research activities. 978-3-902823-48-9/2013 © IFAC

536

The vehicle propulsion system as shown in Fig. 1 consists of a conventional friction braking system (on front and rear axle) and of two single wheel traction drives (EM) on the rear axle. The two actuators, i.e. the friction brake and the traction machine, are labeled as “hybrid actuator system”. All the actuators are controlled using one electronic control unit (ECU), which also hosts the energy management algorithms. As exemplarily shown in Fig. 1 and with reference to the abbreviations listed in Table 1, the application of a friction brake torque TBrk and/or electric recuperation torque TEM causes tire forces, denoted by Fx . According to Fig. 2 both torques result from the energy management reference torques TB and TE . If the vehicle is operated on different road surfaces, the tire force potential may vary. In case of too high reference torques, the wheel slip λ will exceed a threshold λref . This causes a loss of traction force and potentially results in an unstable driving situation. Therefore a further increase of λ has to be avoided Tanelli et al. (2006). The promising results published in Ringdorfer and Horn (2011) motivate the employment of electric traction drives to keep λ within reasonable bounds. This can be achieved by using a control structure as shown in Fig. 2. The wheel slip controller calculates every 2ms a torque Tλ , which counteracts the reference torques delivered by the energy manager. The controllers for the two actuators are tuned such that the friction brake covers the “slow” wheel dynamics whereas the electric machine is dedicated to the “fast” components of the wheel dynamics. Though different traction forces 10.3182/20130904-4-JP-2042.00014

IFAC AAC 2013 September 4-7, 2013. Tokyo, Japan

Fx,RL

δ

Fx,F L

lF EM

ECU COG

β

lR

v

v

ψ˙ Fx,RR

Fx,F R

Fig. 3. Single track model

Fig. 1. Vehicle topology

Table 2. Vehicle parameters

Table 1. Abbreviations Identifier

Description

Vehicle parameter

Value

Fx Jz TB TBrk TBrk,λ TE TEM Tλ Tz ay β βlim βmax β˙

longitudinal tire force vehicle moment of inertia reference brake torque (energy management) brake torque Tλ related brake torque reference traction machine torque (energy mgmt) traction machine torque wheel slip controller torque yaw torque lateral acceleration vehicle sideslip angle maximum vehicle sideslip angle maximum expected vehicle sideslip angle sideslip angle velocity lateral tire stiffness (front/rear) steering angle yaw rate error distance between COG and front/rear axle wheel slip/reference wheel slip vehicle mass surface friction coefficient yaw rate/reference yaw rate reference yaw rate (sideslip angle controller) reference yaw rate (vehicle model) yaw acceleration vehicle velocity

cF , cR lF , lR Jz m

70000N/rad 1.23m,1.25m 1236kgm2 1135kg

cF /cR δ e lF /lR λ/λref m µ ˙ ψ˙ ref ψ/ ψ˙ C ψ˙ O ψ¨ v

wheel corner controller

λref

TB

wheel slip controller

brake actuator/ controller

Tλ

single track model (see Fig. 3) is used, where front and rear wheels are lumped into one wheel each on the center line of the vehicle. Such an approach is explained e.g. in Milliken and Milliken (1995); Gillespie (1992). The application of the principles of angular and linear momentum results in (1). The state variables of this second order system are the yaw rate ψ˙ and the sideslip angle β, the inputs are the steering angle δ and the torque Tz . The required vehicle parameters are summarized in Table 2. It is assumed, that the hybrid actuator system generates a yaw torque Tz for compensation or enforcement of the road-induced yaw torques. 2 cR l R + cF lF2 ˙ cR lR − cF lF cF l F 1 ψ¨ = − ψ+ β+ δ + Tz Jz v Jz Jz Jz

 cF cF + cR cR l R − cF l F − 1 ψ˙ − β+ δ (1) 2 mv mv mv The reference signal ψ˙ ref for the vehicles yaw rate, i.e. the driver-intended yaw motion is calculated via the vehicle model (1). Therefore the method explained in Khalil (1996) was used. β˙ =

TE traction drive/ controller

TEM

TBrk,λ

wheel corner

λ



3.2 Yaw rate control

TBrk

Fig. 2. Hybrid actuator system control loop Fx cause a yaw torque, which forces the vehicle to rotate around its center of gravity (COG). If this yaw motion does not correspond to the drivers intention, a vehicle dynamics controller (VDC) has to intervene accordingly, i.e. the propulsion torques have to be adapted such, that the real vehicle motion ψ˙ corresponds to the drivers demand ψ˙ ref .

From (1) it can be concluded, that the yaw rate is directly affected by Tz . To minimize the influence of the uncertain vehicle parameters e.g. cR , cF , lF , lR , ..., a robust control approach is essential Zehetner and Horn (2007); Angeringer and Horn (2011). Examples of robust control applications can e.g. be found in Utkin et al. (1999). As proposed in Slotine and Li (1991) a sliding mode control approach was chosen. Introducing a yaw rate error e = ψ˙ − ψ˙ ref ,

(2)

a possible choice for the sliding surface sψ˙ is given by 3. CONTROLLER DESIGN sψ˙ = e + γψ˙

3.1 Vehicle model The development of a VDC requires a mathematical description of the vehicle’s motion. Usually the so-called 537

Z

e dt,

(3)

where γψ˙ is a strictly positive weighting factor. The equivalent yaw torque, i.e. the torque required to keep sψ˙ at constant values, can be easily determined as

IFAC AAC 2013 September 4-7, 2013. Tokyo, Japan

driver input

either chosen from a vehicle model or from the sideslip angle controller, i.e.

˙ v ay , ψ,

vehicle model

ψ˙ ref

driver input

energy management

ψ˙ ref =

λref vehicle

yaw rate controller

ψ˙

Tz

torque coordinator

TE , TB ˙ ay , ψ, v

wheel corner controller

wheel corner

λ

Fig. 4. Yaw rate control loop   2 cR l R + cF lF2 − γψ˙ Jz ψ˙ − cF lF δ + ... Tˆz = v ... + (cF lF − cR lR ) β + γ ˙ Jz ψ˙ ref . ψ

(4)

In order to steer sψ˙ to zero and to cope with the uncertainties, an additional yaw torque component has to be added that the yaw rate control law finally reads as ! sψ˙ ˆ , (5) Tz = Tz − kψ˙ sat φψ˙ where φψ˙ is the boundary layer width, see e.g. Utkin and Lee (2006). To ensure a convergence, i.e. lim e(t) = 0,

t→∞

(6)

the positive constant kψ˙ has to satisfy kψ˙ ≥ |(cR lR − cF lF ) βmax | + ηψ˙

(7)

where ηψ˙ is strictly positive. As shown in Fig. 4 the yaw torque Tz can be used to modify the desired propulsion torques from the energy management. The strategy for combining Tz and the energy management set points depends on the vehicle operation mode (e.g. acceleration, deceleration, steering, straight run,...). Therefore a socalled torque coordinator, which provides the torque vectoring functionality, is required. A rule-based approach was chosen, which roughly determines the yaw potential of each tire like shown in Wagner (2006). Based on each tire potential, the most preferable actuator configuration is selected. The yaw rate controller performance is tested with standardized maneuvers. Exemplarily a steering-step test maneuver was chosen, the corresponding results are discussed in section 4.1.



ψ˙ O , if |β| < |βlim | ψ˙ C , otherwise

(8)

While low sideslip angle values are present, a reference yaw rate ψ˙ ref resulting from the vehicle model is used, see section 3.1. In case of high sideslip angles, a suitable sliding mode controller delivers ψ˙ ref . The exact determination of β requires very costly measurement equipment which is not suitable for serial production cars. Instead an estimation of β is applied Grip et al. (2009). In order to keep the number of controller parameters to be tuned at a minimum, the sliding surface sβ is chosen as Z sβ = β − βlim + γβ (β − βlim ) dt, (9)

where γβ is positive. As β must be bounded by βlim , the equivalent control law reads as (cF + cR ) vβ − cF vδ − γβ (β − βlim ) mv 2 ˆ ψ˙ C = . (10) cR lR − cF lF − mv 2 As some parameters are uncertain the control law   sβ , (11) ψ˙ C = ψˆ˙C − kβ sat φβ with v (cF + cR ) kβ ≥ β (12) max + ηβ 2 cR lR − cF lF − mv guarantees convergence in the presence of parameter uncertainties. Special emphasis has to be put on the selection of the positive constant ηβ . From simulations it was found, that a high ηβ on one hand leads to a fast convergence, on the other hand causes a fast increase of the slip λ. Especially for slow driving on low-µ conditions, this is not conducive. In contrast to higher speeds a low ηβ leads to good performance for low velocities. Therefore a speeddependent choice of ηβ , i.e. ηβ = ηβ (v) (13) is preferable. After stabilization of the car a bumpless transition from sideslip angle control to yaw rate control has to be performed. The performance of the proposed control structure was compared to a benchmark system. The results are shown in subsections 4.2 and 4.3. 4. SIMULATION RESULTS

3.3 Slideslip angle control From the results in section 4.1 it can be concluded, that the hybrid actuator system improves the cornering performance of a vehicle. Although the results are very promising, the yaw motion control has deficiencies during braking maneuvers and driving situations where the vehicle sideslip angle β increases rapidly. As unexperienced driver should also be able to easily handle the vehicle it is proposed to limit the sideslip angle β in such situations, see Isermann (2006); Wong (1993). Investigating (1) leads to the conclusion that Tz has no direct impact on β. Inspired by the results presented in Reichhartinger and Horn (2012), the control loop shown in Fig. 4 is extended by an additional outer control loop, see Fig. 5. The reference yaw rate is 538

All simulations are carried out with the simulation framework Dyna4TM . As the simulations have to account for real world conditions, were the measured signals corrupted by a time delay of 4ms. Additionally, the frequency for the update of the torque set values was assumed to be 500Hz. 4.1 Steering wheel step For the demonstration of the VDC performance, a steering wheel step with constant vehicle velocity was chosen. In order to get a feeling for the potentials of the proposed concept, a comparison with a vehicle (conventional ESC benchmark vehicle) without hybrid actuator system was carried out. The steering step was applied to both vehicles

IFAC AAC 2013 September 4-7, 2013. Tokyo, Japan

driver input

˙ v ay , ψ,

vehicle model

β, βlim sideslip-angle controller

energy management

driver input

ψ˙ O

λref vehicle

ψ˙ ref ψ˙ C

yaw rate controller

torque coordinator

TE , TB ˙ v ay , ψ,

Tz

ψ˙

wheel corner controller

wheel corner

λ

Fig. 5. Sideslip angle control loop

VDC

ψ˙ ref (δ, v)

VDC

ψ˙ ref




high-µ

ay , δ, v

20





0

corridor

−20 12

low-µ

0 140

Yaw rate [◦ /s]

y-Position [m]

ESC

40

ESC VDC

20

60

160

180

200

220

240

260

13

14 15 t [s]

16

17

Fig. 7. Sine with dwell (yaw rate)

Fig. 6. Steering step test maneuver on high-µ and low-µ on high-µ as well as on low-µ. From Fig. 6 it can be seen, that the performances of both systems on highµ are almost identical. The same control approach as proposed in section 3.2 for low-µ conditions, leads to high sideslip angles and therefore needs some refinement based on the ideas of Isermann (2006). As the lateral tire forces are highly nonlinear and depend on µ, it is difficult to determine the reference yaw rate for different road surfaces analytically. Instead, a practicable approach is based on the lateral acceleration ay . By assuming that the whole tire force potential is exploited, a relation between ψ˙ ref and ay can be found for constant velocities and different steering angles at static conditions. Although the reference yaw rate depends on µ, this dependency can be covered by ay . Special requirements according to the signal quality of ay are not given, as the signal quality can be improved with the help of observers. ψ˙ ref is now a function of the lateral acceleration as well, i.e.  ay  ψ˙ ref = min ψ˙ ref (v, δ) , . (14) v In fact, this modification leads to very promising results. As depicted in Fig. 6 the VDC is capable of limiting the ¨ Even the benchmark ESC system is yaw acceleration ψ. not able to suppress this oversteering behavior completely. 4.2 Sine with dwell The aim of the Sine with dwell -maneuver is to provoke an oversteering vehicle behavior. A measure for the performance of the vehicle stability is the dynamics of the yaw rate, after the steering input has returned to the zero 539

Vehicle sideslip angle [◦ ]

x-Position [m] 10

5

0 ESC VDC −5 12

13

14 15 t [s]

16

17

Fig. 8. Sine with dwell (vehicle sideslip angle) position. According to NHTSA (2006), a controller passes the test, if the yaw rate remains in the corridor, plotted in Fig. 7. From Fig. 7 it is obvious, that both controllers pass the test, i.e. the yaw rate remains within the required corridor. Nevertheless the yaw rate of the VDC is driven to zero significantly faster. Also Fig. 8 confirms that the potential for limiting the sideslip angle is impressive. In order to demonstrate the vehicle reaction, the vehicle position can also be displayed from the birds view (see Fig. 9). For an ordinary driver the VDC-equipped car is easier to handle than the benchmark vehicle. 4.3 Split-µ braking / Low-µ braking One of the most common test maneuvers is split-µ braking. One half of the vehicle is operated on ice whereas the second half is on high-µ. For studying the controller behavior in terms of traction machine power, a variation of the machine’s peak output power was carried out. VDC 1 represents high performance traction machines, which are able to provide the entire deceleration torque electrically. VDC 2 displays the same maneuver, where the machines are not able to provide the required torques, due to lack of

5 0 −5

160

180

Traction machine torque [Nm]

y-Position [m]

IFAC AAC 2013 September 4-7, 2013. Tokyo, Japan

200

x-Position [m] y-Position [m]

Zoom 5

ESC

0 VDC 180

190

185

195

200

Rear axle wheel velocity [km/h]

Rear axle brake pressure [bar]

400 200 0 VDC1: µ-high VDC2: µ-high −200 13

14

µ-low µ-low 16

15

17

Fig. 11. Recuperation torque split-µ braking

Fig. 9. Sinus with dwell (vehicle position) ESC: µ-high VDC2: µ-high

µ-low µ-low

40

20

0 13

600

t [s] x-Position [m]

60

800

14

15

16

17

80 left

right

60 40 20 0 13

ESC: µ-low VDC1: µ-low VDC2: µ-low 14

15 t [s]

ESC: µ-high VDC1: µ-high VDC2: µ-high 16

17 13

14

15 t [s]

16

17

Fig. 12. Wheel velocity split-µ braking

t [s]

Fig. 10. Rear axle brake pressure split-µ braking the machine’s peak torque. Therefore a combined control of friction brake and traction machine comes into play. As in the vehicle, only the brake pressure can be measured it is displayed in Fig. 10 and Fig. 13 instead of TBrk . From Fig. 10 it can be seen, that the brake pressure can be lowered if a hybrid braking system is used. This means, that kinetic energy can be recovered for charging the electric energy storage system. VDC 1 is not displayed, as it does not access the friction brake at all. Only the traction machines have to adapt their recuperation torques for limiting the wheel slips. From Fig. 11 it can be seen, that the energy manager demands high recuperation torques. When applying the requested machine torque on the lowµ side, the wheel starts to skid. The wheel slip controller intervenes and reduces the recuperation torque on the lowµ side immediately, while the recuperation torque on the high-µ side remains unaffected. According to the different traction force potential, a yaw motion is induced. At t = 14.2s the sideslip angle exceeds βlim , so the VDC corrects this yaw motion via Tz . The torque coordinator calculates the yaw torque potential of each wheel and distributes Tz to the appropriate traction machines. It commands the reduction of the recuperation torque on the high-µ side in order to keep the vehicle motion manageable for the driver. On the low-µ side, the wheel slip control using full recuperation is still in progress. When the vehicle is stabilized, the recuperation on high-µ can be re-enforced to maintain a minimum braking distance. The corresponding wheel velocities can be seen in Fig. 12. The same experiment was carried out using VDC 2. The traction machines cannot provide the vehicle deceleration torques, due to lack of the machine’s peak torque. An 540

additional friction brake intervention (see Fig. 10) is required. The resulting deceleration torques cause the low-µ wheel to skid. Hydraulic brake pressure is reduced immediately, while full recuperation is maintained according to the machines limits. From Fig. 10 and Fig. 11 it can be concluded, that although the wheel slip λ is controlled, the recuperation torque on low-µ is increased continuously. The brake pressures are only applied as short as possible and are as low as required. While wheel slip control is active on the low-µ side, the torque coordinator holds the brake pressure on the high-µ on a constant level, in order to weaken the excitation of undesired yaw motions. Only the traction machine is allowed to increase energy recuperation. At t = 14.6s the sideslip angle exceeds βlim , so the VDC corrects this yaw motion via Tz . The torque coordinator counteracts by lowering the friction brake torque in a first step, and if required, by lowering the recuperation torque in a second step. In order to minimize the braking distance and to keep the vehicle stable only the high-µ side is affected. After stabilizing the vehicle, the recuperation is re-enforced, the friction brake is inactive. Additionally a low-µ braking maneuver was carried out. Starting from a constant velocity v, the vehicle is decelerated as fast as possible. As stated in the split-µ braking scenario, the experiment was carried out with the ESCsystem, with VDC 1 and VDC 2. The hybrid braking system, permits low brake pressures or even keeps them at zero, see Fig. 13. In case of pure recuperative braking, a very short braking distance can be achieved (see Table 3). If the friction brake is actuated due to machine limits, the braking distance still is reduced. In both cases (split-µ and low-µ) the proposed concept permits • to reduce the braking distance

Rear axle brake pressure [bar]

IFAC AAC 2013 September 4-7, 2013. Tokyo, Japan

it is intended to investigate the controller performance in case of actuator malfunction. Finally the integration of the controller into a prototype car is planned.

40 30

ACKNOWLEDGEMENTS 20

The authors gratefully acknowledge the support of the “Austrian Research Promotion Agency (FFG)” and the “Magna Projecthouse Europe”.

10

0 13

ESC: VDC2: 14

15

16

REFERENCES 18

17

t [s]

Traction machine torque [Nm]

Fig. 13. Rear axle brake pressure low-µ braking 800 600 400 200 0 VDC1: VDC2: −200 13

14

15

17

16

18

t [s]

Rear axle wheel velocity [km/h]

Fig. 14. Recuperation torque low-µ braking 80 left

right

60 40 20 0

ESC: VDC1: VDC2:

ESC: VDC1: VDC2:

14

16 t [s]

18 13

14

15 16 t [s]

17

18

Fig. 15. Wheel velocity low-µ braking Table 3. System comparison System

Maneuver

Braking Distance

ESC VDC 1 VDC 2

split-µ / low-µ split-µ / low-µ split-µ / low-µ

39.5m / 49.6m 37.7m / 48.1m 38.5m / 48.3m

• to ensure vehicle stability and • to guarantee full energy recuperation. 5. CONCLUSION AND FUTURE WORK The integration of electric traction drives into vehicle stability control offers new degrees of freedom. It is shown, that cascaded sliding mode controllers are suitable for vehicle dynamics control. Especially in combination with the presented hybrid actuator system energy saving and yaw stability can be brought in line. In the near future 541

Angeringer, U. and Horn, M. (2011). Sliding mode drive line control for an electrically driven vehicle. Proc. of IEEE Multi-Conference on System and Control. Gillespie, T. (1992). Fundamentals of Vehicle Dynamics. Society of Automotive Engineers. Grip, H., Imsland, L., Johansen, T., Kalkkuhl, J., and Suissa, A. (2009). Vehicle sideslip estimation. IEEE Control Systems Magazine, 36–52. Isermann, R. (ed.) (2006). Fahrdynamik-Regelung. Friedrich Vieweg & Sohn Verlag, 1st edition. Jurgen, R.K. (1999). Automotive electronics handbook. McGraw-Hill handbooks. Khalil, H. (1996). Nonlinear Systems. Prentice Hall, second edition. Milliken, W. and Milliken, D. (1995). Race Car Vehicle Dynamics. Society of Automotive Engineers. NHTSA (2006). Proposed fmvss no.126 electronic stability control systems - preliminary regulatory impact analysis. Reichhartinger, M. and Horn, M. (2012). Cascaded slidingmode control of permanent magnet synchronous motors. Proc. of International Workshop on Variable Structure Systems. Ringdorfer, M. and Horn, M. (2011). Development of a wheel slip actuator controller for electric vehicles using energy recuperation and hydraulic brake control. Proc. of IEEE Multi-Conference on System and Control. Slotine, J.J.E. and Li, W. (1991). Applied Nonlinear Control. Prentice Hall. Tanelli, M., Sartori, R., and Savaresi, S. (2006). Sliding mode slip-deceleration control for brake-by-wire control systems. European Journal of Control. Utkin, V., Guldner, J., and Shi, J. (1999). Sliding Mode Control in Electromechanical Systems. CRC Press London. Utkin, V. and Lee, H. (2006). The chattering analysis. Proc. of International Power Electronics and Motion Control Conference. Wagner, M. (2006). Gleichzeitige Nutzung von l¨ angs-, quer- und vertikaldynamisch wirkenden Regelsystemen f¨ ur Personenkraftwagen. VDI Verlag GmbH. Wong, J. (1993). Theory of Ground Vehicles. John Wiley and Sons. Zehetner, J. and Horn, M. (2007). Vehicle dynamics control with torque-vectoring and active rear steering using sliding mode control. Advances in Automotive Control.