Method, arrangement and system for estimating vehicle cornering stiffness
A method, arrangement and system are described for estimating one or more vehicle cornering stiffness parameters (c f , c r ) in a linear vehicle operating region. The method includes reading sensor data representative of at least vehicle ( 1 ) longitudinal velocity (v x ), vehicle lateral acceleration (a y ), vehicle yaw rate (ω z ) and vehicle steering angle (δ), determining from the read sensor data if the cornering stiffness parameters (c f , c r ) are observable, and if so providing an estimate of the cornering stiffness parameters (c f , c r ) using a bicycle model that includes a model of tire relaxation dynamics.
1. A method for estimating one or more vehicle cornering stiffness parameters in a linear operating region of a vehicle, the method comprising:
retrieving from a vehicle longitudinal velocity sensor, a vehicle lateral acceleration sensor, a vehicle yaw rate sensor, and a vehicle steering angle sensor data representative of at least a vehicle longitudinal velocity, a vehicle lateral acceleration, a vehicle yaw rate, and a vehicle steering angle;
sending the sensor data representative of at least the vehicle longitudinal velocity, the vehicle lateral acceleration, the vehicle yaw rate and the vehicle steering angle to a control system;
determining, by the control system, from the sensor data when vehicle cornering stiffness parameters are observable; and
when vehicle cornering stiffness parameters are observable, generating, by the control system, a cornering stiffness parameter signal based on an estimate of the cornering stiffness parameters provided using a bicycle model that includes a model of tire relaxation dynamics describing the delay between when a slip angle is introduced and when a resulting lateral force reaches a steady state value.
2. The method according to claim 1 wherein determining cornering stiffness parameter observability further comprises:
determining if the vehicle longitudinal velocity exceeds a minimum threshold;
determining if the vehicle lateral acceleration is below a maximum threshold;
determining if the vehicle yaw rate exceeds a minimum threshold; and
determining if the vehicle steering angle exceeds a minimum threshold.
3. The method according to claim 1 wherein providing the estimate of the cornering stiffness parameters further comprises formulating and solving a weighted linear least squares problem using a standard recursive least squares approach.
4. The method according to claim 3 wherein the weighted linear least squares problem, in order to involve the cornering stiffness parameters and tire relaxation dynamics, is formulated based on a description of a lateral motion of the vehicle that includes a relation between a first slip angle and a first lateral tire force at a center of a tire and a second slip angle and a second lateral tire force at a point of contact between the tire and a road surface.
5. The method according to claim 4 wherein the description of the vehicle lateral motion includes a first order filter model for the relation between the first slip angle and the first lateral tire force at the center of the tire and the second slip angle and the second lateral tire force at the point of contact between the tire and the road surface according to
α f t =H ( s )α f
α r t =H ( s )α r
where
H
(
s
)
=
1
1
+
s
τ
and the notation with an exponent or superscript t, (term) t , indicates that the term is expressed in a tire coordinate system.
6. The method according to claim 4 wherein the description of the lateral motion of the vehicle is defined as
c
f
H
(
s
)
(
δ
-
ω
z
l
f
+
l
r
v
x
)
+
c
f
(
ml
f
a
y
-
I
z
ω
.
z
)
c
r
(
l
f
+
l
r
)
=
ml
r
a
y
+
I
z
ω
.
z
l
f
+
l
r
where c f is the front cornering stiffness parameter; c r is the rear cornering stiffness parameter; ω z is the vehicle yaw rate; {dot over (ω)} z is the vehicle yaw acceleration; δ is the vehicle steering wheel angle; l f is the distance between a vehicle center of gravity and the front axle; l r is the distance between the vehicle center of gravity and the rear axle; I z is the vehicle yaw moment of inertia; m is the mass of the vehicle; v x is the longitudinal velocity of the vehicle; and a y is the lateral acceleration of the vehicle at the vehicle center of gravity.
7. The method according to claim 3 wherein the weighted linear least squares problem is formulated to provide an estimation of both a front cornering stiffness and a rear cornering stiffness of the vehicle.
8. The method according to claim 3 wherein the weighted linear least squares problem is formulated to provide an estimation of a front cornering stiffness only.
9. The method of claim 1 further comprising preprocessing the sensor data before using the sensor data for providing the estimate of the cornering stiffness parameters.
10. An arrangement for estimating one or more vehicle cornering stiffness parameters in a linear operating region of a vehicle, the arrangement comprising:
a vehicle longitudinal velocity sensor for providing a vehicle longitudinal velocity signal;
a vehicle lateral acceleration sensor for providing a vehicle lateral acceleration signal;
a vehicle yaw rate sensor for providing a yaw rate signal of the vehicle;
a steering angle sensor for providing a steering angle signal of the vehicle;
a cornering stiffness parameter observability determination unit arranged to determine from the sensor data when vehicle cornering stiffness parameters are observable; and
a cornering stiffness parameter estimation unit arranged to generate, when vehicle cornering stiffness parameters are observable, a cornering stiffness parameter signal using a bicycle model that includes a model of tire relaxation dynamics describing the delay between when a slip angle is introduced and when a resulting lateral force reaches a steady state value.
11. A system for estimating one or more vehicle cornering stiffness parameters in a linear operating region of a vehicle, the system comprising:
a vehicle longitudinal velocity sensor for providing a vehicle longitudinal velocity signal;
a vehicle lateral acceleration sensor for providing a vehicle lateral acceleration signal;
a vehicle yaw rate sensor for providing a yaw rate signal of the vehicle;
a steering angle sensor for providing a steering angle signal of the vehicle;
a control system comprising a processor and associated memory storing computer executable instructions, wherein the instructions when executed by the processor cause the processor to read sensor data including the vehicle longitudinal velocity signal, the vehicle lateral acceleration signal, the yaw rate signal and the steering angle signal;
determine from the sensor data read when vehicle cornering stiffness parameters are observable; and
when vehicle cornering stiffness parameters are observable, generate a cornering stiffness parameter signal based on an estimate of the cornering stiffness parameters provided using a bicycle model that includes a model of tire relaxation dynamics describing the delay between when a slip angle is introduced and when a resulting lateral force reaches a steady state value.