Method and system for tracking normal force in active downforce control
A method for downforce control includes receiving vehicle inputs. The method includes determining a first normal-force request at the front axle and a second normal-force request at the rear axle using the plurality of vehicle inputs and a prediction model. The prediction model is a combined state space model that integrates a half-car state space model and an actuator state space model, the half-car state space model is developed using a half-car model, and the actuator state space model is developed using a neural network model. The method further includes determining a first position of the first aerodynamic body relative to the vehicle body and a second position of the second aerodynamic body relative to the vehicle body based on the first normal-force request and the second normal-force request, respectively.
1 . A method for downforce control, comprising:
receiving a plurality of vehicle inputs from a vehicle, wherein the plurality of vehicle inputs includes sensor data from a plurality of sensors of the vehicle, the vehicle includes a vehicle body, a front axle coupled to the vehicle body, a rear axle coupled to the vehicle body, a first aerodynamic actuator coupled to the vehicle body, and a second aerodynamic actuator coupled to the vehicle body, the first aerodynamic actuator includes a first aerodynamic body movable relative to the vehicle body, the second aerodynamic actuator includes a second aerodynamic body movable relative to the vehicle body;
determining a first normal-force request at the front axle and a second normal-force request at the rear axle using the plurality of vehicle inputs and a prediction model, wherein the prediction model is a combined state space model that integrates a half-car state space model and an actuator state space model for modeling the first aerodynamic actuator and the second aerodynamic actuator, the half-car state space model is developed using a half-car model, and the actuator state space model is developed using a neural network model, wherein the combined state space model serves as the prediction model for controlling the first aerodynamic actuator and the second aerodynamic actuator based on the plurality of vehicle inputs, and wherein the neural network model is trained using at least one aero map of the vehicle, the at least one aero map determines front and rear downforce as a function of ride heights, air speeds, and positions of the first aerodynamic actuator and the second aerodynamic actuator, and the actuator state space model is a linear time invariant state space model converted from the neural network model by calculating partial derivatives of states at a next step time with respect to all the inputs and also states at a current step time using auto-differentiation;
determining a first position of the first aerodynamic body relative to the vehicle body and a second position of the second aerodynamic body relative to the vehicle body based on the first normal-force request and the second normal-force request, respectively;
commanding the first aerodynamic actuator to move the first aerodynamic body to the first position relative to the vehicle body; and
commanding the second aerodynamic actuator to move the second aerodynamic body to the second position relative to the vehicle body.
2 . The method of claim 1 , wherein the combined state space model includes a state vector and an output vector, and the state vector is defined by a following formula:
X
ah
(
k
+
1
)
=
[
[
A
a
]
[
D
s
2
[
c
1
c
3
]
0
D
s
2
[
L
f
c
1
-
L
r
c
3
]
0
]
[
B
h
]
[
A
h
]
]
6
x
6
[
X
ah
(
k
)
]
+
[
B
a
0
]
6
x
2
[
U
ah
]
+
[
D
s
2
0
]
6
x
2
[
c
2
c
4
]
2
x
1
+
[
D
x
2
D
h
]
6
x
1
︸
D
where:
k is a time step;
X ah is the state vector of the combined state space model;
A a is a state matrix of the actuator state space model;
B h is an input matrix of the half-car state space model;
A h is the state matrix of the actuator state space model;
D s2 is a first feedthrough matrix of the actuator state space model;
D x2 is a second feedthrough matrix of the actuator state space model;
c 1 is a front ride height conversion factor at the front axle;
c 3 is a rear ride height conversion factor at the rear axle;
L f is a distance from a center of gravity of the vehicle to the front axle;
L r is a distance from the center of gravity of the vehicle to the front axle;
B a is an input matrix of the actuator state space model;
U ah is an input matrix of the combined state space model;
c 2 is a front ride height at the front axle while the vehicle is subjected to curb loading;
c 4 is a rear ride height at the rear axle while the vehicle is subjected to curb loading;
D h is a feedthrough matrix of the half-car model; and
D is a feedthrough factor.
3 . The method of claim 2 , wherein the output vector of the combined state space model is defined by the following formula:
Y
ah
(
k
)
=
C
ah
X
ah
(
k
)
where:
k is the time step;
Y ah is the output vector of the combined state space model;
X ah is the state vector of the combined state space model; and
C ah is an output matrix of the combined state space model.
4 . The method of claim 3 , further comprising training the neural network model by testing the vehicle on a road.
5 . A tangible, non-transitory, machine-readable medium, comprising machine-readable instructions, that when executed by a processor, cause the processor to:
receive a plurality of vehicle inputs from a vehicle, wherein the plurality of inputs includes sensor data from a plurality of sensors of the vehicle, the vehicle includes a vehicle body, a front axle coupled to the vehicle body, a rear axle coupled to the vehicle body, a first aerodynamic actuator coupled to the vehicle body, and a second aerodynamic actuator coupled to the vehicle body, the first aerodynamic actuator includes a first aerodynamic body movable relative to the vehicle body, and the second aerodynamic actuator includes a second aerodynamic body movable relative to the vehicle body;
determine a first normal-force request at the front axle and a second normal-force request at the rear axle using the plurality of vehicle inputs and a prediction model, wherein the prediction model is a combined state space model, the combined state space model integrates a half-car state space model and an actuator state space model for modeling the first aerodynamic actuator and the second aerodynamic actuator, the half-car state space model is developed using a half-car model, and the actuator state space model is developed using a neural network model, wherein the combined state space model serves as the prediction model for controlling the first aerodynamic actuator and the second aerodynamic actuator based on the plurality of vehicle inputs, and wherein the neural network model is trained using at least one aero map of the vehicle, the at least one aero map determines front and rear downforce as a function of ride heights, air speeds, and positions of the first aerodynamic actuator and the second aerodynamic actuator, and the actuator state space model is a linear time invariant state space model converted from the neural network model by calculating partial derivatives of states at a next step time with respect to all the inputs and also states at a current step time using auto-differentiation;
determine a first position of the first aerodynamic body relative to the vehicle body and a second position of the second aerodynamic body relative to the vehicle body based on the first normal-force request and the second normal-force request, respectively;
command the first aerodynamic actuator to move the first aerodynamic body to the first position relative to the vehicle body; and
command the second aerodynamic actuator to move the second aerodynamic body to the second position relative to the vehicle body.
6 . The tangible, non-transitory, machine-readable medium of claim 5 , wherein the combined state space model includes a state vector and an output vector, and the state vector is defined by a following formula:
X
ah
(
k
+
1
)
=
[
[
A
a
]
[
D
s
2
[
c
1
c
3
]
0
D
s
2
[
L
f
c
1
-
L
r
c
3
]
0
]
[
B
h
]
[
A
h
]
]
6
x
6
[
X
ah
(
k
)
]
+
[
B
a
0
]
6
x
2
[
U
ah
]
+
[
D
s
2
0
]
6
x
2
[
c
2
c
4
]
2
x
1
+
[
D
x
2
D
h
]
6
x
1
︸
D
where:
k is a time step;
X ah is the state vector of the combined state space model;
A a is a state matrix of the actuator state space model;
B h is an input matrix of the half-car state space model;
A h is the state matrix of the actuator state space model;
D s2 is a first feedthrough matrix of the actuator state space model;
D x2 is a second feedthrough matrix of the actuator state space model;
c 1 is a front ride height conversion factor at the front axle;
c 3 is a rear ride height conversion factor at the rear axle;
L f is a distance from a center of gravity of the vehicle to the front axle;
L r is a distance from the center of gravity of the vehicle to the front axle;
B a is an input matrix of the actuator state space model;
U ah is an input matrix of the combined state space model;
c 2 is a front ride height at the front axle while the vehicle is subjected to curb loading;
c 4 is a rear ride height at the rear axle while the vehicle is subjected to curb loading;
D h is a feedthrough matrix of the half-car model; and
D is a feedthrough factor.
7 . The tangible, non-transitory, machine-readable medium of claim 5 , wherein the tangible, non-transitory, machine-readable medium further comprising machine-readable instructions, that when executed by the processor, causes the processor to train the neural network model by testing the vehicle on a road.
8 . A vehicle, comprising:
a vehicle body;
a front axle coupled to the vehicle body;
a rear axle coupled to the vehicle body;
a plurality of sensors disposed within the vehicle body;
a first aerodynamic actuator coupled to the vehicle body, wherein the first aerodynamic actuator includes a first aerodynamic body movable relative to the vehicle body;
a second aerodynamic actuator coupled to the vehicle body, wherein the second aerodynamic actuator includes a second aerodynamic body movable relative to the vehicle body; and
a vehicle controller disposed within the vehicle body, wherein the vehicle controller is in communication with the plurality of sensors, and the vehicle controller is programmed to:
receive a plurality of vehicle inputs from the vehicle, wherein the plurality of vehicle inputs includes sensor data from a plurality of sensors of the vehicle;
determine a first normal-force request at the front axle and a second normal-force request at the rear axle using the plurality of vehicle inputs and a prediction model, wherein the prediction model is a combined state space model that integrates a half-car state space model and an actuator state space model for modeling the first aerodynamic actuator and the second aerodynamic actuator, the half-car state space model is developed using a half-car model, and the actuator state space model is developed using a neural network model, wherein the combined state space model serves as the prediction model for controlling the first aerodynamic actuator and the second aerodynamic actuator based on the plurality of vehicle inputs, and wherein the neural network model is trained using at least one aero map of the vehicle, the at least one aero map determines front and rear downforce as a function of ride heights, air speeds, and positions of the first aerodynamic actuator and the second aerodynamic actuator, and the actuator state space model is a linear time invariant state space model converted from the neural network model by calculating partial derivatives of states at a next step time with respect to all the inputs and also states at a current step time using auto-differentiation;
determine a first position of the first aerodynamic body relative to the vehicle body and a second position of the second aerodynamic body relative to the vehicle body based on the first normal-force request and the second normal-force request, respectively;
command the first aerodynamic actuator to move the first aerodynamic body to the first position relative to the vehicle body; and
command the second aerodynamic actuator to move the second aerodynamic body to the second position relative to the vehicle body.
9 . The vehicle of claim 8 , wherein the combined state space model includes a state vector and an output vector, and the state vector is defined by a following formula:
X
ah
(
k
+
1
)
=
[
[
A
a
]
[
D
s
2
[
c
1
c
3
]
0
D
s
2
[
L
f
c
1
-
L
r
c
3
]
0
]
[
B
h
]
[
A
h
]
]
6
x
6
[
X
ah
(
k
)
]
+
[
B
a
0
]
6
x
2
[
U
ah
]
+
[
D
s
2
0
]
6
x
2
[
c
2
c
4
]
2
x
1
+
[
D
x
2
D
h
]
6
x
1
︸
D
where:
k is a time step;
X ah is the state vector of the combined state space model;
A a is a state matrix of the actuator state space model;
B h is an input matrix of the half-car state space model;
A h is the state matrix of the actuator state space model;
D s2 is a first feedthrough matrix of the actuator state space model;
D x2 is a second feedthrough matrix of the actuator state space model;
c 1 is a front ride height conversion factor at the front axle;
c 3 is a rear ride height conversion factor at the rear axle;
L f is a distance from a center of gravity of the vehicle to the front axle;
L r is a distance from the center of gravity of the vehicle to the front axle;
B a is an input matrix of the actuator state space model;
U ah is an input matrix of the combined state space model;
c 2 is a front ride height at the front axle while the vehicle is subjected to curb loading;
c 4 is a rear ride height at the rear axle while the vehicle is subjected to curb loading;
D h is a feedthrough matrix of the half-car model; and
D is a feedthrough factor.
10 . The vehicle of claim 9 , wherein the output vector of the combined state space model is defined by the following formula:
Y
ah
(
k
)
=
C
ah
X
ah
(
k
)
where:
k is the time step;
Y ah is the output vector of the combined state space model;
X ah is the state vector of the combined state space model; and
C ah is an output matrix of the combined state space model.
11 . The vehicle of claim 8 , wherein the vehicle controller is programmed to train the neural network model by testing the vehicle on a road.