Keywords

1 Introduction

Electronic Stability Control (ESC) has been introduced to prevent cars from losing driveability [1,2,3,4] and vehicle (or body) sideslip angle is of paramount importance in such algorithm [5,6,7]. In this paper the estimation performances of sideslip estimators are outlined at first [8,9,10]. A yaw rate based stability control is then presented and the results outlined. Virtual methods provide powerful tools to speed up the development process following the V-model approach [11, 12]; in this work such methodology has been applied for the evaluation of both estimation and control achievements. This paper outlines at first an overview of the system, development environments and use cases considered for this activity. Then the adopted estimation, control strategies and dedicated KPIs are introduced for evaluation of the performances. A comparison between results on different development environments is illustrated. Finally, the conclusions portrays the main outcomes and summary of the achieved results.

2 System Overview, Virtual Environments and Use Cases

This work has been accomplished following the V-model approach by leveraging the information from several development environments with decreasing virtualization levels (Fig. 1). Simulation activities have been performed in a completely virtual Model-In-the-Loop (MIL) environment while Driver-Hardware-In-the-Loop (DHIL) tests on a COMPACT Simulator by VI-grade [13]. The virtual environment development results of this activity have been achieved based on a vehicle model provided by VI-grade CarRealTime software [14]. Vehicle activities have been carried out on a AWD fully electric vehicle equipped with Brembo braking system [15,16,17] portrayed in Fig. 1. The designated use case for this activity is the Lane Change maneuver following test protocol as in ISO 3888-1 [18].

Fig. 1.
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(Left) Brembo braking system. (Right) V-model diagram.

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Fig. 2.
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(Left) Example of a vehicle test during a Lane Change manouver (ISO 3888-1). (Right) KPI to assess body slip angle estimation performances (VEH = vehicle, GT = Ground-Truth, m = mean, std = standard deviation).

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3 Vehicle (or Body) Sideslip Angle Estimation

Vehicle (or body) sideslip angle is of great importance in the development of stability control algorithms. In this work, the following body sideslip angle (\(\beta \)) estimators have been adopted and compared: BSAE presented in [8, 9] and BSAA outlined in [10] and results are illustrated in Fig. 2. Main idea is to confront such methods in order to assess the best appropriate solution for the control purposes and to determine whether consistent results can be achieved in environments with different level of virtualization. To evaluate the estimation performances, the EAM (Error At Maximum) indicator delineated in (1) has been adopted: it focuses on the relative error between the estimated sideslip angle at the time instant \(\overline{t}\) when the ground-truth (GT) signal is at its maximum value; ground-truth signal is provided by VI-grade CarRealTime software on MIL and DHIL environments, Kistler Correvit S-Motion optical sensor on vehicle. Although this is not a complete evaluation of the estimation behaviour and features of the algorithms, it provides a concise assessment of the estimation outcomes during several repetitions of lane-change maneuvers where the maximum sideslip angle (\(\beta \)) is a major concern. The closer the EAM is to the unit value 1, the better the estimation performances. Based on this criteria, BSAA outperforms BSAE in terms of both mean value and standard deviation in all environments; thus, it is the most suitable solution for the purposes of stability control. Furthermore, this analysis shows coherent results among different development environments demostrating the effectiveness of using a virtualization approach to anticipate road testing activities.

$$\begin{aligned} EAM [-] = \frac{BSAx(\overline{t})}{GT(\overline{t})}, x=\{E,A\} \end{aligned}$$
(1)
Fig. 3.
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Yaw rate based stability control scheme where \(\beta \) = body sideslip angle, ref = reference, r = yawrate, \(\lambda \) = wheel slip, \(F_b\) = brake force, X = {Front,Rear}, Y = {Left,Right}

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4 Yaw Rate Based Stability Control

The stability control adopted for this activity is portrayed in Fig. 3 where both the wheel slip controller and the yaw rate controller are based on a PID algorithm enhanced with additional non linear contributions. The methodologies behind these logics are similar to the ones described in [19, 20] and [21, 22] respectively. The reference generator is developed starting from the definition of maximum admissible yaw rate as in [23]. The vehicle state observer (VSO) provides the information required by the stability control but not included among the available measurements; the estimators of the sideslip angle (\(\beta \)) presented in the previous section are included in this block. The stability control exploits the benefits of the independent wheels braking system generating a reference brake force for each corner (\(F_{b,XY}^{ref}\)) in order to enhance performance and safety.

The tuning of the yaw rate controller is the main goal of this work. For this purpose, four different set of parameters have been defined based on an increasing degree of control intervention: standard control intervention (SD), less invasive control intervention (LC), more invasive control intervention (MC) and stability control deactivated (OFF). In order to take into account environments with the variability of the driver’s inputs only, driving simulator (DHIL) environment and vehicle testing have been considered. To carry out this analysis, the following objective criteria have been applied: (1) vehicle (body) sideslip angle peak defined as the maximum absolute value of the measured angle during the maneuver; this criteria focuses on the vehicle lateral stability; (2) yaw rate peak defined as the maximum absolute value of the yaw rate during the maneuver; this criteria highlights the vehicle steerability; (3) speed loss ratio defined as the ratio between the minimum speed within the maneuver and the speed at the beginning of maneuver, this criteria aims to measure the level of the brake intervention. Since vehicle activities have been carried out on a mixed dry and wet/dry condition, DHIL manouvers have been performed using 2 grip levels (1, 0.8) to take into account the tire-road grip (mu) variability during road testing. As outlined in Fig. 4, results follow the expected behaviour: increasing the degree of control leads to decrease both body sideslip angle and yaw rate peaks, while speed loss ratio tends to increase. In terms of comparison between development environments, the results show a consistent trend between driving simulator (DHIL) and the vehicle.

Fig. 4.
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Stability control results: comparison between vehicle data and DHIL tests (mu refers to the tire-road grip) during Lane Change manouvers (ISO 3888-1).

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5 Conclusions

In this work the tuning and validation of a yaw rate based stability control has been described. The strategy have been carried out based on virtual methods following the V-model approach which has been used to assess the most suitable estimation algorithm and parameter sets to be tested on vehicle. Despite a significant effort is required to implement realistic virtual environments and define representative KPIs to evaluate the outcomes, the results have shown that virtual methods provide useful information in order to support and speed up the development of vehicle estimation and control strategies prior to any vehicle activity leading to significant time and cost reduction.