Method for synthesising an h-infinity controller for a motion control system of a vehicle

Abstract

The invention relates to a method for synthesising an H ∞ controller for a motion control system of a vehicle, comprising the steps of: - modelling a generalised system (501) to be controlled, - defining controlled inputs and outputs of the generalised system, - calculating the controller (502) via H ∞ synthesis, wherein modelling of the generalised system to be controlled comprises: - generating a reference yaw rate (formula (I)) using a first model (504) for modelling the vehicle, - generating an actual yaw rate (formula (II)) using a second model (503) for modelling the vehicle different from the first, - calculating a difference (ε(t)) between the reference yaw rate (formula (I)) and actual yaw rate (formula (II)), and feeding this difference as input to the high-level controller during synthesis. The invention also relates to the use of the controller in a vehicle.

Description

DESCRIPTION: Method for synthesizing a type H-infinity controller for a vehicle motion control system. Technical domain:

[0001] The invention lies in the field of motor vehicle actuator control, and more specifically relates to a method for synthesizing (or defining) an infinite H-type controller (or ^ ^ ) for a vehicle motion control system (in English "Vehicle Motion Control", VMC), the vehicle comprising at least one actuator.

[0002] The invention also relates to a vehicle using the synthesized controller. Prior art:

[0003] An actuator is a device that can be installed in a vehicle and whose role is to convert an electrical command signal into an action. The invention relates to the control of such actuators in a vehicle. It is described in the context of a motor vehicle, but is generally applicable to any type of vehicle (motorcycle, airplane, boat, etc.). For illustrative purposes, it is subsequently described in the specific case of controlling the rear wheel steering for a four-wheel steering (4WS) motor vehicle and controlling the differential braking. However, the invention is not limited to these actuators and can be applied mutatis mutandis to any actuator in the vehicle, for example, a longitudinal speed actuator (engine).

[0004] In four-wheel steering vehicles, the steering of the two rear wheels is typically implemented by a single actuator, but can also be implemented by two separate actuators, each acting on one of the two rear wheels. For differential braking, each brake on the vehicle is controlled by a dedicated actuator to adjust the braking pressure between the right and left wheels, for example, for ABS (Antiblockiersystem, or anti-lock braking system) functions. Confidential C

[0005] Figure 1 shows the block diagram of a state-of-the-art motion control system for controlling the rear wheel steering angle and differential braking of a motor vehicle. Such a system transforms a setpoint ^ ^ steering wheel angle and a guideline ^ ^The vehicle's speed is controlled by the actions of the vehicle's actuators, in this example, the wheel brake actuators and a rear wheel steering actuator. The objective is to optimize the vehicle's stability and maneuverability by coordinating the use of the differential braking and the rear steering system. However, the invention applies equally to the control of the various actuators of a vehicle.

[0006] The motion control system relies on a reference model 101, which models the vehicle's chassis dynamics, to determine a reference yaw rate corresponding to the time derivative of the yaw angle. ^^^ reference (the desired yaw angle). Calculations are performed based on the instruction ^ ^ steering wheel angle, from the instruction ^ ^vehicle speed, and possibly other inputs, such as an estimate of the road friction coefficient. The reference model used for a motor vehicle is typically the bicycle model, shown in Figure 2, where the wheels of the same wheel set are modeled as a single wheel located on the axis of the vehicle's center of gravity. This bicycle model allows the vehicle's chassis dynamics to be modeled in order to deduce the commands to be applied to the various actuators. It uses: - ^ ^ and ^ ^ : the drift angles of the front and rear wheels; - ^ ^^ , ^ ^^ : the cornering rigidity of the front and rear tires; - ^ ^ : the angle of the front wheel; - ^ ^^ , ^ ^^ : the lateral forces applied to the front and rear wheels; - ^ ^ : the longitudinal velocity vector; - ^ ^: moment of inertia; - ^ : mass of the vehicle; - ^ : vehicle drift, which is also the angle of the velocity vector with respect to the vehicle axis; - ^ : yaw angle of the vehicle; Confidential C - ^ ^ , ^ ^ : the distance between the center of gravity and the front (rear) axle of the vehicle; - ^ ^ : the moment of the lace.

[0007] The matrix state-space representation of the bicycle model can be defined as: where: - the state variables are the vehicle's drift and yaw rate, - the control input is the yaw moment ! .

[0008] Returning to Figure 1, a high-level software controller 102 determines a yaw moment ^ !from the difference between the reference yaw rate ^^ ^^^ and the actual yaw rate ^^ of the vehicle (i.e. the difference between the target yaw rate and that of the vehicle).

[0009] A command allocation unit 103 implements a command allocation process to distribute the yaw moment ^ ! forces to be applied to the differential braking actuators of the four wheels (with here ^ , ^ ^, ^^ , ^ ^, ^, , ^ ^, ^^ the braking forces respectively associated with the front left, front right, rear left and rear right wheels) and on the actuator controlling the rear wheel steering (^ ^, ^ ), taking into account the limitations of chassis 104.

[0010] Low-level software controllers 106 and 107 translate these force commands into acceleration and braking respectively. -^. / ^for each of the four wheels, and in the steering angle of the rear wheels ^ ^ Sensors positioned on vehicle 108 measure the vehicle's movement, specifically its effective yaw rate. This yaw rate is compared to the reference yaw rate, and the difference is passed to the higher-level controller 102 for the next iteration. Confidential C

[0011] Thus, the system in Figure 1 operates in a closed loop to optimally allocate commands to the differential braking and rear wheel steering actuators, the goal being for the vehicle to follow a reference yaw rate ^^ ^^^.

[0012] The present invention relates to an improvement of block 102 of a high-level software controller, which takes as input the difference between the reference yaw rate and the effective yaw rate of the vehicle. In state-of-the-art motion control calculation methods, this controller is implemented by a PID (Proportional, Integral, Derivative) type controller, tuned using parameter tables based on the vehicle's longitudinal speed and lateral acceleration, derived from exhaustive tests and fine-tuned on-vehicle by specialists to achieve the desired yaw rate.

[0013] One object of the invention is to improve the robustness of the high-level PID software controller, while making it faster and providing better tracking performance. Summary of the invention:

[0014] To this end, the present invention describes a method for synthesizing an infinite H-type controller, or ^^ For a vehicle motion control system, the synthesis process comprises: - a modeling step of a generalized system to be controlled 0(2), - a step of defining the inputs 4(5) of said generalized system, - a step of defining the controlled outputs 6(5) of the generalized system, - a step of calculating the controller 7(2) by a synthesis of type ^ ^ .

[0015] The particularity of the synthesis process according to the invention is that the modeling of the generalized system to be controlled 0(2) comprises: - the generation of a reference yaw rate ^^ ^^^ using a first vehicle modeling model, Confidential C - the generation of an effective yaw rate ^^ using a second vehicle modeling model, the first and second modeling models being different, - the calculation of a difference 8(5) between the reference yaw rate ^^ ^^^ and the effective yaw rate ^^ , and the use of this difference as input to the high-level controller 7(2) during synthesis.

[0016] More specifically, the calculation step of a high-level controller 7(2) by a synthesis of type ^ ^ includes the determination of the high-level controller 7(2) which minimizes the influence of the inputs 4(5) of the generalized system on the outputs 6 ( 5 ) of the generalized system.

[0017] According to one embodiment, the second vehicle modeling model is a bicycle model.

[0018] According to a compatible embodiment of the preceding one, the first vehicle modeling model is a bicycle model modified to make one or more vehicle parameters variable.

[0019] Advantageously, the output of the high-level controller 7(2) is a yaw moment ^ ! of the vehicle.

[0020] According to a particular embodiment in which the controller of type ^ ^ is configured to control a differential brake actuator and a rear wheel steering actuator; a matrix state-space representation of the first vehicle modeling model is: with: - ^ ^^^ the vehicle's drift, - ^ ^^^ the vehicle's shoelace, Confidential C - ^ ^^,^^^ and ^ ^^,^^^the respective front and rear cornering stiffnesses, - ^ ^,^^^ and ^ ^,^^^ the distance between the center of gravity and the front and rear axles respectively, - ^ the mass of the vehicle, - ^ ^ the longitudinal velocity vector of the vehicle, - ^ ! the moment of inertia of the vehicle, - ^ ^,^^^ the angle of the vehicle's rear wheel, - ^ ! the yaw point of the vehicle.

[0021] Advantageously, the second vehicle modeling model takes an angle as input ^ ^ steering angle of the vehicle's front wheels calculated from the yaw moment ^ ! .

[0022] The invention also addresses a computer program comprising program code instructions for executing the first, second, third, and fourth steps of a method for synthesizing a controller of type ^ ^according to the invention when the program is executed on a computer, as well as a computer-readable recording medium comprising the computer program.

[0023] The invention also relates to a vehicle comprising a motion control system with: computing means configured to implement: - a reference model configured to generate a reference yaw rate to be followed by the vehicle, - a high-level controller configured to determine a yaw moment ! based on a difference between the reference yaw rate and the effective yaw rate of the vehicle, - a command allocation unit configured to transform the yaw moment ! force commands to be applied to at least one actuator, - at least one low-level controller configured to translate the force commands into movement of at least one actuator, Confidential C and -at least one sensor configured to measure the effective yaw rate of the vehicle, the vehicle's high-level controller being developed beforehand by a controller synthesis process of type ^ ^ according to the invention.

[0024] In one embodiment, this is a four-wheel drive vehicle comprising a differential brake actuator and a rear-wheel steering actuator. Brief description of the figures:

[0025] The invention will be better understood, and other features, details, and advantages will become clearer upon reading the following description, given by way of example, and with the help of the accompanying figures, of which: - Figure 1 shows a block diagram of a motion control system for controlling the rear wheel steering angle and differential braking of a motor vehicle according to the prior art; - Figure 2 shows the linear bicycle model, widely used in the prior art; - Figure 3 shows the functional diagram of a controller of the type ^ ^ , known from the prior art; - Figure 4 represents a block diagram of a synthesis process for a controller of type ^ ^ according to the invention; - Figure 5 represents the elements implemented by the synthesis process of a high-level controller of type ^ ^according to the invention, in an embodiment aimed at controlling differential braking and rear axle steering actuators of the vehicle; - Figure 6 compares the yaw moment calculated by a high-level controller defined by a synthesis method of type ^ ^ according to the state of the art and according to the invention. Confidential C Detailed description:

[0026] One way to improve the performance of the high-level software controller 102 in Figure 1 is to replace it with an infinite H-type controller, or ^ ^ , which represents a modern alternative to PID-type controllers. The principle of a controller ^ ^ is well known and described for example in the thesis of Moad Kissai: “Optimal Coordination of Chassis Systems for Vehicle Motion Control”, Automatic Control Engineering, Université Paris Saclay (COmUE), 2019.

[0027] A robust controller must guarantee the system's performance and stability despite varying operating conditions and model uncertainties (e.g., variations in vehicle mass). The control ^ ^ specifically aims for robustness by minimizing the standard ^ ^ , which corresponds to the maximum singular value of the system's frequency response. This represents the worst-case gain, that is, the most amplified disturbance in the system across all frequencies: with ;(<=) the system gain on all frequencies.

[0028] In control, the generalized system is an extended representation of a system that includes not only the dynamics of the system to be controlled, but also the weights and models of external signals, such as disturbances and noise. The generalized system is used to formulate robust control problems, such as the control ^ ^ .

[0029] Figure 3 represents the elements required for the synthesis (or development) of a high-level controller of type ^ ^ namely: - 0(2) the modeling of the generalized system, i.e., the system to be controlled, in which weights can be used to increase or decrease the weights of the inputs / outputs, - 7(2) the high-level controller of the system (i.e., box 102 in Figure 1), which aims to stabilize the generalized system 0(2). This is the controller that will be implemented in block 102 of system 100 in Figure 1 in vehicles, - 4(5) the inputs of the generalized system, for example, the reference that the controller must follow, disturbances, and noise. Confidential C - 6(5) the controlled outputs of the system, i.e. controller quality estimators, used during synthesis to constrain the performance of controller 7(2).

[0030] The main objective of the synthesis ^^ is to determine the stabilization controller 7(2) which, based on the information measured in D(5) by the generalized system 0(2), generates the control signal E(5) minimizing the influence of the undesirable signals 4(5) on the controlled variable 6(5). This is done by minimizing the norm ^ ^ of the closed-loop transfer function F !G below a specified optimal value H. This objective can be formulated as follows: 7(2) = arg m M(i Nn ) H 2.5. ‖F!G(2)‖^ ≤ Hoù st means "subject to", or "under constraint that" in French.

[0031] La fonction de transfert en boucle fermée F!G(2) inclut les contributions du system to be controlled;(2) , of the controller 7(2) as well as the weighting functions which define the performance and robustness requirements.

[0032] Performance models define the desired performance criteria, such as tracking accuracy, disturbance rejection, and noise attenuation. These criteria are translated into weighting functions that penalize deviations from the desired performance.

[0033] The use of a ^ type controller ^ replacing the high-level software controller 102 in Figure 1 improves the robustness of motion control calculation, its speed and tracking accuracy compared to a PID controller.

[0034] Once the generalized system 0(2) and the inputs / outputs 4(5) and 6(5) are defined, the synthesis can be done in the usual way for the person in the trade.

[0035] In practice, it turned out that a 7(2) type controller ^ ^proves too powerful to be implemented in a vehicle. For example, in the context of a controller driving differential braking and rear axle control actuators, the yaw moments calculated by the controller and converted into braking and angle commands by component 103 in Figure 1, cause excessively abrupt braking of the vehicle to be undrivable. Confidential C

[0036] To address this problem, the inventors developed a method for synthesizing a high-level controller of the ^ type ^ for a vehicle motion control system described below. Such a controller is robust to disturbances and noise, while exhibiting a sufficiently flexible response to be implemented in a vehicle, particularly a motor vehicle.

[0037] Figure 4 represents a block diagram of a synthesis process for a controller of type ^ ^ according to the invention. This method includes a first step 401 of modeling a generalized system to be controlled 0(2).

[0038] This step consists of describing the generalized system 0(2) which will be controlled and stabilized by the controller 7(2). The inventors discovered that if the use of a controller of type ^ ^ This is not suitable for controlling a motor vehicle because the reference model is not taken into account during the synthesis of 7(2). Indeed, the error 8(5) = ^^ ^^^ − ^^ is an input to the generalized system, and the controller does not know its actual dynamics. It therefore tends to oversize its setpoints.

[0039] The invention integrates the reference model (i.e., the model generating the reference yaw rate ^^ ^^^) into the generalized system 0(2), so that the controller has information on the dynamics of the deviation 8(5). The setpoint received at the controller input is then more realistic with respect to the dynamics achievable by the vehicle.

[0040] The other steps in the synthesis process of a high-level controller of type ^ ^ According to the invention, the usual steps for this type of controller are: - a step 402 of defining inputs 4(5) of the generalized system, - a step 403 of defining controlled outputs 6(5) of the generalized system, - a step 404 of calculating the high-level controller 7(2) of type ^ ^ .

[0041] Step 404 can be implemented by following Riccati's equations. Alternatively, matrix calculation tools such as Matlab® software can be used to calculate the high-level stability controller 7(2) once the system is generalized and its inputs / outputs are defined.

[0042] Figure 5 represents the elements implemented by the synthesis process of a high-level controller of type ^ ^ according to the invention, in an embodiment Confidential C a specific device aimed at controlling differential braking and rear axle steering actuators of the vehicle.

[0043] Le système généralisé 0(2) 501 comprend un modèle ;(2) 503 du véhicule allowing the calculation of an effective yaw rate ^^ of the vehicle. The model ;(2) is typically a bicycle model as described previously, taking the steering angle as input of the vehicle. It corresponds to the modeling of the behavior of gearboxes 103 to 107 in Figure 1.

[0044] Le système généralisé 0(2) 501 comprend également un modèle ;^^^(2) 504configured to calculate a reference yaw rate of the vehicle, which will subsequently be called the reference model. The reference model; ^^^ (2) differs from the bicycle model. It can, for example, be obtained by making one or more parameters of the bicycle model variable, or by using a model other than the bicycle model. The output of (2) corresponds to the reference yaw rate calculated by box 101 in Figure 1.

[0045] In the embodiment considered by way of illustration, the reference model is obtained from the bicycle model, by making three parameters variable, selected for their link with differential braking and rear steering control: - the wheelbase ratio PQ: the variation of the wheelbase ratio, typically between 0.5 and 1.5, makes it possible to generate a reference yaw rate which would be typical of a larger or smaller vehicle.This variation is of interest because it allows the vehicle's behavior to be adapted to its environment: a shorter wheelbase is more suitable for city driving and a longer wheelbase is more suitable for highway driving; - RS angular dynamics: the variation in angular dynamics allows the vehicle's understeer / oversteer behavior to be varied, which is of interest when accelerating or braking in a corner; - specific front / rear drifts, respectively T. UN and T ^N Varying the specific front / rear drifts allows for adjusting the synchronization between the front and rear axles of the vehicle. Confidential C

[0046] It thus implements a state matrix close to that of the bicycle model, in which the front / backward cornering stiffnesses ^ ^^ and ^ ^^, and the distance between the center of gravity and the front / rear axle ^ ^ and ^ ^ are defined as follows: ^^,^^^ = ^^ ∗ PQ W ^^^ = W ∗ PQ with L being the vehicle's wheelbase (i.e., the distance between the front axle and the rear axle), and

[0047] The final state space of the reference model; ^^^ (2) is then defined as: where the state variables are the vehicle's drift and yaw rate, and the control input is the yaw moment. ! The rear wheel angle is ^ ^,^^^ .

[0048] Alternatively, the reference model can be adapted to vary only one of these parameters, or to vary other parameters such as vehicle mass, drift angles, etc. Any other type of model, for example a four-wheeled vehicle model, that allows for determining a yaw rate setpoint can be implemented in the generalized system. Confidential C

[0049] In the embodiment described by way of illustration, the reference model ;^^^(2) takes as input the steering angle ^^ of the rear wheels. The input type depends on the reference model chosen.

[0050] In the embodiment considered by way of illustration, the inputs defined during step 402 are as follows: - the angle ^ ^ rear wheel steering, - input disturbances T Y .

[0051] The controlled outputs defined in step 403 are as follows: - suivi, - 6(5) which contains the tracking error multiplied by an error weighting function, and the front wheel angle multiplied by a control weighting function.

[0052] In the embodiment considered as an illustration, it was chosen to emulate the ^ command ^ from the lace moment command ^ ! This choice is linked to the search for the best possible frequency response.

[0053] Yaw moment conversion ^ ! on order ^ ^ is done by applying a gain such that:

[0054] To form the standard structure for the controller ^ ^The weighting functions P^(2), P̂(2), and Pc(2) shown in Figure 5 are defined to characterize, respectively, the performance objectives, the actuator limitations, and the disturbance rejection. Their development is the result of the expertise and know-how of the automation engineer.

[0055] As an example, these weighting functions can be chosen as follows: - P ^ (2) is used to filter the output signal 6 U weighted yaw rate error. This is the yaw rate tracking performance. The weighting P ^ (2) can, for example, take the form of a high-pass filter whose cutoff frequency is the attenuation level for low frequencies. This filter's role is to adjust Confidential C The maximum static error and the maximum amplitude of the controller's sensitivity function, -P̂ (2), is used to filter the 6^ signal of the front wheel angle attenuation. This weighting can, for example, take the form of a low-pass filter whose cutoff frequency is the attenuation level for high frequencies and whose maximum value serves as an upper limit for the controller's sensitivity function, in order to prevent actuator saturation. - P c ( 2 ) is used to filter the input disturbance T Y This weighting can, for example, take the form of a simple gain of 0.01, which impacts the sensitivity functions of the controller.

[0056] Figure 6 compares the yaw moment calculated by a high-level controller defined by a synthesis process of type ^ ^According to the prior art 601 and according to the invention 602, extracted from a record of measurements taken under real-world conditions, it is observed that the controller 602 synthesized with the reference model exhibits a lower yaw moment amplitude and a slightly slower response compared to the controller 601 synthesized without the reference model, thus offering better tracking performance and energy savings since less yaw moment is required to achieve the same performance.

[0057] If the controller according to the invention may appear to have lower performance compared to a controller ^ ^In conventional tests conducted on a vehicle operating under real-world conditions, the 601 controller proved too powerful for satisfactory driving. Conversely, the 602 controller, synthesized with the reference model, performed perfectly in the various environments where it was tested. It proved robust to system variations and different driving modes. The high-level controller of type ^ ^ 602, synthesized by taking into account the reference model in the generalized system, is therefore more suitable for implementation in a vehicle than controller 601.

[0058] The invention relates to a method for synthesizing a controller of type ^ ^in which the reference model used to generate the reference is defined within the generalized O(2) system. The method is implemented on digital computing means, such as, for example, a microprocessor associated with a memory containing the code instructions of the method according to the invention. Confidential C

[0059] It also relates to a computer program comprising program code instructions for executing steps 401 to 404 of the synthesis process of a controller of type ^ ^ according to the invention when said program is executed on a computer.

[0060] It also relates to a computer-readable recording medium on which is recorded a computer program comprising program code instructions for the execution of steps 401 to 404 of the synthesis process of a controller of type ^ ^ according to the invention.

[0061] Finally, the invention relates to a vehicle, for example a motor vehicle, comprising a motion control system 100 with: computing means such as one or more processors, configured to implement: - a reference model 101 configured to generate a reference yaw rate to be followed by the vehicle, - a high-level controller 102 configured to determine a yaw moment from a difference between said reference yaw rate and an effective yaw rate of the vehicle, - a command allocation unit 103 configured to transform the yaw moment !in force commands to be applied to at least one actuator, - at least one low-level controller 105, 106 configured to translate the force commands into movement of at least one actuator, and - at least one sensor 107 configured to measure the effective yaw rate of the vehicle, where the high-level controller 102 is developed beforehand (i.e., prior to the use of the vehicle and then installed on the vehicle) by a method of synthesizing a controller of type ^ ^ according to the invention, wherein the modeling of the generalized system comprises the reference model. Confidential C

[0062] According to a particular embodiment of the invention, the vehicle is a four-wheel drive motor vehicle, and at least one actuator comprises a differential braking actuator and a rear-wheel steering actuator. Confidential C

Claims

CLAIMS 1. Method for synthesizing an infinite H-type controller, or ^ ^ , for a vehicle motion control system (100), the synthesis process comprises: - a step (401) of modeling a generalized system to be controlled (0(2)), - a step (402) of defining inputs (4(5)) of said generalized system, - a step (403) of defining controlled outputs (6(5)) of the generalized system, - a step (404) of calculating the controller (7(2)) by a synthesis of type ^ ^said synthesis process being characterized in that the modeling of the generalized system to be controlled (0(2)) comprises: - the generation of a reference yaw rate ^^ ^^^ using a first vehicle modeling model (504), - the generation of an effective yaw rate ^^ using a second vehicle modeling model (503), the first and second modeling models being different, - the calculation of a difference (8(5)) between the reference yaw rate ^^ ^^^ and the effective yaw rate ^^, and the use of this difference as input to the high-level controller (7 ( 2 ) ) during synthesis.

2. Synthesis process for a controller of type ^ ^ according to claim 1, wherein the calculation step (404) of a high-level controller (7(2)) by a synthesis of type ^ ^includes determining the high-level controller (7(2)) that minimizes the influence of the inputs (4(5)) of the generalized system on the outputs (6(5)) of the generalized system.

3. Method for synthesizing a controller of type ^ ^ according to any one of claims 1 to 2, wherein the second vehicle modeling model (503) is a bicycle model.

4. Method for synthesizing a controller of type ^ ^ , in which the first vehicle modeling model (504) is a bicycle model modified to make one or more vehicle parameters variable. Confidential C 5. Method for synthesizing a controller of type ^ ^ , in which the output of the high-level controller (7(2)) is a yaw moment ^ ! of the vehicle.

6. Method for synthesizing a type ^ controller ^according to any one of claims 1 to 5 for the control of a differential braking actuator and the control of a rear wheel steering actuator, wherein a matrix state-space representation of the first vehicle modeling model is: with: - ^ ^^^ the vehicle's drift, - ^ ^^^ the vehicle's yaw, - ^ ^^,^^^ and ^ ^^,^^^ the respective front and rear cornering stiffnesses, - ^ ^,^^^ and ^ ^,^^^ the distance between the center of gravity and the front and rear axles respectively, - ^ the mass of the vehicle, - ^ ^ the longitudinal velocity vector of the vehicle, - ^ ! the moment of inertia of the vehicle, - ^ ^,^^^ the angle of the vehicle's rear wheel, - ^ ! the yaw moment of the vehicle.

7. Method for synthesizing a controller of type ^ ^according to claim 6, wherein the second vehicle modeling model takes as input an angle ^ ^ steering angle of the vehicle's front wheels calculated from the yaw moment ^ ! 8. Computer program comprising program code instructions for the execution of the first (401), second (402), third (403) and fourth (404) Confidential C steps in a process for synthesizing a controller of type ^ ^ according to any one of claims 1 to 7 when said program is executed on a computer.

9. Computer-readable recording medium on which is recorded a computer program comprising program code instructions for executing the first (401), second (402), third (403), and fourth (404) steps of a method for synthesizing a controller of type ^ ^according to any one of claims 1 to 7.

10. Vehicle comprising a motion control system (100) with computing means configured to implement: - a reference model (101) configured to generate a reference yaw rate to be followed by the vehicle, - a high-level controller (102) configured to determine a yaw moment from a difference between said reference yaw rate and an effective yaw rate of the vehicle, - a command allocation unit (103) configured to transform the yaw moment !in force commands to be applied by at least one actuator, - at least one low-level controller (105), (106) configured to translate the force commands into movement of at least one actuator, and - at least one sensor (107) configured to measure the effective yaw rate of the vehicle, the vehicle being characterized in that the high-level controller (102) is developed beforehand by a method of synthesizing a controller of type ^ ^ according to any one of claims 1 to 7.

11. Four-wheel drive vehicle according to claim 10, comprising a differential brake actuator and a rear-wheel steering actuator. Confidential C

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