Method for calibrating a Kalman filter estimator for controlling a fault detection and isolation device on a measurement channel of a redundant sensor
Patent Information
- Application Number
- FR2023002775
- Authority / Receiving Office
- FR · FR
- Patent Type
- Patents
- Current Assignee / Owner
- Filing Date
- 2023-03-23
- Publication Date
- 2025-03-07
- Estimated Expiration
- 2043-03-23
Smart Images
Figure 00000020_0000
Abstract
Description
Title of the invention: Method for calibrating a Kalman filter estimator for controlling a fault detection and isolation device on a measurement channel of a redundant sensor Technical field
[0001] The technical field of the invention is control systems, in particular integrated into aircraft, and more specifically control systems with Kalman filter estimator comprising a redundant sensor. Previous techniques
[0002] LVDT sensors (acronym for "Linear Variable Differential Transformer") are sensors for measuring linear displacement based on the operating principle of an electrical transformer. In the aeronautical field, such sensors are used to determine the linear position of actuators, such as cylinders, in particular for fuel metering or controlling the variable geometry of compressor blades.
[0003] Such LVDT sensors are used in control loops that are carried out in two parts:
[0004] - a first, global part, calculating instructions of an actuator involving a cylinder equipped with an LVDT sensor depending on a model,
[0005] - a second, local part, carrying out the actuator instructions according to a actuator response curve.
[0006] The application to the aeronautical field generally involves the redundancy of the controls, or at least of the measurement sensors. Thus, each LVDT sensor is generally redundant to provide resistance to errors and drifts of the actuator. The redundant LVDT sensor then comprises two measurement channels, one called local, the other called cross.
[0007] However, each redundant LVDT sensor can also suffer from errors and drifts. In such cases, a position measurement deviation appears between the two redundant channels of the same sensor. If this deviation exceeds a predefined threshold, called the cross-check threshold, the deviation must be taken into account.
[0008] During such a "cross-check" failure, it may then be necessary to select one of the two measurement channels of the redundant sensor, or an average of the two measurement channels. To ensure the accuracy and reliability of the measurement provided by the sensor, it is necessary to ensure proper localization of an erroneous or faulty measurement channel.
[0009] From the state of the prior art, documents US20200201312 are known, CN110118128 and US2009043447, each of which describes the detection of the failure of a sensor measuring one quantity in relation to other sensors measuring different quantities, in particular through a particular architecture of Kalman filters. These documents describe the use of "banks" (i.e. several different Kalman filters) used with the same sensors. The interpretation of the residuals (i.e. differences between the model outputs and the sensor measurements) makes it possible to detect the faulty sensor, but does not always make it possible to locate a faulty measurement channel.
[0010] In order to determine a faulty channel of a redundant LVDT sensor by applying a single Kalman filter, it is necessary to have an optimal calibration of said Kalman filter estimator, making it possible to have a capacity to choose the healthy measurement channel more quickly and reliably than in the case of arbitrary calibration of the estimator. Statement of the invention
[0011] The subject of the invention is a method for calibrating a Kalman filter estimator included in a control system of a device provided with at least one piece of equipment, the control system comprising at least one redundant sensor configured so as to determine a quantity of the at least one piece of equipment, the redundant sensor comprising two redundant measurement channels, the calibration method comprising the following steps:
[0012] a. identification of a set of reference commands of the device,
[0013] b. determination of a cost function depending on a set of time constants also defining the Kalman filter, of a threshold of difference in measured quantity between the two channels of the same redundant sensor beyond which it is considered that a fault is present, of a compromise parameter defining the priority given to the speed of convergence or to the precision of the estimator, and of the difference for each item of equipment between measured quantity and quantity estimated by the Kalman filter estimator, the difference being calculated for at least two instants included in the duration of the set of reference commands,
[0014] c. optimization by minimizing the value of the cost function by varying the set of time constants for a given compromise parameter value,
[0015] d. repeating the optimization by minimization for at least one other trade-off parameter value, and
[0016] e. determination of the set of time constants associated with a compromise parameter value of which the root mean square error between the measured value and the estimated value of the position of the equipment and the sum of the time constants are each less than a threshold, said set of time constants calibrating the Kalman filter estimator.
[0017] To determine the value taken by the cost function for a set of time constants, the following sub-steps can be carried out:
[0018] a. determination of the gain of the Kalman filter for the set of time constants and for each operating point around which the device has been linearized,
[0019] b. determining the estimated value of the measurement of the redundant sensor associated with each piece of equipment of the device by means of the Kalman filter estimator in the entire set of reference commands identified and for the at least two instants included in the duration of the set of reference commands.
[0020] To achieve optimization by minimizing the value of the cost function, a genetic algorithm can be used.
[0021] Another object of the invention is a method for controlling a device provided with at least one item of equipment, said device being further provided with at least one sensor capable of each measuring an operating quantity of the device, and a redundant sensor for each item of equipment so as to have two measurement channels for each physical quantity measured, the control method comprising the following steps: a. a Kalman filter estimator is calibrated by the calibration method as described above, b. a selected measurement is determined for the at least one controlled equipment, by the calibrated Kalman filter estimator, as a function of the at least one measurement of the operating quantity of the device and the measurements of the measurement channels of the redundant sensor for the controlled equipment, then c. a command is determined for the at least one piece of equipment based on the at least one measurement of the operating quantity of the device and the measurement selected for the controlled piece of equipment, and d. a failure of one of the measuring channels of the redundant sensor is detected so as to exclude the measuring channel.
[0022] The invention also relates to a system for controlling a device provided with at least one piece of equipment, the control system comprising at least one sensor capable of each measuring an operating quantity of the device, and a redundant sensor for each piece of equipment, at least one nested control means configured to determine a command to the at least one piece of equipment as a function of the measurement of at least one operating quantity of the device and a measurement selected for the controlled equipment, the control system further comprising a calculation means configured to determine the measurement selected for the at least one controlled equipment, by a Kalman filter estimator, as a function of the at least one measurement of the operating quantity of the device and measurements of the measurement channels of the redundant sensor for the controlled equipment, the calculation means being further configured to detect a failure of one of the measurement channels of the redundant sensor so as to exclude the measurement channel, in which the Kalman filter estimator is calibrated by the calibration method as described above.
[0023] The device may be an aircraft engine and the measurement channels of the redundant sensor may measure the position of the variable geometry cylinders, the position of the fuel metering valve, the variable timings of the stators of the high pressure compressor of the engine, the measurement of the temperature at the inlet of the high pressure compressor of the engine, or the measurement of static pressure at the inlet of the combustion chamber of the engine.
[0024] The equipment may be an actuator of the aircraft engine, for example a jack.
[0025] The redundant sensor may be an LVDT sensor.
[0026] The invention also relates to an aircraft equipped with a control system as described above. Brief description of the drawings
[0027] Other aims, characteristics and advantages of the invention will appear on reading the following description, given solely by way of non-limiting example and made with reference to the appended drawings in which:
[0028] - figure [Fig.l] illustrates the main steps of a calibration process according to a exemplary embodiment of the invention. Detailed description
[0029] A device can be modeled by a state representation, based on a vector of the states of the device, noted x, a vector of the commands applied to the device, noted u and a vector of the measurements of the device, noted y.
[0030] In an ideal case, the modeling of the device is linear and the state representation can then be written:
[0031] [Math.l] xk+1 = A xk +B uk yk-C xk + Duk
[0032] With:
[0033] A,B,C,D: adjustment matrices, specifying the contribution of each value of the vectors x and u on the values of the vector x at the following iteration and on the values of the vector y.
[0034] In reality, the modeling of a device is often non-linear. We then note the state representation of the device as follows:
[0035] [Math.2] . yk=h{^^)
[0036] The resolution of the system of equations included in the modeling of a device can then be long and complex depending on the nature of the functions f and h.
[0037] A device (for example, a motor), or equipment it comprises (for example, an actuator), generally operates over a reduced range of values, also called the operating regime. We then seek to linearize the functions f and h by limited development around a defined operating point n0} included in the operating regime. Considering that / (xq, w0) = x0 and h(xQ, Uq) = due to the operation in steady state, and considering that _ df(xM), g _ _ a / iGyd , and p „ 3k(x,u), we obtain the system of equations dx of the dx of the [Math 3] below after having carried out the limited development of the functions f and h of the system of equations [Math 2].
[0038] If it is necessary to have modeling over a wider range of values, for example to accommodate a wider operating regime, it is then appropriate to carry out other linearizations around other operating points covering the wider range of values.
[0039] For the operating point {xq, , the values of the states, commands and outputs are constant and have respectively the value 3 o- The modeling of the device can then be represented in the following way:
[0040] [Math.3] ' - *0 = A ( xk ~xo) + B ( ltk - ) ■ yk ■ >'o = C (xk - x0) + D (- Uo)
[0041] Knowing this representation of the device around the operating point {jt'o, Wo], we now seek to make an estimate of it.
[0042] An estimator, in the context of state representation, is an algorithm for estimating a state for one of the following reasons:
[0043] - the state is measured with high uncertainty,
[0044] - the state is not measured, and we do not want to add a sensor to the device, or
[0045] - the state corresponds to an intrinsic quantity that is impossible to measure di directly (for example, efficiency, section, convection coefficient, etc.).
[0046] The estimator of the measurement of a redundant LVDT sensor of an equipment i of the device will now be described.
[0047] We set the difference e of a quantity measured by the LVDT sensor of the equipment i equal to the difference between the measured value LVDTj mes of this quantity and the actual value L VDTi reei of this quantity.
[0048] [Math.4] z = LVDTireel-LVDTimes
[0049] We seek to reduce this gap by iterative calculation.
[0050] We note the function which links the real position of the equipment i and the quantity x that one wishes to control via the equipment i.
[0051] [Math.5] x, = gi(LVDTiml)
[0052] The function is bijective so that TV DT- { =
[0053] We then introduce 8 which represents the difference between the value of the command effect tively applied to the system and the value of the command corresponding to the LVDT measurement. We then obtain a system of equations of the following form.
[0054] [Math.6] « = VDT, - g^LVDT, J
[0055] We thus obtain a new set of vectors, comprising the state vector x, the control vector u and the measurement vector y between which the quantities x, the LVDTi measurements and the 0 commands are distributed.
[0056] The state representation is used to predict the measurements yk that should be obtained. The quantities y are measured by the redundant LVDT sensors. A deviation £ is determined for each quantity as a function of the predicted value and the corresponding measurement of the redundant LVDT sensor, then each command 9 is estimated as a function of the measurements yk and the quantities y and the deviation £.
[0057] These steps are carried out twice in parallel, once for the data from the local channel of each redundant LVDT sensor and once for the data from the cross channel of each redundant LVDT sensor. It is recalled that a redundant LVDT sensor comprises two redundant measurement channels, called local channel and cross channel, normally carrying close values.
[0058] A difference between the values of the local channel and the cross channel of the same redundant LVDT sensor can be determined and this difference can be compared to a so-called cross-check threshold. If the difference is greater than the cross-check threshold, a fault is present and one of the two channels must be chosen as the healthy channel. This is achieved by considering the healthy channel as the one having the value with the smallest difference compared to the estimate of the measured quantity LV DT, meas.
[0059] To be able to estimate them, we add to the vector of states x the values 0 of the differences between the command deduced from the LVDT position measurement and the actual command applied to the device. These 0 values are called disturbances in the rest of this document.
[0060] Adding these perturbations to the vector of states x makes it possible to reformulate the representation state representation of the equation [Math 3]. The state representation taking into account the per turbations is then as follows.
[0061] L0 ■■■ 0 0
[0062]
[0063]
[0064]
[0065] With : HAS ■■■ 0 1 ■■■ 0 0 B 1, ■■■ 0 ■■■ 0. D],
[0066] DP=[CD].
[0067] A state estimator of a dynamical system is defined by the fundamental equation next:
[0068] [Math. 8] +D(uk-uo) - (zk-y0) )
[0069] With:
[0070] : the estimated value of the state,
[0071] zk ; the measurements of the quantities obtained by the sensors at time k
[0072] The value of the state is updated with the equation of the dynamics of the model ( A(^-.ï0) + B(z^ - Mo)), corrected by the difference between the predicted values of the measured quantities ((7 ( ) + D( / ¾ - Uq) - Zj, - y P ct 'cs values actually measured ">0).
[0073] In equation [Math 8], the matrix K, called the gain of the estimator, allows us to
[0074] weight the corrective term. In other words, the K matrix allows us to weight the trade-off between model and measurements. When the values of the matrix K are small, the estimated value - x0 will depend mainly on the term A ( xk - x0 ) + B (uk- ) and little on the term C(Xk -XQ) + DÇ Uk - Uq) - yj In other words, the estimated value depends more of the model than of the measurement. The estimate then converges slowly but is more robust to measurement errors.
[0075] Conversely, when the values of the matrix K are strong, the estimated value xk+\ - Xq depends essentially on the term C(xk - Xo) + D(lik - Uq ) - ( and little of the term A ( xk - x0 ) 4- B ( uk - w0 ). The estimated value then depends more on the measurement than on the model. The estimate converges quickly but is more sensitive to errors in measure.
[0076] The operation of determining the matrix K is called synthesis of the estimator. Among the different methods of estimator synthesis, the resolution of the algebraic Riccati equation will be preferred, making it possible to arrive at a Kalman filter. These disturbances are generally linked to the internal disturbances of the disturbance model, to the sampling frequency T of the estimation, and to the time constants Ti of the calculation means implementing the estimator.
[0077] [Math.9] ' x&k + && ' ^k . ek = c0-xek+D0-(jk
[0078] With:
[0079] Ae = Id
[0080] B0 = Teld
[0081] C^Id
[0082] [t, ■■■ 0' d» = ; \ ; .0 ■ ' ' T n _
[0083] Id = identity matrix
[0084] The values x0( with i = k or k+1 correspond to the value of the internal disturbances in the disturbance model. The values 0, are used to feed the model. The value Te corresponds to the sampling frequency of the estimation. The values ' / are time constants, calibrated by the implementer, and which correspond to the dynamics that we wish to assign to the estimation of the disturbance on the corresponding equipment. The values C are virtual inputs, assigned to each equipment.
[0085]
[0086]
[0087] We then carry out the serialization of the disturbance model [Math 7] with the device model [Math 3]. In other words, we determine the disturbances as a function of the virtual input values by the disturbance model and then we inject these disturbances 0, into the linearized model as a control vector u. We then obtain a new system of equations having a form similar to the previous model of the device, but dependent on the virtual inputs of the equipment and represented by the following system of equations. [Math. 10] ' Xk+Ï " X0 “ ' ( Xk ~ A'o) ^3' X^k+l = A&-X0k+BP<7k yk "*0 = C' - ¾) + D' (Q' - «0)
[0088]
[0089] Note that the device is always modeled around the operating point
[0090] The system of equations [Math 10] can then be reexpressed by simplifying the identity matrices, and so as to remove the second equation. We then obtain the following equation. [Math. 11] AB / x\M0\ 0 ■■■ 0 1 ■■■ \x0Jk+i : ■. : : .0 ■■■ 0 0 ■■■ 0 1. B - Dq
[0091]
[0092]
[0093]
[0094] The algebraic Riccati equation, in a discrete context, is written as follows: [Math. 12] A^PAP-P- (APT PP p + T) (C^P.Cp + V)4(CjPAp + Tt)+W = Q Where: AB 1,
[0095]
[0096]
[0097]
[0098]
[0099] L0 ■■■ 0 0 ■■■ 11 CP=[CD], P: the covariance of the steady-state estimation error. V: the covariance of the measurement noise with itself, W: the covariance of the model noise with itself, T; the covariance of the measurement noise with the model noise.
[0100]
[0101]
[0102]
[0103]
[0104]
[0105]
[0106]
[0107]
[0108]
[0109] We recall that the matrix P is the unknown of the equation, of which we are looking for the value. Considering the matrices \ B • Dg and (D • of the equation [Math 11] we Bt defines the following matrices V, W and T: [Math. 13] B-DtA ÎB-Dg B, R Be After solving the system of equations [Math 12], [Math 13], we obtain the matrix P. Knowing the matrix P, we can then determine the matrix K; [Math. 14] K = PC / .V'1 We can then implement the Kalman Filter defined by the equation [Math 8]. The compromise between speed of convergence of the estimate and robustness to measurement errors can be adjusted using the calibratable parameters available, i.e. the time constants Ti of the matrix De. If the time constants 1 i have high values, the convergence of the estimate will be longer, which will filter out measurement noise but also high frequency model errors. If the time constants 1 i have small values, the estimate will converge very quickly but will be vulnerable to both measurement noise and high-frequency model errors. Once the Kalman filter is determined, it remains to be calibrated by determining the associated time constants r'. It should be noted that the linearization of a nonlinear system as described above is a widely used technique with many advantages. However, it suffers from a major flaw in that the device only behaves linearly around the point of Ibnctionncmcnt^q^ around which the linearization was carried out. This assumption does not represent a major problem for the state xo, and for the neighboring states x. These dynamic quantities vary continuously with a certain inertia, which implies that the deviations xk ~ xo are by nature small. This is not the case for the control, which can vary abruptly during transient operation of the device. In such transient regimes, it is common to observe the appearance of high frequency modeling errors, likely to profoundly alter the quality of the estimation if the Kalman filter, and therefore its time constants, are not calibrated appropriately.
[0110] The following calibration method makes it possible to obtain robust equipment control at such transient regimes. Figure [Fig.l] illustrates the main steps of the calibration method according to an exemplary embodiment.
[0111] During a first step 1, a set of reference commands of the device giving rise to transient operation is identified. The set of reference commands comprises at least two commands to the device carried out in a predetermined duration, between an initial time t=0 and a final time tf. In other words, a reference maneuver of the device or a scenario of use of said device is identified generating a transient operating regime of at least one physical quantity of equipment included in said device, measured by an LVDT sensor.
[0112] During a second step 2, a cost function is defined as a function of a given set of time constants T'. The given set of time constants T< included in the matrix D^ described above in connection with the system of equations [Math 9] makes it possible to define the Kalman estimator through the gain K. The cost function J is expressed by the following equation.
[0113] [Math. 15] . J = aV T( + ( 1-a)ttf-LVDT,ev / i))2 \ 1 11 ieGV / Iwv ( vy \ * r&nx / t lm\ JJ
[0114] Where:
[0115] GV; all the equipment considered included in the modeled device
[0116] Tî: time constant associated with the equipment / included in the GV set of equipment
[0117] LVDT Threshold i ; the cross-check threshold for the LVDT sensor of equipment i
[0118] LV DT ; real ; the actual position of the cylinder of equipment i measured by the sensor LVDT of equipment i,
[0119] LVDTj is; the estimated position of the cylinder of equipment i estimated by the filter of Kalman,
[0120] a E [0; 1]: the weighting between the speed of convergence of the estimator and the robustness of the estimation, also called the compromise parameter
[0121] tf: duration of T set of reference commands
[0122] The cross-check threshold SeuilLVDT-, is the position measurement deviation threshold between the two redundant measurement channels of a redundant sensor beyond which a fault is considered to be present. As this cross-check threshold value is different for each piece of equipment, it allows the contributions to be normalized relative estimation errors on each piece of equipment.
[0123] For a set {rj of time constants, the following sub-steps are carried out:
[0124] During a first sub-step 2a, the gain K of the Kalman filter is determined for the set { t- ) of time constants and for each operating point {xq, around which the modeling of the device was linearized, by application of the equation [Math 14].
[0125] During a second sub-step 2b, the estimated value LVDT j is determined from the measurement of each redundant sensor measuring a quantity of equipment i by applying the Kalman filter ([Math 8]) in the entire set of reference commands identified in the first step and as a function of the gain K determined in the first sub-step.
[0126] During this second sub-step 2b, the value of the real disturbances on the local and cross channels of the position measurements of the redundant sensor of each equipment i is set to zero. Since no measurement noise is simulated, any disturbance estimate by the Kalman filter is the image of a modeling error. It is specified that the disturbance estimate, called the RMSE value (an English acronym for “root mean square error” or “root mean square error” in French), is here equal to:
[0127] [Math. 16] RM SE=
[0128] To be as robust as possible, we therefore want the estimated value of all disturbances, or RMSE value, to be as close as possible to zero throughout the simulation.
[0129] During a third step 3, we determine the value of the cost J for a given value of the parameter a and for the set {rj of time constants.
[0130] For a given value of the parameter a, that is to say for a given compromise between speed and robustness of the estimator, the optimal estimation performances are allowed by the set (rj of time constants which minimizes the cost function J [Math 15]. We therefore seek to solve the following numerical optimization problem:
[0131] [Math. 17] min {z,} ) under the constraints: {r,} >0 fr.i \ll,ieGV / 1 'LeôV * 1 ' i&GV
[0132] It appears that this non-convex optimization problem admits local minima in addition to its global minimum. We recall that it is known that the derivative of the cost function is zero both at the level of the global minimum and at the level of each local minimum in such circumstances. The aim of the optimization being to de complete the global minimum, the preferred optimization algorithm should therefore not be based on canceling the derivative of the cost function. A genetic algorithm is preferably used, particularly as described in Goldberg, David E., Genetic Algorithms in Search, Optimization & Machine Learning, Addison-Wesley, 1989.
[0133] The third step 3 is repeated for different values of the parameter a, in order to determine a profile of the RMSE value ([Math 16]) as a function of the sum of the values of the set [rj GV of time constants.
[0134] Each point of the profile thus corresponds to a resolution of the equation [Math 17] for a given value of the parameter a.
[0135] Depending on the requirements of the application in question, it is up to the designer to choose one of the points obtained by optimization, and therefore a speed / robustness compromise. The estimation performance obtained by the Kalman Filter resulting from the choice of the set gv of time constants will be optimal, in the sense of the compromise defined by the value of a chosen.
[0136] The profile of the RMSE value as a function of the sum of the values of the set {T;} of time constants having a hyperbolic profile, it is possible to determine a set {rj . of time constants as a function of the profile determined at the end of the second step, as a function of a threshold of RMSE value not to be exceeded and a threshold of sum of the values of the set [rj of time constants not to be exceeded.
[0137] During a fourth step 4, a threshold of RMSE value not to be exceeded and a threshold of sum of the values of the set [tJ of time constants not to be exceeded are defined. The set {rj of time constants, corresponding to a value of a, whose RMSE value and the sum of the values of the set {rj of time constants satisfy each of these two thresholds respectively, are then determined. If several sets {Tj} cv of time constants satisfy these two thresholds, the set chosen is the one having the sum of the lowest time constants.
[0138] The method of calibrating a Kalman filter estimator described above can be used to perform fault detection on measurements from a redundant sensor measuring a quantity of equipment of a device. Depending on the application, the device can be an aircraft engine and the equipment can be a fuel meter or a variable geometry turbine control.
[0139] More precisely, such a control system is based on the use of the same Kalman filter (but supplied by different measurement channels) to detect and locate a simple failure of a redundant sensor in order to accommodate acquisition on the healthy channel instead of arbitrarily choosing a channel and potentially selecting the wrong channel. In an aircraft application, and in aircraft engine control, it is then possible to avoid an engine event, such as a loss of thrust control LOTC (acronym "Loss of Thrust Control").
[0140] A calculation means comprises an observer based on a Kalman filter, making it possible to determine a selected measurement as a function of signals from the sensors of each piece of equipment and of the device. The observer is built from a model representative of the observed device and of the at least one piece of equipment and makes it possible to isolate a faulty measurement channel coming from one of the redundant sensor measurement channels measuring each piece of equipment.
[0141] The selected measurement is obtained by adding additive biases to the measurements of the redundant sensors of each piece of equipment. The Kalman filter then makes it possible, by varying in real time the additive biases on each of the model inputs, to converge the model outputs with the device measurements. Convergence makes it possible to obtain a zero residual. The biases obtained then directly represent the difference between the actual measurement of the controlled equipment (determined by observation via its effect on the device) and the chosen measurement from one of the measurement channels of the redundant equipment sensors.
[0142] The calculation means comprises an observer by Kalman filter, a comparison means, and a selection device.
[0143] The observer makes it possible to determine, taking into account one or more measurements of the device's magnitude, an estimate of the bias of the measurement of the first measurement channel of the redundant sensor and an estimate of the bias of the measurement of the second measurement channel of the redundant sensor.
[0144] The comparison means is configured to determine a selection signal as a function of the comparison of the estimate of the bias of the first measurement channel with a first threshold, of the estimate of the bias of the second measurement channel with a first threshold, and of the estimate of the bias of the first measurement channel with the estimate of the bias of the second measurement channel. The Boolean signals associated with these comparisons are transmitted to a predetermined truth table so as to determine the selection signal sel of the value to be transmitted as the selected measurement.
[0145] The control system has been described in relation to a single quantity measured by two specific measurement channels of a redundant sensor. However, the control system can be extended to at least two quantities each measured by two specific measurement channels of redundant sensors. In this case, the same Kalman filter observer is used to determine the estimation of the bias of the measurement channels for each quantity taken into account.
[0146] For each quantity, we then have two bias estimates, a means of comparison with its own truth table and with its own comparison threshold, as well as a means of selection.
[0147] The control system allows: • to isolate, for each redundant sensor, the faulty channel from the healthy channel and thus be able to reconfigure itself, • to use the same Kalman filter fed by different measurement channels. Thus, unlike the state of the art which uses a bank of different Kalman filters, this allows the control system to be optimized (reducing the impact on memory or CPU load) • to obtain an estimate of the bias directly dependent on the measurements and easily interpretable subsequently (unlike the residuals used in the state of the art)
[0148] Applied to an aircraft, and in particular to the control of an aircraft engine, the control system makes it possible to be robust to failure during flight and to provide a diagnosis for replacement at the end of the mission.
Claims
1. Claims Method for calibrating a Kalman filter estimator included in a control system of a device equipped with at least one piece of equipment, the control system comprising at least one redundant sensor configured to determine a physical quantity of the at least one piece of equipment, the redundant sensor comprising two redundant measurement channels, the calibration method comprising the following steps: a. identification of a set of reference commands of the device carried out in a predetermined duration, b. determination of a cost function based on a set of time constants, a threshold of difference in measured quantity between the two channels of the same redundant sensor beyond which a fault is considered to be present, a compromise parameter defining the priority given to the speed of convergence or to the robustness of the estimator, and the difference for each piece of equipment between the measured quantity and the quantity estimated by the Kalman filter estimator, the difference being calculated for at least two instants included in the predetermined duration of the set of reference commands, the set of time constants also defining the gain of the Kalman filter estimator c. optimization by minimizing the value of the cost function by varying the set of time constants for a compromise parameter value, d. repeating the minimization optimization for at least one other trade-off parameter value, and e. determination of the set of time constants associated with a compromise parameter value whose root mean square error between the measured value and the estimated value of the position of the equipment, and the sum of the time constants, are each less than a threshold, said set of time constants calibrating the Kalman filter estimator.
2. Calibration method according to claim 1, wherein, to de- To complete the value taken by the cost function for a set of time constants, the following sub-steps are carried out: a. determination of the gain of the Kalman filter for the set of time constants and for each operating point around which the device has been linearized, b. determination of the estimated value of the measurement of the redundant sensor associated with each device equipment by means of the Kalman filter estimator in the entire set of reference commands identified and for the at least two instants included in the duration of the set of reference commands.
3. Calibration method according to one of claims 1 or 2, in which, to carry out the optimization by minimizing the value of the cost function, a genetic algorithm is used.
4. Calibration method according to any one of claims 1 to 3, in which the cost function denoted J is expressed by the following equation: J ( { T'} teGV ) ~ ^ieGV1 i + E / =0Lfec v Seuil IVDT i reefà " LVDTj esfe) ) “ where: GV is the set of equipment considered included in the device, Ti is the time constant associated with equipment i included in the set GV of equipment, SeuilLVDT i is the cross-check threshold for the sensor associated with equipment i, LVDTj real is a real position of a cylinder of equipment i measured by the sensor associated with equipment i, LVDTiest is an estimated position of a cylinder of equipment i estimated by the Kalman filter. a is the weighting between the speed of convergence of the estimator and the robustness of the estimation, called the trade-off parameter, tf is a duration of the set of reference commands.
5. Method for controlling a device equipped with at least one piece of equipment, said device also being equipped with at least one sensor capable of each measuring an operating quantity of the device, and a redundant sensor for each piece of equipment so as to have two measurement channels for each physical quantity measured, the control method comprising the following steps: a. a Kalman filter estimator is calibrated by the calibration method according to any one of claims 1 to 4, b. a selected measurement is determined for the at least one controlled equipment, by the calibrated Kalman filter estimator, as a function of the at least one measurement of the operating quantity of the device and the measurements of the measurement channels of the redundant sensor for the controlled equipment, then c. a command is determined for the at least one equipment as a function of the at least one measurement of the operating quantity of the device and the selected measurement for the controlled equipment, and d. a failure of one of the measuring channels of the redundant sensor is detected so as to exclude the measuring channel.
6. System for controlling a device provided with at least one piece of equipment, the control system comprising at least one sensor capable of each measuring an operating quantity of the device, and a redundant sensor for each piece of equipment, at least one nested control means configured to determine a command to the at least one piece of equipment as a function of the measurement of at least one operating quantity of the device and a measurement selected for the controlled equipment, the control system further comprising a calculation means configured to determine the measurement selected for the at least one controlled equipment, by a Kalman filter estimator, as a function of the at least one measurement of the operating quantity of the device and the measurements of the measurement channels of the redundant sensor for the controlled equipment,the calculation means being further configured to detect a failure of one of the measurement channels of the redundant sensor so as to exclude the measurement channel therefrom, in which the Kalman filter estimator is calibrated by the calibration method according to any one of claims 1 to 4.,
7. A control system according to claim 6, wherein the device is an aircraft engine and the measurement channels of the redundant sensor measure the position of the variable geometry actuators, and / or the position of the fuel metering valve, and / or the variable timings of the stators of the engine's high pressure compressor, and / or the measurement of the temperature at the inlet of the engine's high pressure compressor, and / or the measurement of static pressure at the inlet of the engine's combustion chamber.
8. The control system of claim 7, wherein the redundant sensor is an LVDT sensor.
9. Control system according to one of claims 7 or 8, in which the equipment is an actuator of the aircraft engine, for example a jack.
10. Aircraft provided with a control system according to any one of claims 6 to 9.