Method for determining an energy-efficient optimized control for controlling at least one actuator

Abstract

Method for determining an energy-efficient optimized control for at least one actuator. The invention relates to a computer-implemented method for determining a control (u) for at least one actuator (20, 30) for a system, said method comprising the following steps: Provision (100) of a physical model (M10) of the system; Provision (200) of a driven model (M20, M30) of the dynamics of at least one actuator (20, 30); Determination (300) of a hybrid model (MH10) of the system by concatenating the physical model (M10) of the system and the model (M20, M30) of the dynamics of at least one actuator (20, 30); Determination (400) of a control (u) by minimizing a constrained quadratic criterion taking into account the hybrid model, and comprising: a first part involving the control ( of the system, a second part making to intervene a difference () between a reference instruction and a response of the system.(Figure 1).

Description

Title of the invention: Method for determining an energy-efficient optimized control for controlling at least one actuator

[0001] The present invention relates to the field of mechanics, and more specifically to the automotive sector, and more precisely concerns a method for determining an optimized control system for at least one actuator in a system, for example, a vehicle. The invention aims to take into account the actual dynamics of each actuator in order to ensure, on the one hand, efficient control of the actuators and therefore of the vehicle in which they are implemented, and on the other hand, to guarantee the energy efficiency of the control system as a whole. The invention is particularly applicable to systems that use one or more electric motors as actuators.We can distinguish between rotary electric motors, which convert an electrical command into energy corresponding to the product of a torque and an angular displacement, and linear electric motors, which convert an electrical command into energy corresponding to the product of a force and a linear displacement.

[0002] In what follows, the invention will be described in its automotive application. However, as will become clear from the description of the invention, the invention can also be applied in other technical fields where it is necessary to electronically control an actuator such as an electric motor, as is the case, for example, in systems such as airplanes, trains, electric bicycles, motorcycles, lifting systems, and household appliances. Furthermore, the application of the invention is not limited to transportation systems. It can also be applied in the field of manufacturing, since there too, different actuators with different dynamics must be electronically controlled to achieve a target or reference trajectory.

[0003] An actuator is a component that acts on a system in such a way as to modify its state or behavior. In the automotive field, an actuator can be defined as a motor used by driver assistance software to assist the driver, the system then being the vehicle. The invention applies particularly to actuators that are electric motors controlled by a digital command. According to various embodiments, the actuator(s) can be braking actuators, steering actuators, motors, etc., for a controlled system that can be any type of vehicle, robot, or electronic device comprising one or more actuators.

[0004] According to current estimates, an average annual increase of 1.6% in global transport energy demand is expected between 2007 and 2030. This increase in energy demand must be considered as an important factor in the design of mechatronic systems, particularly the control devices associated with them.

[0005] One way to reduce the electrical energy of mechatronic systems using electric motors as actuators would be to optimize the control devices of these motors while ensuring good performance and better energy efficiency.

[0006] Unfortunately, most of the control laws currently designed lose their efficiency in terms of electrical energy because these control laws are designed without taking into account the actual dynamics of the controlled motors.

[0007] Indeed, each actuator exhibits its own unique dynamics, resulting from the technical solution implemented to perform its intended function. An actuator's dynamics correspond to the time it takes to execute a command and its ability to reach the given setpoint. For example, for a wheel, the setpoint is the steering angle, and the dynamics consist of the time required to reach this target steering angle and the accuracy relative to the setpoint. In most of the various control laws used in motor vehicles, actuators are considered ideal for the sake of simplicity. Therefore, when designing a control system, it is assumed that this control will be applied instantaneously, without amplitude or phase distortion.

[0008] This is not entirely accurate, but the loss of efficiency created by this simplifying assumption has not been considered significant until now. However, in the current context of the energy crisis, and even more so in the future, vehicle control based on multiple actuators will need to be energy-efficient.

[0009] In existing control solutions, the control laws are designed without taking into account the actual dynamics of the actuators. These laws correct the vehicle's behavior to follow a given setpoint or trajectory by addressing, through closed-loop control, the inaccuracies introduced by the actuator dynamics.

[0010] It is therefore understood that this correction is made at the expense of the overall electrical energy required to carry out the mission. This correction, although effective, is all the more significant (and therefore energy-intensive) because the behavioral models used to design the correctors are developed without taking into account the dynamics of the actuators.

[0011] The invention aims to overcome all or part of the problems mentioned above by designing an optimal control law ensuring performance and energy efficiency by taking advantage of the integration of the real dynamics of the controlled motors in the basic model used to design the control laws and by determining a control on a minimized difference between an output data of the system and its input setpoint.

[0012] The invention thus optimally solves the vehicle control problem from an energy perspective by introducing dynamic models of all the actuators onboard the vehicle into the control models. This results in personalized, and therefore perfectly efficient, control.

[0013] To this end, the invention relates to a computer-implemented method for determining a command to control at least one actuator for a system, said method comprising the following steps: - Provision of a physical model of the system; - Provision of a model of the dynamics of at least one actuator; - Determination of a hybrid model of the system by concatenating the physical model of the system and the model of the dynamics of at least one actuator; - Determining a control by minimizing a constrained quadratic criterion taking into account the hybrid model, and including: • a first part involving the control of the system, • a second part involving a difference between a reference setpoint and a response of the system.

[0014] Thanks to these characteristics, the control is obtained from a control law that is based both on the physical model of the system and on the actuator dynamics model(s) to simultaneously optimize the energy efficiency of the actuators and the tracking of the reference setpoint. The control law thus takes into account the system dynamics and the actual dynamics of the actuators, which avoids having to correct for inaccuracies that would be introduced by assuming perfect actuator operation. This results in a dual effect: on the one hand, improved vehicle stability and performance are achieved since the control law generates a command that responds as closely as possible to the setpoint, and on the other hand, energy efficiency in vehicle operation is increased since the control law sends a setpoint that is precisely what is needed for the actuators.

[0015] Advantageously, the quadratic criterion comprises a weighted sum of the first part and the second part. By adjusting the weighting factors, it It is possible to give more weight to trajectory tracking or to efficiency. energy control for the system.

[0016]

[0017]

[0018]

[0019]

[0020] According to a particular embodiment: the quadratic criterion (j(u. e)) constant equal to ^ti(uTRu + eTQ&)dt - the constraint is Xa — "f Bjl y — CaXa ey fy J rej J with : - the difference between the reference setpoint and the system response (y), - R a symmetric positive matrix, - Q is a non-negative symmetric matrix, - and if integration times, - Au is a state matrix, Ba a control matrix and Ca an observation matrix of the state representation of the hybrid model (MH10), - is the state variable of the hybrid model, and Xa its derivative. According to an optional feature of the invention, the actuator dynamics model is a trained model obtained through machine learning. This model takes as input a set of actuator input data and a set of actuator output data associated with the input data. The machine learning process allows for the introduction of real input and output data into an initially selected model and the adaptation of its parameters to best match the model's output data with the actual actuator output data. According to an optional feature of the invention, the step of determining a model of the actuator dynamics comprises: - a first sub-step of choosing a model defined by initial parameters; - a second sub-step of feeding the model with a first input data from the actuator to obtain a first output data from the model; - a third sub-step of determining a difference between the first output data of the model and the first output data of the actuator associated with the first input data of the actuator; - a fourth sub-step of adjusting the initial parameters and carrying out the second and third sub-steps until the gap is less than a first predefined value.

[0021] By proceeding in this way, a model of the actuator dynamics is determined by iteration on the basis of a set of real data.

[0022] According to an optional feature of the invention, the step of determining a model of the actuator dynamics further comprises a fifth substep for validating the actuator dynamics model, defined by performing the second substep with a second input data point, distinct from the first input data point, to obtain a second output data point for the model, and performing the third substep with the second output data point. If the deviation is greater than a second predefined value, a sixth alert substep is performed. If the deviation is less than this second predefined value, then the actuator dynamics model is validated.

[0023] This fifth substep allows for the consideration of a second set of input / output data to consolidate the actuator dynamics model. In the event of a significant discrepancy between the output data from the actuator dynamics model and the actual output data from the actuator, the parameters of the actuator dynamics model are adjusted. This substep therefore serves to validate the model and ensure the robustness of the method of the invention. The warning substep, which may be optional, alerts a user to the fact that the actuator dynamics model may have deficiencies.

[0024] In one embodiment of the invention, the actuator dynamics model is a linear time-invariant model.

[0025] In another embodiment of the invention, the actuator dynamics model is a linear model with varying parameters.

[0026] The invention also covers a vehicle comprising at least one actuator and computing means configured to implement the method described above, in which the system is the vehicle.

[0027] The invention also relates to a computer program comprising instructions for the execution of such a method, when the program is executed by a processor.

[0028] Finally, the invention also relates to a processor-readable recording medium on which is recorded a program containing instructions for the execution of said method, when the program is executed by a processor.

[0029] Other features and advantages of the invention will become apparent from the following description on the one hand, and from several embodiments given as examples. indicative and not exhaustive, with reference to the attached schematic drawings, on which:

[0030] [Fig. 1] schematically represents the main steps of the method for determining an order according to the invention,

[0031] [Fig.2] schematically represents the sub-steps of the step of determining a model of the actuator dynamics according to the invention,

[0032] [Fig.3] schematically represents the sub-steps of the step of determining a model of the actuator dynamics according to the invention with an optional sub-step of validating the model of the actuator dynamics,

[0033] [Fig.4] represents a control which controls the yaw rate of a vehicle and the associated braking torque without and with application of the method of the invention.

[0034] The features, variants, and different embodiments of the invention, as described or as they will be presented in the detailed description that follows, can be combined in various ways, provided that they are not incompatible or mutually exclusive. In particular, variants of the invention may be conceived comprising only a selection of features described hereafter in isolation from the other described features, if this selection of features is sufficient to confer a technical advantage and / or to differentiate the invention from the prior art.

[0035] For the sake of clarity, the same elements are designated by the same references in the different figures.

[0036] As already mentioned, the invention is described in its automotive application to determine a command to control an actuator, and particularly an electric motor, for a vehicle, but is by no means limited to it and can be applied to an actuator for any type of system.

[0037] Figure 1 schematically represents the main steps of the method for determining a control signal (denoted u) according to the invention. The method for determining a control signal is implemented by computer. The control signal allows for the control of at least one actuator 20, 30 for a system, in particular a vehicle 10. The actuators are typically electric motors driven by a digital setpoint, but may be other types of actuators. The determination method according to the invention includes a step 100 of providing a physical model M10 of the vehicle 10. The physical model M10 may be a physical model of the vehicle, based on the laws of physics, such as those used in current solutions for controlling a vehicle. The case of a model relating to a vehicle for the purpose of determining a yaw rate of the vehicle will be considered for the remainder of the description, by way of illustration only.

[0038] This model results from Newton's first two laws, which allow us to obtain the equations of vehicle dynamics, referenced below as (6) and (9). The table below presents the physical parameters and signals characterizing a physical model of a four-wheeled vehicle. Symbol Description Distance from center of gravity to front axle L2 Distance from center of gravity to rear axle Front axle drift stiffness ^2 Rear axle drift stiffness F Road friction coefficient Vx Longitudinal speed ni Vehicle mass 0 Vehicle drift angle Front axle drift angle <52 Rear axle drift angle Yaw rate Sf Front wheel steering angle 5r Rear wheel steering angle (4WS) Mz Yaw moment Ff Front axle lateral force Fr Rear axle lateral force

[0039] According to Newton's first law: the sum of the external forces is equal to the mass multiplied by the acceleration (equation (1)) and we obtain: Ff + L = + ra / ¾¾ + 1¾¾ = + ¢) (3) 8, (4) 82=Sr-$+^> (5)

[0040] The operator * denotes the derivative of x, and * the second derivative of x.

[0041] According to Newton's second law, the sum of the moments of the external forces is equivalent to the derivative of the angular momentum at the center of gravity of the vehicle (equation (7)). We then obtain: = (7) <8> —---p---—;--—• < / ?+'——------—LU t" — (’J) -s -Z'k'C 'Z '' k <2

[0042] Starting from equations (6) and (9), we obtain the mathematical description of the bicycle model of the vehicle in the form of a referenced state representation (10): (10)

[0043]

[0044] where:

[0045] x = ( ) is the state variable,

[0046] " / \ is the command vector, with <5 / the front wheel steering, the "~ 5r \ Mz / DAE (short for Electric Assisted Steering), or the steering of the rear wheels, the 4WS or 4 Wheels Steering (for 4 steering wheels), and Mz the overall yaw moment to be allocated to the braking actuators or to the IWM (In Wheel Motor) or to any other actuator capable of achieving this yaw moment.

[0047] y _ is the output of the model,

[0048] A, B and C are respectively the state, control and observation matrices of the state representation of the model.

[0049] The determination method according to the invention includes a step 200 of providing a model M20, M30 of the dynamics of at least one actuator 20, 30. If the vehicle implements only one actuator 20, the method includes providing the Model M20. If the vehicle uses a single actuator 30, the method includes providing model M30. If the vehicle uses both actuators 20 and 30, the method includes providing models M20 and M30. Of course, a similar approach can be used with a plurality of actuators, for example, 10, 50, or 100.

[0050] By way of example, for longitudinal control, the actuators involved may be motor or braking actuators. For vertical control, the actuators involved may be active or semi-active suspension actuators.

[0051] Lateral or yaw control of the vehicle usually employs a linear dynamic model, commonly called the bicycle model of the vehicle. The bicycle model is the most widely used for trajectory generation and the development of control laws for vehicle control.

[0052] For the remainder of the description, we will take the example of a braking actuator for the differential braking of a vehicle, as an illustration only.

[0053] For each actuator 20 (respectively 30), the actuator dynamics model can be obtained by means of machine learning, taking as input a set of input data E20 (respectively E30) for actuator 20 (respectively 30) and a set of output data S20 (respectively S30) for actuator 20 (respectively 30) associated with the input data E20 (respectively E30). In this case, we refer to it as a trained model. Alternatively, the actuator dynamics model can be obtained from manufacturer data. We will detail the determination of a trained model in the following sections.

[0054] For each actuator 20, 30, input data E20, E30 and output data S20, S30 are collected. Based on this data, a machine learning technique is used to produce a model of the dynamics of the actuators involved in controlling the vehicle.

[0055] The determination of the trained model (step 205) will be detailed below.

[0056] Next, the method of the invention includes a step 300 of determining a hybrid model MH10 of vehicle 10 by concatenation of the physical model M10 of vehicle 10 and the model M20, M30 of the dynamics of at least one actuator 20, 30.

[0057] The hybrid model is a concatenation of the previously provided physical model of the vehicle and the actuator dynamics model obtained previously by Machine Learning or from data provided by the manufacturer.

[0058] Finally, the method of the invention includes a step 400 of determining a control (denoted u) by an optimal control law Le, by minimizing a constrained quadratic criterion taking into account the hybrid model, and comprising a first part involving the control (u) of the system and a second part involving a difference e between a reference setpoint and a system response. In other words, the control determination is based on a control law Le derived from the hybrid model MH 10, a reference input setpoint (y_ref) applied to system 10, and a system output (y) obtained from the input setpoint applied to system 10. The control law aims to minimize the difference between the system output and the input setpoint. Step 400, the determination of the control u, will be described below.

[0059] The determination of the actuator dynamics model, when it is a driven model, and the determination of the hybrid model will first be explained.

[0060] Fig. 2 schematically represents the sub-steps of the step of determining a model of the dynamics of the actuator according to the invention in an embodiment where this dynamics is obtained by supervised learning.

[0061] As described previously, the dynamics model of at least one actuator can be obtained using machine learning, which takes as input a set of input data E20, E30 from actuator 20, 30 and a set of output data S20, S30 from actuator 20, 30 associated with the input data E20, E30 (step 205). Step 205 is a dynamic model determination step that is implemented offline, prior to the control determination. This model can be obtained using machine learning techniques based on the input and output data of each actuator. The model is obtained solely through data, hence the name Data Driven Model, as opposed to a physical model obtained through the laws of physics.

[0062] In the context of the invention, the Data Driven Model approach is identical to the Supervised Machine Learning approach or to System Identification. It consists of estimating the parameters of the actuator dynamics model from the input and output signals.

[0063] Step 205 of determining a model M20, M30 of the dynamics of the actuator 20, 30 includes a first substep 210 of choosing a model Mi defined by initial parameters Pi. In order to limit the complexity of the calculations, a reduced-order model may be used, but the invention applies identically to higher-order models.

[0064] For actuators, a reduced-order LTI (Linear Time Invariant) model is suitable, but other types of models can be used, for example the LPV (Linear Model with Variing Parameters).

[0065] The inputs should preferably sweep across the entire amplitude of the actuator, in order to obtain a model that is reliable over the entire operating range of the actuator.

[0066] Step 205 of determining a model M20, M30 of the dynamics of the actuator 20, 30 includes a second substep 220 of feeding the model Mi with a first input data El of the actuator to obtain a first output data SMI of the model Mi.

[0067] This second substep 220 is carried out following the activation of each actuator in predefined configurations (with variable amplitudes and frequencies) to obtain corresponding input and output data sequences. This data is processed according to modeling assumptions: frequency filtering, bias elimination, weighting of data sequences, etc. For example, for a wheel steering actuator, the input is the steering setpoint, and the output is the actuator's response (i.e., the actual steering angle applied). After obtaining the input / output data pairs, the model Mi is successively fed an input data El to produce an output data for the SMI model.

[0068] Step 205 of determining a model M20, M30 of the actuator dynamics 20, 30 includes a third substep 230 of determining a gap 40 between the first SMI output data of the model and the first SI output data of the actuator associated with the first El input data of the actuator. In other words, the SMI output data of the model is compared with the actual SI output data of the actuator to determine a gap between the output signal measured on the actuator and the output signal of the model subjected to the same input signal. If the gap is greater than a predefined value, it is then necessary to adjust the characteristics of the model in order to minimize the gap.

[0069] Step 205 of determining a model M20, M30 of the dynamics of the actuator 20, 30 includes a fourth substep 240 of adjusting the initial parameters Pi and performing the second and third substeps 220, 230 until the gap 40 is less than a first predefined value 50. For convex optimization, the identified parameters of the model are those that minimize the L2 norm (least squares norm) of the gap between the model and reality. This means that the parameters Pi of the model are modified, and then the substeps of feeding the model with the input data and determining the gap between the output data from the model and the actual data are repeated until the resulting gap is less than the predefined value 50.

[0070] The learning phase, i.e., step 205 of determining a model of the actuator dynamics, is done "offline", prior to the use of the vehicle. It is done once for the entire range of vehicles.

[0071] Figure 3 schematically represents the substeps of the actuator dynamics model determination step according to the invention, with an optional actuator dynamics model validation substep. In addition to the steps presented previously, the actuator dynamics model determination step 205 further includes a fifth actuator dynamics model validation substep 250 defined by carrying out the second substep 220 with a second input data E2, distinct from the first input data E1, to obtain a second output data SM2 of the model, and carrying out the third substep 230 with the second output data SM2, S2, and if the deviation 40 is greater than a second predefined value 51, a sixth alert substep 260.

[0072] This substep allows the obtained model to be identified and validated by verifying its predictive nature, that is, its ability to account for the actuator output, for input sequences different from those used for identification. This step is optional and allows the model's quality to be ensured.

[0073] The step of determining the hybrid model will now be explained. As an example, a model of the actuator dynamics determined in step 205 may have an LTI-type structure. Such a model is first-order and allows approximating the actuator dynamics. Such a model for the 4WS (four-wheel steering) application may have the following structure: 1 “F * &

[0074] with Kp 41^5, the actuator gain; rp_ws, its response time constant, and s the Laplacian. As an example, the actuator gain can take the value 1 and the time constant can take the value 0.05.

[0075] It can be noted that the values ​​of Kp 4^5 and tp-4ws can be obtained theoretically, without resorting to machine learning. The model is thus simpler to implement, but proves to be less accurate.

[0076] Previously, the method for identifying the dynamics of the actuators was illustrated with the example of the 4WS actuator. The hybrid model used for the design of the control law is a concatenation of the physical model of the vehicle and the model of the dynamics of the different actuators of the vehicle.

[0077] To construct this hybrid model, a physical model of the vehicle and a dynamic model of each actuator implemented in the vehicle are required. The physical model of the vehicle has been presented previously (see referenced equation (10)). Regarding the actuator dynamics model, based on the example of the 4WS actuator, the corresponding state representation is:

[0078] With 4 - 1 . D - Fp_4K-5

[0079] "«ws is the actuator excitation input (i.e., the setpoint), and the actuator output

[0080] The Data Driven approach applied to braking actuators that perform the overall yaw moment gives the state representation:

[0081] with: 4 1 • p _Rp_Brafee T > Da_8rake~ ■ ■a.K'flfe"1 * OA t

[0082] ua_Brake is the excitation input of the brake actuator, and the output of the actuator Rmke=xa_Brake.

[0083] The Data Driven approach applied to DAE gives the following state representation:

[0084] with: ^a. Brafcë”” Z ' 4 SA£””“ nâ)7 ®^a

[0085] u«_dae is the excitation input of the DAE actuator, and the output of the actuator

[0086] In the specific case of controlling 4WS, braking, and DAE actuators, the hybrid model is obtained by concatenating v_, jws=xajWS, xa_Brake, and yaj)AE=x“PAE. Denoting by a the index pertaining to the hybrid model, the new state variable is:

[0087] xa_DAE xaj^V% \ xaJBi-uke /

[0088] The state representation of the hybrid model is obtained:

[0089] ( xa = A^x^ + Baiia I

[0090] with

[0091] —

[0092] Ba-

[0093] and ' (Pj+Pj Dj P2 ' m*vx " 1 ' mVx mVx " DiLy-DiLf D2Ll+DjLl PL. D2L2 j. h " L ■ L I- oo - oo 0 0 0 0 L 0 0 0 0 -JraJ ' 0 0 0 ' 0 0 0 kp^ae , n rpJDAE 0 a V Tp .nS V „ „ ^p_Brake । OV rpjlrake , _ 1 0 0 01 for ^=( n 10 1 0 01 *

[0094] Aa, Ba and Ca are respectively the state, control and observation matrices of the state representation of the hybrid model.

[0095] The control law design used to calculate the control takes into account the hybrid model. Although the DAE actuator, 4WS and braking are used in the hybrid model presented above, the method for obtaining this hybrid model will apply analogously with other actuators.

[0096] Now, step 400 of determining the order will be described.

[0097] The control synthesis of systems according to the prior art is generally provided by a PID (Proportional, Integral, Derivative) controller or equivalent. These controllers allow for efficient control of the system, but are not geared towards energy efficiency.

[0098] As discussed previously, the invention uses a control law Le which allows determining the optimal control (u) for the vehicle so that the vehicle output, for example the yaw rate of the vehicle (which can for example be

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109] measured by vehicle sensors), or equal to or very close to the reference setpoint given to the vehicle, while minimizing energy consumption. Thus, thanks to the method of the invention, which is based on a hybrid model of the vehicle and actuators, optimal control in terms of electrical energy of the electric motors is determined, allowing the system to respond as closely as possible to the input setpoint. The optimal control is obtained by aligning the system output with the input setpoint. This involves minimizing the difference e between the reference setpoint yref and the measured value J at the system output, with s ~ yref ~ y. The 400 control determination step (u) includes a constrained quadratic minimization step of a function depending on a control of at least one actuator of the system and the difference £. Therefore, the quadratic criterion must be minimized: J\u, £] = ^jt(urRu + sTQ e)dt With : • R: a symmetric positive matrix • Q: a non-negative, symmetric matrix • h and tf are the integration times • M: the command vector • : the difference between the reference setpoint yref and the measured value 4 The R and Q matrices have a size that depends on the number of sensors (if two sensors are used, they will be 2x2 matrices). They correspond to weighting factors that are established depending on whether one seeks precise tracking of the reference trajectory (in which case a significant weight is given to the Q matrix) or maximum energy efficiency (in which case a significant weight is given to the R matrix). The optimization of the quadratic criterion is performed under the following constraint: Xa = Aaxa + Bau y — CaXa ey j rej The optimal control u, solution of the quadratic criterion and subject to the constraint indicated above, is a minimal control in terms of electrical energy consumed, while ensuring good control performance since it is obtained for the lowest absolute value of s ~ yref ' J. The equation below illustrates this constrained optimization: / ed \ III 1 uop = argmin (J(u, s)) = argmin (ô L. (u + eTQ e)dt]

[0110] where argmin is the minimization function of the quadratic criterion J.

[0111] The solution of this minimization, u°p (optimal control obtained for 11), takes into account the dynamics of the hybrid model, via the term uTR u which involves the control of the system and via the term eTQ t' which involves the control error£ “ yref~^ where is provided by the hybrid model by a physical sensor or a software sensor.

[0112] The proposed quadratic criterion offers a compromise between reducing the difference from the reference and minimizing electrical energy consumption. This compromise can be adjusted by modifying the values ​​of the R and Q matrices. Accuracy increases with the value of Q, while electrical consumption is improved as the value of R increases.

[0113] It is thus understood that in the invention, the known vehicle control model based on the laws of physics (called the physical vehicle model) remains unchanged. It is supplemented or augmented, for each actuator used by the vehicle, by a model of the dynamics of said actuator. This yields the hybrid model. And based on this hybrid model, by using a minimization function of the quadratic criterion J, the optimal control for the vehicle is obtained, both in terms of energy efficiency and adherence to the setpoint trajectory.

[0114] According to the invention, the control determination method is implemented on the vehicle. The step of determining a model of the actuator dynamics, however, is performed offline, prior to determining the control law and before proceeding to vehicle operation. The control determination is done online, in real time by the chassis control system. The control law transforms a setpoint (for example, pressing the brake pedal or a steering wheel angle) into actions to be used by the actuators (braking power, wheel rotation, etc.) using the hybrid model of the actuator and the vehicle.

[0115] Figure 4 shows a control system that regulates the yaw rate of a vehicle (upper graph) and the associated braking torque (lower graph) with and without application of the method of the invention. The results shown in Figure 4, obtained from a numerical simulation, represent a control system for a vehicle equipped with an electric motor, in this case, differential braking actuators. The yaw rate of this vehicle is controlled with the control (curve Lc_MH_syst) obtained by the determination method according to the invention and without the control of the invention, i.e., with a traditional control (curve Lc_M_syst). The upper graph of Figure 4 illustrates the system output as a function of the reference setpoint (y_ref) for the two control laws, y_MH_syst being the system output obtained with a control law according to the invention, and y_M_syst being the The system output obtained with a traditional control law. In terms of control, we see that the control obtained by the method of the invention is better than that obtained in a traditional way since it exhibits fewer overshoots compared to the reference setpoint. Each time the reference setpoint is exceeded (in absolute value), it results in undue energy consumption. The control law used by the method of the invention thus provides better energy efficiency for the system.

[0116] The lower graph of [Fig. 4] representing the braking torque highlights that the control law used by the method of the invention makes it possible to significantly reduce the required braking torque compared to a traditional control law. Indeed, the braking torque associated with the control law used by the invention (curve Lc_MH_syst) is almost always lower in absolute value than the braking torque associated with a traditional control law (curve Lc_M_syst).

[0117] Thanks to the method of the invention, in addition to allowing the input setpoint to be reproduced as accurately as possible, the method of the invention also ensures, due to the use of the hybrid model and the consideration of the control of the system in the control law, a lower energy consumption, resulting in an increase in battery autonomy.

[0118] The method of the invention makes it possible to reduce the energy consumed during system commands. This results in a reduction of control energy, which means an increase in battery life. The method of the invention contributes to a reduction in actuator wear since they are subjected to only the minimum required load. This also implies an increase in the lifespan of energy storage systems because they undergo fewer charge and discharge cycles.

[0119] The invention also relates to a vehicle comprising at least one actuator and computing means configured to implement the method of determining a command to control at least one actuator 20, 30 for the vehicle.

[0120] The invention also covers a computer program comprising instructions for executing the method according to the invention as described above, when the program is executed by a processor.

[0121] The invention also relates to a processor-readable recording medium on which is recorded a program comprising instructions for executing the method of determining a command to control at least one actuator for a system, when the program is executed by a processor.

[0122] Although not limited to such applications, the embodiments of the invention are particularly advantageous for implementation in a vehicle, and particularly an autonomous vehicle.

[0123] A person skilled in the art understands that the system or subsystems according to embodiments of the invention can be implemented in various ways in the form of hardware, software, or a combination of hardware and software, in particular in the form of program code that can be distributed as a program product in various forms. In particular, the program code can be distributed using computer-readable media, which may include computer-readable storage media and communication media. The processes or methods described herein can, in particular, be implemented in the form of computer program instructions that can be executed by one or more processors in a computer processing device. These computer program instructions can also be stored in computer-readable media.

[0124] Of course, the invention is not limited to the examples just described, and many modifications can be made to these examples without departing from the scope of the invention. In particular, the features of different embodiments of the invention can be combined to carry out the invention, provided that these embodiments are not incompatible with each other.

Claims

1.

2.

3. Demands A computer-implemented method for determining a command (“ ) to control at least one actuator (20, 30) for a system (10), said method comprising the following steps: - Provision (100) of a physical model (M10) of the system (10); - Supply (200) of a model (M20, M30) of the dynamics of at least one actuator (20, 30); - Determination (300) of a hybrid model (MH 10) of the system (10) by concatenation of the physical model (M10) of the system (10) and the model (M20, M30) of the dynamics of at least one actuator (20, 30); - Determination (400) of a control (u) by minimizing a constrained quadratic criterion taking into account the hybrid model, and comprising: • a first part involving the system's control (") • a second part involving a difference (£) between a reference setpoint and a system response. Method according to claim 1, wherein the quadratic criterion comprises a weighted sum of the first part and the second part. Method according to claim 1 or 2, wherein: - the quadratic criterion (j(u, e)) is equal to ^ti{uTRu^eTQe}dt - the constraint is %a — "FB^U y — Caxa ey .--y - rej J with : - £ the difference between the reference setpoint and the system response (y), - R a symmetric positive matrix, - Q a non-negative symmetric matrix, - h and if integration times, - Aa a state matrix, Ba a control matrix and Ca an observation matrix of a state representation of the hybrid model (MH 10), - is the state variable of the hybrid model, and Xa its derivative.

4. A method according to any one of claims 1 to 3, wherein the model of the dynamics of at least one actuator is a trained model obtained by means of machine learning receiving as input a set of input data (E20, E30) of the actuator (20, 30) and a set of output data (S20, S30) of the actuator (20, 30) associated with the input data (E20, E30) (step 205).

5. A method according to claim 4, wherein the step (205) of determining a model (M20, M30) of the dynamics of the actuator (20, 30) comprises: - a first substep (210) of choosing a model (Mi) defined by initial parameters (Pi); - a second substep (220) of supplying the model (Mi) with a first input data (El) of the actuator to obtain a first output data (SMI) of the model (Mi); - a third substep (230) of determining a gap (40) between the first output data (SMI) of the model and the first output data (SI) of the actuator associated with the first input data (El) of the actuator; - a fourth sub-step (240) of adjusting the initial parameters (Pi) and carrying out the second and third sub-steps (220, 230) until the gap (40) is less than a first predefined value (50).

6. A method according to claim 5, wherein the step (205) of determining a model of the actuator dynamics further comprises a fifth substep (250) of validating the model of the actuator dynamics defined by performing the second substep (220) with a second input (E2), distinct from the first input (E1), to obtain a second output data (SM2) of the model and the execution of the third substep (230) with the second output data (SM2, S2), and if the deviation (40) is greater than a second predefined value (51), a sixth substep (260) of alert.

7. Method according to any one of claims 4 to 6, wherein the actuator dynamics model is a time-invariant linear model or a linear model with varying parameters.

8. Vehicle comprising at least one actuator and computing means configured to implement the method according to claim 1 wherein the system (10) is the vehicle and the at least one actuator is an electric motor equipping the vehicle.

9. A computer program comprising instructions for carrying out the method according to any one of claims 1 to 7, when the program is executed by a processor.

10. Processor-readable recording medium on which is recorded a program containing instructions for executing the method according to any one of claims 1 to 7, when the program is executed by a processor.