Integrated chassis control with AFS, ARS and ESC under lateral force constraint on AFS
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This paper presents an integrated chassis control with active front steering (AFS), active rear steering (ARS) and electronic stability control (ESC) under lateral force constraint on front wheels. The control yaw moment is calculated using sliding mode control. A weighted pseudo-inverse-based control allocation (WPCA) is used for yaw moment distribution. On low-friction road, AFS has little effect on control performance since the lateral tire forces of front wheels are easily saturated. To overcome the problem, the lateral force generated by AFS is limited to its maximum, and the braking force of ESC and the angle of ARS, obtained from WPCA, are applied. To check the effectiveness of the proposed method, simulation was performed on the vehicle simulation package, CarSim. From simulation, it was verified that the proposed method can enhance the maneuverability and lateral stability, if the lateral forces on front wheels are saturated.
KeywordsIntegrated chassis control Active front steering Active rear steering Electronic stability control Lateral force saturation
List of symbols
Lateral acceleration (m/s2)
- Cf, Cr
Cornering stiffness of front/rear tires (N/rad)
- Fyf, Fyr
Lateral tire forces of front and rear wheels (N)
- Fyfc, Fyrc
Lateral tire force generated by AFS and ARS (N)
Longitudinal tire forces generated by ESC (N)
Gravitational constant (= 9.81 m/s2)
- H, D
Effectiveness matrix in WPCA
Yaw moment of inertial (kg·m2)
Gain in sliding mode control
Pressure–force constant (N·m/MPa)
- lf, lr
Distance from C.G. to front and rear axles (m)
Vehicle total mass (kg)
- ΔMB, ΔMN
Control yaw moment (Nm)
Brake pressure of ESC (MPa)
- x, y
Vector of tire forces in WPCA
Radius of a wheel (m)
- tf, tr
Track width of front and rear axles (m)
- vx, vy
Longitudinal and lateral velocities of a vehicle (m/s)
Vehicle speed (m/s)
- W, V
Weighting matrix in WPCA
- αf, αr
Tire slip angles of front and rear wheels (rad)
Side-slip angle (rad)
Weight on a particular tire force in WPCA
- δf, δr
Front and rear steering angles (rad)
Corrective steering angle of AFS (rad)
- γ, γd
Real and reference yaw rates (rad/s)
Tuning parameters on yaw rate error and side-slip angle
Tire–road friction coefficient
Vector of variable weights in WPCA
Generally, vehicle stability control (VSC) is designed to enhance maneuverability and lateral stability of a vehicle . The maneuverability means that a vehicle follows the driver’s intention. Driver’s intention is represented by the reference yaw rate, algebraically calculated from the steering wheel angle. So, vehicle stability control improves the maneuverability by making the error between the real and reference yaw rates zero. Lateral stability means that the vehicle has small side-slip angle because the large side-slip angle stands for loss of stability. So, vehicle stability control maintains the lateral stability by reducing the side-slip angle within a certain level. Generally, the side-slip angle is restricted within 3° by vehicle stability control .
Vehicle stability controller has a two-level control structure: upper- and lower-level controllers . The upper-level controller calculates control yaw moment, needed to stabilize a vehicle, using vehicle models such as 2-DOF bicycle model or 3-DOF planar model. Controller design methodologies such as LQ optimal control, sliding mode control and fuzzy control have been applied to it [3, 4, 5]. Lower-level controller determines the tire forces of several actuators, needed to generate the control yaw moment calculated from the upper-level controller. This is called yaw moment distribution .
In the lower-level controller, several actuators can be used for yaw moment distribution. The most representative actuator is electronic stability control (ESC), developed in the early 1990s . ESC uses braking in generating the control yaw moment. ESC has known to be effective for vehicle stability, since it has been developed and commercialized. As a result, installation of ESC became mandatory in the late 2000s. Other devices used for yaw moment generation are active front steering (AFS), active rear steering (ARS), and torque vectoring devices (TVD) [7, 8, 9]. These devices have been adopted solely or together with ESC. If there are multiple actuators for yaw moment generation, it is called integrated chassis control (ICC). In this paper, the integrated chassis control with AFS, ARS and ESC is considered .
The lower-level controller of ICC should determine the corrective steering angles of AFS and ARS and the braking force of ESC to generate the control yaw moment. Up to date, several methods have been proposed for yaw moment distribution. Typical method is to apply optimization algorithm to determine the tire forces generated by ESC, AFS and ARS. The unified chassis control (UCC) with optimum distribution was proposed for yaw moment distribution . In the method, the quadratic objective function was set to minimize the tire forces of ESC. The equilibrium condition between the control yaw moment and the tire forces was set as the equality constraint. The friction circle on tire forces was set as the inequality constraint. The constrained quadratic programming problem was solved algebraically by applying KKT optimality condition. Another optimization-based method for yaw moment distribution is the weighted pseudo-inverse-based control allocation (WPCA) [1, 10, 12]. In WPCA, the quadratic objective function with tire forces generated by ESC, AFS and ARS was set. The equilibrium condition between the control yaw moment and the tire forces was set as the equality constraint. This problem is the quadratic programming with single equality constraint, which can be algebraically solved. In this paper, the weighted pseudo-inverse-based control allocation (WPCA) is adopted for yaw moment distribution. With the variable weights of WPCA, it is easy to represent several actuator configurations used for yaw moment distribution [1, 10].
When applying WPCA for yaw moment distribution, the smaller weight on AFS makes ICC use only AFS. If only AFS is used for yaw moment distribution, the smaller speed reduction and the enhanced ride comfort can be achieved because the braking of ESC is not used . However, the sole use of AFS can make the lateral tire force of front wheels easily saturated because the corrective steering angle of AFS is added to that of driver. Under the situation, AFS cannot generate the lateral tire force needed to generate the control yaw moment . So, it is necessary to limit the lateral tire force of AFS, and to compensate the loss of the control yaw moment using ESC and ARS.
For the purpose, several researches have done up to date. Yim proposed the WPCA-based scheme to cope with the saturation of lateral tire forces on front wheels . In the other research, Yim proposed the method by combining the UCC and WPCA to cope with the problem . In these researches, ESC and AFS were used as an actuator to generate the control yaw moment. ARS or TVD has not been used for yaw moment distribution up to date under that condition.
Recent advances of ARS can make the performance of the vehicle stability control be enhanced . Especially, the lateral stability, represented by the side-slip angle, can be drastically improved by ARS. So, ARS is adopted as an actuator to generate the control yaw moment in this paper. Nagai et al. proposed ICC with ARS and braking-based DYC . Yim proposed the ICC with ESC, AFS and ARS [10, 17, 18]. However, there have been little researches on ICC with ESC, AFS and ARS under the saturation of lateral tire forces on front wheels.
This paper proposes a method which copes with the saturation of lateral tire forces on front wheels, caused by the excessive application of AFS. Contrary to the previous works, the ICC proposed in this paper uses ESC, AFS and ARS. The proposed method compensates the loss of the control yaw moment, caused by the saturated lateral tire force of AFS, by re-applying WPCA with ESC and ARS if the lateral tire forces of front wheels are saturated. Since WPCA algebraically calculates the optimum solution, it is easy to implement WPCA in real vehicles.
This paper is organized as follows: Sect. 2 presents the design procedure of the integrated chassis controller. New method to compensate the saturated lateral tire forces of front wheels is proposed in Sect. 3. To validate the proposed method, simulation is performed in Sect. 4. Finally, Sect. 5 concludes this paper.
2 Design of the integrated chassis controller
In this section, the integrated chassis controller with ESC, AFS, and ARS is designed. Direct yaw moment control and WPCA are adopted for control yaw moment generation and yaw moment distribution in the upper- and lower-level controllers, respectively. Variable weights in WPCA are defined for several purposes.
2.1 Design of an upper-level controller
2.2 Design of a lower-level controller
Once the control yaw moment ΔMB is computed in the upper-level controller, it should be distributed into braking forces of ESC and steering angles of AFS and ARS. In this paper, a WPCA is adopted to distribute the control yaw moment into the tire forces generated by ESC, AFS and ARS .
In Eq. (10), the vertical tire forces should be estimated because these cannot be easily measured. The vertical tire forces can be estimated with the longitudinal and lateral accelerations, as given in the previous work .
In Eq. (10), ρ is the vector of fictitious variable weights ρi. In this paper, the variable weight ρ is used for several purposes [1, 10]. Firstly, ρ is used to capture several actuator combinations such as ESC, AFS, ARS, ESC + AFS, ESC + ARS, ESC + AFS + ARS, and AFS + ARS. Secondly, ρ is used to limit excessive tire slip ratio and slip angle when ESC, AFS and ARS are applied. Thirdly, ρ is used to improve the maneuverability and lateral stability with simulation based tuning. The detailed roles of ρ will be explained later.
In this paper, four actuator configurations, ESC, AFS, ARS and ESC + ARS, are considered. For these actuator combinations, a particular constraint on yaw moment distribution is needed. For example, if only ESC is available and the control yaw moment is positive, then the longitudinal braking forces of left wheels, i.e., Fx1 and Fx3 in Fig. 2, should be generated and those of right wheels, i.e., Fx2 and Fx4, should not be generated.
To capture these actuator configurations, the vector of variable weights, ρ, in Eq. (10) is introduced [1, 10]. If the variable weight ρi in ρ is decreased, then the corresponding tire force Fxi or Fyfc or Fyrc is increased, and vice versa. Using this fact, the distribution scheme can be set for each actuator combination. Let us assume that all the variable weights in ρ are set to 1e−4. In this situation, if only ESC is available and the control yaw moment ΔMB is positive, the braking pressure can be applied to the left wheels. For this purpose, ρ1, ρ2, ρ4 and ρ6 should be set to a high value, e.g., 1, as shown in Eq. (12). As a result of this setting, only Fx1 and Fx3 can be generated from WPCA. Following the fact, the sets of variable weights for actuator configurations, ESC, AFS, ARS and ESC + ARS, can be determined, as given from (12) to (15) .
In the actuator configuration of ESC + ARS, the variable weights, ε1, ε2 and ε3, correspond to the use of ARS and ESC on the front and rear wheels, respectively. If a particular variable weight increases, then the corresponding actuator will be less used. For instance, if ε1 increases, lesser AFS will be used for yaw moment distribution.
2.3 Determination of corrective angles of AFS and ARS
3 Compensation of the saturated lateral tire forces of front wheels
Parameters and values of a small-sized SUV model in CarSim
1302.1 kg m2
v x i
150 N m/MPa
70 N m/MPa
To compensate the saturated lateral tire force of the front wheels, ESC and ARS are used. Regarding the actuator configuration, four cases, CASE1, CASE2, CASE3, and CASE4, are considered in simulation. CASE1 uses only AFS for yaw moment distribution without considering the saturation of the front lateral tire forces. CASE2, CASE 3 and CASE4 use ESC, ARS and ESC + ARS for yaw moment distribution with considering the saturation of the front lateral tire forces, respectively. WPCA is used for CASE1, and CWPCA is used for CASE2, CASE3 and CASE4. Simulation with four cases can make it clear which actuator combination is the best for yaw moment distribution under the saturation of the front lateral tire forces.
Summary of the simulation results for all cases
Maximum |γ − γd| (°/s)
Maximum |β| (°)
Minimum vx (km/h)
As shown in Fig. 5, the controlled vehicles did not lose its stability. Coordinated control with CASE2, CASE3 and CASE4, considering the saturation of the front lateral tire forces, gave satisfactory results in terms of the yaw rate error and side-slip angle. Especially, the side-slip angles were significantly reduced by the proposed method. This is caused by the fact that the front lateral tire forces were not saturated by AFS, and that ESC and ARS compensated the loss of control yaw moment. As shown in Fig. 7, the front lateral tire forces generated by AFS were limited to its maximum Fyf,max by CWPCA for CASE2, CASE3, and CASE4. As a result, the corrective steering angles of AFS were reduced, as shown in Fig. 6a. Every case with CWPCA has nearly identical yaw rate errors angles and side-slip angles, as given in Table 2. However, the vehicle speeds are different from one another, as shown in Fig. 5c. This is caused by the fact that the brake pressures of ESC are applied in CASE2 and CASE4, as shown in Fig. 6c. On the other hand, CASE3 shows the largest vehicle speed because there were no braking pressures of ESC by virtue of ARS. So, CASE3 shows the best performance in yaw moment distribution. The effect of the coordination between ESC and ARS is clear as given in Fig. 6b, c. In other words, the ARS angle of CASE4 is smaller than that of CASE3 by virtue of the braking pressure of ESC. If one tries to maintain the vehicle speed under the control, it is desirable to use CASE 3. On the other hand, if one tries to reduce the ARS angle, it is desirable to use CASE4.
In this paper, the integrated chassis control with ESC, AFS and ARS, designed to compensate the saturated lateral tire force of front wheels with WPCA, was proposed. With WPCA, the control yaw moment, calculated from the upper-level controller, was distributed into the tire forces generated by ESC, AFS and ARS. Several actuator configurations are represented by the variable weights of WPCA. Especially, only AFS is adopted for enhanced ride comfort and smaller speed reduction. Constrained WPCA was proposed to cope with the saturated lateral tire force of front wheels caused by excessive steering. ESC and ARS were used to compensate the loss of the control yaw moment in CWPCA. From simulation results, it was checked that the proposed method can limit the corrective steering angle of AFS, and increase the braking force of ESC or steering angle of ARS using CWPCA.
This study was supported by Seoul National University of Science and Technology.
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