Method for configuring a digital filter for attenuating a frequency associated with a torsional mode of a power transmission line of a turbomachine

Abstract

The present invention relates to a method for configuring a digital filter for attenuating the torsional modes of a power transmission line of an aircraft turbomotor (1), the modes being associated with a frequency F_T falling within a confidence interval le, the digital filter being a low-pass filter and: - described by a causal transfer function which is stable and equal to the quotient N(z) / D(z), - intended to be integrated into a pre-existing control loop of the turbomotor (1) in order to filter a signal sampled at a frequency F_E, the loop being closed and the absolute value of the gain increasing by a value V in its bandwidth. Furthermore, the method comprises: - step (100) of calculating the zeros of N(z) so that the filter attenuates the frequency F_T, - step (200) of updating the zeros of N(z) so that the gain of the filter satisfies a first gain margin in the interval le, - step (300) of determining the poles of D(z) so that in the bandwidth of the loop: - the phase of the filter satisfies a phase margin, - the gain of the filter satisfies a second gain margin.

Description

BACKGROUND OF THE INVENTION

[0001] The present invention pertains to the field of aircraft turbine engines such as airplanes or helicopters. More specifically, it relates to a method for parameterizing a digital filter model for attenuating the torsional modes of the power transmission lines of an aircraft turbine engine. The present invention finds particularly advantageous applications in the case of turbine engines including unducted propulsion devices, but is not limited thereto.

[0002] In the design of civil and military aircraft such as airplanes and helicopters, the implementation of turbine engines is now common. Turbine engines indeed allow the development of the power required for the flight of aircraft whose mass typically reaches several tens of tons.

[0003] Turbine engines are available in different versions (gas turbines, turbojets, turboprop engines, etc.), all of which are controlled by the same operating principle, namely the conversion of kinetic and thermal energy derived from gas production (usually by burning hydrocarbons) into mechanical energy, which is intended to rotate at least one shaft coupled to the propulsion device (such as a rotor provided with a propeller).

[0004] Traditionally, a turbine engine includes a gas generator and a linked or free turbine, which is located downstream of the gas generator with reference to the flow direction of the gas in the turbine engine. This turbine is driven to rotate by the generated gas flow, thereby causing the transmission line (also referred to as the "power transmission line") to rotate. The transmission line includes, in a known manner, at least one shaft directly coupled to the turbine, also referred to as the "turbine shaft", and at least one output shaft coupled to the propulsion device. Optionally, a planetary reduction gear connects the turbine shaft to the output shaft to reduce the rotational speed of the propulsion device.

[0005] The operation of a turbine engine is generally guided by a set of logics forming so-called engine control. Among these logics, some rely on feedback to form closed-loop monitoring logics. Such loops are intended to monitor the operating parameters of the turbine engine, such as, for example, the rotational speed of the rotor of the propulsion device, in order to respond to a pre-established guidance strategy. To this end, the loop performs measurements of said parameters and compares these measurements with setpoints. The possible deviation between the measurement and the setpoint is transmitted to a control device capable of generating a control signal, which is transmitted to the turbine engine to compensate for said deviation, and then the monitoring process is repeated along said loop.

[0006] Thus, the control signals generated by the control device affect the operation of the turbine, which particularly includes a component formed by a turbine, a transmission line, and a propulsion device. However, like any mechanical system, this component is particularly characterized by a certain stiffness - here rotation - which may not be sufficient for the high-inertia elements at its ends in terms of dimensional constraints. This problem is further complicated by an increase in the length of the transmission line or an increase in the number of its components (e.g., via the introduction of a speed reducer). The transmission line then has torsional modes, whose frequencies are typically outside the operating bandwidth of the transmission line but still relatively close to it. Therefore, there is a risk that commands generated by the control device will excite the torsional modes of the transmission line or amplify the resonance after excitation outside the closed loop. This configuration is problematic because torsional oscillations may have amplitudes capable of significantly reducing the fatigue strength of the transmission line, thus leading to premature wear of the equipment and causing plasticization or rupture of the shaft.

[0007] At least conceptually, and in order to limit the excitation of the transmission line along its torsional modes, it can be envisaged that, according to a first alternative, the mechanical design and sizing of the turbine engine are oriented such that said torsional modes are far enough from the bandwidth of the monitoring loop. In this way, the power of the control signal will be sufficiently attenuated at the frequencies of said torsional modes.

[0008] According to a second alternative, it can be envisaged that, without modifying the mechanical architecture of the turbine engine, the knowledge (frequency, amplitude) of the torsional modes is taken into account when designing the monitoring loop of the turbine engine. In other words, once the design of the turbine engine has been finalized and the torsional modes have been identified, the monitoring loop is designed such that it does not excite said torsional modes.

[0009] However, these two alternatives run counter to the traditional design cycle of the turbine engine. In fact, the sizing of the turbine engine is aimed at defining the overall production constraints, that is, the constraints imposed when considering the turbine engine as a whole (or even, ideally, when considering the environment in which it is intended to be integrated). These constraints are related to, for example, mass, cost, space requirements, operating and usage modes, etc. However, the turbine engine is a complex architectural system because it is manufactured from a large number of parts, so it is difficult to list all these high-level constraints for each of the different parts and to predict the behavior of the final machine before producing them.

[0010] Therefore, once all the said parts have been produced and assembled, the complex dynamic behavior associated with the integration effects is often discovered late in the design cycle and only verified during engine testing.

[0011] Thus, it can be understood that if the initial dimensions are determined not to allow avoiding the torsional mode of the line, it is necessary to review the mechanical design and / or the regulation logic associated with the monitoring loop, which is particularly long and expensive and should therefore be avoided. Summary of the Invention

[0012] An object of the present invention is to overcome all or part of the drawbacks of the prior art, in particular those mentioned above, by proposing a solution that allows attenuating the torsional mode of the power transmission line of a turbomachine, so as to avoid any substantial sizing of the turbomachine and any change to the pre-existing operating regulation logic of the turbomachine.

[0013] To this end, and according to a first aspect, the present invention relates to a method for parameterizing a digital filter for attenuating the torsional mode of a power transmission line of an aircraft turbomachine, the mode being associated with a frequency F_T included in a confidence interval Ic,

[0014] The digital filter is of low-pass type and:

[0015] - is described by a z-transfer function, which is causal, stable and equal to the quotient N(z) / D(z), where N and D are polynomial functions and the order of N is strictly greater than 1,

[0016] - is intended to be integrated into a pre-existing monitoring loop of the turbomachine in order to filter a control signal generated by the control device of the loop and sampled at a frequency F_E, the loop being closed and associated with a bandwidth in which the absolute value of the gain of the loop increases by a value V.

[0017] Furthermore, the method is implemented by a parameterization device and comprises:

[0018] - a step of calculating the complex numbers forming the zeros of N(z) as a function of the frequencies F_T and F_E so that the filter attenuates the frequency F_T,

[0019] - a step of updating the zeros of N(z) so that the gain of the filter satisfies a first predetermined gain template as a function of the amplitude of the torsional mode in the confidence interval Ic,

[0020] - a step of determining the real numbers forming the poles of D(z) so that in the bandwidth of the loop:

[0021] - the phase of the filter satisfies a predetermined phase template as a function of the frequency F_E,

[0022] - the gain of the filter satisfies a second predetermined gain template as a function of the value V.

[0023] The steps for calculating the zeros of N(z) allow for the parametric design of the filter to precisely target the frequency F_T to be attenuated. At this stage, the frequency behavior of the filter phase is not considered.

[0024] After the calculation step, the update step allows for the release of the attenuation that has so far been targeted only at the frequency F_T, in order to take into account the confidence interval Ic that includes said frequency F_T. In other words, this step allows for the consideration of the uncertainty associated with the value of the frequency F_T, thus making the final attenuation sought by the digital filter more robust with respect to this uncertainty.

[0025] It should be noted that at this stage, the frequency behavior of the filter phase is likewise not considered. On the other hand, the behavior of the filter gain essentially stops on its own and may only change slightly during the subsequent steps of determining the poles of D(z). More specifically, the fact that the modulus of the gain decreases in absolute value and within the interval Ic during the update step is countered by the fact that it increases again during the step of determining the poles of D(z).

[0026] Finally, the step of determining the poles of D(z) aims to place the poles of D(z) in order to monitor the evolution of the filter phase over the bandwidth of the loop, which ultimately allows for the monitoring of the filter phase over the entire spectrum (regions A, B, and C) envisioned. Additionally, the fact that the filter gain is constrained within the bandwidth of the loop allows for ensuring that the useful information contained in the control signal can continue to be transmitted to the actuators of the turbomachine.

[0027] Thus, the present invention allows for the integration of a digital filter at the output of the control device of a closed loop, which is configured to attenuate the torsional modes associated with the power line, without physically sizing the turbomachine and without modifying the pre-existing regulation logic (i.e., the operation of the monitoring system operating according to said pre-existing closed loop). The digital filter obtained by the parametric method merely supplements the pre-existing regulation logic.

[0028] It should be noted that the parametric design of the digital filter is advantageously carried out by decoupling the positions of the zeros of the numerator N(z) used to ensure sufficient attenuation within the interval Ic from the positions of the poles of the denominator D(z) used to primarily monitor the phase of the digital filter.

[0029] This decoupling is advantageous because it allows for the obtaining of a discrete linear filter, and also a good compromise between the expected behavior of the filter and a low filter order. The filter obtained in this way is also very easily implementable in computer software from a library of elementary functions known to those skilled in the art, and is commonly used in the production of certified aviation software.

[0030] In a particular implementation mode, the parameterization method may also include one or more of the following features, either alone or in any technically possible combination.

[0031] In a particular implementation mode, the step of updating the zeros of N(z) includes a sub-step of reducing the corresponding modulus of the zeros at a predetermined spacing, and this reduction sub-step is iteratively executed as long as the first amplitude template is not satisfied.

[0032] Thus, reducing the corresponding modulus of the zeros determined during the calculation step allows them to be moved away from the unit circle, and thus widens the filter attenuation region to take into account the confidence interval Ic. This further allows for a good compromise to be obtained between the efficiency and complexity of the parameterization.

[0033] In a particular implementation mode, all the poles of D(z) are considered to be equal to each other, and the pole determination step includes:

[0034] - a sub-step of selecting poles that are strictly included between -1 and 1,

[0035] - a sub-step of translating the selected poles along the real axis at a predetermined spacing to obtain translated poles,

[0036] The translation sub-step is iteratively executed as long as the phase template and the second gain template are not satisfied, and the poles selected during the iteration correspond to the translated poles obtained during the previous iteration.

[0037] Thus, determining the poles of D(z) advantageously allows monitoring the evolution of the phase of the filter over the bandwidth of the loop, which ultimately allows monitoring the phase of the filter over the entire spectrum. In addition, the fact that the gain of the filter is also constrained in the bandwidth of the loop and thus normalized ensures that the useful information contained in the control signal can continue to be transmitted to the actuators of the turbomachine.

[0038] In a particular implementation mode, the first gain template corresponds to an increase opposite to the amplitude of the torsional mode in the gain value within the confidence interval Ic.

[0039] In a particular implementation mode, the phase template corresponds to an increase in the phase shift introduced by the filter in the bandwidth of the closed loop.

[0040] In a particular implementation mode, the order of N(z) is equal to 2 so that the zeros z_1 and z_2 are obtained according to the following formula during the calculation step:

[0041] z_1 = exp((2×i×π×F_T) / F_E) and z_2 = exp((-2×i×π×F_T) / F_E).

[0042] The fact that the order of N(z) is equal to 2 allows the complexity of the filter to be limited, and in particular for the frequency F_T to be attenuated.

[0043] In a particular implementation mode, the order of D(z) is equal to 3.

[0044] The fact that the order of D(z) is equal to 3 advantageously allows the complexity of the filter to be limited while allowing a filter with strict cleanliness.

[0045] In a particular implementation mode, the frequency F_T and the confidence interval Ic are predetermined during a series of tests on a test bench for the oscillatory behavior of the power transmission line.

[0046] In a particular implementation mode, the method includes, after the step of determining the real numbers forming the poles of D(z), a step of verifying the time behavior of the digital filter, the verification step including verifying that the time response of the filter to a step signal is monotonically increasing.

[0047] According to a second aspect, the invention relates to a monitoring system intended to be installed on an aircraft comprising a turbomachine, said turbomachine including a power transmission line having a torsional mode associated with the frequency F_T included in the confidence interval Ic, said system including means for receiving a setpoint related to a predetermined parameter, a control device configured to generate a control signal sampled at the frequency F_E, and means for measuring said parameter, the monitoring system forming a closed monitoring loop associated with a bandwidth, in which the absolute value of the gain is increased by the value V. Furthermore, the monitoring loop includes a digital filter parameterized by the method according to the invention, said digital filter being integrated into the loop in order to filter the control signal.

[0048] According to a third aspect, the invention relates to a computer program comprising a set of program code instructions which, when they are executed by a processor, configure said processor to implement the parameterization method according to the invention.

[0049] According to a fourth aspect, the invention relates to a computer-readable recording medium on which is recorded the computer program according to the invention.

[0050] According to a fifth aspect, the invention relates to a device for parameterizing a digital filter, said filter being intended to attenuate the torsional mode of the power transmission line of an aircraft turbomachine, said mode being associated with the frequency F_T included in the confidence interval Ic,

[0051] The digital filter is of the low-pass type and:

[0052] - Described by a z-transfer function, which is causal, stable and equal to the quotient N(z) / D(z), where N and D are polynomial functions and the order of N is strictly greater than 1,

[0053] - Intended to be integrated into a pre-existing monitoring loop of a turbomachine in order to filter a control signal generated by the control device of said loop and sampled at a frequency F_E, said loop being closed and associated with a bandwidth in which the absolute value of the gain of the loop increases by a value V,

[0054] The device comprises:

[0055] - A calculation module configured to calculate the complex numbers forming the zeros of N(z) as a function of the frequencies F_T and F_E so that the filter attenuates the frequency F_T,

[0056] - An update module configured to update the zeros of N(z) so that the gain of the filter satisfies a first predetermined gain template as a function of the torsional mode amplitude in a confidence interval Ic,

[0057] - A determination module configured to determine the real numbers forming the poles of D(z) so that in the bandwidth of the loop:

[0058] - The phase of the filter satisfies a predetermined phase template as a function of the frequency F_E,

[0059] - The gain of the filter satisfies a second predetermined gain template as a function of the value V.

[0060] According to a sixth aspect, the invention relates to an aircraft comprising a turbomachine, said turbomachine comprising a power transmission line having a torsional mode associated with a frequency F_T included in a confidence interval Ic. Furthermore, the aircraft comprises a monitoring system according to the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Other features and advantages of the invention will become apparent from the following description with reference to the non-limiting drawings illustrating exemplary embodiments of the invention. In the drawings:

[0062] Figure 1 Schematically represents an exemplary embodiment of a system called a power transmission system of an aircraft turbomachine;

[0063] Figure 2 Schematically represents an example of operation in a nominal mode of a monitoring system of a turbomachine known to those skilled in the art;

[0064] Figure 3 Schematically represents the gain of a transfer function associated with a closed monitoring loop, Figure 2The monitoring system is configured according to this loop;

[0065] Figure 4 Figure showing an implementation mode of a method for parameterizing a digital filter according to the invention, said method making it possible to attenuate the torsional modes of the power line of a turbomachine;

[0066] Figure 5 Schematically represents according to the invention Figure 4 Preferred implementation mode of the parameterization method, wherein said method comprises a step of verifying the time behavior of the digital filter;

[0067] Figure 6A Represents the evolution of the gain of the digital filter obtained during the parameterization method according to the invention after calculating the zeros of said filter;

[0068] Figure 6B Represents the evolution of the phase of the digital filter obtained during the parameterization method according to the invention after calculating the zeros of said filter;

[0069] Figure 7A Represents the evolution of the gain of the digital filter obtained during the parameterization method according to the invention after the step of updating the zeros of said filter;

[0070] Figure 7B Represents the evolution of the phase of the digital filter obtained during the parameterization method according to the invention after the step of updating the zeros of said filter;

[0071] Figure 8A Represents the evolution of the gain of the digital filter obtained during the parameterization method according to the invention after the step of determining the poles of said filter;

[0072] Figure 8B Represents the evolution of the phase of the digital filter obtained during the parameterization method according to the invention after the step of determining the poles of said filter. Detailed implementation

[0073] The present invention belongs to the field of turbomachines for aircraft, and more particularly to the damping of one or more mechanical elements forming part of a turbomachine.

[0074] "Damping" here refers to the control of the oscillation amplitude, as long as these may be associated with frequencies equal to or at least close to the frequencies characteristic of the eigenmodes of the assembly formed by said mechanical elements, which mode may cause premature wear of said assembly during its long-term maintenance or repeated excitation. In other words, the concept of damping corresponds to the fact of seeking to damp the oscillations evolving at a predetermined frequency and which may damage the mechanical elements under consideration.

[0075] Figure 1 Schematically represents an exemplary embodiment of a system 10, referred to as a power transmission system, of an aircraft turbomachine 1.

[0076] In practice, the power transmission system 10 may also include other elements different from Figure 1 those represented in , however they are outside the scope of the present invention.

[0077] As Figure 1 illustrated but not limited to in , the power transmission system 10 includes a gas generator 11. This generator 11 generally corresponds to a combustion chamber in which hydrocarbons are ignited to generate gas at high temperature and high speed. The gas generated is then conveyed to a turbine referred to as a power turbine 12, which is thus set in motion. This power turbine 12 can be designated by those skilled in the art by the expression "free turbine" in some engine architectures.

[0078] The turbine shaft is coupled at its respective ends to the power turbine 12 and to a planetary reduction gear 13. Another shaft, referred to as the output shaft, which is opposite the turbine shaft with respect to the reduction gear 13, extends by itself between the reduction gear 13 and the propulsion means 14 of the aircraft.

[0079] Thus, the turbine shaft is rotated by the power turbine 12. The reduction gear 13 itself allows the output shaft to rotate at a speed lower than that of the turbine shaft. Finally, the propulsion means 14 is driven by the output shaft.

[0080] The assembly formed by the turbine and the output shaft and the reduction gear 13 is generally referred to as the "power transmission line". It can indeed be understood that this assembly is responsible for ensuring the transmission of rotational energy from the power turbine 12 to the propulsion means 14.

[0081] The remainder of the present specification relates more specifically but not limited to a turboprop-type turbomachine 1 for an aircraft. Thus, the main thrust of the turbomachine 1 is obtained by the rotation of at least one propeller comprising a plurality of blades. For example and preferably, the propulsion means 14 includes two ducted contra-rotating propellers, which in particular allows the propulsion efficiency to be increased.

[0082] However, following other examples not detailed herein, it is not excluded to consider other types of turbomachines, such as for example turbojets. The present invention is indeed applicable to any type of turbomachine whose operation is desired to be monitored so that the transmission line is not excited according to its specific torsional modes. It is also not excluded to consider another type of turbine, such as for example a linked turbine of a type known per se, downstream of the gas generator, and another type of aircraft such as a helicopter.

[0083] Note that the torsional mode of the transmission line results not only from its torsional flexibility, which is a function of the material used in its manufacture, its length and its diameter, but also from the fact that it rotates between the power turbine 12 and the propulsion device 14, which, for their part, are elements having an inertia much greater than the inertia of the transmission line (and of the reduction gear 13 in this example). In other words, during the nominal operation of the turbomachine 1, the transmission line is likely to be subjected to torsional torques capable of exciting its torsional mode according to the eigenfrequency F_T associated with its torsional mode.

[0084] The operation of the turbomachine 1 is generally guided by a monitoring system 20 on board the aircraft.

[0085] Figure 2 Schematically represents an example of the monitoring system 20 of the turbomachine 1 known to those skilled in the art operating in the nominal mode. Such a figure is also designated by the expression "servo-control block diagram".

[0086] "Nominal mode" herein refers to the mode according to which the monitoring system 20 acts on the turbomachine 1 when the turbomachine 1 is subject to constraints that may affect its operation, but these constraints have been taken into account in the design of the turbomachine 1 before performing the dynamic response tests of the transmission line.

[0087] Traditionally and as Figure 2 shown in, the monitoring system 20 includes an input device 21 for receiving setpoints of a type known per se, such as for example a computer. According to this exemplary embodiment, the setpoint represents the desired rotational speed of the rotor of the propulsion device. However, it should be noted that other physical parameters can be considered to define the setpoint, such as for example the predetermined orientation of the aircraft. The choice of parameters depends in particular on the monitoring strategy chosen to ensure the thrust of the aircraft.

[0088] Such a monitoring system 20 includes a control device 22 configured to generate control signals intended to be transmitted to an actuator of the aircraft ( Figure 2 not shown in). Such an actuator is for example a device configured to deliver a determined quantity of hydrocarbon to the gas generator 11, such as for example a fuel metering valve.

[0089] The control device 22 includes for example one or more processors and storage means (magnetic hard disk, electronic memory, optical disk, etc.) in which data and computer programs are stored in the form of a set of program code instructions which are executed in order to achieve all or part of the guidance of the operation of the turbomachine 1. Alternatively or additionally, the control device 22 also includes one or more programmable logic circuits of the FPGA, PLD type, etc., and / or an application specific integrated circuit (ASIC), and / or a set of discrete electronic components, etc., which are suitable for implementing the guidance of the operation of the turbomachine 1.

[0090] In other words, the control device 22 includes a set of means configured in software (a specific computer program) and / or hardware (FPGA, PLD, ASIC, etc.) to implement the guidance of the operation of the turbine engine 1.

[0091] In a particular exemplary embodiment, the control device 22 is configured according to a "PID" (Proportional, Integral, Derivative) type model known to those skilled in the art on how to implement. However, such an exemplary embodiment only constitutes an alternative embodiment and does not exclude a control device configured according to different types of models not detailed herein.

[0092] The monitoring system 20 also includes, at the output, a measurement of the rotational speed of the rotor of the propulsion device 14, which is typically due to a dedicated sensor 23, such as, for example, a tone wheel. This measured speed is redirected to the input of the monitoring system 20 so that the latter operates according to a closed-loop monitoring logic.

[0093] The control device 22 is an integral part of the closed monitoring loop and is thus configured to generate a control signal based on the deviation between the speed setpoint and the speed measurement. Thus, the speed setpoint is servo-controlled, and the control device acts as a corrector for compensating for said deviation. The control signal is then transmitted to the actuator, which has an impact on the turbine engine 1 and thus ultimately also on the transmission line (changes in the rotational speeds of the turbine shaft and the output shaft, and thus the rotational speed of the propulsion device 14).

[0094] It should be noted that the control signal generated in response to the setpoint deviation corresponds to a digital signal. The sampling frequency of the control signal generated during the operation of the turbine engine 1 is denoted as F_E in the remainder of the specification and is, for example, equal to 50 Hz. However, according to other examples not detailed herein, it is not excluded to consider a sampling frequency F_E other than 50 Hz.

[0095] Hitherto known and illustrated in Figure 2 The monitoring loop is associated with a transfer function that represents the frequency response of the assembly formed by the actuator and the turbine engine 1 to the control signal. Insofar as this assembly corresponds to a physical assembly in the real world, the transfer function here is of the low-pass type.

[0096] Those skilled in the art will appreciate that the expressions "gain of the monitoring loop" and "gain of the transfer function associated with the monitoring loop" have the same meaning in the following description.

[0097] Figure 3Schematically represents the gain of the transfer function associated with the closed monitoring loop and corresponds to a graph (Bode plot) on a semi-logarithmic scale. The abscissa of this graph represents the frequency f in hertz (Hz), and the ordinate represents the gain GdB of the filter in decibels (dB).

[0098] As Figure 3 illustrated therein, the evolution of the gain as a function of frequency includes three regions, namely:

[0099] - Region A corresponding to the bandwidth of the transfer function (in this example, it extends between 0 Hz and substantially 1 Hz), and where the absolute value of the gain of the loop increases by a value V, for example equal to 0 dB,

[0100] - Region C corresponding to the attenuation band of the transfer function (in this example, it extends beyond substantially 10 Hz),

[0101] - Region B corresponding to the transition band of the transfer function and located between Region A and Region C.

[0102] The frequency F_T of the torsional mode is located in Region B. Moreover, the frequency F_T is close enough to Region A so that it is necessary to envisage attenuating it to avoid the excitation of the associated torsional mode and thus eliminate any risk of premature wear of the device. The present invention proposes a solution to this problem that does not require modifying the mechanical architecture of the turbomachine or the pre-existing regulation logic of the turbomachine operation.

[0103] For example, the frequency F_T is equal to 7 Hz and is associated with a confidence interval Ic, the corresponding bounds of which are 6.5 Hz and 7.5 Hz. According to other examples not detailed herein, other values of the frequency F_T and the confidence interval Ic are not excluded from consideration.

[0104] It should be noted that the frequency F_T is associated with the confidence interval Ic. The existence of such a confidence interval Ic is because the frequency F_T cannot be known with absolute accuracy in the case of possible scatter between engines during mass production.

[0105] Thus, according to a preferred example, the frequency F_T is determined during a series of tests on a test bench of the dynamic behavior of the power transmission line. It should be noted that such a series of tests is carried out once the mechanical sizing of the turbomachine and the design of the regulation logic have been completed. Thus, the confidence interval Ic depends on the accuracy of the measurements performed during the tests and also on the number of tests carried out according to statistical methods known to those skilled in the art, and since it is outside the scope of the present invention, it is not detailed here.

[0106] However, other methods for obtaining the frequency F_T and its confidence interval Ic are not excluded. For example, they can be obtained by numerical simulation, which therefore requires a fine modeling of the different mechanical parts forming the turbomachine and of the mathematical simulation models representing the dynamic behavior of these parts.

[0107] For the choice of Ic, no other parameter is excluded either, which will be identified as a source of variation of the frequency F_T, such as for example the scatter related to the method of manufacturing the parts forming the power transmission line or the evolution of these parameters during the service life of said parts.

[0108] Figure 4 Flowchart representing an implementation mode of a method for parameterizing a digital filter to attenuate the torsional mode associated with the frequency F_T.

[0109] The parameterization method is implemented by a parameterization device (not shown in the figure), which includes for example one or more processors and storage means (magnetic hard disk, electronic memory, optical disk, etc.), in which data and computer programs are stored in the form of a set of program code instructions, which set of program code instructions is executed in order to implement all or part of the steps of the parameterization method. Alternatively or additionally, the parameterization device also includes one or more programmable logic circuits of the FPGA, PLD, etc. type, and / or application-specific integrated circuits (ASICs), and / or a set of discrete electronic components, etc., which are suitable for implementing all or part of the steps of the parameterization method.

[0110] In other words, the parameterization device includes a set of means configured in software (specific computer program) and / or hardware (FPGA, PLD, ASIC, etc.) to implement the various steps of the parameterization method.

[0111] The digital filter parameterized by the parameterization method is intended to be integrated into a pre-existing monitoring loop in order to filter the control signal generated by the control device 22. In other words, the digital filter is intended to be integrated, for example in software, at the output of the control device 22.

[0112] The digital filter according to the invention is sought in the form of a low-pass filter, in particular so as not to disturb the behavior of the transfer function associated with the monitoring loop.

[0113] One further seeks digital filters such that the transfer function associated therewith is causal, stable and equal to the quotient N(z) / D(z), where N and D are polynomial functions and the order of N is strictly greater than 1. Thus the transfer function is a rational fraction. Due to causality, this means that the order of the denominator is strictly greater than the order of the numerator. The stability criterion itself means that the poles of D(z) are all contained within the unit circle of the complex plane. Those skilled in the art will also be aware that the argument z of the functions N(z) and D(z) corresponds to the symbol of a complex variable which is commonly used to manipulate discrete signals, the link with the continuous representation being done through the z-transform. Then we have the following formula:

[0114] z = exp(2iπ×p / F_E)

[0115] where p is the Laplace variable.

[0116] The roots of the numerator N(z) and of the denominator D(z) are respectively called zeros and poles.

[0117] The parameterization method comprises several steps. In its general principle, the method first comprises placing the zeros of the numerator so as to provide attenuation for the frequency F_T. These zeros are then updated so as to take into account the uncertainty of the value of the frequency F_T. Only after the parameterization of the numerator is completed is the denominator then parameterized by the position of its poles, mainly to adjust the phase of the digital filter.

[0118] The parameterization method first comprises step 100 of calculating the complex numbers forming the zeros of N(z) as a function of the frequencies F_T and F_E so that the filter attenuates the frequency F_T.

[0119] The purpose of step 100 is a first placement of the zeros of N(z) so as to ensure attenuation of the frequency F_T.

[0120] In a preferred implementation mode, the order of N(z) is equal to 2. This means that N(z) comprises two zeros respectively denoted z_1 and z_2. These zeros z_1 and z_2 are calculated during calculation step 100 according to the following formulae:

[0121] z_1 = exp((2×i×π×F_T) / F_E) and z_2 = exp((-2×i×π×F_T) / F_E).

[0122] Calculating the zeros z_1 and z_2 in this way amounts to determining a digital filter which specifically takes the frequency F_T as the frequency to be attenuated. The fact of first determining such zeros on the unit circle represents poor damping of the power transmission line for the frequency F_T.

[0123] However, it is not excluded that the zeros z_1 and z_2 are calculated in a different way during step 100, as they allow to exclude a frequency region centered essentially on the frequency F_T associated with the torsional mode. Preferably, the zeros are determined during step 100 close to the unit circle (and thus the modulus is essentially equal to 1), ideally on the unit circle, in order to start the parameterization method in a simple way.

[0124] The fact that the order of N(z) is chosen to be equal to 2 allows to limit the complexity of the filter. However, it should be noted that this choice only constitutes an alternative implementation mode of the present invention. For example, N can be parameterized so that the order is strictly greater than 2, for example equal to 4, as long as the constraints on which the causality of the filter is based are satisfied.

[0125] Then, the parameterization method includes a step 200 of updating the zeros of N(z) so that the gain of the filter satisfies a first amplitude template predetermined as a function of the amplitude of the torsional mode in the confidence interval Ic.

[0126] This step 200 of updating the zeros allows to take into account the uncertainty associated with the value of the frequency F_T, and thus makes the final attenuation sought for the digital filter more robust with respect to this uncertainty.

[0127] In a particular implementation mode, the step 200 of updating the zeros of N(z) includes a sub-step of reducing the respective modulus of the zeros at a predetermined spacing. The fact of reducing the respective modulus of the zeros determined during the calculation step 100 allows to move the zeros away from the unit circle (the interior of the unit circle), and thus to widen the attenuation region of the filter in order to take into account the confidence interval Ic.

[0128] Then, the sub-step of modulus reduction is iterated as long as the first gain template is not satisfied.

[0129] For example, the modulus reduction spacing is set to be equal to 0.01. In this way, and during the first iteration of the reduction sub-step, the updated zeros have a modulus equal to 0.99. It should also be understood that if the reduction sub-step is iterated, for example, five times, the zeros obtained at the end of the update step 200 will have a modulus equal to 0.95.

[0130] However, following other examples not detailed here, it is not excluded to consider a spacing greater than or less than 0.01. It is also not excluded to consider reducing the modulus in a non-additive type, for example multiplicative type.

[0131] The fact of gradually reducing the modulus iteratively allows to obtain a good compromise between the calculation time and the complexity of the parameterization.

[0132] However, it should be noted that this way of proceeding only constitutes an alternative implementation mode of the present invention. For example, the update of the zeros of step 100 can be performed by an optimization algorithm (such as a shape optimization algorithm) aimed at optimizing a predetermined cost function as a function of the amplitude of the torsional mode. However, such an optimization algorithm increases the complexity of step 200 of updating the zeros of N(z).

[0133] As a non-limiting example, the first gain template corresponds to a preferably strict increase in the gain value in the confidence interval Ic, which increase is opposite to the amplitude of the resonance of the torsional mode. For example, if the torsional mode causes a 3 dB peak on the Bode plot of the system at the frequency F_T, the filter is designed such that the gain is compensated to a minimum for such amplification. In terms of the template, this results in a maximum constraint of -3 dB at the frequency F_T.

[0134] In fact, compared to the gain obtained at the end of a single calculation step 100, the update of the zeros according to the present invention reduces the absolute value of the amplitude of the filter gain. Therefore, setting such a first gain template allows providing a constraint to stop the update of the zeros so that the filter will completely attenuate the frequency F_T in the confidence interval Ic.

[0135] The choice of such a first gain template only constitutes an alternative implementation mode of the present invention. Therefore, other alternatives can be envisaged, such as for example having a first gain template corresponding to the gain value in the interval Ic, which gain value is greater than or equal to the opposite value of the amplitude of the torsional mode. For example, the first gain template can correspond to a gain value between 90% and 95% of the amplitude of the torsional vibration mode. In fact, the steps (described later) after the zero update step 200 have the effect of further reducing the gain of the digital filter at the frequency F_T, thus allowing a trade-off between the amplitude of the torsional mode, the gain of the filter at the end of step 200, and the length of the interval Ic.

[0136] Therefore, it can be understood that steps 100 and 200 are mainly aimed at parameterizing the digital filter in order to calibrate its gain near the frequency F_T, and subsequently calibrating the phase and gain on the rest of the spectrum, especially on the bandwidth of the closed loop.

[0137] To this end, the parameterization method includes a step 300 of determining the real numbers forming the poles of D(z). The fact of finding the poles of D(z) in real form allows ensuring the damping behavior of the filter.

[0138] The step 300 of determining the poles of D(z) is performed under a constraint, i.e., such that in the bandwidth of the loop:

[0139] - the phase of the filter satisfies a predetermined phase template as a function of the frequency F_E,

[0140] - The gain of the filter satisfies a second predetermined gain template as a function of the value V.

[0141] Thus, step 300 aims to place the poles of D(z) so as to monitor the evolution of the phase of the filter over the bandwidth of the monitoring loop, which ultimately allows the phase of the filter to be monitored over the entire spectrum (regions A, B, and C) envisaged. Moreover, the fact that the filter gain is constrained in the bandwidth of the loop in this way ensures that the useful information contained in the control signal can continue to be transmitted to the actuators of the turbomachine 1 without attenuation.

[0142] In a preferred implementation mode, all the poles of D(z) are considered to be equal. Considering all the poles to be equal to each other allows a favorable compromise to be obtained between the complexity of the parameterization (and thus the calculation time and the necessary calculation means) and the accuracy of the filter behavior. However, it should be noted that choosing poles that are all equal to each other only constitutes an alternative implementation mode of the present invention. For example, real poles can be determined so as to be completely different from each other, or only some of the poles are equal to each other.

[0143] In a particular implementation mode, step 300 of determining the poles of D(z) includes:

[0144] - A sub-step of selecting poles strictly included between -1 and 1,

[0145] - A sub-step of translating the selected poles along the real axis at a predetermined spacing in order to obtain translated poles.

[0146] Then, the translation sub-step is iterated as long as the phase template and the second gain template are not satisfied. To perform such an iteration, the poles selected during the iteration correspond to the translated poles obtained during the previous iteration.

[0147] For example, the said translation spacing along the real axis is set to be equal to 0.01 in the direction of decreasing real numbers. In this way, and during the first iteration of the translation sub-step, if the initially selected pole is equal to 0.9, then the pole is equal to 0.89. It can also be understood that if the translation sub-step is iterated, for example, five times, if the first selected pole is equal to 0.9, then the pole obtained at the end of step 300 will be equal to 0.85.

[0148] However, following other examples not detailed here, it is not excluded to consider a spacing greater than or less than 0.01, as well as a translation in the direction of increasing real numbers. Generally, the direction of translation depends on the position of the initially selected poles with respect to the boundaries -1 and 1. It is not excluded that the direction of translation along the real axis changes between at least two iterations, for example in the case where the direction of translation is determined by an optimization algorithm that aims to optimize a predetermined cost function as a function of the frequency F_E and the value V.

[0149] The fact that the poles of D(z) are determined by translational iteration allows for a good compromise between the computational time and complexity of the parameterization.

[0150] However, it should be noted that this mode of proceeding constitutes only an alternative implementation mode of the present invention. Thus, based on considerations similar to those in the case of step 200 described above, the determination of the poles of D(z) can be performed by an optimization algorithm, such as, for example, a shape optimization algorithm. However, such an optimization algorithm increases the complexity of step 300.

[0151] As a non-limiting example, the phase template corresponds to an increase in the phase shift introduced by the filter over region A, which corresponds to the bandwidth of the closed loop. For example, this increase corresponds to a predetermined multiple of the product of the period 1 / F_E and the maximum impulse bounding region A.

[0152] The fact of increasing the phase shift in the loop bandwidth allows for avoiding excessive distortion of the phase during the monitoring of the operation of the turbomachine 1. In other words, proceeding in this way advantageously limits the effect of the introduced phase shift without disrupting the existing detection loop, understanding that any digital processing necessarily has an impact on the phase.

[0153] Furthermore, the fact of normalizing the gain of the filter does not affect the gain of the closed loop at low frequencies.

[0154] In a preferred implementation mode, the numerator D(z) is parameterized such that its order is equal to 3. This choice advantageously allows for meeting the requirements while limiting the complexity of the filter. However, it should be noted that this choice constitutes only an alternative implementation mode of the present invention. For example, D(z) can be parameterized such that its order is strictly greater than 3, for example equal to 5, as long as the constraints on which the causality of the filter is based are met.

[0155] Figure 5 Schematically represents a preferred implementation mode of the parameterization method, wherein the method includes, after step 300 of determining the real numbers forming the poles of D(z), a step 400 of verifying the time behavior of the digital filter. By "verification of the time behavior", reference is made here to confirm that the output of the digital filter follows the expected behavior over time in response to a known input signal.

[0156] In other words, the verification step 400 allows for ensuring that the digital parameterized filter according to the present invention does not have an inappropriate behavior.

[0157] In the preferred implementation mode, the verification step 400 includes: verifying that the time response of the filter to a step signal (Heaviside function) is monotonically increasing. This verification step corresponds to the study of the unit step response of a digital filter. Therefore, it will not be elaborated here. It is only specified that the time behavior of the filter is effectively verified when the time response is monotonically increasing.

[0158] Once the verification step 400 is completed, and when the time behavior of the parameterized filter is ultimately not satisfactory, as long as the behavior of the digital filter has not been verified, the pole D(z) determination step 300 and the verification step 400 are repeated. In other words, the poles of D(z) are readjusted. To readjust the poles of D(z), step 300 can be performed, for example, by selecting all the same real poles, but the first pole selected before any translation is different from the pole selected during the first implementation of this method, which results in a filter with unsatisfactory behavior.

[0159] Figure 6A 、 Figure 6B 、 Figure 7A 、 Figure 7B 、 Figure 8A 、 Figure 8B represent the corresponding evolutions of the gain ( Figure 6A 、 Figure 7A 、 Figure 8A ) and phase ( Figure 6B 、 Figure 7B 、 Figure 8B ) of the digital filter obtained step by step during an example of implementing the parameterized method.

[0160] In this embodiment, the frequencies F_E and F_T are equal to 50 Hz and 7 Hz respectively. The interval Ic here corresponds to [6.5 Hz, 7.5 Hz], and the value V is equal to 0 dB. In addition, the filter transfer function is sought in the form of the quotient N(z) / D(z), where the order of N is 2 and the order of D is 3, and all the poles are equal to each other.

[0161] Figure 6A Schematically represents the frequency evolution of the gain of the digital filter at the end of step 100 of the parameterized method. As Figure 6A illustrates, the absolute value of the gain increases significantly at the frequency F_T, which indeed corresponds to the expected behavior of the target attenuation.

[0162] Figure 6B itself schematically represents the frequency evolution of the phase of the digital filter at the end of step 100 of the parameterized method. As Figure 6B illustrates, the phase of the filter has not been controlled at this stage, because for frequencies above F_T, it increases by more than 180°.

[0163] Note that the zeros of N(z) determined at the end of step 100 are equal to 0.637 + i*0.771 and 0.637 - i*0.771, respectively.

[0164] It should also be noted that, due to the parameterization device, Figure 6A and Figure 6B are obtained by simulating the behavior of a digital filter.

[0165] Once the step 200 of updating the zeros has been executed, Figure 7A and Figure 7B correspond to the corresponding updates of Figure 6A and Figure 6B .

[0166] As can be observed in Figure 7A , the absolute value of the gain of the digital filter decreases near the frequency F_T, more specifically in the interval Ic. Nevertheless, the absolute value of this gain remains greater than the amplitude of the torsional mode.

[0167] For its part, as Figure 7B is illustrated, the phase hardly evolves.

[0168] In addition, the updated zeros associated with the cases of Figure 7A and Figure 7B are 0.606 + i*0.732 and 0.606 - i*0.732, respectively. Thus, a decrease in the modulus of the zeros with respect to those obtained at the end of step 100 and associated with Figure 6A and Figure 6B is indeed observed.

[0169] Once the step 300 of determining the poles has been executed, Figure 8A and Figure 8B correspond to the corresponding updates of Figure 7A and Figure 7B . It should be noted that at the end of step 300, all the poles are determined to be equal to 0.5.

[0170] As can be observed in Figure 8A , the absolute value of the gain of the digital filter increases near the frequency F_T, more specifically in the interval Ic. Thus, there is a strong targeted attenuation of the torsional mode of the power transmission line. In addition, the gain in the bandwidth remains below 0 dB, which means that the digital filter modifies the low-frequency control signal very little.

[0171] For its part and as Figure 8BAs illustrated, the absolute value of the phase remains between 0° and 180° over the entire spectrum considered (regions A, B, and C), which allows any side effects to be avoided during the execution of the monitoring loop, such as, for example, too large a phase shift that could cause the control signal to invert.

[0172] In general, the invention of course still applies to torsional modes that are not located in region B but are also located in region A or region C.

[0173] Thus, the invention allows the digital filter to be advantageously parameterized in order to effectively attenuate the torsional mode of the power transmission line near the frequency of said torsional mode, by limiting the phase shift effect introduced without reducing the gain of the pre-existing monitoring loop over the rest of the spectrum and without introducing any undesired temporal behavior into the pre-existing regulation logic. Furthermore, the parameterization method allows a very effective digital filter of reasonable order to be obtained, generally less than 5, for example equal to 3, which is compatible with real-time implementation in the pre-existing regulation logic.

[0174] Finally, it should be noted that the transfer function associated with the digital filter parameterized according to the invention can be easily implemented in the pre-existing regulation software. To this end, a person skilled in the art can access a function library that allows such a digital filter to be generated at the output of the control device 22 of the monitoring loop.

Claims

1. A method for parameterizing a digital filter for attenuating torsional modes of a power transmission line of an aircraft turbomachine (1), said modes being associated with a frequency F_T included in a confidence interval Ic, said digital filter being of the low-pass type and: - comprising a z-transfer function which is causal, stable and equal to the quotient N(z) / D(z), where N and D are polynomial functions and the order of N is strictly greater than 1, - intended to be integrated into a pre-existing monitoring loop of said turbomachine (1) in order to filter a control signal generated by a control device (22) of said loop and sampled at a frequency F_E, said loop being closed and associated with a bandwidth in which the absolute value of the gain of said loop increases by a value V, said method being implemented by a parameterization device and comprising: - a step (100) of calculating complex numbers forming the zeros of N(z) as a function of said frequencies F_T and F_E so that the filter attenuates said frequency F_T, - a step (200) of updating the zeros of N(z) so that the gain of the filter satisfies a first predetermined gain template as a function of the amplitude of said torsional mode in said confidence interval Ic, - a step (300) of determining real numbers forming the poles of D(z) so that in the bandwidth of said loop: - the phase of the filter satisfies a predetermined phase template as a function of said frequency F_E, - the gain of the filter satisfies a second predetermined gain template as a function of said value V.

2. The method according to claim 1, wherein the step (200) of updating the zeros of N(z) comprises a sub-step of reducing the corresponding modulus of the zeros at a predetermined spacing and iteratively performing said reducing sub-step as long as the first amplitude template is not satisfied.

3. The method according to claim 1, wherein all the poles of D(z) are considered to be equal to each other, and the pole determination step (300) comprises: - a sub-step of selecting a pole strictly included between -1 and 1, - a sub-step of translating the selected pole along the real axis at a predetermined spacing in order to obtain a translated pole, iteratively performing said sub-step of translating the selected pole along the real axis at a predetermined spacing in order to obtain a translated pole as long as the phase template and the second gain template are not satisfied, and the pole selected during the iteration corresponding to the translated pole obtained during the previous iteration.

4. The method according to any one of claims 1 to 3, wherein the first gain template corresponds to an increase opposite to the amplitude of the torsional mode of the gain value in said confidence interval Ic.

5. The method according to any one of claims 1 to 3, wherein the phase template corresponds to an increase in the phase shift introduced by the filter in the bandwidth of said loop.

6. The method according to any one of claims 1 to 3, wherein the order of N(z) is equal to 2 so that during the step (100) of calculating the complex numbers forming the zeros of N(z), the zeros z_1 and z_2 are obtained according to the following formula: z_1 = exp((2×i×π×F_T) / F_E) and z_2 = exp((-2×i×π×F_T) / F_E), wherein, i is the imaginary unit and π is the ratio of the circumference of a circle to its diameter.

7. The method according to any one of claims 1 to 3, wherein the order of D(z) is equal to 3.

8. The method according to any one of claims 1 to 3, wherein the frequency F_T and the confidence interval Ic are predetermined during a series of tests on a test bench for the dynamic behavior of the power transmission line.

9. The method according to any one of claims 1 to 3, the method comprising, after the step (300) of determining the real numbers forming the poles of D(z), a step (400) of verifying the time behavior of the digital filter, the verification step (400) comprising verifying that the time response of the filter to a step signal is monotonically increasing, as long as the behavior of the digital filter has not been verified, the step (300) of determining the real numbers forming the poles of D(z) and the verification step (400) are iterated.

10. A monitoring system (20) intended to be installed on an aircraft comprising a turbomachine (1), the turbomachine (1) comprising a power transmission line having a torsional mode associated with a frequency F_T included in a confidence interval Ic, the system (20) comprising means (21) for receiving a setpoint related to a predetermined parameter, a control device (22) configured to generate a control signal sampled at a frequency F_E, and means (23) for measuring the parameter, the monitoring system (20) forming a closed-loop monitoring loop associated with a bandwidth, wherein the absolute value of the gain is increased by a value V, the system being characterized in that the monitoring loop comprises a digital filter parameterized by the method according to any one of claims 1 to 9, the digital filter being integrated in the loop in order to filter the control signal.

11. A computer program product comprising a set of program code instructions which, when executed by a processor, configure the processor to implement the method for parameterizing a digital filter according to any one of claims 1 to 9.

12. A computer-readable recording medium on which is recorded the computer program product according to claim 11.

13. A device for parameterizing a digital filter, the filter being intended to attenuate the torsional mode of the power transmission line of an aircraft turbomachine (1), the mode being associated with a frequency F_T included in a confidence interval Ic, the digital filter being of the low-pass type and: - described by a z transfer function which is causal, stable and equal to the quotient N(z) / D(z), where N and D are polynomial functions and the order of N is strictly greater than 1, - Intended to be integrated into a pre - existing monitoring loop of the turbomachine (1) in order to filter a control signal generated by a control device (22) of the loop and sampled at a frequency F_E, the loop being closed and associated with a bandwidth in which the absolute value of the gain of the loop increases by a value V, The device comprises: - a calculation module configured to calculate complex numbers forming the zeros of N(z) as a function of the frequencies F_T and F_E so that the filter attenuates the frequency F_T, - an update module configured to update the zeros of N(z) so that the gain of the filter satisfies a first predetermined gain template as a function of the amplitude of the torsional mode in the confidence interval Ic, - a determination module configured to determine real numbers forming the poles of D(z) so that in the bandwidth of the loop: - the phase of the filter satisfies a predetermined phase template as a function of the frequency F_E, - the gain of the filter satisfies a second predetermined gain template as a function of the value V.

14. An aircraft comprising a turbomachine, the turbomachine comprising a power transmission line having a torsional mode associated with a frequency F_T included in a confidence interval Ic, the aircraft further comprising the monitoring system according to claim 10.

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