Lateral Vehicle Dynamics Control Based on Tyre ... - Semantic Scholar
52nd IEEE Conference on Decision and Control December 10-13, 2013. Florence, Italy
Lateral Vehicle Dynamics Control Based On Tyre Utilization Coefficients and Tyre Force Measurements Anil Kunnappillil Madhusudhanan, Matteo Corno, and Edward Holweg Typical VDC
Abstract— In assessing and controlling vehicle dynamics, tyre forces are the most important variables as they are the only point of interaction with the road. Estimating tyre forces is difficult for their nonlinear characteristics and most vehicle dynamics controllers are therefore based on indirect measurements as yaw rate. With the invention of tyre force sensors, direct measurement of tyre forces is possible. In this work, a tyre force based lateral vehicle dynamics controller is proposed. The controller, applying an independent steering correction, controls the lateral tyre forces so to better distribute the force on the four tyres. This is obtained equating the tyre utilization coefficients. The proposed controller is tested in a simulation environment using CarSim and Simulink.
I. INTRODUCTION Vehicle safety requirements are increasing day by day in order to reduce the number of accidents [1]. Traffic rules alone cannot guarantee safe driving, especially when an average skilled driver tries to push the vehicle close to its physical limits unknowingly. For example, consider a scenario where the vehicle is going at a high speed and an average skilled driver applies a high steering angle. The vehicle could spin out of control and possibly meet with an accident. To avoid such situations from happening, Vehicle Dynamics Controllers (VDC) are used [2]–[5]. The literature on VDC is rich and diverse. Most of the VDC’s are kinematic based. Sensors measure inertial variables (accelerations and yaw rates) and the controller acts (according to different actuation schemes) based on those variables. Lateral stability of a vehicle is typically measured in terms of yaw rate deviation from a reference value [6]–[8] or in terms of vehicle side slip [9]. The yaw rate based approaches are limited because a reasonable yaw rate reference model requires the knowledge of the surface. Side-slip based approaches are more robust to changes of surface, but a reliable, robust and cost-effective estimation of the side-slip is still an open problem [10], [11]. The recent introduction of tyre force sensing technology [12] has opened a third way: tyre force based control, Fig. 1. See page 2 of [12] for more details on the available force measurement. This paradigm avoids the need of complex estimation algorithms and at the same time directly accounts A. K. Madhusudhanan is with the Intelligent Automotive Systems Group, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands [email protected] M. Corno is with the Dipartimento di Elettronica e Informazione, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy
[email protected] E. Holweg is with the Intelligent Automotive Systems Group, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands, and also with the SKF Automotive Division, Nieuwegein 3430 DT, The Netherlands [email protected]
978-1-4673-5716-6/13/$31.00 ©2013 IEEE
Tyre force based VDC
Actuators
Driver inputs
Actuators
Control
Tyre forces
Control
Tyre force ref
ɺ ψ
ψɺ ref
Fig. 1.
Typical vs Tyre force based VDC
for road conditions. Tyre force based control has proven successful in longitudinal vehicle dynamics control [12]– [14]; this paper proposes an investigation of the potential of force based lateral vehicle control. In particular, the benefits of tyre force sensing coupled with 4 Wheel Steering (4WS) are explored. The advantages of 4WS in the context of more classical sensing architectures have been documented in the past. In [15], a feed-forward control 4WS is proposed to steer the rear wheels in the same direction as the front ones to reduce the delay in the vehicle lateral acceleration. In [16], a feedback scheme is proposed where rear wheel steer proportional to the vehicle yaw rate is used in order to modify the vehicle dynamics for improving the vehicle stability. In [17], rear wheel steering is used in order to keep the vehicle side slip angle close to zero. In [18], toe-in angles of rear wheels are controlled to improve yaw stability. In this work the potential of 4WS and tyre force measurement is investigated. A lateral vehicle dynamics control system is presented; the underlining idea is that of improving vehicle stability by equalizing the tyre utilization coefficients (TUC). TUC is an indication of how much the tyre is engaged with respect to the maximum force it can exert. A four wheeled vehicle equipped with independent steering and tyre force sensors is assumed. The vehicle model used is a multibody model with 15 mechanical degrees of freedom (DOF) from CarSim simulation package [19]. The CarSim model uses a nonlinear tyre model with dependency on slip, load, and camber. See the vehicle configuration Ind Ind: B-Class, Hatchback: No ABS in CarSim for more details about the vehicle model. The basic principle used is to control the TUCs such that on each axle, equal TUCs are utilized from the respective left and right tyre. By doing so, saturation during cornering can be avoided or delayed,
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tyre αF L and the front right tyre αF R are also shown. In this set of simulations, the left tyre is the inner tyre and the radius of curvature is 100 m. 0.8
Fy2 Fx2 + Fx2max Fy2max
Friction ellipse
Fig. 2.
k
Fxmax
Definition of tyre utilization coefficient k using friction ellipse
=
Fx2 Fx2max
+
Fy2 Fy2max
, where 0
Lateral Vehicle Dynamics Control Based On Tyre Utilization Coefficients and Tyre Force Measurements Anil Kunnappillil Madhusudhanan, Matteo Corno, and Edward Holweg Typical VDC
Abstract— In assessing and controlling vehicle dynamics, tyre forces are the most important variables as they are the only point of interaction with the road. Estimating tyre forces is difficult for their nonlinear characteristics and most vehicle dynamics controllers are therefore based on indirect measurements as yaw rate. With the invention of tyre force sensors, direct measurement of tyre forces is possible. In this work, a tyre force based lateral vehicle dynamics controller is proposed. The controller, applying an independent steering correction, controls the lateral tyre forces so to better distribute the force on the four tyres. This is obtained equating the tyre utilization coefficients. The proposed controller is tested in a simulation environment using CarSim and Simulink.
I. INTRODUCTION Vehicle safety requirements are increasing day by day in order to reduce the number of accidents [1]. Traffic rules alone cannot guarantee safe driving, especially when an average skilled driver tries to push the vehicle close to its physical limits unknowingly. For example, consider a scenario where the vehicle is going at a high speed and an average skilled driver applies a high steering angle. The vehicle could spin out of control and possibly meet with an accident. To avoid such situations from happening, Vehicle Dynamics Controllers (VDC) are used [2]–[5]. The literature on VDC is rich and diverse. Most of the VDC’s are kinematic based. Sensors measure inertial variables (accelerations and yaw rates) and the controller acts (according to different actuation schemes) based on those variables. Lateral stability of a vehicle is typically measured in terms of yaw rate deviation from a reference value [6]–[8] or in terms of vehicle side slip [9]. The yaw rate based approaches are limited because a reasonable yaw rate reference model requires the knowledge of the surface. Side-slip based approaches are more robust to changes of surface, but a reliable, robust and cost-effective estimation of the side-slip is still an open problem [10], [11]. The recent introduction of tyre force sensing technology [12] has opened a third way: tyre force based control, Fig. 1. See page 2 of [12] for more details on the available force measurement. This paradigm avoids the need of complex estimation algorithms and at the same time directly accounts A. K. Madhusudhanan is with the Intelligent Automotive Systems Group, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands [email protected] M. Corno is with the Dipartimento di Elettronica e Informazione, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy
[email protected] E. Holweg is with the Intelligent Automotive Systems Group, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands, and also with the SKF Automotive Division, Nieuwegein 3430 DT, The Netherlands [email protected]
978-1-4673-5716-6/13/$31.00 ©2013 IEEE
Tyre force based VDC
Actuators
Driver inputs
Actuators
Control
Tyre forces
Control
Tyre force ref
ɺ ψ
ψɺ ref
Fig. 1.
Typical vs Tyre force based VDC
for road conditions. Tyre force based control has proven successful in longitudinal vehicle dynamics control [12]– [14]; this paper proposes an investigation of the potential of force based lateral vehicle control. In particular, the benefits of tyre force sensing coupled with 4 Wheel Steering (4WS) are explored. The advantages of 4WS in the context of more classical sensing architectures have been documented in the past. In [15], a feed-forward control 4WS is proposed to steer the rear wheels in the same direction as the front ones to reduce the delay in the vehicle lateral acceleration. In [16], a feedback scheme is proposed where rear wheel steer proportional to the vehicle yaw rate is used in order to modify the vehicle dynamics for improving the vehicle stability. In [17], rear wheel steering is used in order to keep the vehicle side slip angle close to zero. In [18], toe-in angles of rear wheels are controlled to improve yaw stability. In this work the potential of 4WS and tyre force measurement is investigated. A lateral vehicle dynamics control system is presented; the underlining idea is that of improving vehicle stability by equalizing the tyre utilization coefficients (TUC). TUC is an indication of how much the tyre is engaged with respect to the maximum force it can exert. A four wheeled vehicle equipped with independent steering and tyre force sensors is assumed. The vehicle model used is a multibody model with 15 mechanical degrees of freedom (DOF) from CarSim simulation package [19]. The CarSim model uses a nonlinear tyre model with dependency on slip, load, and camber. See the vehicle configuration Ind Ind: B-Class, Hatchback: No ABS in CarSim for more details about the vehicle model. The basic principle used is to control the TUCs such that on each axle, equal TUCs are utilized from the respective left and right tyre. By doing so, saturation during cornering can be avoided or delayed,
2816
tyre αF L and the front right tyre αF R are also shown. In this set of simulations, the left tyre is the inner tyre and the radius of curvature is 100 m. 0.8
Fy2 Fx2 + Fx2max Fy2max
Friction ellipse
Fig. 2.
k
Fxmax
Definition of tyre utilization coefficient k using friction ellipse
=
Fx2 Fx2max
+
Fy2 Fy2max
, where 0
