Adaptive observation process integrating a linear predictive model

Abstract

The present invention relates to a method for adaptive observation of a system comprising at a time t: - a set of input quantities comprising the control setpoint ut and modeled in the form of a vector: Ut, - a set of output quantities modeled in the form of a vector: Yt, and - a set of quantities representing the state of the system and modeled in the form of a vector: xt; the method being implemented in a calculation unit and comprising: - a first step E1 of programming a set of linear differential equations between the input quantities, the state quantities of the system and the output quantities, - a step E2 of determining the slowly evolving parameters, and - a step E3 of adaptive observation comprising the numerical calculation of the quantities of the state of the system xt at time t by solving the set of linear differential equations. Figure for the abstract: Figure 6.

Description

Title of the invention: Adaptive observation method integrating a linear predictive model Technical field of the invention

[0001] The present invention relates to the field of industrial systems control and more particularly 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 instruction and an electronic card in which the method of the invention is implemented. Technical background

[0003] Conventionally, the formulation of the control law of an industrial system is carried out in a modeling step upstream of the implementation within the system control unit. It is based on a model presenting modeling uncertainties, which leads to control which is not sufficiently robust for certain applications, for example when the control is applied to a fuel cell electric vehicle system.

[0004] The construction of a reliable model requires taking into account changes in the system over time, linked in particular to aging phenomena. In order to take these changes into account, it is known to carry out empirical recalibrations defined by means of tests on real systems and carried out on test benches. However, these recalibrations can be tedious and the test results may not be representative of all the systems in the same series.

[0005] To overcome these drawbacks, there are solutions consisting of integrating into the system an algorithm for adapting the control law according to the actual state of the system. However, very often, the control laws are based on physical models represented by non-linear equations making the techniques for adapting and identifying parameters complicated or even impossible. In addition, solving non-linear equations requires greater computing power which must be implemented in particularly complex and expensive computers. Summary of the invention

[0006] The invention proposes a method for adaptive observation of a system comprising at a time t: - a set of input quantities including the control instruction ut and modeled in the form of a vector: Ut, - a set of output quantities modeled in the form of a vector: Yt, and

[0007]

[0008] - a set of quantities representing the state of the system and modeled in the form of a vector: xt; the method being implemented in a calculation unit and comprising a first step E1 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] Y, = CWx.r,+ W,)xU, - where 0t = {fl1, 0^, , 0^} are slowly evolving parameters exhibiting a variation in time slower than Ut, Yt and xt and - where A(0t), B(0t), C(0t) and D(0t) are matrices containing the slowly evolving parameters {g', 0~, 03, ... , or 1, -1 or 0; - a step E2 of determining the slowly evolving parameters 0t = {01, 0^, 0^, ... , 0^} by minimizing the difference e between the measured values ​​of the output quantities (Yt)mes. and the values ​​calculated using the mathematical equation. 13 of the output quantities Yt: [Math. 14] e = (Xt) - yz the process comprising: - a step E3 after step E2 or simultaneously with step E2, of adaptive observation including the numerical calculation of the quantities of the state of the system xt at time t by numerical resolution of the mathematical equations. 13 taking into account the minimum deviation e at time t. In step E2 or in step E3, the slowly evolving parameters 0t = {^, 0^, 0^, ... , 0^} or the quantities of the state of the system xt are obtained numerically after several iterations of solving the equations math. 13 and minimizing the gap e. The invention also relates to a method for determining at least one control instruction ut of a system at a time t comprising: - steps E1, E2 and E3 of the adaptive observation method according to the invention, - a step E4 of determining the optimal control setpoint using the quadratic programming method over a time window [To, T0+NAT] comprising N samples using the following quadratic criterion to be optimized: [Math. 15] [r-^t=Tn+NAT , yt / \ Lr=Ta (xlxQxXf+Ut xRxUt)^(xideal-xN) K\xideai-xNJ - where xideai is the vector representing the target state of the system - where xf, jj? and v \r, are the transposed vectors of the vectors xt, Ut, and 'X-^ideal And - where Q, R and K are weighting matrices of the quadratic criterion to be optimized, - where N is a natural whole number, the control instruction ut then being obtained for N samples to come from the present instant Tp, the instruction being expressed for each sample of the instant Tp+i =Tp+iAT as a function of: A(9Tp+1), B(0Tp+1), C(9Tp+1) and D(9Tp+1), xTp+1, Q, R and K.

[9999] The method may comprise a new iteration of step E4 of determining the optimal control setpoint using the quadratic programming method when one of the slowly evolving parameters 9t = {^, ... , varies.

[9919] The method may comprise a step E5 of sending to a control unit of the system the optimal control setpoint of the following instant Tp+i after each new iteration of step E4 of determining the optimal control setpoint.

[9911] The method can be implemented in a fuel cell system comprising: - a battery, - a fuel cell, and - an electric motor, with [Math. 16] - Ibat 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] Or : mm - 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] _ [ x _ Or : - SoC is the state of charge of the battery, - mH2 is the consumption of dihydrogen in the fuel cell, - Vioss is the voltage linked to electrical losses in the system which characterizes the aging state of the fuel cell, so that the linear equation math. 13 adapted online models the dynamics of Vioss aging of the fuel cell.

[9912] The matrices A, B, C and D can have the following form:

[0013]

[0014]

[0015] [Math. 19] '1 0 A= 0 1 LO 0 0 0 e4 [Math. 20] [Math.20] 'O1 0 0 0 e2 e3 oo e5 [Math. 21] [Math.21] O6 0 0 ' 0 0-1 .0 1 0 . [Math. 22] [Math.22] LO 1 0 08" 1 0 0 0.

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023] The method can be implemented in a system exhibiting fouling effects, or frictional forces. The invention also relates to an electronic card in which the method according to the invention is implemented. Brief description of the figures Other characteristics and advantages of the invention will appear during the reading of the detailed description which follows for the understanding of which reference will be made to the appended drawings in which: [Fig.l] 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 method according to an embodiment of the invention; [Fig.2] is a flowchart representing the sequence of steps of a method according to one embodiment of the invention; [Fig.3] is a flowchart representing steps E2 and E3 of the process of [Fig.2] [Fig.4] is a flowchart representing the sequence of steps E2 to E5 of the method of [Fig.2]; [Fig.5] is a schematic representation of the operation of the components of a fuel cell electric vehicle system to which the method of the invention can be applied;

[0024] [Fig.6] is a flowchart schematically representing the application of the method of the invention to the system of [Fig.5]. Detailed description of the invention

[0025] In the following description, identical, similar or analogous elements will be designated by the same reference numbers.

[0026] [Fig.l] 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 by means of the method of the invention allowing 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.

[0027] The method of the invention makes it possible to calculate, for each future time step in a given time window, an optimal control setpoint uk. The calculation is carried out during a step E4 of the method which will be detailed later. The calculation implements a direct quadratic programming method known per se.

[0028] Each iteration of step E4 makes it possible to calculate a set of optimal control setpoint values ​​uk for the future time steps in a given time window. The set of values ​​obtained after an iteration of step E4 constitutes a control trajectory. The graph in [Fig.l] comprises several control trajectories resulting from the different iterations of step E4. Each control trajectory is represented by a specific line of varying darkness.

[0029] A new control trajectory is calculated, i.e. a new iteration of step E4 is performed, only when a parameter 0k of the system varies. 0k represents, for example, a parameter which evolves under the effect of the aging of the system. In the example, between steps k=2 and k=3, the parameters 0k do not vary, i.e. 03 =02. The control trajectory is therefore not recalculated at step k=3, but it is recalculated for the other steps.

[0030] The dotted line represents the control setpoint uk actually sent to the system control unit. For each step k, the control setpoint uk actually sent to the system control unit corresponds to the last control setpoint value calculated for the step k in question.

[0031] [Fig.l] shows that the method of the invention makes it possible to carry out the control of a system by predictive model by determining an optimal control instruction adapted according to the real behavior of the system.

[0032] [Fig.2] represents the steps of a method according to an embodiment of the invention in the form of a flowchart.

[0033] The method of the invention is implemented in a calculation unit of a system comprising for example a generic processor or a microprocessor or even an electronic circuit. The calculation unit may be an integral part of a control unit of the system or may comprise wired or radio communication means with a control unit of the system. In addition, the calculation unit in which the method is implemented comprises a memory capable of storing values ​​for certain quantities involved in the algorithm of the method.

[0034] The method 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 for determining the slowly evolving parameters; - a third stage E3 of adaptive observation 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 the optimal control instruction for the following instant to the system.

[0035] The first step El corresponds to the implementation of the system behavior model in the system calculation unit.

[0036] The first step E1 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 state quantities and the output quantities. The equations are in the form: [Math.l] ^ = 4e^x,+^xu, Yt = c(et)xxt+D(et)xul - where 0t = {01, gj, ... , tf} are slow-changing 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 the slowly evolving parameters {^, 0^, ... , 0^}, or 1, -1 or 0.

[0037] The slow-changing parameters 0t = {0*, 0%, 0^, • • • , 0^} are parameters which do not necessarily have a physical meaning and which vary slowly over time, in particular as a function of the aging and wear phenomena occurring in the components of the system.

[0038] The second step E2 corresponds to the identification of parameters of the system. The second step E2 includes the determination of the slowly evolving parameters 0t = {01, 02, ^ ... , 0^}.

[0039] Step E2 is based on reasoning which consists of considering that the measured values ​​of the output quantities (Yt)mes must be equal in theory to the values ​​of the output quantities Yt calculated using equation 1. Thanks to the introduction of the measured values ​​into the equations and the resolution of the system of equations, it is possible to deduce unknowns of the system.

[0040] In practice, the slow-changing 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 difference e is expressed in the following form: [Math.2] e = (Yt) - Yt. KL / mes. 1

[0041] Obtaining a zero deviation 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 persistence of excitation of the input quantities ut. This is guaranteed by adding to the optimal control setpoint uk a signal of very low amplitude rich in frequency. The low amplitude makes it possible to have a neglected impact on the cost function J that we wish to optimize.

[0042] The third step E3 corresponds to adaptive observation, i.e. an estimation of the state of the system based on a model adapted during the life of the system. The model is adapted, i.e. updated based on the evolution of the behavior of the system, in particular with aging.

[0043] The third step E3 is carried out after step E2 in order to have available during step E3 the slow-evolving parameters 0t to calculate the values ​​characterizing the state of the system. Step E3 comprises 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 and the slow-evolving parameters 0t obtained in step E2.

[0044] Alternatively, steps E2 and E3 are carried out simultaneously by a global resolution of the equations.

[0045] The fourth step E4 corresponds to the expression of optimal control.

[0046] The fourth step E4 involves determining the optimal control setpoint ut using the quadratic programming method. The quadratic programming method is applied on a time window [To, T0+NAT] comprising N samples using the following quadratic criterion to be optimized: [Math.3] J = (# x Qx xt + Uj xRxUt) - where xideai is the vector representing the target state of the system - where xf, , and are the transposed vectors of the vectors xt, Ut, and (Xideal " XW)-' and - where Q, R and K are weighting matrices of the quadratic criterion to be optimized, - where N is a natural integer.

[0047] Each term of the quadratic criterion involves the product of a vector by its transposed vector, hence the name “quadratic”.

[0048] 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. Also, the details of the calculations implemented in the quadratic programming method are not included in this description.

[0049] By calculating the minimum of the quadratic criterion J, the control instruction ut is obtained for N samples to come from the present instant Tp, the instruction being expressed for each sample of the instant Tp+i =Tp+iAT, i being between 0 and N, as a function of: A(0Tp+i), B(0Tp+i), C(0Tp+i) and D(0Tp+i), xTp+i, Q, R and K which are terms that can be expressed numerically, in particular thanks to step E2 which allows us to obtain 0Tp+i and step E3 which allows us to obtain xTp+i numerically.

[0050] The fifth step E5 corresponds to the control of the system by predictive model.

[0051] The fifth step E5 comprises sending to a control unit of the system the optimal control setpoint uTp+i of the following instant Tp+i. The sending of the optimal control setpoint is carried out after each new iteration of step E4 of determining the optimal control setpoint.

[0052] The system control strategy by predictive model is robust insofar as it is constantly adapted to the actual operation of the system, taking into account in particular the evolution of the operation of the system with aging.

[0053] Steps E2 to E5 are carried out during 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.

[0054] [Fig. 3] represents in the form of a flowchart the steps E2 and E3. The step E2 of identification of system parameters and the step E3 of adaptive observation are two strongly linked steps. In these steps E2 and E3, the estimators of state xk+i and of parameters 0k+i produce at each time step k the values ​​predicted at the following time step k+1.

[0055] [Fig.3] shows that to perform the estimation at the next time step k+1, the adaptive observer needs input data: - the values ​​of the input quantities Uk sent to the control unit or measured, - the difference e between the values ​​of the output quantities (Yk) measured and the values ​​of the output quantities Yk calculated, the difference being provided for example by a comparator 12, - values ​​of the state quantities of the system xk and of the parameters 0k at the present time step k stored in a memory 10.

[0056] The state of the system xk+i and the parameters 0k+i estimated for the following instant 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+b

[0057] In step E2, the slowly evolving parameters 0t = {^, ^3, , can be obtained numerically after several iterations of solving equations 1 and minimizing the gap e in the time window [To, T0+NAT]. Indeed, a recursive calculation allows an asymptotic convergence towards the correct values ​​of 0t.

[0058] 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 difference e in the time window [To, To+NAT].

[0059] [Fig.4] represents the sequence of steps E2 to E5 in the form of a flowchart. The predictive model control strategy which is at the origin of 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.

[0060] [Fig.4] shows in a three-column table at which level each step is located. The steps are distributed across the three levels as follows: - steps E2 and E3 are at the level of adaptive observation, i.e. the determination of the state of the system based on updated measurements, - step E4 is at the level of the optimization algorithm, i.e. expression of optimal control, and - step E5 is at the level of system control by predictive model, i.e. at the command level.

[0061] After steps E2 and E3, the performance of step E4 of determining the optimal control setpoint is subject to the verification of a logic test 14 whose condition is the following: 0k+i^ 0k. In other words, step E4 is triggered when one of the slowly changing parameters 0t = {#', oj, ... , varies. Step E5 of 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 updating of the command is deactivated as shown in step E6.

[0062] Indeed, if the slowly evolving parameters 0t remain constant, then the updating of the optimal control setpoint is deactivated to avoid unnecessary calculations since the control setpoint values ​​ut calculated for the N samples from the instant Tp remain unchanged. Thus, the control unit takes into account at each instant Tp+i =Tp+iAT the last control setpoint uTp+i calculated for this instant.

[0063] 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 carried out since the instant TP.

[0064] The predictive model control strategy uses an internal model adapted over the life of the system using an adaptive observation method.

[0065] [Fig. 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 can be any other type of vehicle such as a boat or an airplane.

[0066] The system 16 comprises: - a junction box or junction box 18 allowing the centralization of electrical connections between different electrical devices; - a 20 battery, - a fuel cell 22, - auxiliary components 24 of the fuel cell, and - a 26 electric motor.

[0067] The arrows represent the exchanges of electrical power between the components.

[0068] The battery 20 is capable of providing or storing electrical energy, which is represented by a two-way arrow pointing both towards the battery 20 to symbolize that it is receiving electrical energy to be stored in a storage mode or pointing towards the junction box 18 to symbolize that the battery 20 is providing electrical energy in a supply mode.

[0069] The fuel cell 22 makes it possible to provide electrical energy by means of the oxidation on one electrode of a reducing fuel, for example dihydrogen, coupled with the reduction on the other electrode of an oxidant, such as oxygen from the air. The fuel cell 22 transmits the electrical energy produced to the junction box 18.

[0070] The auxiliary components 24 of the fuel cell, for example, comprise 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 another different voltage level. The auxiliary components 24 consume a portion of the electrical energy.

[0071] The electric motor 26 consumes electrical energy to provide engine torque but it can also provide electrical energy when it operates as a generator, for example during deceleration.

[0072] The power balance at the terminals of the junction box 18 is expressed by the equation below.

[0073] [Math.4] PWFC + Pwba[ = PWreq -Pwaux

[0074] Where: - PwFC is the power supplied by the fuel cell 22, - Pwbat is the power supplied by battery 20 (positive sign in power supply mode and negative 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.

[0075] The system comprises: - a set of input quantities modeled in the form of a vector: Ut, - a set of output quantities modeled in the form of a vector: Yt, and - a set of quantities representing the state of the system and modeled in the form of a vector: xt.

[0076] The input quantities, the output quantities and the quantities representing the state of the system are quantities which depend on time t. In the following writings, the index "t" indicating the time dependence is sometimes omitted to simplify the writings.

[0077] The input quantities and the output quantities are quantities that can be measured or deduced using known information about the system.

[0078] The input quantities include: - the intensity of the supply current of the IFC fuel cell which constitutes 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 to the extent that the journey to be made by the vehicle is known.

[0079] The intensity of the supply current of the fuel cell IFC determines the operating regime of the fuel cell. Thus, the greater the intensity of the supply current of the fuel cell IFC, the greater the quantity of electrical energy produced by the fuel cell and therefore the greater the instantaneous power delivered by the fuel cell PwFC. Consequently, the greater the higher the current intensity of the IFC fuel cell supply, the higher the consumption of dihydrogen to provide the PwFC power.

[0080] The power to be delivered to the electric motor Pwreq is linked 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 the knowledge of the journey to be made 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.

[0081] [Fig.6] is a flowchart representing the application of the method of the invention to the system 16 of [Fig.5].

[0082] The input quantities are modeled by the vector U below:

[0083] [Math.5] [ A„ 1 L i J Or : - Ibat is the intensity of the electric current in the battery, - The is the intensity of the electric current in the fuel cell, - f(IFc) is a function of Le involved in the calculation of VFC. More precisely, it is the voltage current characterization when the fuel cell system is in new condition (without aging or Vloss=0).

[0084] The output quantities include: - the electrical voltage in the battery Vbat, - the electrical voltage in the fuel cell VFC, - the consumption of dihydrogen in the fuel cell mH2. The output quantities are modeled by the vector Y below:

[0085] [Math.6] y _ 'Vc 2 - mH2 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.

[0086] The quantities representing the state of the system include: - the state of charge of the SoC battery, - the consumption of dihydrogen in the fuel cell mH2, - the voltage linked 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:

[0087]

[0088] [Math.7] [soc i I V, iw 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] ^=A(B^xxt + B(0t)x Ut Yt = C(0^xt+D{Dt)xVt

[0089]

[0090] X = A(6)x + B(0)U [ xk+l - Ad ( 0k ) xk + Bd ( 6k ) Uk K=cd(ek >k + Dd(0k)Uk fxk+1 -FLUENT d (0 k )x k +B d (0 k )U k discrete form -* A , x . |Y k = C d (Sure k + D d (0 k )U k SoC(k+l)-SoC(k)+eVlbat mH,(k+ 1) = mfk(k) + 92^ IFC(k ) VUk+l)= 63k*IFC+ ù4k^Vloss+05k T / 1 \ ('PwUkj-WkW^ \ =» Lut 1 k ) = [------—v^~------- I VUk) = e6k*SoC(k) + 07k*Ibat(k) +6sk vFC(k)=f(Mk))-vloss(k) rîiH2(k) = mH / k)

[0091] / Pwreq ( k ) − læ ( k ) '-V( k ) V FC «H, u= IFC f(Wk)) SoC' mH2

[0092] L 1 The matrices A, B, C, and D have the following form:

[0093] [Fig.9] [Matt. 10]

[0094] [Fig. 10] 0 0 0' 0 2 0 0 0 3 0 Q 5 . [Math. 11]

[0095] [Math. 11] 0 -1 0 . [Math. 12] [Math. 12] ô7 0 .0 0 9 8 " 1 0 0 0.

[0096] The slowly changing 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.

[0097] Other equations make it possible to translate the operating constraints of the system 16. Thus, the relationships between current and voltage within the battery 20 are translated. Similarly, the relationships between current and voltage within the fuel cell 22 are translated.

[0098] In the quadratic criterion J to be optimized, that is to say minimized, the first term involving xt reflects the aging of the system 16 and the second term involving Ut reflects the consumption, in particular of dihydrogen. Thus, minimizing the quadratic criterion J does indeed result in an optimization, that is to say a minimization, of both the aging of the system and its consumption.

[0099] The algorithm makes it possible to calculate, through the intensity of the electric current IFC in the fuel cell 22, the energy to be supplied by the fuel cell 22 so as 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.

[0100] The algorithm is implemented in an electronic card controlling the power flows at the junction box 18.

[0101] The invention can be used in other systems. For example, the invention can be used to design the optimal control of systems such as:

[0102] - cooling circuit systems based on heat exchangers for be more robust against the effects of fouling of the exchangers;

[0103] - electrical machines so that they are more robust against the forces of friction.

[0104] For these two examples, it is the dynamic model which will be modified and adapted to the input, output and state quantities of the system which intervene in the system considered.

[0105] The invention has numerous advantages described below.

[0106] The control setpoint determination method proposed by the invention is robust and precise because it is adaptive and based on actual measurements made within the system.

[0107] The method is based on finding a mathematical model linking the inputs and outputs of the system in a linear form so as to obtain a sufficiently precise model and which allows the implementation of an adaptation and parameter identification algorithm.

[0108] The formulation of the control setpoint as a function of: A(0Tp+i), B(0Tp+i), C(0Tp+i) and D(0Tp+i), xTp+i, Q, R and K allow a relatively simple implementation of the determination algorithm in the calculation unit. In particular, the measurement step is quite quick to perform and the implementation of the resolution algorithms is inexpensive in terms of calculation time. Thus, the implementation of the method does not pose a priori any real-time implementation problem.

[0109] Therefore, the method of the invention can be implemented by computing and control units comprising relatively simple and inexpensive processors.

[0110] The invention proposes a reliable on-board solution for optimizing the energy consumption and aging of a system, in particular a fuel cell electric vehicle.

Claims

Claims

1. Method for adaptive observation of a system comprising at a time t: - a set of input quantities including the control instruction ut and modeled in the form of a vector: Ut, - a set of output quantities modeled in the form of a vector: Yt, and - a set of quantities representing the state of the system and modeled in the form of a vector: xt; the method being implemented in a calculation unit and comprising a first step E1 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] $ = a(i0 xx,+b(0) xu, Y, = c(e^x,+D{e^u, - where 0t = {01, 0^, 0^, ... , 0^} are slow-changing parameters with 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 slow-changing parameters {^, 0^, ... , 0^}, or 1, -1 or 0; - a step E2 of determining the slowly evolving parameters 0t = { , 0^, thanks to the minimization of the gap e between the values measured output quantities (Yt)mes and the values ​​calculated using the equation [ _ A(^) X xt + X Ut of the output quantities Yt: [Math. 14] e = (ïQ - KJc process being characterized in that it comprises: - a step E3 after step E2 or simultaneously with step E2, of adaptive observation comprising the numerical calculation of the quantities of the state of the system xt at time t by numerical resolution of the equations § =A(e^xx,+ B(0t)x Ut Yt^c(et)xxj+D(et)x ut minimum at time t. taking into account the difference e

2.

3.

4.

5. Method according to the preceding claim, characterized in that in step E2 or in step E3, the slowly evolving parameters 0t = {^, #2, ... , ^} or the quantities of the state of the system xt are obtained nu mechanically after several iterations of solving ÿ = Afa) X xt + X Ut and minimization of the gap e. Y^C^xxt + D^xUt Method for determining at least one control instruction ut of a system at a time t characterized in that it comprises: - steps E1, E2 and E3 of the adaptive observation method according to any one of claims 1 or 2, - a step E4 of determining the optimal control setpoint using the quadratic programming method over a time window [To, To+NAT] comprising N samples using the following quadratic criterion to be optimized: [Math. 15] J = [Lf=2-0 (xf x Q x xt + U} XRX Ut ) j+(xideaJ - xN) K\xideal - - where Xideai is the vector representing the target state of the system - where xf, u?, and (x Xf^, are the transposed vectors of the vectors xi - where Q, R and K are weighting matrices of the quadratic criterion to be optimized, - where N is a natural whole number, the control instruction ut then being obtained for N samples to come from the present instant Tp, the instruction being expressed for each sample of the instant Tp+i =Tp+iAT as a function of: A(0Tp+1), B(0Tp+1), C(0Tp+1) and D(0Tp+1), xTp+1, Q, R and K. Method according to claim 3, characterized in that it comprises a new iteration of step E4 of determining the optimal control setpoint by means of the quadratic programming method when one of the slowly evolving parameters 0t = {. , f^} varies. Method according to any one of claims 3 or 4, characterized in that it comprises a step E5 of sending to a control unit of the system the optimal control setpoint of the following instant Tp+i after each new iteration of step E4 of determining the optimal control setpoint.

6. Method according to any one of the preceding claims, characterized in that it is implemented in a fuel cell system (16) comprising: - a battery (20), - a fuel cell (22), and - an electric motor (26), with [Math. 16] Or : - Ibat is the intensity of the electric current in the battery (20), - 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] Or : - Vbat is the electrical voltage in the battery (20), - VFC is the electrical voltage in the fuel cell (22), - mH2 is the consumption of dihydrogen in the fuel cell (22). with [Math. 18] . _ 1 where:

7. - SoC is the state of charge of the battery (20), - mH2 is the consumption of dihydrogen in the fuel cell (22), - Vioss is the voltage related to electrical losses in the system which characterizes the aging state of the fuel cell (22), so that the linear equation ÿ - A^ X xt + B^t) X Ut adapted online models the Yt=c(et)xxt+D(et)*ut Vioss aging dynamics of the fuel cell. Method according to the preceding claim, characterized in that the matrices A, B, C and D have the following form: [Math. 19] A= 0 1 LO 0 0' 0 0 4 . [Math.20] • 1 61 0 0 0 B = o e2 o 0 .0 o3 () 0 5 « [Math.21] [Math.21] 06 0 o' C = 0 0-1 .0 1 0 . [Math.22] [Math.22] ô7 0 0 0 8' D- 0 0 1 c 0 1 0 c

8.

9. Method according to any one of claims 1 to 5, characterized in that it is implemented in a system having fouling effects, or friction forces. Electronic card in which the method according to any one of claims 1 to 8 is implemented.

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