- Email: [email protected]
Relaxed static stability based on tyre cornering stiffness estimation for all-wheel-drive electric vehicle
Control Engineering Practice 64 (2017) 102–110
Contents lists available at ScienceDirect
Control Engineering Practice journal homepage: www.elsevier.com/locate/conengprac
Relaxed static stability based on tyre cornering stiffness estimation for all-wheel-drive electric vehicle Jun Ni, Jibin Hu n, Changle Xiang National Key Lab of Vehicle Transmission, Beijing Institute of Technology, Beijing, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 7 August 2016 Received in revised form 20 April 2017 Accepted 20 April 2017
A novel dynamics control approach for all-wheel-drive electric vehicle (EV), relaxed static stability (RSS) approach is proposed with two advantages. Firstly, it allows vehicle lateral dynamics system to be inherent unstable to improve configuration flexibility. Secondly, handling performance could be improved based on closed-looped pole assignment with additional yaw moment. In this paper, basic control framework of RSS is proposed, including ‘Desired Pole Location’, ‘Pole Assignment’ and ‘Tyre Cornering Stiffness Estimation’ modules. The tyre cornering stiffness is estimated online to improve the robustness of the controller. The experiments based on an EV testbed show the performance and efficiency of RSS. & 2017 Elsevier Ltd. All rights reserved.
Keywords-: Electric Vehicle (EV) All-wheel-drive Vehicle Relaxed Static Stability Yaw Moment Control Vehicle Dynamics
1. Introduction All-wheel-drive (AWD) electric vehicle (EV), which applies independent motor to drive each wheel, is becoming widely focused with unique features. It employs independent motors to directly drive the wheels without any mechanical link. The torque acting on each wheel can be controlled independently, which provides great convenience to conduct vehicle dynamics control, such as Traction Control (TC), Direct Yaw Control (DYC) or integrated control (Wong et al., 2016; Chan, 2008; Zhang, Zhang & Wang, 2016; Wang, Zhang & Wang, 2014; Ivanov, Savitski, & Shyrokau, 2015; Jalali et al., 2016; Ni & Hu, 2017). Moreover, since the acting torque information on each wheel is available, it also boosts the research of tyre-road adhesion condition and vehicle behavior parameter observation (Wang, Fujimoto, & Hara, 2016; Hu, Yin, & Hori, 2011; Doumiati, Victorino, & Charara, 2011; Nam, Fujimoto, & Hori 2012) DYC is one of the most popular topics among the dynamics control technologies of AWD EV (Shuai, Zhang & Wang, 2014a, 2014b; Shibahata, Shimada, & Tomari, 1993). The main principle is to generate additional yaw moment to control the vehicle to track the desired behavior to improve the handling performance. M. Nagai proposes a model matching controller to control the vehicle to follow the desired 2DOF lateral dynamic model (Nagai et al., 1997). Y. Hori claims that it's necessary to calculate the desired n
Corresponding author. E-mail address: [email protected] (J. Hu).
http://dx.doi.org/10.1016/j.conengprac.2017.04.011 0967-0661/& 2017 Elsevier Ltd. All rights reserved.
behavior based on 2DOF lateral dynamic model because of the safety concern (Sakai & Hori, 1998). Goodarzi discusses the performance of optimal controller on yaw moment generating (Goodarzi & Mohammadi, 2014). Xiong proposes an optimal controller with real-time online estimation of the tyre cornering stiffness to improve the control accuracy against tyre uncertainties (Xiong, Yu, & Wang, 2012). Hedrick uses sliding mode control during the process of yaw moment generating, and the driver behavior is also taken into consideration (Chen, Hedrick, & Guo, 2012). To deal with DYC control problem in high nonlinear maneuver condition, Hori proposes a controller based on body slip angle fuzzy observer (Geng, Mostefai, & Hori, 2009), and he further proposes a slip angle estimation block using the lateral tire force sensors (Nam, Fujimoto, & Hori, 2012, 2014). Shuai investigates the time-varying delay of CAN network in DYC and Active Front Steer (AFS) systems, and he proposes an H1 based delay-tolerant controller (Shuai et al., 2014a; 2014b). H. Zhang proposes a generalized Proportional-integral (PI) controller to deal with uncertainties of longitudinal velocity in AFS and DYC combined control systems (Zhang & Wang, 2016) Above researchers’ work have made great contributions. However, DYC still have apparent deficiency, which will be discussed in details later. In this paper, a novel lateral dynamics control approach-relaxed static stability (RSS) will be proposed based on our previous work (Ni & Hu, 2016a; 2016b; Ni et al., 2015; Ni & Hu, 2016a; 2016b). The major novelty and contribution of RSS lies on: 1) RSS's basic principle is totally different from that of DYC. It can be considered as novel overall theory of ground
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
vehicle. The main idea is that the vehicle's lateral dynamics system can be designed as unstable (inherent oversteer), which is significant for improving structure configuration flexibility. 2) RSS utilizes pole assignment approach to improve the closed-looped handling performance. The desired pole locations of closed-looped lateral dynamics system could be easily adjusted to meet different handling demand of different type vehicles, such as safety demand for passenger car, or agility demand for combat vehicle. In this paper, following sections are organized. In Section 2, the necessity to use RSS in ground vehicle field is claimed compared to the history of flight control. In Section 3, the control framework of RSS is described, including ‘Desired Pole Location’, ‘Pole Assignment Controller’ and ‘Tyre Cornering Stiffness Estimation’ modules. In Section 4, the experiments based on an EV testbed show the efficiency of RSS.
2. CCV to improve configuration flexibility 2.1. Inspiration of airplane design and flight control Control Configured Vehicle (CCV) concept has been widely used in flight control area. The control methods of CCV concept include relaxed static stability, envelope limit control, maneuver load control and active structural mode control (Anderson & Mason). For the traditional design process of airplane. The airplane configuration only depends on the propulsion system design, aerodynamic system design and other mechanical systems design. The flight control system design process is on the outside of the primary configuration and optimization loop. The control system has no influence on the structure configuration. In other words, the control system will not be designed until after the final airplane configuration has been selected. The airplane design process under CCV concept is totally different (Anderson & Mason). It includes the control system design in parallel with other subsystems for final configuration. The control system directly affects configuration selection. The combination of mechanical and control systems leads to the maximization of the overall performance. Take RSS control method as example. For traditional airplane, the aerodynamic center must be in the back of C.G to achieve enough longitudinal static stability. By using CCV concept, if a feedback active control system is utilized to provide artificial stability, the airplane's longitudinal stability can be relaxed. Therefore, the C.G location can be placed in the back of aerodynamic center, which significantly improves the configuration flexibility. The down tail loads can even result in an up-loaded tail so that the wing loads are reduced. The size and weight of horizontal tail can be reduced to achieve reduced fuel consumption, reduced drag, and better maneuvering capability. Previous ground vehicle overall design process is same to traditional process of airplane. The configuration selection of the ground vehicle only takes mechanical systems into consideration. The control system design process is separated from the mechanical systems. After the overall configuration is determined, various control systems will be added, such as TC, ABS or DYC systems. The history of airplane overall configuration principle could provide significant guidance. With more control systems involved, it's necessary to utilize CCV concept in ground vehicle to improve the overall performance. 2.2. Pole location discussion-configuration flexibility improvement According to vehicle dynamics theory (Milliken & Milliken, 1994), the vehicle should be understeer to achieve stable handling response. It is usually described by Static Margin (S.M.): (Milliken & Milliken, 1994).
S.M. =
103
lf Cr − Cf + Cr L
(1)
Where Cf and Cr is front and rear tyre cornering stiffness. lf is the distance from front axle to C.G. L is the wheelbase. When S.M. is higher than 0, the vehicle will be inherent understeer. The higher the S.M. value is, the more understeer the vehicle will be. The value of S.M. depends on the configuration of the vehicle. Understeer is a basic principle to configure the vehicle's structure. Traditional vehicles easy to achieve inherent understeer according to Eq. (1). The engine and transmission systems are usually located at the front of the vehicle, which decreases the value of lf, and consequently enhances the understeer characteristics. However, for some new type vehicles, such as AWD EVs, it is hard to configure them to be inherent understeer. Heavy battery pack is usually located at the middle of the vehicle, and the independent motors are separated near the wheels, which leads to a back C.G. location. As mentioned in (Esmailzadeh, Goodarzi, & Vossoughi , 2003), the configuration problem is a common problem for EVs, which leads to inherent handling instability. CCV concept and RSS control provides great idea to solve this problem. Like how it works in airplane field, it allows the vehicle lateral dynamics system to be inherent unstable to improve the configuration flexibility, and to be closed-looped stable based on the yaw moment feedback. How much RSS can improve the configuration flexibility should be discussed. The pole location of the lateral dynamics system will be discussed to give a clearer observation. The state-space of 2DOF lateral dynamic model is described as (Milliken & Milliken, 1994):
(2)
ẋ = Ax + Bδ Where:
⎡ β⎤ x = ⎢ ⎥, ⎣ r⎦
⎡ C ⎤ ⎢− f ⎥ ⎢ mu ⎥ B=⎢ lC ⎥ ⎢− f f ⎥ ⎣⎢ Iz ⎦⎥
⎡ C +C l f Cf − lr Cr r ⎢ f − mu ⎢ mu2 A=⎢ l2f Cf + lr2Cr ⎢ l f Cf − lr Cr ⎢⎣ Iz Izu
(3)
⎤ 1⎥ ⎥ ⎥ ⎥ ⎥⎦
(4)
Where lr is the distance from rear axle to C.G. r is the yaw velocity. β is the side slip angle. m is the vehicle mass. Iz is the yaw inertia. u is the vehicle speed. The pole locations can be described as:
p1,2 =
(
)
(
)
Iz Cf + Cr + m l2f Cf + lr2Cr ±
Δ
2Izmu
(5)
Where: 2 Δ = ⎡⎣ Iz Cf + Cr − m l2f Cf + lr2Cr ⎤⎦
(
)
(
) )(
−4Izm⎡⎣ mu2 − l f Cf − lr Cr ⎤⎦ l f Cf − lr Cr
(
)
(6)
To show the pole distributions of inherent understeer vehicle, a front-drive passenger car's specifications will be used as Table 1 shows. In order to discuss how CCV and RSS improves the configuration flexibility, the variation of poles location when configuration changes should be discussed. Fig. 1(a) shows the case when C.G location changes. The original C.
104
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
Table 1 Conventional Passenger Car Specifications. Specification
Value
m L Iz Cf Cr lf lr
900 kg 2.54 m 1138 kg*m2 57000N/rad 42000N/rad 0.89 m 1.65 m
stable tendency. However, for AWD EV, the traction force also acts on rear tyres, which makes the stiffness of rear tyres much lower than that of conventional vehicle. Apparently, the traditional vehicle dynamics theory strictly constrains the distribution of the tyre cornering stiffness, which further constrains the traction force distribution for AWD EV. Above discussion shows how traditional understeer principle constrains the overall configuration. Actually, understeer principle also constrains the suspension adjustment, steering system adjustment, and wheel camber or toe angle adjustment, et al. The configuration problem is one of the biggest problems for AWD EV. The application of CCV and RSS could solve this problem by allowing lateral dynamics system to be inherent unstable configured
3. Hierarchical control framework of RSS
(a) C.G Location
(b) Wheelbase
Fig. 1. Poles When Specifications Change(100 km/h).
G. location is 65%:35%. The original pole locations are ( 4.1, 74), which are noted by red points. When it moves forward to 90%:10% (red solid arrows), the distance from poles to the origin becomes larger. When it moves backward to 40%:60% (red dash arrows), the system becomes overdamped, and the poles become double negative real poles. When the C.G location is 40%:60%, a positive real pole occurs, which indicates the system is unstable. The inherent understeer principle constrains the C.G location must be between 100%:0 to 40%60%. It constrains the configuration of the EV, as well as the location of the subsystem, such as battery back. Fig. 1(b) shows the case when wheelbase changes. The direction when the value increases is noted by solid arrows, and the decrease is noted by dash arrows. During the change of wheelbase (50%-150%), the system remains two conjugate complex poles, which shows the system is underdamped. Although it is stable, it still has great influence on handling transient response. For AWD EV, wheelbase is always larger than conventional vehicle, so that damping ratio becomes higher. According to the transient performance demand, the wheelbase needs to be designed short enough to obtain desired damping ratio. In Fig. 2, the red solid arrows show the stiffness increases, and the dash arrows show the stiffness decreases. When cornering stiffness of front tyres reaches 150% as origin, a positive real pole occurs, which indicates instability. When cornering stiffness of rear tyres decreases to 40% as origin, a positive real pole occurs. For traditional front-drive vehicle, the traction force makes the stiffness of front tyres lower than rear tyres, which leads to a more
In this section, the control framework of RSS will be proposed as Fig. 3 shows. The desired pole locations of the vehicle lateral dynamics system will be predefined as a function of u, which can be adjusted according to different handling demand. A pole assignment controller is used to calculate the desired yaw moment. The feedback of tyre cornering stiffness is utilized to improve the robustness against uncertainties during high acceleration maneuver condition.
3.1. Pole assignment controller against uncertainties 2DOF model is utilized to design the pole assignment controller. Assume the vehicle is operating in the low lateral acceleration condition and the tyres are operating in the linear region. Consider yaw moment provided by the independent motors M as control input, the dynamics model can be described as Eq. (7) regardless of uncertainties (Sakai & Hori, 1998):
(7)
ẋ = Ax + Bδ + CM Where:
⎡ 0⎤ ⎢ ⎥ C = ⎢ 1⎥ ⎢⎣ Iz ⎥⎦
(8)
The definition of x and B has been shown in Eq. (3). State feedback control will be applied in this paper. Consider M as feedback according to state vector x. Let F be state feedback vector and F¼[f1, f2]:
(9)
M = − Fx The closed-looped dynamics model can be described as:
ẋ = (A − CF )x + Bδ
(10)
Substitute Eqs. (4) and (8) into Eq. (10), it can be obtained:
δ
Desired Pole Location
u
(a) Front tyre Cornering Stiffness
(b) Rear tyre Cornering Stiffness
Fig. 2. Poles When Specifications Change(100 km/h).
P
Pole Controller
ur β
M
Force Distribution
T
Vehicle State Tyre Cornering Stiffness Estimation
Fig. 3. RSS Control Framework.
Fz α
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
⎤ ⎡ Cf + Cr l f Cf − lr Cr ⎢ − 1⎥ 2 mu ⎥ ⎢ mu A − CF = ⎢ ⎥ 2 2 l C l C f l C l C f − − + − f f r r f f r r 1 2⎥ ⎢ ⎥⎦ ⎢⎣ Iz Izu
105
(11)
Eq. (11) represents the characteristics matrix of closed-looped dynamics system. After manipulation, the closed-looped pole locations can be described as:
p1′ ,2′ =
(
)
(
)
Iz Cf + Cr + m l2f Cf + lr2Cr + f2 mu ±
Δ2
2Izmu
(12)
Where: 2 Δ2 = ⎡⎣ Iz Cf + Cr − m l2f Cf + lr2Cr − f2 mu⎤⎦
(
)
(
) ) (
−4Izm⎡⎣ mu2 − l f Cf − lr Cr ⎤⎦ ⎡⎣ l f Cf − lr Cr + f1⎤⎦
(
)
(13)
(aa) Longitudinal Characteristics C
By equating Eq. (12) to equation of target closed-looped pole locations, the value of f1 and f2 can be obtained and the state feedback control can be applied through Eq. (9). According to Eqs. (12) and (13), it can be seen that the closed-looped pole locations of vehicle lateral dynamics system is determined by both vehicle specifications and control parameters. This is the key concept of CCV. The dynamics behavior and stability of the vehicle not only depends on the mechanical system configuration, but also depends on the control system. If the mechanical parts of the vehicle are configured to be inherent unstable, the control system can be adjusted to obtain closed-looped stability and achieve better dynamics behavior based on pole assignment. Above calculation neglects the uncertainties during vehicle motion. Actually, some parameters vary a lot during the motion, which leads to unmodelled uncertainties, especially the tyre cornering stiffness. When the lateral acceleration is high, the tyre forces will no longer be linearly proportional to the tyre slip angle. Therefore, the cornering stiffness value will not be constant and it will vary when nonlinear property occurs. Consider the tyre cornering stiffness uncertainties
⎧ C′f = Cf + ΔCf ⎨ ⎪ ⎩ Cr′ = Cr + ΔCr
(a) Lateral Chaaracteristics Fig. 4. Magic Formula Tyre Model.
⎪
(14)
Where Cf’, Cr’ represent real cornering stiffness of front and rear tyre. ΔCf’, ΔCr’ represent additional uncertainties due to the tyre nonlinearity. The solving process of state feedback control parameters needs the accurate value of tyre cornering stiffness. Therefore, in this paper, based on the independent motor information, GPS/INS sensor information and pre-conducted tyre property tests, the real time value of tyre cornering stiffness will be estimated and feedback to the controller. 3.2. Tyre Cornering Stiffness Estimation The tyre used in the testbed was tested through the test rig. With the cooperation with Formula SAE Tire Test Consortium (Kasprzak et al., 2006), plenty of tests were conducted to obtain tyre raw data in longitudinal, lateral and combination condition. The cornering tests were run with a free-rolling tyre, while drive/ brake tests hold constant slip angle while varying slip ratio. Both tests are conducted under five loads (50 lb, 100 lb, 150 lb, 250 lb and 350 lb), five inclination angles (0°, 1°, 2°, 3° and 4°). During the tyre modeling in this paper, the data of 12 psi is used. Based on test raw data, the nonlinear characteristics of tyre force is described by Magic Formula model after fitting work:
F = D sin {C1arctan[B1X − E(B1X − arctan(B1X ))]}
(15)
Where B1 is stiffness factor. C1 is shape factor. D is peak factor. E is curvature factor. X is slip ratio or slip angle. Fig. 4 shows the pure longitudinal and lateral characteristics of the tyre according to the Magic Formula model. The combinedcondition Magic Formula model can be described as:
⎧ ⎪ Fx0 = ⎨ ⎪F = ⎩ y0
σx Fx σ σy Fy σ
(16)
Where Fx and Fy is the pure longitudinal and lateral force. Fx0 and Fy0 is the combined longitudinal and lateral force. s is the normalized combined slip ratio. sx is the normalized longitudinal slip ratio. sy is the normalized lateral slip angle:
⎧ ⎪σ = ⎪ ⎪ ⎨ σx = ⎪ ⎪ σ = ⎪ ⎩ y
σx2 + σy2 s 1+s tan α 1+s
(17)
Where s is the slip ratio. α is the lateral slip angle. According to the combined Magic Formula model, the nominal real time tyre cornering stiffness can be estimated through:
106
C0 =
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
∂Fy0 ∂α
(18)
The estimating process of C0 needs the feedback of tyre slip ratio s, slip angle α and vertical load Fz. The tyre slip ratio s can be estimated through:
⎧ ωR −u ⎪ sa = t t ⎪ ωt Rt ⎨ ⎪ u − ωt Rt s = ⎪ ⎩ b u
(19)
Where sa, sb is the tyre slip ratio during accelerating and braking condition, respectively. ωt is the rotation speed of the wheels. Rt is the tyre radius. The vehicle speed u is feedback by the GPS/INS sensor, and ωt is feedback by the independent motor information. The tyre slip angle α can be estimated through:
⎧ lr ⎪ α11 = α12 = f + β − δ ⎪ u ⎨ ⎪ lr α = α22 = β − r ⎪ ⎩ 21 u
(20)
Where α11, α12 is the lateral slip angle of front left and right tyres. α21, α22 is the lateral slip angle of rear left and rear tyres. Steering wheel angle δ is feedback by the sensor. The yaw rate r and sideslip angle β is feedback by the GPS/INS system. The vertical load of each tyre is estimated through:
⎧ ma y ⎛ hKϕf l ⎞ ⎪ F = − ma xh + ⎜⎜ + r ⎟⎟ z11 ⎪ L B ⎝ Kϕf + Kϕr Lhrf ⎠ ⎪ ⎛ ⎪ ma y hKϕf ma xh l ⎞ ⎜⎜ ⎪ Fz12 = − − + r ⎟⎟ L B ⎝ Kϕf + Kϕr Lhrf ⎠ ⎪ ⎨ ⎪ ma y ⎛ hKϕr lf ⎞ ma xh ⎜⎜ ⎟⎟ + + ⎪ Fz21 = + L B K K Lh ⎝ ϕf ⎪ rr ⎠ ϕr ⎪ ma y ⎛ hKϕr lf ⎞ ⎪ ma xh ⎪ Fz22 = L − B ⎜⎜ K + K + Lh ⎟⎟ ⎝ ϕf rr ⎠ ϕr ⎩
(21)
Where Fzii (i¼1,2) is the vertical load of four wheels, respectively. ax, ay is the longitudinal and lateral acceleration of the vehicle. h is the height of C.G. B is the track width. KΦf, KΦr is the roll stiffness of front and rear suspension. hrf, hrr is the suspension roll center of front and rear suspension. ax, ay is feedback by the GPS/INS system. The constant Magic Formula model parameters are pre-defined in the controller. However, the nominal stiffness is obtained according to the test data in the test rig, and the actual road condition varies a lot, which cannot be the same as the belt in test rig. Therefore, the road friction condition should be estimated and the tyre cornering stiffness should be adjusted according to the friction condition online. Assume the variation of cornering stiffness is in proportional to the variation of road fiction.
Cai = λC0
Hong, 2015; Lee, Nakano, & Ohori, 2015; Sado, Sakai, & Hori, 1999). The real time friction coefficient is easy to be estimated. Consider the dynamics motion equation of driving wheel:
Fd =
1 (T − Itω̇t ) Rt
(24)
Where It is the inertial of the wheel. T is the acting torque which can be easily obtained by measuring motor current, torque constant and gear ratio. Based on Eq. (24), the driving force Fd of each wheel can be estimated, and a low pass filter is utilized to eliminate noise caused by taking differential of wheel rotation speed. Then the real time value of μa can be estimated by:
μa =
Fd Fz
(25)
The vertical load of each wheel is obtained according to Eq. (21). After the value of λ is obtained, the actual cornering stiffness of each tyre can be estimated according to Eq. (22) 3.3. Desired pole locations RSS utilizes the desired pole locations of lateral dynamics system as control goal. The pole locations represent the dynamics behavior of the system. It's convenient to adjust the desired pole locations to satisfy different handling performance demand. For example, for passenger car, stability is the most important so that the desired pole locations could be designed accordingly. For military vehicle or racing car, fast response is most important so that the desired pole locations could be designed as critical damping to obtain fastest transient response. These two kinds of desired pole locations are utilized as examples as Fig. 5 shows. Fig. 5 shows the desired pole locations in ‘Stable Mode’ and ‘Agile Mode’. In ‘Stable Mode’, there are conjugate complex values arranged in straight lines, which divide 2nd and 3rd quadrants. It means the system is optimal damping ratio as 0.707. The desired vehicle handling response is assumed to be with constant optimal damping ratio during the whole speed range, which could significantly increase the handling stability. The desired pole locations in ‘Stable Mode’ can be expressed as:
pd1 =
d ( 1 ± i) u
(26)
The distance from desired pole location is in inverse proportional to vehicle speed u. Parameter d is used to adjust the desired pole location. Shadow circles represent the desired pole locations in ‘Agile Mode’. In each speed case, the desired pole locations are assumed to be one single negative real value, which indicates critical damping ratio. According to reference (Milliken & Milliken, 1994),
(22)
Where Cai is the actual cornering stiffness of each tyre.
λ=
μa μ0
(23)
Where μa is the real time friction coefficient. μ0 is the friction coefficient with the same slip ratio according to the tyre test data. Value of μ0 can be predefined as table form in the controller, and the value of μa has to be estimated online. For independent motor driven electric vehicle, a great advantage is that the torque and speed information of each wheel is observable (Kim, Hahn, &
Fig. 5. Desired Pole Locations.
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
neutralsteer vehicle has greatest handling transient response, which is also the reason why Formula 1 race car is always designed to be neutralsteer. Moreover, neutralsteer vehicle is always critical damped. The desired pole locations can be expressed as:
pd2 =
d u
107
Planetary Gearbox Drive Axle
Independent Motor
Suspension
(27)
4. Experiments validation Fig. 7. Independent Motor and Gearbox.
In this section, RSS control will be validated through experiments based on an independent-motor-driven EV testbed, which is completely designed and built by the authors. Inherent stability of the testbed vehicle will be adjusted to validate the RSS control performance in both ‘Agile Mode’ and ‘Stable Mode’. 4.1. Introduction of the testbed vehicle Figs. 6 and 7 show the pictures of testbed EV. Each wheel is independently driven by a motor, which is mounting in the vehicle body. The maximum power of each independent motor is 60 kW. With a 4-gearratio planetary gearbox, the independent motor could provide high traction force. Four drive axles are utilized to drive the wheels. The testbed vehicle is powered by LiFePo4 battery pack. The battery voltage is 400 V and the capacity is 8kWh. Each battery cell is equipped with a Battery Management System (BMS) chip to monitor the battery sates, such as State of Charge (SOC). Each motor is controlled by its own motor controller, and 4 motor controllers are controlled by a rapid ECU controller through CAN bus. The ECU controller is powered by a 400V-24V DC/DC convertor. A Differential GPS/INS system and two antennas are equipped to collect the information of position, vehicle speed, yaw velocity, side slip angle, longitudinal and lateral acceleration. The IMU is located at the front of the vehicle. Two antennas are located at both front and rear of the vehicle to obtain longer baseline. Main parameters are shown in Table 2. 4.2. J-turn experiments with inherent oversteer configuration At first, the ‘Stable Mode’ RSS control for the inherent oversteer configuration will be validated. The battery pack locates at the rear of the body, which leads to a back C.G location. The distance from front axle to the C.G location is 1 m and the distance from rear axle to the C.G location is 0.6 m. It can be calculated that the testbed vehicle is inherent oversteer. It is meaningful to show the handling behavior of an inherent oversteer vehicle under ‘Stable Mode’ control. During the experiments, the vehicle is controlled to accelerate to 80 km/h, and then a step steer angle will be input. The parameter d defined in Eq. (26) is assumed to be 120 in the experiment.
GPS Antenna Rapid ECU IMU Sensor Independent Motor
GPS Antenna
Battery Pack Fig. 6. Independent-motor-driven EV Testbed.
Table 2 Testbed EV Specification. Parameters
Value
Total Mass Maximum Speed Wheelbase Track Width Height of C.G Tire Radius
400 kg 120 km/h 1.6 m 1.3 m 0.4 m 230mm
Fig. 8(a) shows the comparison of yaw velocity and Fig. 8(b) shows the comparison of vehicle sideslip angle between uncontrolled and under control cases. According to Fig. 8(c), it can be seen that the vehicle accelerates to 80 km/h at 8 s, and then a step steer angle is input at about 8.5 s. Based on simple calculation it can be concluded that 80 km/h has exceeded the critical speed of the vehicle. After the steer angle is input, the uncontrolled vehicle loses stability and spins simultaneously. The yaw velocity of the uncontrolled vehicle increases rapidly to 1.2 rad/s and continues to increase from 9 s to 11 s. The sideslip angle of uncontrolled vehicle is also very large and continues to increase to 0.2 rad. However, the vehicle under RSS control remains stable and shows good handling behavior. The phase portrait of yaw velocity against side slip angle is plotted in Fig. 8(d). The phase portrait of uncontrolled vehicle has exceeded the stable boundary and becomes divergent. Fig. 8(e) shows the trace of C.G location, which is measured by the GPS/INS system. The red dash line shows the spin phenomenon of the uncontrolled vehicle. From 0 to about 120 m, the vehicle is accelerating to 80 km/h. After the steer angle is inputted, the vehicle spins and the radius becomes smaller due to the instability. Fig. 8(f) and (g) show the estimation results of tyre cornering stiffness, which have been smoothed to calculate the desired yaw moment. Only the front left and rear left tyre is shown. The results over the whole experiment period are shown in Fig. 8(f) to observe the accuracy of the result. From 0 to 8 s, the vertical load transfers to rear axle due to the longitudinal acceleration, hence the cornering stiffness of rear tyre is larger than that of front tyre. After the steer angle is inputted at 8.5 s, the tyre cornering stiffness decreases rapidly. After 9 s, the cornering stiffness of both front and rear tyres is around 0 which indicates the tyres are becoming saturated and the vehicle consequently loses stability and spins. Fig. 8(g) shows the result in RSS control case, the adhesion situation in RSS control case is much better, which indicates the vehicle is in better handling performance. Fig. 8(h) shows the desired yaw moment. It peaks about 600Nm, which is acceptable for the independent motors torque capability. The torque of each independent motor is calculated based on adding the torque demand TLi according to accelerate pedal and the torque demand TYi according to desired yaw moment.
108
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
(a) Comparison of Yaw Velocity
(b) Comparison of Vehicle Sideslip Angle
(c) Vehicle Speed
(d) Comparison of Phase Portrait
(e) Trace of C.G Location
(f) Tyre Cornering Stiffness Estimation Result in Uncontrolled Case
(g) Tyre Cornering Stiffness Estimation Result in RSS Control Case
(h) Desired Yaw Moment
(i) Comparison of Pole Locations Fig. 8. Experiment Results in 80 km/h J-turn.
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
TLi = ξP
(28)
Where P is the pedal location percentage. ξ is the linear coefficient. The desired yaw moment is distributed to four independent motors by simple equivalent approach:
TYi = ±
2MRt B
(29)
The influence of the steering angle of front wheels are neglected. The moment arms of each wheel's longitudinal force are assumed to be B/2 equally. Therefore, the total torque of each motor is calculated by:
Ti = TLi + TMi
(30)
In Fig. 8(i), the pole locations of vehicle lateral dynamics system on both cases are shown. The pole locations are calculated based on the estimation value of tyre cornering stiffness. The data are collected by 100 Hz sampling frequency, and only the data in cornering condition from 8 s to 11 s are shown. The red hollow points indicate the pole locations in uncontrolled case. It can be seen that a lot real positive poles occur, which indicate the unstable condition due to tyre saturation. The blue solid points indicate the closed-looped pole locations in RSS control case. The desired pole locations are ( 5.4, 75.4). During the experiment, great uncertainties occur due to the tyre nonlinearity. Therefore, the closed-looped locations can not be accurately assigned to be ( 5.4, 75.4). The pole assignment controller shows great performance against the uncertainties because of the tyre cornering stiffness online estimation. All the closed-looped pole locations are separated around ( 5.4, 75.4), despite some points are a little far because of the nonlinearity in such high-acceleration maneuver. It can be concluded that the controller successfully achieves the predefined control goal. 4.3. J-turn experiments with inherent understeer configuration ‘Agile Mode’ is supposed to improve the transient response
109
performance. Therefore, in this section the ‘Agile Mode’ RSS control will be validated with inherent understeer configuration. As above introduced, the testbed vehicle is completely built by the authors. Therefore, it is easy to do the adjustment. The original C.G location is 38%/62%. Before this experiment, the testbed vehicle's C.G location is adjusted to 60%/40% by the balance weight and suspension adjustment. Consequently, the testbed vehicle is changed to inherent understeer configuration. During the experiments, the vehicle is controlled to accelerate to 100 km/h, and then a step steer angle will be input. According to Fig. 9(a), the uncontrolled vehicle remains stable after the steer angle is input. The yaw velocity goes into the steady-state condition as about 0.4 rad/s after an overshoot. The overshoot percentage value peaks about 125%. The reason of such a high overshoot is because the vehicle speed during the experiment is as high as 100 km/h. In RSS control case, it can be seen that the overshoot and oscillation has been greatly eliminated. The time period used to go into steady state cornering condition has been greatly reduced. It can be concluded that the ‘Agile Mode’ RSS control successfully improves the transient handling performance of the vehicle. Fig. 9(b) shows the trace of C.G location in both cases. The vehicle was accelerating to 100 km/h from 0 to 180 m. After the steer angle is input, it can be seen that both the uncontrolled and RSS controlled vehicles go into the steady-state cornering condition. The radius of RSS control case is little higher than that of uncontrolled case. Fig. 9(c) shows the desired yaw moment calculated by the controller. Compared to the yaw moment demand in ‘Stable Mode’ case, it's much lower in ‘Agile Mode’ case. There is also a large overshoot occurs. Apparently, a large negative yaw moment overshoot is supposed to reduce the oscillation and overshoot of the yaw velocity. After that, the desired yaw moment remains constant as about 125Nm. Fig. 9(d) shows the pole locations estimation results on both cases. The data in cornering condition from 9.5 to 13 s are shown. There are no positive real poles occur for uncontrolled vehicle, which indicates the uncontrolled vehicle remains stable during
(a) Comparison of Yaw Velocity
(c) Desired Yaw Moment
(b) Trace of C.G Location
(d) Comparison of Pole Locations
Fig. 9. Experiment Results in 100 km/h J-turn.
110
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
the experiment. The pole locations of uncontrolled vehicle are near to the imaginary axis due to the high vehicle speed, and the damping ratio becomes very low, which indicates bad transient performance. The desired pole locations are ( 3.6,0) as a critical damped system. It can be seen that the pole assignment controller successfully controls the closed-looped pole locations to be located around the desired pole locations. Therefore, the transient handling performance of the vehicle has been improved.
5. Conclusion A novel concept-RSS is proposed for ground vehicle in this paper, which could be considered as CCV concept used in ground vehicle field. RSS and CCV combines the mechanical and control systems to form a novel overall configuration and control concept. Firstly, RSS allows the vehicle to be designed as inherent unstable to significantly improve the overall configuration flexibility. Secondly, RSS can significantly improve the handling performance of the vehicle. The basic control framework of RSS is proposed in this paper. The tyre cornering stiffness value is estimated online to improve the robustness of the controller against the uncertainties due to tyre saturation and nonlinearity. Moreover, RSS provides possibility to define different handling performance demand based on the desired pole location determination. Finally, an EV with independent motors is used to validate the proposed RSS control strategy. The experiment results indicate the great performance and efficiency of RSS control. In inherent oversteer configuration case, RSS controller successfully controls the vehicle to be stable during high-acceleration maneuver. In inherent understeer configuration case, RSS controller successfully controls the vehicle to be an almost critical damped system to improve the transient handling performance.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. U1564210).
References Anderson, M. R., Mason, W. H. An MDO approach to control configured vehicle design. american institute of aeronautics and astronautics. Paper No. 96-4058. Chan, C. C. (2008). The state of the art of electric and hybrid vehicles Jun. IEEE IEEE Transactions on Industrial Electronics, 55(6), 2237–2245 Jun. Chen, Y., Hedrick, K., & Guo, K. (2012). A novel direct yaw moment controller for inwheel motor electric motors. Vehicle System Dynamics, 51(6), 925–942. Doumiati, M., Victorino, A. C., & Charara, A. (2011). Onboard real-time estimation of vehicle lateral tire-road forces and sideslip angle. IEEE/ASME Transaction on Mechatronics., 16(4), 601–614. Esmailzadeh, E., Goodarzi, A., & Vossoughi, G. R. (2003). Optimal yaw moment control law for improved vehicle handling. Mechatronics, 13, 659–675. Geng, C., Mostefai, L., & Hori, Y. (2009). Direct yaw moment control of an in-wheel motored electric vehicle based on body slip angle fuzzy observer. IEEE Transactions on Industrial Electronics, 56(5), 1411–1419. Goodarzi, A., & Mohammadi, M. (2014). Stability enhancement and fuel economy of the 4 wheel drive hybrid electric vehicles by optimal tyre force distribution.
Vehicle System Dynamics, 52(4), 539–561. Hu, J., Yin, D., & Hori, Y. (2011). Fault-tolerant traction control of electric vehicles. Control Engineering Practice, 19, 204–213. Ivanov, V., Savitski, D., & Shyrokau, B. (2015). A survey of traction control and antilock braking systems of full electric vehicles with individually controlled electric motors. IEEE Transaction on Vehicle Technolology, 64(9), 3878–3896. Jalali, M., Khajepur, A., Chen, S., et al. (2016). Integrated stability and traction control for electric vehicles using model predictive control. Control Engineering Practice, 54, 256–266. Kasprzak, M. Edward and D. Gentz. The Formula SAE Tire Test Consortium-Tire Testing and Data Handling. SAE Technical Paper: 2006-01-3606. Kim, C., Hahn, J., & Hong, K. (2015). Estimation of tire-road friction based on onboard 6-dof acceleration measurement. IEEE Trans. Veh. Technol., 64(8), 3368–3377. Lee, S., Nakano, K., & Ohori, M. (2015). On-board identification of tyre cornering stiffness using dual kalman filter and GPS. Vehicle System Dynamics, 53(4), 437–448. Milliken, W. F., & Milliken, D. L. (1994). Race Car Vehicle Dynamics. SAE: Warren Michigan. Nagai, M., Hirano, Y., & Yamanaka, S. (1997). Integrated control of active rear wheel steering and direct yaw moment control. Vehicle System Dynamics, 27, 357–370. Nam, K., Fujimoto, H., & Hori, Y. (2012). Lateral stability control of in-wheel-motordriven electric vehicles based on sideslip angle estimation using lateral tire force sensors. IEEE Transaction on Vehicles Technology, 61(5), 1972–1984. Nam, K., Fujimoto, H., & Hori, Y. (2014). Advanced motion control of electric vehicles based on robust lateral tire force control via active front steer. IEEE/ASME Transaction on Mechatronics, 19(1), 289–299. Ni, J., & Hu, J. (2016a). Handling performance control for hybrid 8-wheel-drive vehicle and simulation verification. Vehicle System Dynamics, 54(8), 1098–1119. Ni, J., & Hu, J. (2016b). Dynamic modeling and experimental validation of a skid steered wheeled mobile robot on pivotal steer condition. Proceedings of the Institution of Mechanical Engineering Part D: The Journal of Automobile Engineering. http://dx.doi.org/10.1177/0954407016652760. Ni, J., & Hu, J. (2017). Dynamics control of autonomous vehicle at driving limits and experiment on an autonomous Formula racing car. Mechanical Systems and Signal Processing, 90, 154–174. Ni, J., Hu, J., & Li, X. (2015). Dynamic modeling, validation and handling performance analysis of skid steered vehicle. Proceedings of the Institution of Mechanical Engineering Part D: The Journal of Automobile Engineering, 232, 1–13. Sado, H., Sakai, S., & Hori, Y. (1999). Road condition estimation for traction control in electric vehicle. IEEE International Symposium on Industrial Electronics, 2, 973–978. S. Sakai, Y. Hori. Robustified model matching control for motion control of electric vehicle. IEEE AMC’98, 1998. Shibahata, Y., Shimada, K., & Tomari, T. (1993). Improvement of vehicle maneuverability by direct yaw moment control. Vehicle System Dynamics, 22, 465–481. Shuai, Z., Zhang, H., Wang, J., et al. (2014a). Lateral motion control for four-wheelindependent-drive electric vehicles using optimal torque allocation and dynamic message priority scheduling. Control Engineering Practice, 24, 55–66. Shuai, Z., Zhang, H., Wang, J., Li, J., & Ouyang, M. (2014b). Combined AFS and DYC control of four-wheel-indepdent-drive electric vehicles over CAN network with time-varying delays. IEEE Transaction on Vehicle Technology, 63(2), 591–602. Wang, R., Zhang, H., & Wang, J. (2014). Linear parameter-varying controller design for four wheel independently-actuated electric ground vehicles with active steering systems. IEEE Transactions on Control Systems Technology, 22(4), 1281–1296. Wang, Y., Fujimoto, H., & Hara, S. (2016). Torque distribution-based range extension control system for longitudinal motion of electric vehicles by LTI modeling with generalized frequency variable. IEEE/ASME Transaction on Mechatronics., 21(1), 443–452. Wong, A., Kasinathan, D., Khajepur, A., et al. (2016). Integrated torque vectoring and power management framework for electric vehicles. Control Engineering Practice, 48, 22–36. Xiong, L., Yu, Z. P., & Wang, Y. (2012). Vehicle dynamics control of four in-wheel motor drive electric vehicle using gain scheduling based on tyre cornering stiffness estimation. Vehicle System Dynamics, 50, 831–846. Zhang, H., & Wang, J. (2016). Vehicle lateral dynamics control through afs/dyc and robust gain-scheduling approach. IEEE Transaction on Vehicle Technolology, 65 (1), 489–494. Zhang, H., Zhang, G., & Wang, J. (2016). H1 observer design for LPV systems with uncertain measurements on scheduling variables: application to an electric ground vehicle. IEEE/ASME Transaction on Mechatronics., vol. 21(3), 1659–1670.
Contents lists available at ScienceDirect
Control Engineering Practice journal homepage: www.elsevier.com/locate/conengprac
Relaxed static stability based on tyre cornering stiffness estimation for all-wheel-drive electric vehicle Jun Ni, Jibin Hu n, Changle Xiang National Key Lab of Vehicle Transmission, Beijing Institute of Technology, Beijing, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 7 August 2016 Received in revised form 20 April 2017 Accepted 20 April 2017
A novel dynamics control approach for all-wheel-drive electric vehicle (EV), relaxed static stability (RSS) approach is proposed with two advantages. Firstly, it allows vehicle lateral dynamics system to be inherent unstable to improve configuration flexibility. Secondly, handling performance could be improved based on closed-looped pole assignment with additional yaw moment. In this paper, basic control framework of RSS is proposed, including ‘Desired Pole Location’, ‘Pole Assignment’ and ‘Tyre Cornering Stiffness Estimation’ modules. The tyre cornering stiffness is estimated online to improve the robustness of the controller. The experiments based on an EV testbed show the performance and efficiency of RSS. & 2017 Elsevier Ltd. All rights reserved.
Keywords-: Electric Vehicle (EV) All-wheel-drive Vehicle Relaxed Static Stability Yaw Moment Control Vehicle Dynamics
1. Introduction All-wheel-drive (AWD) electric vehicle (EV), which applies independent motor to drive each wheel, is becoming widely focused with unique features. It employs independent motors to directly drive the wheels without any mechanical link. The torque acting on each wheel can be controlled independently, which provides great convenience to conduct vehicle dynamics control, such as Traction Control (TC), Direct Yaw Control (DYC) or integrated control (Wong et al., 2016; Chan, 2008; Zhang, Zhang & Wang, 2016; Wang, Zhang & Wang, 2014; Ivanov, Savitski, & Shyrokau, 2015; Jalali et al., 2016; Ni & Hu, 2017). Moreover, since the acting torque information on each wheel is available, it also boosts the research of tyre-road adhesion condition and vehicle behavior parameter observation (Wang, Fujimoto, & Hara, 2016; Hu, Yin, & Hori, 2011; Doumiati, Victorino, & Charara, 2011; Nam, Fujimoto, & Hori 2012) DYC is one of the most popular topics among the dynamics control technologies of AWD EV (Shuai, Zhang & Wang, 2014a, 2014b; Shibahata, Shimada, & Tomari, 1993). The main principle is to generate additional yaw moment to control the vehicle to track the desired behavior to improve the handling performance. M. Nagai proposes a model matching controller to control the vehicle to follow the desired 2DOF lateral dynamic model (Nagai et al., 1997). Y. Hori claims that it's necessary to calculate the desired n
Corresponding author. E-mail address: [email protected] (J. Hu).
http://dx.doi.org/10.1016/j.conengprac.2017.04.011 0967-0661/& 2017 Elsevier Ltd. All rights reserved.
behavior based on 2DOF lateral dynamic model because of the safety concern (Sakai & Hori, 1998). Goodarzi discusses the performance of optimal controller on yaw moment generating (Goodarzi & Mohammadi, 2014). Xiong proposes an optimal controller with real-time online estimation of the tyre cornering stiffness to improve the control accuracy against tyre uncertainties (Xiong, Yu, & Wang, 2012). Hedrick uses sliding mode control during the process of yaw moment generating, and the driver behavior is also taken into consideration (Chen, Hedrick, & Guo, 2012). To deal with DYC control problem in high nonlinear maneuver condition, Hori proposes a controller based on body slip angle fuzzy observer (Geng, Mostefai, & Hori, 2009), and he further proposes a slip angle estimation block using the lateral tire force sensors (Nam, Fujimoto, & Hori, 2012, 2014). Shuai investigates the time-varying delay of CAN network in DYC and Active Front Steer (AFS) systems, and he proposes an H1 based delay-tolerant controller (Shuai et al., 2014a; 2014b). H. Zhang proposes a generalized Proportional-integral (PI) controller to deal with uncertainties of longitudinal velocity in AFS and DYC combined control systems (Zhang & Wang, 2016) Above researchers’ work have made great contributions. However, DYC still have apparent deficiency, which will be discussed in details later. In this paper, a novel lateral dynamics control approach-relaxed static stability (RSS) will be proposed based on our previous work (Ni & Hu, 2016a; 2016b; Ni et al., 2015; Ni & Hu, 2016a; 2016b). The major novelty and contribution of RSS lies on: 1) RSS's basic principle is totally different from that of DYC. It can be considered as novel overall theory of ground
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
vehicle. The main idea is that the vehicle's lateral dynamics system can be designed as unstable (inherent oversteer), which is significant for improving structure configuration flexibility. 2) RSS utilizes pole assignment approach to improve the closed-looped handling performance. The desired pole locations of closed-looped lateral dynamics system could be easily adjusted to meet different handling demand of different type vehicles, such as safety demand for passenger car, or agility demand for combat vehicle. In this paper, following sections are organized. In Section 2, the necessity to use RSS in ground vehicle field is claimed compared to the history of flight control. In Section 3, the control framework of RSS is described, including ‘Desired Pole Location’, ‘Pole Assignment Controller’ and ‘Tyre Cornering Stiffness Estimation’ modules. In Section 4, the experiments based on an EV testbed show the efficiency of RSS.
2. CCV to improve configuration flexibility 2.1. Inspiration of airplane design and flight control Control Configured Vehicle (CCV) concept has been widely used in flight control area. The control methods of CCV concept include relaxed static stability, envelope limit control, maneuver load control and active structural mode control (Anderson & Mason). For the traditional design process of airplane. The airplane configuration only depends on the propulsion system design, aerodynamic system design and other mechanical systems design. The flight control system design process is on the outside of the primary configuration and optimization loop. The control system has no influence on the structure configuration. In other words, the control system will not be designed until after the final airplane configuration has been selected. The airplane design process under CCV concept is totally different (Anderson & Mason). It includes the control system design in parallel with other subsystems for final configuration. The control system directly affects configuration selection. The combination of mechanical and control systems leads to the maximization of the overall performance. Take RSS control method as example. For traditional airplane, the aerodynamic center must be in the back of C.G to achieve enough longitudinal static stability. By using CCV concept, if a feedback active control system is utilized to provide artificial stability, the airplane's longitudinal stability can be relaxed. Therefore, the C.G location can be placed in the back of aerodynamic center, which significantly improves the configuration flexibility. The down tail loads can even result in an up-loaded tail so that the wing loads are reduced. The size and weight of horizontal tail can be reduced to achieve reduced fuel consumption, reduced drag, and better maneuvering capability. Previous ground vehicle overall design process is same to traditional process of airplane. The configuration selection of the ground vehicle only takes mechanical systems into consideration. The control system design process is separated from the mechanical systems. After the overall configuration is determined, various control systems will be added, such as TC, ABS or DYC systems. The history of airplane overall configuration principle could provide significant guidance. With more control systems involved, it's necessary to utilize CCV concept in ground vehicle to improve the overall performance. 2.2. Pole location discussion-configuration flexibility improvement According to vehicle dynamics theory (Milliken & Milliken, 1994), the vehicle should be understeer to achieve stable handling response. It is usually described by Static Margin (S.M.): (Milliken & Milliken, 1994).
S.M. =
103
lf Cr − Cf + Cr L
(1)
Where Cf and Cr is front and rear tyre cornering stiffness. lf is the distance from front axle to C.G. L is the wheelbase. When S.M. is higher than 0, the vehicle will be inherent understeer. The higher the S.M. value is, the more understeer the vehicle will be. The value of S.M. depends on the configuration of the vehicle. Understeer is a basic principle to configure the vehicle's structure. Traditional vehicles easy to achieve inherent understeer according to Eq. (1). The engine and transmission systems are usually located at the front of the vehicle, which decreases the value of lf, and consequently enhances the understeer characteristics. However, for some new type vehicles, such as AWD EVs, it is hard to configure them to be inherent understeer. Heavy battery pack is usually located at the middle of the vehicle, and the independent motors are separated near the wheels, which leads to a back C.G. location. As mentioned in (Esmailzadeh, Goodarzi, & Vossoughi , 2003), the configuration problem is a common problem for EVs, which leads to inherent handling instability. CCV concept and RSS control provides great idea to solve this problem. Like how it works in airplane field, it allows the vehicle lateral dynamics system to be inherent unstable to improve the configuration flexibility, and to be closed-looped stable based on the yaw moment feedback. How much RSS can improve the configuration flexibility should be discussed. The pole location of the lateral dynamics system will be discussed to give a clearer observation. The state-space of 2DOF lateral dynamic model is described as (Milliken & Milliken, 1994):
(2)
ẋ = Ax + Bδ Where:
⎡ β⎤ x = ⎢ ⎥, ⎣ r⎦
⎡ C ⎤ ⎢− f ⎥ ⎢ mu ⎥ B=⎢ lC ⎥ ⎢− f f ⎥ ⎣⎢ Iz ⎦⎥
⎡ C +C l f Cf − lr Cr r ⎢ f − mu ⎢ mu2 A=⎢ l2f Cf + lr2Cr ⎢ l f Cf − lr Cr ⎢⎣ Iz Izu
(3)
⎤ 1⎥ ⎥ ⎥ ⎥ ⎥⎦
(4)
Where lr is the distance from rear axle to C.G. r is the yaw velocity. β is the side slip angle. m is the vehicle mass. Iz is the yaw inertia. u is the vehicle speed. The pole locations can be described as:
p1,2 =
(
)
(
)
Iz Cf + Cr + m l2f Cf + lr2Cr ±
Δ
2Izmu
(5)
Where: 2 Δ = ⎡⎣ Iz Cf + Cr − m l2f Cf + lr2Cr ⎤⎦
(
)
(
) )(
−4Izm⎡⎣ mu2 − l f Cf − lr Cr ⎤⎦ l f Cf − lr Cr
(
)
(6)
To show the pole distributions of inherent understeer vehicle, a front-drive passenger car's specifications will be used as Table 1 shows. In order to discuss how CCV and RSS improves the configuration flexibility, the variation of poles location when configuration changes should be discussed. Fig. 1(a) shows the case when C.G location changes. The original C.
104
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
Table 1 Conventional Passenger Car Specifications. Specification
Value
m L Iz Cf Cr lf lr
900 kg 2.54 m 1138 kg*m2 57000N/rad 42000N/rad 0.89 m 1.65 m
stable tendency. However, for AWD EV, the traction force also acts on rear tyres, which makes the stiffness of rear tyres much lower than that of conventional vehicle. Apparently, the traditional vehicle dynamics theory strictly constrains the distribution of the tyre cornering stiffness, which further constrains the traction force distribution for AWD EV. Above discussion shows how traditional understeer principle constrains the overall configuration. Actually, understeer principle also constrains the suspension adjustment, steering system adjustment, and wheel camber or toe angle adjustment, et al. The configuration problem is one of the biggest problems for AWD EV. The application of CCV and RSS could solve this problem by allowing lateral dynamics system to be inherent unstable configured
3. Hierarchical control framework of RSS
(a) C.G Location
(b) Wheelbase
Fig. 1. Poles When Specifications Change(100 km/h).
G. location is 65%:35%. The original pole locations are ( 4.1, 74), which are noted by red points. When it moves forward to 90%:10% (red solid arrows), the distance from poles to the origin becomes larger. When it moves backward to 40%:60% (red dash arrows), the system becomes overdamped, and the poles become double negative real poles. When the C.G location is 40%:60%, a positive real pole occurs, which indicates the system is unstable. The inherent understeer principle constrains the C.G location must be between 100%:0 to 40%60%. It constrains the configuration of the EV, as well as the location of the subsystem, such as battery back. Fig. 1(b) shows the case when wheelbase changes. The direction when the value increases is noted by solid arrows, and the decrease is noted by dash arrows. During the change of wheelbase (50%-150%), the system remains two conjugate complex poles, which shows the system is underdamped. Although it is stable, it still has great influence on handling transient response. For AWD EV, wheelbase is always larger than conventional vehicle, so that damping ratio becomes higher. According to the transient performance demand, the wheelbase needs to be designed short enough to obtain desired damping ratio. In Fig. 2, the red solid arrows show the stiffness increases, and the dash arrows show the stiffness decreases. When cornering stiffness of front tyres reaches 150% as origin, a positive real pole occurs, which indicates instability. When cornering stiffness of rear tyres decreases to 40% as origin, a positive real pole occurs. For traditional front-drive vehicle, the traction force makes the stiffness of front tyres lower than rear tyres, which leads to a more
In this section, the control framework of RSS will be proposed as Fig. 3 shows. The desired pole locations of the vehicle lateral dynamics system will be predefined as a function of u, which can be adjusted according to different handling demand. A pole assignment controller is used to calculate the desired yaw moment. The feedback of tyre cornering stiffness is utilized to improve the robustness against uncertainties during high acceleration maneuver condition.
3.1. Pole assignment controller against uncertainties 2DOF model is utilized to design the pole assignment controller. Assume the vehicle is operating in the low lateral acceleration condition and the tyres are operating in the linear region. Consider yaw moment provided by the independent motors M as control input, the dynamics model can be described as Eq. (7) regardless of uncertainties (Sakai & Hori, 1998):
(7)
ẋ = Ax + Bδ + CM Where:
⎡ 0⎤ ⎢ ⎥ C = ⎢ 1⎥ ⎢⎣ Iz ⎥⎦
(8)
The definition of x and B has been shown in Eq. (3). State feedback control will be applied in this paper. Consider M as feedback according to state vector x. Let F be state feedback vector and F¼[f1, f2]:
(9)
M = − Fx The closed-looped dynamics model can be described as:
ẋ = (A − CF )x + Bδ
(10)
Substitute Eqs. (4) and (8) into Eq. (10), it can be obtained:
δ
Desired Pole Location
u
(a) Front tyre Cornering Stiffness
(b) Rear tyre Cornering Stiffness
Fig. 2. Poles When Specifications Change(100 km/h).
P
Pole Controller
ur β
M
Force Distribution
T
Vehicle State Tyre Cornering Stiffness Estimation
Fig. 3. RSS Control Framework.
Fz α
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
⎤ ⎡ Cf + Cr l f Cf − lr Cr ⎢ − 1⎥ 2 mu ⎥ ⎢ mu A − CF = ⎢ ⎥ 2 2 l C l C f l C l C f − − + − f f r r f f r r 1 2⎥ ⎢ ⎥⎦ ⎢⎣ Iz Izu
105
(11)
Eq. (11) represents the characteristics matrix of closed-looped dynamics system. After manipulation, the closed-looped pole locations can be described as:
p1′ ,2′ =
(
)
(
)
Iz Cf + Cr + m l2f Cf + lr2Cr + f2 mu ±
Δ2
2Izmu
(12)
Where: 2 Δ2 = ⎡⎣ Iz Cf + Cr − m l2f Cf + lr2Cr − f2 mu⎤⎦
(
)
(
) ) (
−4Izm⎡⎣ mu2 − l f Cf − lr Cr ⎤⎦ ⎡⎣ l f Cf − lr Cr + f1⎤⎦
(
)
(13)
(aa) Longitudinal Characteristics C
By equating Eq. (12) to equation of target closed-looped pole locations, the value of f1 and f2 can be obtained and the state feedback control can be applied through Eq. (9). According to Eqs. (12) and (13), it can be seen that the closed-looped pole locations of vehicle lateral dynamics system is determined by both vehicle specifications and control parameters. This is the key concept of CCV. The dynamics behavior and stability of the vehicle not only depends on the mechanical system configuration, but also depends on the control system. If the mechanical parts of the vehicle are configured to be inherent unstable, the control system can be adjusted to obtain closed-looped stability and achieve better dynamics behavior based on pole assignment. Above calculation neglects the uncertainties during vehicle motion. Actually, some parameters vary a lot during the motion, which leads to unmodelled uncertainties, especially the tyre cornering stiffness. When the lateral acceleration is high, the tyre forces will no longer be linearly proportional to the tyre slip angle. Therefore, the cornering stiffness value will not be constant and it will vary when nonlinear property occurs. Consider the tyre cornering stiffness uncertainties
⎧ C′f = Cf + ΔCf ⎨ ⎪ ⎩ Cr′ = Cr + ΔCr
(a) Lateral Chaaracteristics Fig. 4. Magic Formula Tyre Model.
⎪
(14)
Where Cf’, Cr’ represent real cornering stiffness of front and rear tyre. ΔCf’, ΔCr’ represent additional uncertainties due to the tyre nonlinearity. The solving process of state feedback control parameters needs the accurate value of tyre cornering stiffness. Therefore, in this paper, based on the independent motor information, GPS/INS sensor information and pre-conducted tyre property tests, the real time value of tyre cornering stiffness will be estimated and feedback to the controller. 3.2. Tyre Cornering Stiffness Estimation The tyre used in the testbed was tested through the test rig. With the cooperation with Formula SAE Tire Test Consortium (Kasprzak et al., 2006), plenty of tests were conducted to obtain tyre raw data in longitudinal, lateral and combination condition. The cornering tests were run with a free-rolling tyre, while drive/ brake tests hold constant slip angle while varying slip ratio. Both tests are conducted under five loads (50 lb, 100 lb, 150 lb, 250 lb and 350 lb), five inclination angles (0°, 1°, 2°, 3° and 4°). During the tyre modeling in this paper, the data of 12 psi is used. Based on test raw data, the nonlinear characteristics of tyre force is described by Magic Formula model after fitting work:
F = D sin {C1arctan[B1X − E(B1X − arctan(B1X ))]}
(15)
Where B1 is stiffness factor. C1 is shape factor. D is peak factor. E is curvature factor. X is slip ratio or slip angle. Fig. 4 shows the pure longitudinal and lateral characteristics of the tyre according to the Magic Formula model. The combinedcondition Magic Formula model can be described as:
⎧ ⎪ Fx0 = ⎨ ⎪F = ⎩ y0
σx Fx σ σy Fy σ
(16)
Where Fx and Fy is the pure longitudinal and lateral force. Fx0 and Fy0 is the combined longitudinal and lateral force. s is the normalized combined slip ratio. sx is the normalized longitudinal slip ratio. sy is the normalized lateral slip angle:
⎧ ⎪σ = ⎪ ⎪ ⎨ σx = ⎪ ⎪ σ = ⎪ ⎩ y
σx2 + σy2 s 1+s tan α 1+s
(17)
Where s is the slip ratio. α is the lateral slip angle. According to the combined Magic Formula model, the nominal real time tyre cornering stiffness can be estimated through:
106
C0 =
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
∂Fy0 ∂α
(18)
The estimating process of C0 needs the feedback of tyre slip ratio s, slip angle α and vertical load Fz. The tyre slip ratio s can be estimated through:
⎧ ωR −u ⎪ sa = t t ⎪ ωt Rt ⎨ ⎪ u − ωt Rt s = ⎪ ⎩ b u
(19)
Where sa, sb is the tyre slip ratio during accelerating and braking condition, respectively. ωt is the rotation speed of the wheels. Rt is the tyre radius. The vehicle speed u is feedback by the GPS/INS sensor, and ωt is feedback by the independent motor information. The tyre slip angle α can be estimated through:
⎧ lr ⎪ α11 = α12 = f + β − δ ⎪ u ⎨ ⎪ lr α = α22 = β − r ⎪ ⎩ 21 u
(20)
Where α11, α12 is the lateral slip angle of front left and right tyres. α21, α22 is the lateral slip angle of rear left and rear tyres. Steering wheel angle δ is feedback by the sensor. The yaw rate r and sideslip angle β is feedback by the GPS/INS system. The vertical load of each tyre is estimated through:
⎧ ma y ⎛ hKϕf l ⎞ ⎪ F = − ma xh + ⎜⎜ + r ⎟⎟ z11 ⎪ L B ⎝ Kϕf + Kϕr Lhrf ⎠ ⎪ ⎛ ⎪ ma y hKϕf ma xh l ⎞ ⎜⎜ ⎪ Fz12 = − − + r ⎟⎟ L B ⎝ Kϕf + Kϕr Lhrf ⎠ ⎪ ⎨ ⎪ ma y ⎛ hKϕr lf ⎞ ma xh ⎜⎜ ⎟⎟ + + ⎪ Fz21 = + L B K K Lh ⎝ ϕf ⎪ rr ⎠ ϕr ⎪ ma y ⎛ hKϕr lf ⎞ ⎪ ma xh ⎪ Fz22 = L − B ⎜⎜ K + K + Lh ⎟⎟ ⎝ ϕf rr ⎠ ϕr ⎩
(21)
Where Fzii (i¼1,2) is the vertical load of four wheels, respectively. ax, ay is the longitudinal and lateral acceleration of the vehicle. h is the height of C.G. B is the track width. KΦf, KΦr is the roll stiffness of front and rear suspension. hrf, hrr is the suspension roll center of front and rear suspension. ax, ay is feedback by the GPS/INS system. The constant Magic Formula model parameters are pre-defined in the controller. However, the nominal stiffness is obtained according to the test data in the test rig, and the actual road condition varies a lot, which cannot be the same as the belt in test rig. Therefore, the road friction condition should be estimated and the tyre cornering stiffness should be adjusted according to the friction condition online. Assume the variation of cornering stiffness is in proportional to the variation of road fiction.
Cai = λC0
Hong, 2015; Lee, Nakano, & Ohori, 2015; Sado, Sakai, & Hori, 1999). The real time friction coefficient is easy to be estimated. Consider the dynamics motion equation of driving wheel:
Fd =
1 (T − Itω̇t ) Rt
(24)
Where It is the inertial of the wheel. T is the acting torque which can be easily obtained by measuring motor current, torque constant and gear ratio. Based on Eq. (24), the driving force Fd of each wheel can be estimated, and a low pass filter is utilized to eliminate noise caused by taking differential of wheel rotation speed. Then the real time value of μa can be estimated by:
μa =
Fd Fz
(25)
The vertical load of each wheel is obtained according to Eq. (21). After the value of λ is obtained, the actual cornering stiffness of each tyre can be estimated according to Eq. (22) 3.3. Desired pole locations RSS utilizes the desired pole locations of lateral dynamics system as control goal. The pole locations represent the dynamics behavior of the system. It's convenient to adjust the desired pole locations to satisfy different handling performance demand. For example, for passenger car, stability is the most important so that the desired pole locations could be designed accordingly. For military vehicle or racing car, fast response is most important so that the desired pole locations could be designed as critical damping to obtain fastest transient response. These two kinds of desired pole locations are utilized as examples as Fig. 5 shows. Fig. 5 shows the desired pole locations in ‘Stable Mode’ and ‘Agile Mode’. In ‘Stable Mode’, there are conjugate complex values arranged in straight lines, which divide 2nd and 3rd quadrants. It means the system is optimal damping ratio as 0.707. The desired vehicle handling response is assumed to be with constant optimal damping ratio during the whole speed range, which could significantly increase the handling stability. The desired pole locations in ‘Stable Mode’ can be expressed as:
pd1 =
d ( 1 ± i) u
(26)
The distance from desired pole location is in inverse proportional to vehicle speed u. Parameter d is used to adjust the desired pole location. Shadow circles represent the desired pole locations in ‘Agile Mode’. In each speed case, the desired pole locations are assumed to be one single negative real value, which indicates critical damping ratio. According to reference (Milliken & Milliken, 1994),
(22)
Where Cai is the actual cornering stiffness of each tyre.
λ=
μa μ0
(23)
Where μa is the real time friction coefficient. μ0 is the friction coefficient with the same slip ratio according to the tyre test data. Value of μ0 can be predefined as table form in the controller, and the value of μa has to be estimated online. For independent motor driven electric vehicle, a great advantage is that the torque and speed information of each wheel is observable (Kim, Hahn, &
Fig. 5. Desired Pole Locations.
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
neutralsteer vehicle has greatest handling transient response, which is also the reason why Formula 1 race car is always designed to be neutralsteer. Moreover, neutralsteer vehicle is always critical damped. The desired pole locations can be expressed as:
pd2 =
d u
107
Planetary Gearbox Drive Axle
Independent Motor
Suspension
(27)
4. Experiments validation Fig. 7. Independent Motor and Gearbox.
In this section, RSS control will be validated through experiments based on an independent-motor-driven EV testbed, which is completely designed and built by the authors. Inherent stability of the testbed vehicle will be adjusted to validate the RSS control performance in both ‘Agile Mode’ and ‘Stable Mode’. 4.1. Introduction of the testbed vehicle Figs. 6 and 7 show the pictures of testbed EV. Each wheel is independently driven by a motor, which is mounting in the vehicle body. The maximum power of each independent motor is 60 kW. With a 4-gearratio planetary gearbox, the independent motor could provide high traction force. Four drive axles are utilized to drive the wheels. The testbed vehicle is powered by LiFePo4 battery pack. The battery voltage is 400 V and the capacity is 8kWh. Each battery cell is equipped with a Battery Management System (BMS) chip to monitor the battery sates, such as State of Charge (SOC). Each motor is controlled by its own motor controller, and 4 motor controllers are controlled by a rapid ECU controller through CAN bus. The ECU controller is powered by a 400V-24V DC/DC convertor. A Differential GPS/INS system and two antennas are equipped to collect the information of position, vehicle speed, yaw velocity, side slip angle, longitudinal and lateral acceleration. The IMU is located at the front of the vehicle. Two antennas are located at both front and rear of the vehicle to obtain longer baseline. Main parameters are shown in Table 2. 4.2. J-turn experiments with inherent oversteer configuration At first, the ‘Stable Mode’ RSS control for the inherent oversteer configuration will be validated. The battery pack locates at the rear of the body, which leads to a back C.G location. The distance from front axle to the C.G location is 1 m and the distance from rear axle to the C.G location is 0.6 m. It can be calculated that the testbed vehicle is inherent oversteer. It is meaningful to show the handling behavior of an inherent oversteer vehicle under ‘Stable Mode’ control. During the experiments, the vehicle is controlled to accelerate to 80 km/h, and then a step steer angle will be input. The parameter d defined in Eq. (26) is assumed to be 120 in the experiment.
GPS Antenna Rapid ECU IMU Sensor Independent Motor
GPS Antenna
Battery Pack Fig. 6. Independent-motor-driven EV Testbed.
Table 2 Testbed EV Specification. Parameters
Value
Total Mass Maximum Speed Wheelbase Track Width Height of C.G Tire Radius
400 kg 120 km/h 1.6 m 1.3 m 0.4 m 230mm
Fig. 8(a) shows the comparison of yaw velocity and Fig. 8(b) shows the comparison of vehicle sideslip angle between uncontrolled and under control cases. According to Fig. 8(c), it can be seen that the vehicle accelerates to 80 km/h at 8 s, and then a step steer angle is input at about 8.5 s. Based on simple calculation it can be concluded that 80 km/h has exceeded the critical speed of the vehicle. After the steer angle is input, the uncontrolled vehicle loses stability and spins simultaneously. The yaw velocity of the uncontrolled vehicle increases rapidly to 1.2 rad/s and continues to increase from 9 s to 11 s. The sideslip angle of uncontrolled vehicle is also very large and continues to increase to 0.2 rad. However, the vehicle under RSS control remains stable and shows good handling behavior. The phase portrait of yaw velocity against side slip angle is plotted in Fig. 8(d). The phase portrait of uncontrolled vehicle has exceeded the stable boundary and becomes divergent. Fig. 8(e) shows the trace of C.G location, which is measured by the GPS/INS system. The red dash line shows the spin phenomenon of the uncontrolled vehicle. From 0 to about 120 m, the vehicle is accelerating to 80 km/h. After the steer angle is inputted, the vehicle spins and the radius becomes smaller due to the instability. Fig. 8(f) and (g) show the estimation results of tyre cornering stiffness, which have been smoothed to calculate the desired yaw moment. Only the front left and rear left tyre is shown. The results over the whole experiment period are shown in Fig. 8(f) to observe the accuracy of the result. From 0 to 8 s, the vertical load transfers to rear axle due to the longitudinal acceleration, hence the cornering stiffness of rear tyre is larger than that of front tyre. After the steer angle is inputted at 8.5 s, the tyre cornering stiffness decreases rapidly. After 9 s, the cornering stiffness of both front and rear tyres is around 0 which indicates the tyres are becoming saturated and the vehicle consequently loses stability and spins. Fig. 8(g) shows the result in RSS control case, the adhesion situation in RSS control case is much better, which indicates the vehicle is in better handling performance. Fig. 8(h) shows the desired yaw moment. It peaks about 600Nm, which is acceptable for the independent motors torque capability. The torque of each independent motor is calculated based on adding the torque demand TLi according to accelerate pedal and the torque demand TYi according to desired yaw moment.
108
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
(a) Comparison of Yaw Velocity
(b) Comparison of Vehicle Sideslip Angle
(c) Vehicle Speed
(d) Comparison of Phase Portrait
(e) Trace of C.G Location
(f) Tyre Cornering Stiffness Estimation Result in Uncontrolled Case
(g) Tyre Cornering Stiffness Estimation Result in RSS Control Case
(h) Desired Yaw Moment
(i) Comparison of Pole Locations Fig. 8. Experiment Results in 80 km/h J-turn.
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
TLi = ξP
(28)
Where P is the pedal location percentage. ξ is the linear coefficient. The desired yaw moment is distributed to four independent motors by simple equivalent approach:
TYi = ±
2MRt B
(29)
The influence of the steering angle of front wheels are neglected. The moment arms of each wheel's longitudinal force are assumed to be B/2 equally. Therefore, the total torque of each motor is calculated by:
Ti = TLi + TMi
(30)
In Fig. 8(i), the pole locations of vehicle lateral dynamics system on both cases are shown. The pole locations are calculated based on the estimation value of tyre cornering stiffness. The data are collected by 100 Hz sampling frequency, and only the data in cornering condition from 8 s to 11 s are shown. The red hollow points indicate the pole locations in uncontrolled case. It can be seen that a lot real positive poles occur, which indicate the unstable condition due to tyre saturation. The blue solid points indicate the closed-looped pole locations in RSS control case. The desired pole locations are ( 5.4, 75.4). During the experiment, great uncertainties occur due to the tyre nonlinearity. Therefore, the closed-looped locations can not be accurately assigned to be ( 5.4, 75.4). The pole assignment controller shows great performance against the uncertainties because of the tyre cornering stiffness online estimation. All the closed-looped pole locations are separated around ( 5.4, 75.4), despite some points are a little far because of the nonlinearity in such high-acceleration maneuver. It can be concluded that the controller successfully achieves the predefined control goal. 4.3. J-turn experiments with inherent understeer configuration ‘Agile Mode’ is supposed to improve the transient response
109
performance. Therefore, in this section the ‘Agile Mode’ RSS control will be validated with inherent understeer configuration. As above introduced, the testbed vehicle is completely built by the authors. Therefore, it is easy to do the adjustment. The original C.G location is 38%/62%. Before this experiment, the testbed vehicle's C.G location is adjusted to 60%/40% by the balance weight and suspension adjustment. Consequently, the testbed vehicle is changed to inherent understeer configuration. During the experiments, the vehicle is controlled to accelerate to 100 km/h, and then a step steer angle will be input. According to Fig. 9(a), the uncontrolled vehicle remains stable after the steer angle is input. The yaw velocity goes into the steady-state condition as about 0.4 rad/s after an overshoot. The overshoot percentage value peaks about 125%. The reason of such a high overshoot is because the vehicle speed during the experiment is as high as 100 km/h. In RSS control case, it can be seen that the overshoot and oscillation has been greatly eliminated. The time period used to go into steady state cornering condition has been greatly reduced. It can be concluded that the ‘Agile Mode’ RSS control successfully improves the transient handling performance of the vehicle. Fig. 9(b) shows the trace of C.G location in both cases. The vehicle was accelerating to 100 km/h from 0 to 180 m. After the steer angle is input, it can be seen that both the uncontrolled and RSS controlled vehicles go into the steady-state cornering condition. The radius of RSS control case is little higher than that of uncontrolled case. Fig. 9(c) shows the desired yaw moment calculated by the controller. Compared to the yaw moment demand in ‘Stable Mode’ case, it's much lower in ‘Agile Mode’ case. There is also a large overshoot occurs. Apparently, a large negative yaw moment overshoot is supposed to reduce the oscillation and overshoot of the yaw velocity. After that, the desired yaw moment remains constant as about 125Nm. Fig. 9(d) shows the pole locations estimation results on both cases. The data in cornering condition from 9.5 to 13 s are shown. There are no positive real poles occur for uncontrolled vehicle, which indicates the uncontrolled vehicle remains stable during
(a) Comparison of Yaw Velocity
(c) Desired Yaw Moment
(b) Trace of C.G Location
(d) Comparison of Pole Locations
Fig. 9. Experiment Results in 100 km/h J-turn.
110
J. Ni et al. / Control Engineering Practice 64 (2017) 102–110
the experiment. The pole locations of uncontrolled vehicle are near to the imaginary axis due to the high vehicle speed, and the damping ratio becomes very low, which indicates bad transient performance. The desired pole locations are ( 3.6,0) as a critical damped system. It can be seen that the pole assignment controller successfully controls the closed-looped pole locations to be located around the desired pole locations. Therefore, the transient handling performance of the vehicle has been improved.
5. Conclusion A novel concept-RSS is proposed for ground vehicle in this paper, which could be considered as CCV concept used in ground vehicle field. RSS and CCV combines the mechanical and control systems to form a novel overall configuration and control concept. Firstly, RSS allows the vehicle to be designed as inherent unstable to significantly improve the overall configuration flexibility. Secondly, RSS can significantly improve the handling performance of the vehicle. The basic control framework of RSS is proposed in this paper. The tyre cornering stiffness value is estimated online to improve the robustness of the controller against the uncertainties due to tyre saturation and nonlinearity. Moreover, RSS provides possibility to define different handling performance demand based on the desired pole location determination. Finally, an EV with independent motors is used to validate the proposed RSS control strategy. The experiment results indicate the great performance and efficiency of RSS control. In inherent oversteer configuration case, RSS controller successfully controls the vehicle to be stable during high-acceleration maneuver. In inherent understeer configuration case, RSS controller successfully controls the vehicle to be an almost critical damped system to improve the transient handling performance.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. U1564210).
References Anderson, M. R., Mason, W. H. An MDO approach to control configured vehicle design. american institute of aeronautics and astronautics. Paper No. 96-4058. Chan, C. C. (2008). The state of the art of electric and hybrid vehicles Jun. IEEE IEEE Transactions on Industrial Electronics, 55(6), 2237–2245 Jun. Chen, Y., Hedrick, K., & Guo, K. (2012). A novel direct yaw moment controller for inwheel motor electric motors. Vehicle System Dynamics, 51(6), 925–942. Doumiati, M., Victorino, A. C., & Charara, A. (2011). Onboard real-time estimation of vehicle lateral tire-road forces and sideslip angle. IEEE/ASME Transaction on Mechatronics., 16(4), 601–614. Esmailzadeh, E., Goodarzi, A., & Vossoughi, G. R. (2003). Optimal yaw moment control law for improved vehicle handling. Mechatronics, 13, 659–675. Geng, C., Mostefai, L., & Hori, Y. (2009). Direct yaw moment control of an in-wheel motored electric vehicle based on body slip angle fuzzy observer. IEEE Transactions on Industrial Electronics, 56(5), 1411–1419. Goodarzi, A., & Mohammadi, M. (2014). Stability enhancement and fuel economy of the 4 wheel drive hybrid electric vehicles by optimal tyre force distribution.
Vehicle System Dynamics, 52(4), 539–561. Hu, J., Yin, D., & Hori, Y. (2011). Fault-tolerant traction control of electric vehicles. Control Engineering Practice, 19, 204–213. Ivanov, V., Savitski, D., & Shyrokau, B. (2015). A survey of traction control and antilock braking systems of full electric vehicles with individually controlled electric motors. IEEE Transaction on Vehicle Technolology, 64(9), 3878–3896. Jalali, M., Khajepur, A., Chen, S., et al. (2016). Integrated stability and traction control for electric vehicles using model predictive control. Control Engineering Practice, 54, 256–266. Kasprzak, M. Edward and D. Gentz. The Formula SAE Tire Test Consortium-Tire Testing and Data Handling. SAE Technical Paper: 2006-01-3606. Kim, C., Hahn, J., & Hong, K. (2015). Estimation of tire-road friction based on onboard 6-dof acceleration measurement. IEEE Trans. Veh. Technol., 64(8), 3368–3377. Lee, S., Nakano, K., & Ohori, M. (2015). On-board identification of tyre cornering stiffness using dual kalman filter and GPS. Vehicle System Dynamics, 53(4), 437–448. Milliken, W. F., & Milliken, D. L. (1994). Race Car Vehicle Dynamics. SAE: Warren Michigan. Nagai, M., Hirano, Y., & Yamanaka, S. (1997). Integrated control of active rear wheel steering and direct yaw moment control. Vehicle System Dynamics, 27, 357–370. Nam, K., Fujimoto, H., & Hori, Y. (2012). Lateral stability control of in-wheel-motordriven electric vehicles based on sideslip angle estimation using lateral tire force sensors. IEEE Transaction on Vehicles Technology, 61(5), 1972–1984. Nam, K., Fujimoto, H., & Hori, Y. (2014). Advanced motion control of electric vehicles based on robust lateral tire force control via active front steer. IEEE/ASME Transaction on Mechatronics, 19(1), 289–299. Ni, J., & Hu, J. (2016a). Handling performance control for hybrid 8-wheel-drive vehicle and simulation verification. Vehicle System Dynamics, 54(8), 1098–1119. Ni, J., & Hu, J. (2016b). Dynamic modeling and experimental validation of a skid steered wheeled mobile robot on pivotal steer condition. Proceedings of the Institution of Mechanical Engineering Part D: The Journal of Automobile Engineering. http://dx.doi.org/10.1177/0954407016652760. Ni, J., & Hu, J. (2017). Dynamics control of autonomous vehicle at driving limits and experiment on an autonomous Formula racing car. Mechanical Systems and Signal Processing, 90, 154–174. Ni, J., Hu, J., & Li, X. (2015). Dynamic modeling, validation and handling performance analysis of skid steered vehicle. Proceedings of the Institution of Mechanical Engineering Part D: The Journal of Automobile Engineering, 232, 1–13. Sado, H., Sakai, S., & Hori, Y. (1999). Road condition estimation for traction control in electric vehicle. IEEE International Symposium on Industrial Electronics, 2, 973–978. S. Sakai, Y. Hori. Robustified model matching control for motion control of electric vehicle. IEEE AMC’98, 1998. Shibahata, Y., Shimada, K., & Tomari, T. (1993). Improvement of vehicle maneuverability by direct yaw moment control. Vehicle System Dynamics, 22, 465–481. Shuai, Z., Zhang, H., Wang, J., et al. (2014a). Lateral motion control for four-wheelindependent-drive electric vehicles using optimal torque allocation and dynamic message priority scheduling. Control Engineering Practice, 24, 55–66. Shuai, Z., Zhang, H., Wang, J., Li, J., & Ouyang, M. (2014b). Combined AFS and DYC control of four-wheel-indepdent-drive electric vehicles over CAN network with time-varying delays. IEEE Transaction on Vehicle Technology, 63(2), 591–602. Wang, R., Zhang, H., & Wang, J. (2014). Linear parameter-varying controller design for four wheel independently-actuated electric ground vehicles with active steering systems. IEEE Transactions on Control Systems Technology, 22(4), 1281–1296. Wang, Y., Fujimoto, H., & Hara, S. (2016). Torque distribution-based range extension control system for longitudinal motion of electric vehicles by LTI modeling with generalized frequency variable. IEEE/ASME Transaction on Mechatronics., 21(1), 443–452. Wong, A., Kasinathan, D., Khajepur, A., et al. (2016). Integrated torque vectoring and power management framework for electric vehicles. Control Engineering Practice, 48, 22–36. Xiong, L., Yu, Z. P., & Wang, Y. (2012). Vehicle dynamics control of four in-wheel motor drive electric vehicle using gain scheduling based on tyre cornering stiffness estimation. Vehicle System Dynamics, 50, 831–846. Zhang, H., & Wang, J. (2016). Vehicle lateral dynamics control through afs/dyc and robust gain-scheduling approach. IEEE Transaction on Vehicle Technolology, 65 (1), 489–494. Zhang, H., Zhang, G., & Wang, J. (2016). H1 observer design for LPV systems with uncertain measurements on scheduling variables: application to an electric ground vehicle. IEEE/ASME Transaction on Mechatronics., vol. 21(3), 1659–1670.