FR3127928A1 - SYSTEM FOR CALIBRATION OF A CONTROL BY A TORQUE DISTRIBUTION CONTROL LAW FOR HYBRID VEHICLE LIMITING POLLUTANT EMISSIONS. - Google Patents

Abstract

The invention relates to a system for calibrating a control by a control law for a motor vehicle of the hybrid type, the control system comprising- a means for evaluating an optimal distribution of torques between the electric machine and the heat engine , by considering models of different parameters as a function of operating points of the thermal engine, said evaluation of optimal distribution being made as a function of different values of co-state parameters linked to a state of charge of the battery, and to a temperature of the heat engine, - means for calibrating a control law to apply a setpoint according to the optimum distribution of torques between the electric machine and the heat engine, from given values of said co-state parameters. This control law makes it possible to limit pollutant emissions. The invention also relates to a method and a program based on such a system. Figure 1

Description

SYSTEM FOR CALIBRATION OF A CONTROL BY A TORQUE DISTRIBUTION CONTROL LAW FOR HYBRID VEHICLE LIMITING POLLUTANT EMISSIONS.

The invention relates to the field of traction chains of hybrid motor vehicles, management of the temperature of the internal combustion engine and the minimization of fuel consumption and particle emissions.

The invention finds a particularly advantageous, but not exclusive, application for motor vehicles of the hybrid type comprising a heat engine used in combination with an electric traction machine.

The particles emitted by a combustion engine are in significant quantity when the engine is cold. In addition, the amount of particles is also significant when the engine must provide high torque.

The strategy currently used in motor vehicles of the applicant's PHEV type aims to limit the torque that the internal combustion engine is authorized to supply when cold. This restriction increases with the number of combustions carried out since the start of the engine and we end up allowing the internal combustion engine to provide its maximum torque when it is hot.

The constraint placed on the heat engine makes it possible to limit particulate emissions at the cost of the consumption of electrical energy in the battery. This additional expenditure of electrical energy will have to be compensated later by the heat engine, and this ultimately leads to an increase in fuel consumption. The strategy described above is based on experimental observations and manual calibration, but does not guarantee that the best possible performance is achieved from the point of view of the particle/consumption compromise.

The invention aims to overcome the problems posed by the prior art, in particular the problem of emissions of particles when cold while limiting the consumption of electrical energy when cold. When the engine is cold, it produces a very large quantity of particles, and this phenomenon is amplified for high torques requested.

To achieve this objective, the invention proposes a system for calibrating a control by a control law for a motor vehicle of the hybrid type comprising a heat engine and an electric machine connected to a battery, the calibration system comprising
- a means for evaluating an optimal distribution of torques between the electric machine and the heat engine, by considering a model of fuel consumption as a function of operating points of the heat engine, a model of the state of charge as a function of operating points of the heat engine, a model of particle emissions as a function of operating points of the heat engine and of the temperature of the heat engine, a model of temperature rise of the heat engine as a function of operating points of the heat engine,

said evaluation of optimal distribution being made as a function of different values of a first co-state parameter linked to a state of charge of the battery, and of different values of a second co-state parameter linked to a temperature of the engine thermal,
- a control calibration means for applying a setpoint according to the optimal distribution of torques between the electric machine and the heat engine, the calibration being made from a given value of the first co-state parameter linked to the state of charge of the battery, and a given value of the second co-state parameter linked to the temperature of the heat engine.

The system is for example a set of measuring devices comprising at least one computer.

The invention proposes a system making it possible to calibrate a control by a control law which seeks to optimize the consumption/particle compromise through an optimal engine heating strategy.

According to a variant, the control system is characterized in that

- the fuel consumption model corresponds to the equation (2)

with

fuel consumption at a given time,

the torque provided by the heat engine, and

engine speed;

- the state of charge model corresponds to the equation (3)

with the torque of the electric machine, and

his diet;

- the particulate emissions model corresponds to the equation (6)

with

particle emission values at 4 points of a mesh surrounding any operating point whose emissions are to be calculated,

, speed and torque values which correspond to the mesh thus formed,

mass emissions of particles at the considered point of a mesh, and

the variation of the engine temperature with respect to the ambient temperature;

- the thermal engine temperature rise model corresponds to the equation (7)

Or

is the mass of the coolant,

is the mass heat capacity of the coolant,

represents the temporal variation of the temperature of the cooling system,

is the heat flux produced by the operation of the engine and obtained from a map of speed and torque, and

is the external convection coefficient which represents the heat loss to the surroundings.

This makes it possible to improve the precision of the control law and to use little computation time.

According to a variant, the system is characterized in that

- the optimum distribution of torques is evaluated using the equations (1) (9) (10)

with

the optimal distribution of torques,

the torque of the electric machine,

the torque of the combustion engine,

a function of Hamiltonian type,

a weighting factor to calibrate,

a temporal variation in the state of charge of the battery,

a fuel cost for a possible start,

the co-state linked to the state of charge of the battery,

a variation in engine temperature with respect to the ambient temperature;

- the control calibration means is configured to determine a law according to the optimum distribution of torques.

This makes it possible to obtain a torque distribution value.

According to a variant, the system is characterized in that the means of evaluating the optimal distribution of torques is implemented by solving a minimization of the function (21)

preferably carried out using successive simulations of journeys using the function (20)

with

a calibration value,

a target final SOC value,

{ , } a pair of given values of co-state parameters which allows to minimize the consumption/particle compromise.

This further improves the accuracy of the torque distribution evaluation.

The invention further relates to a method for calibrating a command by a control law for a motor vehicle of the hybrid type, the calibration method comprising a heat engine and an electric machine connected to a battery, the method comprising
- a step of evaluating an optimal distribution of torques between the electric machine and the heat engine, by considering a model of fuel consumption as a function of operating points of the heat engine, a model of the state of charge as a function of operating points of the heat engine, a model of particle emissions as a function of operating points of the heat engine and of the temperature of the heat engine, a model of temperature rise of the heat engine as a function of operating points of the heat engine,

said evaluation of optimal distribution being made as a function of different values of a first co-state parameter linked to a state of charge of the battery, and different values of a second co-state parameter linked to a temperature of the heat engine ,

- a control calibration step for applying a setpoint according to the optimal distribution of torques between the electric machine and the heat engine, the calibration being made from a given value of the first co-state parameter linked to the state of charge of the battery, and a given value of the second co-state parameter linked to the temperature of the heat engine.

According to a variant, the method is characterized in that

- the fuel consumption model corresponds to the equation (2)

with

fuel consumption at a given time,

the torque provided by the heat engine, and

engine speed;

- the state of charge model corresponds to the equation (3)

with the torque of the electric machine, and

his diet;

- the particulate emissions model corresponds to the equation (6)

with

particle emission values at 4 points of a mesh surrounding any operating point whose emissions are to be calculated,

, speed and torque values which correspond to the mesh thus formed,

mass emissions of particles at the considered point of a mesh, and

the variation of the engine temperature with respect to the ambient temperature;

- the thermal engine temperature rise model corresponds to the equation (7)

Or

is the mass of the coolant,

is the mass heat capacity of the coolant,

represents the temporal variation of the temperature of the cooling system,

is the heat flux produced by the operation of the engine and obtained from a map of speed and torque, and

is the external convection coefficient which represents the heat loss to the surroundings.

According to a variant, the method is characterized in that

- the optimum distribution of torques is evaluated using the equations (1) (9) (10)

with

the optimal distribution of torques,

the torque of the electric machine,

the torque of the combustion engine,

a function of Hamiltonian type,

a weighting factor to calibrate,

a time variation of the battery charge state,

a fuel cost for a possible start,

the co-state linked to the state of charge of the battery,

a variation in engine temperature with respect to the ambient temperature;

- the control calibration step is carried out to determine a law according to the optimal distribution of torques.

According to a variant, the method is characterized in that the step of evaluating the optimal distribution of torques is implemented by solving a minimization of the function (21)

preferably carried out using successive simulations of paths using the function (20)

with

a calibration value,

a target final SOC value,

{ , } a pair of given values of co-state parameters which allows to minimize the consumption/particle compromise.

The invention further relates to a computer program comprising program code instructions for performing the steps of a calibration method according to the invention, when said program is running on a computer.

Another object of the invention relates to a kit of motor vehicle calibration devices comprising a calibration system according to the invention.

The invention will be further detailed by the description of non-limiting embodiments, and on the basis of the appended figures illustrating variants of the invention, among which:

schematically illustrates an interpolation of an operating point in a mesh of engine speed and torque values;

schematically illustrates a pattern of second co-state parameters calculated and approximated as a function of temperature; And

schematically illustrates normalized values of particulate emissions and consumption for different values of a weighting factor.

The invention relates to a control system that can be implemented in a hybrid-type motor vehicle on-board computer.

The invention relates in particular to a control law.

The invention takes its context in the field of energy and pollutant management of hybrid vehicles. This technical problem corresponds to the following question: how to determine at each instant the distribution of the driver's torque demand between the internal combustion engine and the electric machine(s) of the hybrid vehicle considered? The answer to this question takes the form of a control law, the aim of which will be to minimize both fuel consumption and particle emissions. The desire to also minimize particles, rather than just consumption, comes from two phenomena inherent in plug-in hybrid vehicles (PHEV):

These vehicles, with an electric range of approximately 50km, are likely to carry out long phases of electric driving, which can thus lead to the cooling of the internal combustion engine during the journey.

In addition, as the electric motorization of these vehicles is important, they are likely to increase in speed and torque before having to start their heat engine. This aspect is very important since, unlike a conventional vehicle, the engine of which will begin to heat up while idling, the engine of a PHEV vehicle may have to be started in order to provide direct and cold high power, which will result in very high particulate emissions.

Note the torque distribution Thus : (1)

with the torque of the electric machine, and the torque of the heat engine.

With a view to producing a control law thus making it possible to calculate the distribution of the torque between the heat engine and the electric machine so as to jointly minimize fuel consumption and particle emissions, the following steps will be followed:
- We make models of the quantities that interest us (modeling part),
- We propose an optimal off-line control law, that is to say a control law allowing to minimize the consumption/particles compromise in an ideal context where we know perfectly a priori the cycle or the path to come (part offline),
- An online control law is deduced from this off-line control law, that is to say that can be used in a vehicle, while driving (on-line part).

The determination of the control law is the purpose of the invention.

Regarding the modeling part, we use a model of the powertrain, and models of fuel consumption, battery charge, particulate emissions, and engine temperature rise.

Consumption is given by a map, i.e. a table of values taken from experimental data, which here depends on the speed and torque provided by the combustion engine: (2)

with fuel consumption at a given time, the torque provided by the heat engine, and the engine rotation speed.

The state of charge of the battery (State Of Charge, noted SOC) varies according to the speed and the torque supplied by the electric machine of the traction chain. This variation is also calculated using a speed and torque map: (3)

with the torque of the electric machine and his diet.

Particulate emissions are dependent on engine temperature, torque and rpm. Preferably, the term “engine temperature” here and hereinafter means the temperature of the coolant, which is measured in the vehicle. In the same way as for consumption, the entire engine field is mapped, i.e. the operating points {rpm, torque} that the engine can reach. For each point, we start with a cold engine to also obtain the impact of temperature on particulate emissions. From the experimental data thus obtained, it is possible to identify for each operating point of the {speed/torque} mesh visited the parameters of the following model: (4)

with mass emissions of particles at the considered point of the mesh, a variation in engine temperature with respect to the ambient temperature, and , And parameters to be identified from experimental data, the value of which comes from a map of the speed and the torque. To obtain the value of the emissions at any speed/torque operating point, it is necessary to apply equation (4) to the four points of the mesh framing the latter, then to perform an interpolation which will for example be linear.

This interpolation is detailed below, because its mathematical expression will be reused later. We have : (6)

with the value of the particle emissions at the 4 points of the mesh framing any operating point whose emissions are to be calculated. are the speed and torque values that correspond to the mesh thus formed, as illustrated in the .

Finally, we use a model of the engine temperature rise, which is expressed as follows: (7)

here is the mass of the coolant, is the mass heat capacity of the coolant, represents the temporal variation of the temperature of the cooling system, is the heat flux produced by the operation of the engine and obtained from a map of speed and torque, and is the external convection coefficient which represents the heat loss to the environment.

This model therefore makes it possible to calculate the fuel consumption and particle emissions of the vehicle, and to simulate the rise in temperature of its engine. It will be used as part of the control strategy aimed at jointly minimizing consumption and particulate emissions detailed below.

Regarding the offline part, to begin with, the criterion that we seek to minimize is written as follows: (8)

The Pontryagin Maximum Principle (PMP) is applied to the system, which results in the introduction of a function, called Hamiltonian, and defined below from equation (8): (9)

here we have the torque distribution defined in equation (1), a weighting factor to calibrate, the temporal variation of the state of charge of the battery (State Of Charge), therefore of the electrical energy available, the fuel cost of a possible start, and finally And which are called co-states, linked respectively to the and to , whose value and variation will be determined later. The PMP principle stipulates that the command allowing to minimize the criterion chosen is obtained by seeking at each instant the minimum of the Hamiltonian of equation (9) as a function of the control signal , i.e. the torque distribution: (10)

To be able to solve the problem of equation (10), it is necessary to know the values of the co-states And . To do this, in the offline framework where we know perfectly the cycle and the operating points to come, we must solve a differential equation for each of the co-states, given by the PMP: (11) (12)

One must first calculate equations (11) and (12), then find an initial or final condition in both cases to solve the differential equations.

With regard to equation (11), it turns out that the term is close to zero, so we usually make the approximation ; So we have constant. To obtain this constant value, the value of the SOC is used. Indeed, in the context of the energy management of hybrid vehicles, we want to end the cycle or the journey at a final target value, which in fact corresponds to an empty battery plus a safety margin. We denote this final target SOC , which will serve us in the process that will solve both equations (11) and (12). We therefore want to satisfy the following condition: (13)

Concerning equation (12), we can develop the derivative of the Hamiltonian and simplify it as follows: (14)

We define a third term of equation (7): (16)

So there remains the term to be determined in equation (14). We will obtain it from the particle emission model of equations (5) and (6). The derivatives of the terms which represent the particle emissions corresponding to the 4 points of the mesh surrounding the current operating point are expressed as follows: (17)

We then deduce: (18)

We therefore have all the terms of equation (14), and we can therefore, knowing the current value of , calculate its evolution step by step using equation (12). It will therefore be necessary to determine a limit value, in this case the initial value , to determine throughout the journey.

There is no final constraint on as is the case with the SOC. In this case, the PMP principle implies the following boundary condition: (19)

To simultaneously satisfy equations (13) and (19), we will base ourselves on successive simulations of the journey to come, which will make it possible to converge towards the appropriate values of (which is constant on the path) and (only an initial value that serves as a starting point for equation (12) with the aim of satisfying equation (19) at the end of the journey).

We therefore introduce the following function: (20)

with a calibration value which will typically be equal to 1. When calling the function , the entire path considered is simulated; this implies that at each moment of the trip the control of the traction chain is calculated by solving the minimization of equation (10), from the values of the co-states (constant) and (obtained with equation (12)). At the end of the simulation of the route, we thus obtained the final values of the SOC and , which allow us to calculate the value of in equation (20).

In this way, we can find the pair { , } to satisfy the conditions of equations (13) and (19) by solving the following minimization problem: (21)

Equation (21) can be solved typically using a genetic algorithm, or any other numerical optimization algorithm.

According to the PMP principle, it is by using the pair thus obtained { , } that it is possible to minimize the chosen optimization criterion, that is to say here the consumption/particle compromise defined in equation (8). This solves the off-line optimal control problem. We are now interested in how we can apply this result to any path, which we do not know in advance.

Concerning the online part, it is the application of the invention, that is to say a control law aimed at minimizing the compromise of equation (8), without a priori information on the path . As before, the optimal control is obtained at each instant by solving the minimization of equation (10); It is then necessary to determine the values of And , without being able to simulate the journey to come.

Re , we use a method widespread in the scientific literature: we give ourselves an SOC instruction to follow during the journey, which will typically be constant and will be worth, for example, 20%. The value of is then obtained using a Proportional-Integral (PI) regulator: (22)

Or , And are values to be calibrated.

Re , we will use the result obtained in the previous part. If we plot the curve of the value of depending on the temperature , it turns out that the appearance of the graph varies little between different routes. We can therefore solve the optimal control problem described in the previous part for a path, then deduce a relation allowing us to deduce only from , whatever the conditions. In particular, we obtain a good approximation of using the following mathematical form: (23)

with the value of which will be chosen at the current instant, and , , And are parameters to be identified from the value of obtained offline. This is illustrated on the .

Here we see in irregular curve the value of obtained during the offline resolution of a reference path by considering a value of of 500. In a regular curve, it looks like after identification. For temperatures below 25°C, the value of at the value reached at 25° C., that is to say for example here at -992.

In summary, during any trip, the distribution of the torque between heat engine and electric machine is calculated at each instant by solving the minimization of equation (10). To do this, we need two values: , obtained with equation (22), and , obtained with equation (23). Figure 3 illustrates the achievable gains for different values of . The reference Cn relates to a standardized criterion.

It can be seen that for large values of , it is possible to greatly reduce particle emissions (decreasing curve in Figure 3) at the cost of a slight increase in consumption (very slightly increasing curve in Figure 3). For example, for , mass particulate emissions are reduced by 85% and consumption is increased by 2.7% compared to .

The invention includes two methods: a method of linked to the design of the control law, to be carried out offline beforehand, and a second method which is the invention strictly speaking, that is to say the law of order used online in the vehicle.

In the off-line design process, all the modeling operations described in the modeling part are carried out. We use the obtained models to perform the operations described in the offline part. From this we deduce the coefficients of equation (23), which allow us to know at any time the value of .

In the command line method, in the vehicle being driven, the value of the command is obtained at each instant by solving the minimization of equation (8) or preferably (10). To do this, we calculate using equation (22) and using equation (23).

The preferred variant is that described above. Other possible variants are:

Regarding the models used, the choices of model structures made above represent the preferred variant, but it is possible to make other choices:
- Fuel consumption can be represented by a Willans model rather than a map.
- The variation of the SOC can be deduced from the power that the electric machine must provide and from a map of the efficiency of the latter, rather than directly using a map of torque and speed.
- The particle emissions model is here a map of the speed and the torque, and the values constituting this map come from the exponential model of equation (4). The emission value is obtained using a linear interpolation in this map. It is possible to do otherwise: by keeping the cartography it is possible to use another type of interpolation. It is also possible to change the model by using, for example, a three-dimensional map whose inputs would be the speed, the torque and the engine temperature, which would make it possible to dispense with equation (4).
- Here in the thermal model of equation (7), the temperature of the motor is assimilated to that of its cooling system. It is possible to make this model more complex by estimating the temperature of the cylinder walls rather than simply measuring the temperature of the cooling system.

Regarding the resolution of the offline problem: it involves the resolution of the optimization problem of equation (21). If this problem is solved here using a genetic algorithm (preferred variant), it can be solved using any other method or algorithm: Nelder-Mead algorithms, Particles Swarm Optimization type, SQP, Levenberg-Marquardt, Interior-Point. Since there are only two dimensions, it can even be solved manually by trial and error.

Concerning the resolution of the online problem, if the PI regulator described in equation (22) represents the preferred variant, it is possible to use any regulator, in a non-exhaustive manner: proportional (P), Proportional- Integral-Derivative (PID), error and integral function mapping, etc.

Furthermore, regarding obtaining the value of , the exponential model described in equation (23) is preferred. Another model could however be used, in particular a one-dimensional mapping, depending on .

The invention makes it possible to greatly reduce particulate emissions, which facilitates the validation of pollution standards such as Euro standards.

Claims (10)

System for calibrating a control by a control law for a motor vehicle of the hybrid type comprising a heat engine and an electric machine connected to a battery, the calibration system comprising
- a means for evaluating an optimal distribution of torques between the electric machine and the heat engine, by considering a model of fuel consumption as a function of operating points of the heat engine, a model of the state of charge as a function of operating points of the heat engine, a model of particle emissions as a function of operating points of the heat engine and of the temperature of the heat engine, a model of temperature rise of the heat engine as a function of operating points of the heat engine,
said evaluation of optimal distribution being made as a function of different values of a first co-state parameter linked to a state of charge of the battery, and of different values of a second co-state parameter linked to a temperature of the engine thermal,
- a control calibration means for applying a setpoint according to the optimal distribution of torques between the electric machine and the heat engine, the calibration being made from a given value of the first co-state parameter linked to the state of charge of the battery, and a given value of the second co-state parameter linked to the temperature of the heat engine. Calibration system according to Claim 1, characterized in that
- the fuel consumption model corresponds to the equation (2) with
fuel consumption at a given time,
the torque provided by the heat engine, and
engine speed;
- the state of charge model corresponds to the equation (3) with the torque of the electric machine, and
his diet;
- the particulate emissions model corresponds to the equation (6) with
values of particle emissions at 4 points of a mesh surrounding any operating point whose emissions are to be calculated,
, speed and torque values which correspond to the mesh thus formed,
mass emissions of particles at the considered point of a mesh, and
the variation of the engine temperature with respect to the ambient temperature;
- the thermal engine temperature rise model corresponds to the equation (7) Or
is the mass of the coolant,
is the mass heat capacity of the coolant,
represents the temporal variation of the temperature of the cooling system,
is the heat flux produced by the operation of the engine and obtained from a map of speed and torque, and
is the external convection coefficient which represents the heat loss to the surroundings. Calibration system according to any one of claims 1 to 2, in which
- the optimum distribution of torques is evaluated using the equations (1) (9) (10) with
the optimal distribution of torques,
the torque of the electric machine,
the torque of the combustion engine,
a Hamiltonian type function,
a weighting factor to calibrate,
a temporal variation in the state of charge of the battery,
a fuel cost for a possible start,
the co-state linked to the state of charge of the battery,
a variation in engine temperature with respect to the ambient temperature;
- the control calibration means is configured to determine a law according to the optimum distribution of torques. Calibration system according to any one of Claims 1 to 3, characterized in that the means for evaluating the optimal distribution of torques is implemented by solving a minimization of the function (21) preferably carried out using successive simulations of paths using the function (20) with
a calibration value,
a target final SOC value,
{ , } a pair of given values of co-state parameters which allows to minimize the consumption/particle compromise. Method for calibrating a control by a control law for a motor vehicle of the hybrid type comprising a heat engine and an electric machine connected to a battery, the method comprising
- a step of evaluating an optimal distribution of torques between the electric machine and the heat engine, by considering a model of fuel consumption as a function of operating points of the heat engine, a model of the state of charge as a function of operating points of the heat engine, a model of particle emissions as a function of operating points of the heat engine and of the temperature of the heat engine, a model of temperature rise of the heat engine as a function of operating points of the heat engine,
said evaluation of optimal distribution being made as a function of different values of a first co-state parameter linked to a state of charge of the battery, and different values of a second co-state parameter linked to a temperature of the heat engine ,
- a control calibration step for applying a setpoint according to the optimal distribution of torques between the electric machine and the heat engine, the calibration being made from a given value of the first co-state parameter linked to the state of charge of the battery, and a given value of the second co-state parameter linked to the temperature of the heat engine. Calibration method according to claim 5, in which
- the fuel consumption model corresponds to the equation (2) with
fuel consumption at a given time,
the torque provided by the heat engine, and
engine speed;
- the state of charge model corresponds to the equation (3) with the torque of the electric machine, and
his diet;
- the particulate emissions model corresponds to the equation (6) with
values of particle emissions at 4 points of a mesh surrounding any operating point whose emissions are to be calculated,
, speed and torque values which correspond to the mesh thus formed,
mass emissions of particles at the considered point of a mesh, and
the variation of the engine temperature with respect to the ambient temperature;
- the thermal engine temperature rise model corresponds to the equation (7) Or
is the mass of the coolant,
is the mass heat capacity of the coolant,
represents the temporal variation of the temperature of the cooling system,
is the heat flux produced by the operation of the engine and obtained from a map of speed and torque, and
is the external convection coefficient which represents the heat loss to the surroundings. Calibration method according to any one of Claims 5 to 6, in which
- the optimum distribution of torques is evaluated using the equations (1) (9) (10) with
the optimal distribution of torques,
the torque of the electric machine,
the torque of the combustion engine,
a function of Hamiltonian type,
a weighting factor to calibrate,
a temporal variation in the state of charge of the battery,
a fuel cost for a possible start,
the co-state linked to the state of charge of the battery,
a variation in engine temperature with respect to the ambient temperature;
- the control calibration step is carried out to determine a law according to the optimal distribution of torques. Method according to any one of Claims 5 to 7, characterized in that the step of evaluating the optimal distribution of torques is implemented by solving a minimization of the function (21) preferably carried out using successive simulations of paths using the function (20) with
a calibration value,
a target final SOC value,
{ , } a pair of given values of co-state parameters which allows to minimize the consumption/particle compromise. A computer program comprising program code instructions for performing the steps of a calibration method according to any one of claims 5 to 8, when said program is running on a computer. Kit of motor vehicle calibration apparatus comprising a calibration system according to any one of claims 1 to 4.