Optimal control method for a system based on a predictive model incorporating an adaptive observer

Abstract

The present invention relates to a method for determining at least one control setpoint ut of a system comprising, at time t: - a set of input quantities including the control setpoint ut and modeled as a vector: Ut, - a set of output quantities modeled as a vector: Yt, and - a set of quantities representing the state of the system and modeled as a vector: xt; the method being implemented in a computing unit and comprising: - a first step E1 of programming a set of linear differential equations between the input quantities, the system state quantities, and the output quantities, and - a step E4 of determining the optimal control setpoint using the quadratic programming method. Figure 6 for the abstract.

Description

Title of the invention: Optimal control method for a system based on a predictive model incorporating an adaptive observer. Technical field of the invention

[0001] The present invention relates to the field of industrial system control and more particularly to the automated optimization of the control law of a system.

[0002] The invention relates more specifically to a method for determining at least one control setpoint and an electronic card in which the method of the invention is implemented. Technical background

[0003] Traditionally, the formulation of the control law for an industrial system is carried out in a modeling step prior to implementation within the system's control unit. It relies on a model with modeling uncertainties, which leads to control that is not sufficiently robust for certain applications, for example when the control is applied to a fuel cell electric vehicle system.

[0004] Constructing a reliable model requires taking into account changes in the system over time, particularly those related to aging phenomena. To account for these changes, it is known to perform empirical recalibrations defined through tests on real systems conducted on test benches. However, these recalibrations can be tedious, and the test results may not be representative of all systems within the same series.

[0005] To overcome these drawbacks, solutions exist that involve integrating an algorithm into the system to adapt the control law according to the system's actual state. However, control laws are often based on physical models represented by nonlinear equations, making adaptation and parameter identification techniques complicated or even impossible. Furthermore, solving nonlinear equations requires significantly greater computing power, which must be implemented in particularly complex and expensive computers. Summary of the invention

[0006] The invention proposes a method for determining at least one control setpoint ut of a system comprising at a time t: - a set of input quantities including the control setpoint ut and modeled as a vector: Ut, - a set of output quantities modeled as a vector: Yt, and - a set of quantities representing the state of the system and modeled as a vector: xt; the process being implemented in a computing unit and comprising a first step El of programming a set of linear differential equations between the input quantities, the state quantities of the system and the output quantities in the form: [Math. 13] '^=4e t )xx t +^e t )xu t '.y t =c(e t )xx t +D(e t )xu t - where 0t = {g^, ... , g^} are slowly evolving parameters exhibiting a variation over time slower than Ut, Yt and xt and - where A(0t), B(0t), C(0t) and D(0t) are matrices with slowly evolving parameters {$1, ​​gj. @3 or jes -1 or 0; the process being characterized in that it comprises: - a step E4 for determining the optimal control setpoint using the quadratic programming method over a time window [To, To+NAT] containing N samples using the following quadratic criterion to be optimized: [Math. 14] J= ( x t xQxx t +u{xRx U t )]+(x ideal -x N ) T K[x ideaI -x N ^ - where Xideai is the vector representing the target state of the system, - where xT, and / \T, are the transposes of the vectors xt, Uet \xideal ~ xNI [xideal " - where Q, R and K are weighting matrices of the quadratic criterion to be optimized, - where N is a natural integer, The control setpoint ut is then obtained for N future samples from the present time Tp, the setpoint being expressed for each sample at time Tp +i = Tp + iAT as a function of: A(0t p+iX B(0t p+i), C(0t p+i) and D(0t p+i), Xy p+i, Q, R and K..

[0007] The process may further include: - a step E2, between steps E1 and E4, for determining the slowly evolving parameters 0t = {g^, g%, g^, ... , g^} by minimizing the difference e between the measured values ​​of the output quantities (Yt)mes and the values ​​calculated using mathematical equation 13 of the output quantities Yt: [Math. 15] e = (yf) - Yf v umes. 1

[0008] In step E2, the slowly evolving parameters 0t = {g2, ... , are obtained numerically after several iterations of solving equations 1 and minimizing the gap e in the time window [To, T0+NAT].

[0009] The method may include a further iteration of step E4 of determining the optimal control setpoint using the quadratic programming method when one of the slowly evolving parameters 0t = {01, g2, ... , ttt varied.

[0010] The method may include a step E5 of sending to a control unit of the system the optimal control setpoint of the next instant Tp +[ after each new iteration of the step E4 of determining the optimal control setpoint.

[0011] The method may further include: - a step E3 after step E2 or simultaneously with step E2, of adaptive observation including the numerical calculation of the state of the system xt at time t by numerical resolution of equations 1 taking into account the minimum deviation e at time t.

[0012] The process can be implemented in a fuel cell system comprising: - a battery, - a fuel cell, and - an electric motor, - Iba t is the intensity of the electric current in the battery, - IFC is the intensity of the electric current in the fuel cell, - f(IFC) is a function of IFC used in the calculation of VFC, with [Math. 17] 1 where: V" __ v FC ! 1 ~ mH2 J - Vbat is the electrical voltage in the battery, - VFC is the electrical voltage in the fuel cell. - mH2 is the consumption of dihydrogen in the fuel cell. with [Math. 18] F mL: ] where: X = V L v loss J - SoC is the state of charge of the battery, - mH2 is the consumption of dihydrogen in the fuel cell. - Vioss is the voltage related to electrical losses in the system.

[0013] Matrices A, B, C and D can have the following form: [Math. 19] 0 0' 1 0 o e4. [Math. 20] [Math. 21] 0 ' -1 0. [Math. 22] e7 o , o o e8' 1 oo o.

[0014] The method can be implemented in a system exhibiting effects fouling, or friction forces.

[0015] The invention also relates to an electronic card in which the method according to the invention is implemented. Brief description of the figures

[0016] Other features and advantages of the invention will become apparent upon reading the detailed description that follows, for an understanding of which reference should be made to the accompanying drawings in which:

[0017] [Fig-1] is a graph which represents a set of values ​​for a control setpoint of a system as a function of time, the values ​​being obtained by a process according to an embodiment of the invention;

[0018] [Fig.2] is an organizational chart representing the sequence of steps of a process according to an embodiment of the invention;

[0019] [Fig.3] is a flowchart representing steps E2 and E3 of the process of [Fig.2]

[0020] [Fig.4] is a flowchart representing the sequence of steps E2 to E5 of the process of [Fig.2];

[0021] [Fig.5] is a schematic representation of the operation of the components of a fuel cell electric vehicle system to which the process of the invention can be applied;

[0022] [Fig.6] is a flowchart schematically representing the application of the process from the invention to the system of the [Fig.5]. Detailed description of the invention

[0023] In the description that follows, identical, similar or analogous elements will be designated by the same reference numerals.

[0024] Figure 1 is a graph representing a set of values ​​for a control setpoint ut of a system as a function of time. The values ​​are obtained using the method of the invention, which enables the control of a system by predictive model. Values ​​were calculated for each time step k, k ranging from 0 to N in the example.

[0025] The method of the invention makes it possible to calculate, for each future time step within a given time window, an optimal control setpoint uk. The calculation is performed during a step E4 of the method, which will be detailed later. The calculation implements a direct quadratic programming method known per se.

[0026] Each iteration of step E4 calculates a set of optimal control setpoint values ​​uk for the upcoming time steps within a given time window. The set of values ​​obtained after an iteration of step E4 constitutes a control trajectory. The graph in [Fig. 1] shows several control trajectories resulting from the different iterations of step E4. Each control trajectory is represented by a specific line of varying darkness.

[0027] A new control trajectory is calculated, i.e., a new iteration of step E4 is performed, only when a parameter 0k of the system changes. 0k represents, for example, a parameter that evolves due to the aging of the system. In the example, between steps k=2 and k=3, the parameters 0k do not change, i.e., 03 = 02. The control trajectory is therefore not recalculated at step k=3, but it is recalculated for the other steps.

[0028] The dotted line represents the control setpoint uk actually sent to the system's control unit. For each step k, the control setpoint uk actually sent to the system's control unit corresponds to the last control setpoint value calculated for that step k.

[0029] Fig. 1 shows that the method of the invention makes it possible to control a system by predictive model by determining an optimal control setpoint adapted according to the actual behavior of the system.

[0030] Figure 2 represents the steps of a process according to one embodiment of the invention in the form of a flowchart.

[0031] The method of the invention is implemented in a computing unit of a system comprising, for example, a generic processor, a microprocessor, or an electronic circuit. The computing unit may be an integral part of a system control unit or may include means for wired or wireless communication with a system control unit. Furthermore, the computing unit in which the method is implemented includes a memory capable of storing values ​​for certain quantities involved in the algorithm of the method.

[0032] The process comprises the following steps: - a first step El of programming a set of linear differential equations between the input quantities, the state quantities of the system and the output quantities; - a second step E2 of determining the slowly evolving parameters; - a third adaptive observation step E3 including the numerical calculation of the state of the system at time t; - a fourth step E4 of determining the optimal control setpoint using the quadratic programming method; - a fifth step E5 of sending to the system the optimal control setpoint for the next instant.

[0033] The first step El corresponds to the implementation of the system behavior model in the system's computing unit.

[0034] The first step El involves programming a set of linear differential equations in the system's computing unit. The linear differential equations establish relationships between the input quantities, the system's state quantities, and the output quantities. The equations are in the form: [Math.l] ;%=jty;ixx t +B(e;ixu t ,Y t =c(e t )xx t +D(e t )xut - where 0t = {^2, g3, g^j are slowly evolving parameters exhibiting a slower variation over time than Ut, Yt and xt and - where A(0t), B(0t), C(0t) and D(0t) are matrices with slowly evolving parameters {^1, g2, g3, ... , 0$}, or 1, -1 or 0. ttt

[0035] Slowly evolving parameters 0t = {$2, @3 ... , g^} are parameters that do not necessarily have a physical meaning and that vary slowly in the time, in particular depending on the aging and wear phenomena occurring in the system components.

[0036] The second step E2 corresponds to the identification of system parameters. The second step E2 involves determining the slowly evolving parameters 0t =

[0037] Step E2 is based on reasoning which consists of considering that the measured values ​​of the output quantities (Yt)mes should theoretically be equal to the values ​​of the output quantities Yt calculated using equation 1. By introducing the measured values ​​into the equations and solving the system of equations, it is possible to deduce unknowns of the system.

[0038] In practice, the slowly evolving parameters 0t are obtained by minimizing the difference e between: - the measured values ​​of the output quantities (Yt)mes; and - the values ​​calculated using equation 1 of the output quantities Yt. The deviation e is expressed in the following form: [Math.2] e = (yj - Yf ' "mes. 1

[0039] Obtaining a zero error e is an indicator of good convergence of the identification algorithm towards the correct values ​​of the parameters 0t. This convergence is subject to conditions of excitation persistence of the input quantities ut. This is guaranteed by adding to the optimal control setpoint uk a very low amplitude, frequency-rich signal. The low amplitude allows for a negligible impact on the cost function J that we wish to optimize.

[0040] The third step E3 corresponds to adaptive observation, that is, an estimation of the system's state based on a model adapted over the system's lifetime. The model is adapted, that is, updated according to changes in the system's behavior, particularly with aging.

[0041] The third step E3 is performed after step E2 in order to have the slowly evolving parameters 0t available during step E3 for calculating the values ​​characterizing the state of the system. Step E3 involves the numerical calculation of the system state xt at time t by numerically solving equations 1, taking into account the minimum deviation e at time t and the slowly evolving parameters 0t obtained in step E2.

[0042] Alternatively, steps E2 and E3 are carried out simultaneously by a global solution of the equations.

[0043] The fourth step E4 corresponds to the expression of optimal control.

[0044] The fourth step E4 involves determining the optimal control setpoint ut using the quadratic programming method. The quadratic programming method is applied to a time window [To, To+NAT] containing N samples using the following quadratic criterion to be optimized: [Math.3] / =x Q* x t+ UfXRx U t )]+(x ideal -x N ) T K[x ideal -x N ) - where Xideai is the vector representing the target state of the system - where xT, TTt, and / \T, are the transposes of the vectors xt, Uet f \x ideal " x Ni [xideal ” ^v) ' - where Q, R and K are weighting matrices of the quadratic criterion to be optimized, - where N is a natural integer.

[0045] Each term of the quadratic criterion involves the product of a vector by its transpose vector, hence the name "quadratic".

[0046] The direct quadratic programming method is well known in the literature and is mainly applied to obtain an optimal control setpoint for linear models over a time window of N observations. Therefore, the details of the calculations implemented in the quadratic programming method are not included in this description.

[0047] By calculating the minimum of the quadratic criterion J, the control setpoint ut is obtained for N future samples from the present time Tp, the setpoint being expressed for each sample at time Tp +i =Tp+iAT, i being between 0 and N, as a function of: A(0T p+i), B(0t p+i), C(0t p+i) and D(0t p+i), xt p+b Q, R and K which are terms which can be expressed numerically, in particular thanks to step E2 which allows to obtain 0T p+ i and step E3 which allows to obtain xT ^numerically.

[0048] The fifth step E5 corresponds to the control of the system by predictive model.

[0049] The fifth step E5 involves sending the system control unit optimal control setpoint uTp+i of the next instant Tp +b The sending of the optimal control setpoint is carried out after each new iteration of the step E4 of determination of the optimal control setpoint.

[0050] The predictive model control strategy of the system is robust insofar as it is constantly adapted to the actual operation of the system, taking into account in particular the evolution of the system's operation with aging.

[0051] Steps E2 to E5 are carried out during the operation of the system. They can be implemented in an embedded manner, i.e. in a computing unit and a control unit integrated into the system.

[0052] Figure 3 represents steps E2 and E3 in flowchart form. Step E2, which identifies system parameters, and step E3, which involves adaptive observation, are closely linked. In these steps E2 and E3, the state estimators xk + [ and parameter estimators 0k + [ produce, at each time step k, the values ​​predicted at the following time step k+1.

[0053] Figure 3 shows that to perform the estimation at the next time step k+1, the adaptive observer requires the following input data: - the values ​​of the input quantities Uk sent to the control unit or measured, - the difference e between the values ​​of the measured output quantities (Yk) and the calculated output quantities Yk, the difference being provided for example by a comparator 12, - values ​​of the system state quantities xk and parameters 0k at the present time step k stored in a memory 10.

[0054] The state of the system xk+[ and the parameters 0k+i estimated for the next time k+1 are output data from steps E2 and E3 which will then be used in step E4 to update the optimal control setpoint uk+i.

[0055] In step E2, the slowly evolving parameters 0t = {01, ^2, g3, ... , 0^} can ttt can be obtained numerically after several iterations of solving equations 1 and minimizing the gap e in the time window [To, To+NAT]. Indeed, a recursive calculation allows asymptotic convergence towards the correct values ​​of 0t.

[0056] Similarly, in step E3, the values ​​of the state quantities of the system xt can be obtained numerically after several iterations of solving equations 1 and minimizing the gap e in the time window [To, To+NAT].

[0057] Figure 4 represents the sequence of steps E2 to E5 in the form of a flowchart. The predictive model control strategy that underlies this sequence of steps E2 to E5 aims to establish a link between the updated model and the optimal control setpoint in order to obtain a robust optimizer.

[0058] Figure 4 shows, in the form of a three-column table, the level at which each step is situated. The steps are distributed across the three levels as follows: - steps E2 and E3 are at the level of adaptive observation, i.e., determining the state of the system based on updated measurements, - step E4 is at the level of the optimization algorithm, i.e., expressing the optimal control, and - Step E5 is at the level of system control by predictive model, that is to say at the level of control.

[0059] After steps E2 and E3, the execution of step E4, which determines the optimal control setpoint, is subject to verification by a logic test 14 whose condition is as follows: 0k+i^ 0k- In other words, step E4 is triggered when one of the slowly changing parameters 0t = {^1, $2, $3, , varies. The step E5, sending the optimal control setpoint to the system, is automatically triggered at the end of step E4. Thus, if the condition 0k+i^ 0k is not verified, the command corresponding to the setpoint uk+i intended to be sent at step k+1 is not modified with respect to the setpoint value uk+i already in memory and the update of the command is disabled as shown in step E6.

[0060] Indeed, if the slowly evolving parameters 0t remain constant, then the update of the optimal control setpoint is disabled to avoid unnecessary calculations, since the control setpoint values ​​ut calculated for the N samples from time Tp remain unchanged. Thus, the control unit takes into account, at each time Tp + i = Tp + iAT, the last control setpoint uTp + i calculated for that time.

[0061] A new iteration of step E5 can be planned at the end of the time window Tp+NAT if no update of the optimal control setpoint ut has been made since the time TP.

[0062] The predictive model control strategy uses an internal model adapted over the life of the system by means of an adaptive observation method.

[0063] Figure 5 schematically represents the operation of the components of a fuel cell electric vehicle system 16 to which the method of the invention can be applied. In the example, the vehicle is a car or a truck. Alternatively, the vehicle could be any other type of vehicle such as a boat or an airplane.

[0064] System 16 comprises: - a junction box or distribution box 18 allowing the centralization of electrical connections between different electrical devices; - a 20V battery, - a fuel cell 22, - auxiliary components 24 of the fuel cell, and - an electric motor 26.

[0065] The arrows represent the exchange of electrical power between the components.

[0066] The battery 20 is capable of supplying or storing electrical energy, which is represented by a double-headed arrow pointing both towards the battery 20 for symbolize that it receives electrical energy to be stored in a storage mode or pointing towards the junction box 18 to symbolize that the battery 20 provides electrical energy in a supply mode.

[0067] The fuel cell 22 provides electrical energy through the oxidation of a reducing fuel, for example dihydrogen, at one electrode, coupled with the reduction of an oxidant, such as oxygen from the air, at the other electrode. The fuel cell 22 transmits the electrical energy produced to the junction box 18.

[0068] The auxiliary components 24 of the fuel cell include, for example, a compressor and a DC-DC converter, which is a power converter that converts a direct current (DC) source from a specified voltage level to a different voltage level. The auxiliary components 24 consume a portion of the electrical energy.

[0069] The electric motor 26 consumes electrical energy to provide motor torque but it can also provide electrical energy when it operates as a generator, for example during deceleration.

[0070] The power balance across the terminals of the junction box 18 is expressed by the equation below.

[0071] [Math.4] PW FC +Pw bat = PWreq~Pw auX

[0072] Where: - PwFc is the power supplied by the fuel cell 22, - Pwbat is the power supplied by the battery (positive sign in power mode and negative sign in storage mode), - Pwreq is the power supplied to the electric motor 26 (positive sign if the electric motor 26 consumes energy and negative sign when the electric motor 26 operates as a generator), - Pwaux is the power consumed by the auxiliary components 24.

[0073] The system comprises: - a set of input quantities modeled as a vector: Ut, - a set of output quantities modeled as a vector: Yt, and - a set of quantities representing the state of the system and modeled as a vector: xt.

[0074] The input quantities, the output quantities and the quantities representing the state of the system are quantities that depend on time t. In the following writings, the index "t" indicating the dependence on time is sometimes omitted to simplify the writings.

[0075] Input quantities and output quantities are quantities that can be measured or deduced from known information about the system.

[0076] The input quantities include: - the intensity of the IFC fuel cell supply current, which is the variable to be controlled and regulated, and for which we seek to calculate an optimal control setpoint ut, and - the power to be delivered to the electric motor Pwreq which is not a controllable quantity but which is assumed to be known insofar as the route to be taken by the vehicle is known.

[0077] The current intensity supplied to the IFC determines the fuel cell's operating regime. Thus, the higher the current intensity supplied to the IFC, the greater the amount of electrical energy produced by the fuel cell, and therefore the greater the instantaneous power delivered by the PwFC. Consequently, the higher the current intensity supplied to the IFC, the greater the hydrogen consumption required to provide the PwFC power.

[0078] The power to be delivered to the electric motor Pwreq is related to the powers PwFC, Pwbat, and Pwaux by the power balance at the terminals of the junction box 18 expressed above. Consequently, since Pwreq can be deduced from knowledge of the path to be followed by the vehicle, it is possible to introduce into the input variables the quantities involved in the calculation of PwFC, Pwbat, and Pwaux, namely Ibat and IFC.

[0079] The [Fig.6] is a flowchart representing the application of the process of the invention to system 16 of the [Fig.5].

[0080] The input quantities are modeled by the vector U below:

[0081] [Math.5] ' 4 ' U= 1 Or : - Iba t is the intensity of the electric current in the battery, - IFC is the intensity of the electric current in the fuel cell, - f(IFC) is a function of IFC used in the calculation of VFC. More precisely, it is the voltage-current characterization when the fuel cell system is in a new state (without aging or Vloss=0).

[0082] The output quantities include: - the electrical voltage in the battery (Vbat), - the electrical voltage in the VFC fuel cell, - the consumption of dihydrogen in the mH2 fuel cell. The output quantities are modeled by the vector Y below:

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] [Math.6] Or : - Vbat is the electrical voltage in the battery, - VFC is the electrical voltage in the fuel cell. - mH2 is the consumption of dihydrogen in the fuel cell. The quantities representing the state of the system include: - the state of charge of the SoC battery, - the consumption of dihydrogen in the mH2 fuel cell, - the voltage related to electrical losses in the Vioss system which characterizes the aging state of the fuel cell. The quantities representing the state of the system are modeled by the vector x below: [Math.7] [SoC ' V, loss J Or : - SoC is the state of charge of the battery, - mH2 is the consumption of dihydrogen in the fuel cell. - Vioss is the voltage related to electrical losses in the system. In the system of figures 5 and 6, equations 1 translate as follows: [Math. 8] ^=4th t )xx t +B(e t )xu t ,Y t =c(e t )xx t +D(e^ut [X = A(9)x+B(9)U „ , . ^^(9^+6^(3⁄4)3⁄4 or \ discrete shape ~ x l Y = C(9 )x+D(9)U 1 Yk=Cd(ek)xk+D <l(9t)Uli SoC(k+l)=SoC(k)+e1k*Ibat xk+l_ Let ( $k) xk + ( 9k ) Uk Yk= Cd(0k )xk+Dd(0k)Uk mH;!(k+1) = mH,(k) +02k* IFC(k) Vloss(k+1) = 03k*IFC + 04k*Vloss+95k T MX (PMkHKWbBl W*) “ ( V„al ) Vbat(k)= 06k*SoC(k) + 07k*Ibat(k)+98k VFC(k)=f(IFC(k))-V10SS(k) mH2(k) = mH2(k)

[0089]

[0090] week / Pwreq(k> IFC(k)*Vrc(k) \ ^FC f(IFc(k)) I 1 i The matrices A, B, C, and D have the following form: [Matt. 9] 0 0' 1 0 or e4. [Matt. 10] 0 0' 0 o or e5, [Matt. 11] 96 0 c = o 0 0 ' -1 0 . SoC W2 ^Joss, [Math. 12] o e8' io 0 0.

[0091]

[0092]

[0093] The slowly evolving parameters are linked to the aging of the battery 20 and the fuel cell 22. Indeed, the behavior of the battery 20 and that of the fuel cell 22 vary as they are used. Other equations allow us to translate the operating constraints of system 16. Thus, the relationships between current and voltage within battery 20 are translated. Similarly, the relationships between current and voltage within fuel cell 22 are translated. In the quadratic criterion J to be optimized, that is, minimized, the first term involving xt reflects the aging of system 16, and the second term involving Ut reflects consumption, particularly of dihydrogen. Thus, minimizing the quadratic criterion J does indeed lead to optimization, that is, a minimization, of both the aging of the system and its consumption.

[0094] The algorithm makes it possible to calculate, through the intensity of the IFC electric current in the fuel cell 22, the energy to be supplied by the fuel cell 22 in order to achieve several objectives, namely: - minimize the consumption of dihydrogen along a known route, - minimize the aging of the system and in particular the aging of the fuel cell 22 and the battery 20.

[0095] The algorithm is implemented in an electronic board controlling the power flows at the level of the junction box 18.

[0096] The invention can be used in other systems. For example, the invention can be used to design optimal control of systems such as:

[0097] - cooling circuit systems based on heat exchangers for to be more robust against the effects of fouling of the heat exchangers;

[0098] - electrical machines so that they are more robust against the forces of friction.

[0099] For these two examples, it is the dynamic model that will be modified and adapted to the input, output and state quantities of the system that intervene in the system under consideration.

[0100] The invention has many advantages which are described below.

[0101] The method for determining the control setpoint proposed by the invention is robust and precise because it is adaptive and based on actual measurements taken within the system.

[0102] The method is based on the search for a mathematical model linking the inputs and outputs of the system exhibiting a linear form so as to obtain a sufficiently accurate model and which allows the implementation of an algorithm for adapting and identifying the parameters.

[0103] The formulation of the control instruction as a function of: A(0t p+i), B(0t p+i), C(0t p+i) and D(0t p+i), xt p+i, Q, R and K allow for a relatively simple implementation of the determination algorithm in the computing unit. In particular, the measurement step is quite fast to perform and the implementation of the solution algorithms is computationally inexpensive. Thus, the implementation of the process does not, a priori, pose any real-time implementation problems.

[0104] Consequently, the method of the invention can be implemented by computing and control units comprising relatively simple and inexpensive processors.

[0105] The invention proposes a reliable embedded solution for optimizing energy consumption and aging of a system, in particular an electric vehicle with a fuel cell.

Claims

Demands

1. Method for determining at least one control setpoint ut of a system comprising at time t: - a set of input quantities including the control setpoint ut and modeled as a vector: Ut, - a set of output quantities modeled as a vector: Yt, and - a set of quantities representing the state of the system and modeled as a vector: xt; the method being implemented in a computing unit and comprising a first step El of programming a set of linear differential equations between the input quantities, the state quantities of the system and the output quantities in the form: [Math. 13] ,Yt=c(et)xxt+i^et)xut - where 0t = {^2, $3, , are slowly evolving parameters exhibiting a slower variation over time than Ut, Yt and xt and - where A(0t), B(0t), C(0t) and D(0t) are matrices containing the slowly evolving parameters { ûl, a2 û3, ..., û^}, or 1, -1 or 0; the process being characterized in that it comprises: - a step E4 of determining the optimal control setpoint by means of the quadratic programming method over a time window [To, T0+NAT] comprising N samples using the following quadratic criterion to be optimized: [Math. 14] J = ( x / 'xQxxt+[7^xPxt7t)]4- (xjdeal - xN)TK[xldsal - xJ - where Xideai is the vector representing the target state of the system - where xT, UT, and ( \T, are the transpose vectors of the \xidear xn) vectors xt, U f, and (y. ,_ y Y, and ü \xideal XN) - where Q, R and K are weighting matrices of the quadratic criterion to be optimized,. - where N is a natural integer, the control setpoint ut then being obtained for N samples to come from the present instant Tp, the setpoint being expressed for each sample of the instant Tp+i =Tp+iAT as a function of: A(9t p+1), B(9t p+1), C(9t p+1) and D(9T p+1), xT p+1, Q, R and K, and in that it is implemented in a fuel cell system (16) including: - a battery (29), - a fuel cell (22), and - an electric motor (26), with [Math. 16] Or : (UrFc) 1 - Ibat is the intensity of the electric current in the battery (29), - IFC is the intensity of the electric current in the fuel cell (22), - f(IFC) is a function of IFC used in the calculation of VFC, with [Math. 17] - Vbat is the electrical voltage in the battery (29), - VFC is the electrical voltage in the fuel cell (22), - mH2 is the consumption of dihydrogen in the fuel cell (22). with [Math. 18] [ X = IV, L v !oss Or : - SoC is the state of charge of the battery (29), - mH2 is the consumption of dihydrogen in the fuel cell (22), - Vioss is the voltage related to electrical losses in the system, and in that the matrices A, B, C and D have the following form: [Math. 19] 0 0' 1 0 oe 4 . [Math. 29] [Math. 21] 'e6 0 1 0 c= 0 0 -1 . 0 î 0 . [Math. 22] e7 0 0 E )8' D = 0 0 1 0 . 0 i 0 DJ

2. A method according to the preceding claim, characterized in that it It also includes: - a step E2, between steps E1 and E4, for determining the slowly evolving parameters 0t = {@1, @2, Q3, ... , 0^} thanks to the minimizing the difference e between the measured values ​​of the quantities output (Yt)mes and the values ​​calculated using the equation = Ut output quantities Yt: [Y t = C(0 t xx t +o(e t )xu t [Math. 15] e = (Yt) v Souls.

3.

4. A method according to the preceding claim, characterized in that in step E2, the slowly evolving parameters 0t = {0^, 02, g3 ... , 0^} are obtained numerically after several iterations of solving ,Yt=C(et)xxc+D(9t)xUt and minimizing the gap e in the time window [To, [To+NAT] A method according to any one of claims 2 or 3, characterized in that it comprises a further iteration of step E4 of determining the optimal control setpoint using the quadratic programming method when one of the slowly evolving parameters 0t = {a1, a2, a3, ... , 0^} varies. ttt *

5. Method according to claim 4, characterized in that it comprises a step E5 of sending to a control unit of the system the optimal control setpoint of the next instant Tp +i after each new iteration of the step E4 of determining the optimal control setpoint.

6. A method according to any one of claims 1 to 5, characterized in that it further comprises: - a step E3 after step E2 or simultaneously with step E2, of adaptive observation comprising the numerical calculation of the state of the system xt at time t by numerical resolution of =4et)*xt+B(et)xut '.Y,= C(et)xxt+D(et)>:Ut taking into account the minimum deviation e at time t.

7. A method according to any one of claims 1 to 6, characterized in that it is implemented in a system exhibiting fouling effects, or friction forces.

8. Electronic card in which the method according to any one of claims 1 to 7 is implemented.

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