Method for optimising the energy consumption of a motor vehicle
The invention relates to a method for optimizing the energy consumption of a motor vehicle comprising a battery ( 30 ), an internal combustion engine (M), an electric machine (M E ), a plurality of devices, each characterized by at least one state variable, and a computer ( 40 ) capable of controlling the internal combustion engine (M) and the electric machine (M E ), said method being notable in that it comprises the steps of: a) defining a prediction period, b) determining the maximum theoretical variation of each state variable over the prediction period, c) determining the range of applicable setpoints in which each setpoint value is selected so that the variation of each state variable satisfies the maximum theoretical variation thereof, d) determining the value of an internal combustion setpoint and the value of an electric setpoint, in the range of applicable setpoints, for which the Hamiltonian function is lowest.
1 . A method for optimizing the energy consumption of a motor vehicle including a fuel tank, an electric battery configured to supply electrical energy, an internal combustion engine powered by the fuel tank, at least one electric machine powered by the electrical energy supplied by the battery, at least one first device connected to the internal combustion engine, at least one second device connected to the electric machine, and a computer configured to manage a drive train of the motor vehicle on a predetermined route, the computer being configured to control the internal combustion engine by issuing an internal combustion setpoint and the electric machine by applying an electric setpoint, the internal combustion engine, the electric machine, the at least one first device connected to the internal combustion engine, and the at least one second device connected to the electric machine each being characterized by at least one state variable, each of the at least one state variable describing an operating state of the respective device that the at least one state variable characterizes, each of the at least one state variable being dependent on at least one state constraint and being defined by an initial value at an initial time, each of the setpoints being associated with at least one of the at least one state variable, the method comprising:
defining a prediction period starting from the initial time;
determining a maximum theoretical variation of each of the at least one state variable from the initial value of the respective state variable and over the prediction period so that each respective state variable satisfies all of the state constraints specific thereto;
determining a range of applicable setpoints comprising a set of values for each of the respective setpoints, each setpoint value (u) being selected so that the variation of each of the state variables satisfies the maximum theoretical variation determined for the respective state variable, all of the setpoint values (u) that satisfy one of: (dx/dt(x,u))≥(Xmin−x)/dH and (dx/dt(x,u))≤(Xmax−x)/dH being selected;
determining the value of the internal combustion setpoint and the value of the at least one electric setpoint, in the range of applicable setpoints determined, by carrying out the following operations for each respective setpoint:
determining optimum setpoints by minimizing a Hamiltonian of a system of equations modeling dynamics of the vehicle, in the range of applicable setpoints, and
minimizing a Lagrangian function modeling the dynamics of the vehicle, the Lagrangian function being determined from the determined Hamiltonian and Karush-Kuhn-Tucker parameters (μ) relating to the state constraints, in the full range of setpoints, comprising all of the setpoints, the Karush-Kuhn-Tucker parameters μ being determined so that the solution that minimizes the Hamiltonian in the range of applicable setpoints also minimizes the Lagrangian function in the full range:
1) s i n u >n p then μ=−(A T ·A) −1 ·A T ·b,
2) s i n u <n p then μ=−A T ·(A·A T ) −1 ·A T ·b,
3) s i n u =n p then μ=−A −1 ·b,
where: n u is equal to the number of devices to be controlled,
n p is equal to the number of inequality constraints to be considered,
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controlling internal combustion engine by issuing the determined internal combustion setpoint and the electric machine by applying the determined electric setpoint.
2 . A computer for managing a drive train of a motor vehicle over a predetermined route, the motor vehicle including a fuel tank, an electric battery configured to supply electrical energy, an internal combustion engine powered by the fuel tank, at least one electric machine powered by the electrical energy supplied by the battery, at least one first device connected to the internal combustion engine, at least one second device connected to the electric machine the internal combustion engine, the electric machine, the at least one first device connected to the internal combustion engine, and the at least one second device connected to the electric machine each being characterized by at least one state variable, each of the at least one state variable describing an operating state of the respective device that the at least one state variable characterizes, each of the at least one state variable being dependent on at least one state constraint and being defined by an initial value at an initial time, each of the setpoints being associated with at least one of the at least one state variable, the computer comprising:
at least one processor configured to:
define a prediction period starting from the initial time,
determine a maximum theoretical variation of each of the at least one state variable from the initial value of the respective state variable and over the prediction period so that each respective state variable satisfies all of the state constraints specific thereto,
determine a range of applicable setpoints comprising a set of values for each of the respective setpoints, each setpoint value being selected so that the variation of each of the state variables satisfies each maximum theoretical variation determined for the respective state variable, all of the setpoint values (u) that satisfy one of: (dx/dt(x,u))≥(Xmin−x)/dH and (dx/dt(x,u))≤(Xmax−x)/dH being selected,
determine the value of an internal combustion setpoint and the value of at least one electric setpoint, in the range of applicable setpoints determined, by, for each setpoint:
determining optimum setpoints by minimizing the Hamiltonian of a system of equations modeling dynamics of the vehicle, in the range of applicable setpoints determined, and
minimizing a Lagrangian function modeling the dynamics of the vehicle, the Lagrangian function being determined from the determined Hamiltonian and Karush-Kuhn-Tucker parameters (μ) relating to the state constraints, in the full range of setpoints, comprising all of the setpoints, the Karush-Kuhn-Tucker parameters μ being determined so that the solution that minimizes the Hamiltonian in the range of applicable setpoints also minimizes the Lagrangian function in the full range:
1) s i n u >n p then μ=−(A T ·A) −1 ·A T ·b,
2) s i n u <n p then μ=−A T ·(A·A T ) −1 ·A T ·b,
3) s i n u =n p then μ=−A −1 ·b,
where: n u is equal to the number of devices to be controlled,
n p is equal to the number of inequality constraints to be considered,
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=
∂
h
′
∂
u
(
u
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)
b
=
∂
H
∂
u
(
u
=
u
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n
u
h′ denotes the equation that describes the constraint applied to the variation of the state variable predicted over a prediction period, and
control the internal combustion engine by issuing the determined internal combustion setpoint and the electric machine by applying the determined electric setpoint.
3 . A motor vehicle comprising:
a fuel tank;
an electric battery configured to supply electrical energy;
an internal combustion engine powered by the fuel tank;
at least one electric machine powered by the electrical energy supplied by the battery;
at least one first device connected to the internal combustion engine;
at least one second device connected to the electric machine; and
a computer configured to manage a drive train of a motor vehicle on a predetermined route, the computer being configured to control the internal combustion engine by issuing the internal combustion setpoint and the electric machine by applying the electric setpoint, the internal combustion engine, the electric machine, the at least one first device connected to the internal combustion engine and the at least one device connected to the electric machine each being characterized by at least one of the at least one state variable, each of the at least one state variable describing an operating state of the device that the at least one state variable characterizes, each of the at least one state variable being dependent on the at least one state constraint and being defined by the initial value at the initial time, each of the setpoints being associated with at least one of the at least one state variable, and the computer configured to:
define a prediction period starting from the initial time,
determine a maximum theoretical variation of each of the at least one state variable from the initial value of the respective state variable and over the prediction period so that each respective state variable satisfies all of the state constraints specific thereto,
determine a range of applicable setpoints comprising a set of values for each of the respective setpoints, each setpoint value being selected so that the variation of each of the state variables satisfies each maximum theoretical variation determined for the respective state variable, all of the setpoint values (u) that satisfy one of: (dx/dt(x,u))≥(Xmin−x)/dH and (dx/dt(x,u))≤(Xmax−x)/dH being selected,
determine the value of an internal combustion setpoint and the value of at least one electric setpoint, in the range of applicable setpoints determined, by, for each setpoint:
determining optimum setpoints by minimizing the Hamiltonian of the system of equations modeling dynamics of the vehicle, in the range of applicable setpoints determined, and
minimizing a Lagrangian function modeling the dynamics of the vehicle, the Lagrangian function being determined from the determined Hamiltonian and Karush-Kuhn-Tucker parameters (μ) relating to the state constraints, in the full range of setpoints, comprising all of the setpoints, the Karush-Kuhn-Tucker parameters u being determined so that the solution that minimizes the Hamiltonian in the range of applicable setpoints also minimizes the Lagrangian function in the full range:
1) s i n u >n p then μ=−(A T ·A) −1 ·A T ·b,
2) s i n u <n p then μ=−A T ·(A·A T ) −1 ·A T ·b,
3) s i n u =n p then μ=−A −1 ·b,
where: n u is equal to the number of devices to be controlled,
n p is equal to the number of inequality constraints to be considered,
A
=
∂
h
′
∂
u
(
u
=
u
′
)
:
dim
(
n
u
×
n
p
)
b
=
∂
H
∂
u
(
u
=
u
′
)
:
dim
n
u
h′ denotes the equation that describes the constraint applied to the variation of the state variable predicted over a prediction period, and
control the internal combustion engine by issuing the determined internal combustion setpoint and the electric machine by applying the determined electric setpoint.
4 . A non-transitory computer program product configured to cause one or more processors to execute a set of program code instructions which, when executed by the one or more processors, configure the one or more processors to implement a method for optimizing the energy consumption of a motor vehicle including a fuel tank, an electric battery configured to supply electrical energy, an internal combustion engine powered by the fuel tank, at least one electric machine powered by the electrical energy supplied by the battery, at least one first device connected to the internal combustion engine, at least one second device connected to the electric machine, and a computer configured to manage a drive train of the motor vehicle on a predetermined route, the computer being configured to control the internal combustion engine by issuing an internal combustion setpoint and the electric machine by applying an electric setpoint, the internal combustion engine, the electric machine, the at least one first device connected to the internal combustion engine, and the at least one second device connected to the electric machine each being characterized by at least one state variable, each of the at least one state variable describing an operating state of the respective device that the at least one state variable characterizes, each of the at least one state variable being dependent on at least one state constraint and being defined by an initial value at an initial time, each of the setpoints being associated with at least one of the at least one state variable, the method comprising:
defining a prediction period starting from the initial time;
determining a maximum theoretical variation of each of the at least one state variable from the initial value of the respective state variable and over the prediction period so that each respective state variable satisfies all of the state constraints specific thereto;
determining a range of applicable setpoints comprising a set of values for each of the respective setpoints, each setpoint value being selected so that the variation of each of the state variables satisfies the maximum theoretical variation determined for the respective state variable, all of the setpoint values (u) that satisfy one of: (dx/dt(x,u))≥(Xmin−x)/dH and (dx/dt(x,u))≤(Xmax−x)/dH being selected;
determining the value of the internal combustion setpoint and the value of the at least one electric setpoint, in a range of applicable setpoints determined, by carrying out the following operations for each respective setpoint:
determining optimum setpoints by minimizing a Hamiltonian of a system of equations modeling dynamics of the vehicle, in the range of applicable setpoints, and
minimizing a Lagrangian function modeling the dynamics of the vehicle, the Lagrangian function being determined from the determined Hamiltonian and Karush-Kuhn-Tucker parameters (μ) relating to the state constraints, in the full range of setpoints, comprising all of the setpoints, the Karush-Kuhn-Tucker parameters μ being determined so that the solution that minimizes the Hamiltonian in the range of applicable setpoints also minimizes the Lagrangian function in the full range:
1) s i n u >n p then μ=−(A T ·A) −1 ·A T ·b,
2) s i n u <n p then μ=−A T ·(A·A T ) −1 ·A T ·b,
3) s i n u =n p then μ=−A −1 ·b,
where: n u is equal to the number of devices to be controlled,
n p is equal to the number of inequality constraints to be considered,
A
=
∂
h
′
∂
u
(
u
=
u
′
)
:
dim
(
n
u
×
n
p
)
b
=
∂
H
∂
u
(
u
=
u
′
)
:
dim
n
u
h′ denotes the equation that describes the constraint applied to the variation of the state variable predicted over a prediction period; and
controlling the internal combustion engine by issuing the determined internal combustion setpoint and the electric machine by applying the determined electric setpoint.