FR3093137A1 - Digital filter with variable cut-off frequency - Google Patents

Abstract

The invention proposes a method of filtering a measurement signal (x_m) disturbed by the rotation of a rotating element (12) rotating at a known speed of rotation (Ω), said filtering method using a filter (H) having a cutoff frequency (ωn), said cutoff frequency (ωn) being a function of the speed of rotation (Ω) of the rotating element (12). Figure for the abstract: Fig. 1

Description

Digital filter with variable cutoff frequency

GENERAL TECHNICAL AREA

The invention relates to the management of external disturbances during measurements by sensors, such as electromagnetic disturbances on LVDT ( Linear Variable Differential Transformer ) sensors.

The invention is applicable to all aircraft engines (plane or helicopter in particular) but it will be illustrated in the general context of an open rotor, that is to say an aircraft engine consisting of a generator of gas (turbine) driving two variable-pitch propellers producing thrust.

STATE OF THE ART

The main objective of a regulation system is to ensure the desired thrust by relying on actuators (fuel flow, propeller pitch angles, etc.) which make it possible to control the various engine speeds both at gas generator level than propellers.

The rotating metal masses of the rotors induce electromagnetic disturbances on the voltage measurements of the LVDT ( Linear Variable Differential Transformer ) sensors and thus disturb the servo-controls. These disturbances are correlated to the different rotation regimes and therefore have frequencies linked to these regimes. For example, in the context of a turbojet engine with counter-rotating propellers (also called an open rotor), the rotation speeds of the propellers are relatively low, and the frequencies of the disturbances induced by the rotation of each metal propeller are found in the bandwidth of the different regulations: it is therefore necessary to deal with them.

According to a first aspect, the invention proposes a method for filtering a measurement signal disturbed by electromagnetic disturbances generated by at least one metal mass, in rotation, of a rotating element of a turbomachine, said rotating element being driven at a known speed of rotation, said filtering method using a filter having a variable cut-off frequency, said cut-off frequency being a function of the speed of rotation of the rotating element.

In one embodiment, the filter receives as input the measurement signal and a signal relating to the speed of rotation.

In one embodiment, the variable cut-off frequency ω _n equals ω _n =2П/60×Ω, where Ω is the speed of rotation expressed in revolutions per minute.

In one embodiment, the filter is expressed continuously according to a Notch filter of order 2.

In one embodiment, the 2nd order Notch filter is in the following form:

where ω _n is the cutoff frequency and ξ _n , ξ _d tuning parameters

In one embodiment, a change of variable was performed using the following bilinear transformation:

where T _s is the system sampling frequency, s is the Laplace variable, and z is the discrete operator.

In one embodiment, the rotating element is a turbomachine rotor, such as a propulsion rotor comprising blades or blades, such as a rotor of an open rotor. By open rotor, is meant an unducted fan turbine engine with at least one propulsion rotor with blades.

According to a second aspect, the invention proposes a filter for filtering a measurement signal disturbed by electromagnetic disturbances generated by at least one metal mass, in rotation, of a rotating element of a turbomachine, said rotating element being driven at a known rotational speed, said filter comprising an input receiving the measurement signal and a value relating to the rotational speed, and in which the cut-off frequency of the filter depends on the value relating to the rotational speed.

This filter can be in the form of a computer program product comprising lines of code able to be executed by a calculation unit (typically by the processor of the calculation unit).

According to a third aspect, the invention proposes a control unit for controlling a device, the control unit receiving as input a receiving as input a setpoint, the control unit comprising
a filter as described previously to generate a filtered measurement signal and
a corrector receiving at input an error signal taking into account the setpoint signal and the filtered measurement signal, the corrector generating at output a command intended for the device.

Other characteristics, objects and advantages of the invention will emerge from the description which follows, which is purely illustrative and not limiting, and which must be read in conjunction with the appended drawings.

Figure 1 illustrates a block diagram of an overall embodiment of the invention.

FIG. 2 illustrates a block diagram of an embodiment of a filter according to the invention.

Figure 3 shows a Bode diagram of the filter in Figure 2.

Figures 4a, 4b, 4c and 4d illustrate a result comparison with and without the filter in Figure 3.

Figures 4a, 4b, 4c and 4d illustrate a result comparison with and without the filter in Figure 3.

Figures 4a, 4b, 4c and 4d illustrate a result comparison with and without the filter in Figure 3.

Figures 4a, 4b, 4c and 4d illustrate a result comparison with and without the filter in Figure 3.

Figures 5a, 5b, 5c and 5d show an enlargement of Figures 4a, 4b, 4c and 4d (between about 36 and 37s).

Figures 5a, 5b, 5c and 5d show an enlargement of Figures 4a, 4b, 4c and 4d (between about 36 and 37s).

Figures 5a, 5b, 5c and 5d show an enlargement of Figures 4a, 4b, 4c and 4d (between about 36 and 37s).

Figures 5a, 5b, 5c and 5d show an enlargement of Figures 4a, 4b, 4c and 4d (between about 36 and 37s).

Figures 6a, 6b, 6c and 6d illustrate a result comparison with the filter of Figure 3 and with a fixed cutoff frequency filter.

Figures 6a, 6b, 6c and 6d illustrate a result comparison with the filter of Figure 3 and with a fixed cutoff frequency filter.

Figures 6a, 6b, 6c and 6d illustrate a result comparison with the filter of Figure 3 and with a fixed cutoff frequency filter.

Figures 6a, 6b, 6c and 6d illustrate a result comparison with the filter of Figure 3 and with a fixed cutoff frequency filter.

Referring to Figure 1 has been illustrated in block diagram form an assembly relating to an embodiment of the invention.

Again, we place ourselves within the framework of an aircraft engine 10 (turbomachine for example, of the open rotor type, that is to say with an unducted fan comprising at least one propulsion rotor with a blade) comprising an element rotating 12, which may be a rotor (propeller or rotor of a fan, turbine, compressor, etc.). The speed of rotation Ω of the rotating element 12 is assumed to be known, for example thanks to speed sensors or using a model reconstituting this speed from other parameters.

The assembly comprises a mechanical and/or electrical and/or hydraulic system, such as for example an actuator.

A sensor 22 makes it possible to generate a measurement signal x_m from the output x of the system 20. In the example of the present description, the sensor 22 is an LVDT sensor.

The assembly also includes a driver unit 30, illustrated in fragmented form in Figure 1. The driver unit 30 typically includes a processor and a memory. The control unit 30 implements a filter H, configured to filter the measurement signal x_m from the sensor 22 and output a filtered measurement signal x_mf.

The control unit 30 is also configured to generate an error signal x_e, formed by a setpoint signal x_cons from which the corrected measured signal x_mf has been subtracted (the error signal can be called servo error or feedback or instruction follow-up). The setpoint signal x_cons comes from a setpoint unit (not shown). The control unit 30 also includes a corrector 32, configured to generate a control signal x_com from the error signal x_e. The corrector 32 is not concerned by the invention. The control signal x_com (typically a voltage or a current) allows the activation of the system 20.

The setpoint unit and the control unit 30 can be implemented in a computer (for example of the FADEC type for an aircraft).

The rotating element 12 includes a metal mass 14 which can generate electromagnetic disturbances at the level of the sensor 22. The measured signal x_m is then a disturbed signal. Here, the disturbances are globally sinusoidal with frequencies equal to the speeds of the rotating element 12.

More generally, the rotating element 12 can be any moving part which generates a disturbance on the sensor 22 and for which a frequency can be established.

The filter H receives as input the measurement signal x_m and the rotational speed Ω of the rotating element 12. This rotational speed Ω is generally already available to a computer, therefore easily available to the control unit 30 .

The filter H has a variable cutoff frequency ω _n . This frequency is a function of the speed of rotation Ω of the rotating element 12. In other words, the measurement of the speed of the propellers is used as a variable parameter of the filter H. More precisely, the cut-off frequency ω _n is expressed proportionally at the rotational speed Ω, in particular by the relationship ω _n =2П/60×Ω, Ω is expressed in revolutions per minute.

In this way, the filter adapts to the operating speed of the engine 10 and makes it possible to generate a filtered signal x_mf of better quality than the measurement signal x_m.

A particular embodiment will be given, with results obtained by computer simulation.

Filter H is a Notch filter of order 2. This type of filter is chosen because it makes it possible to have a very narrow rejection band to limit its impact as much as possible in the rest of the frequency domain. Indeed, as the cutoff frequency will follow in real time the evolution of the disturbance to be filtered, we can allow ourselves to limit this rejection band by considering only the precisions and latencies of the acquisition chain to define the width of this band.

Moreover, this filter has the advantage of having a shape with an explicit _{cutoff frequency ω n:}

where ω _n is the cutoff frequency, ξ _n , ξ _d tuning parameters and s the Laplace variable.

The advantage of using a notch filter is that the attenuation can be very large without the need for high order filters. Moreover, adjustment is easy since the adjustment parameters are “physical” in the sense that they can be directly linked to the filtering characteristics (attenuation and passband).

Nevertheless, no equivalent form of this filter where the cutoff frequency ω _n and the adjustment parameters ξ _n , ξ _d are explicit is defined in the discrete domain, which is why it is preferable to start from the continuous form, c ie with a filter defined in continuous domain. To use this filter discretely while still having the explicit presence of the cutoff frequency, the following bilinear transformation is used:

where T _s is the system sampling frequency, s is the Laplace variable, and z is the discrete operator.

This transformation makes it possible to obtain a discrete filter which remains of the second order with always explicit parameters and whose form is given below:

The filter H is placed in an architecture as illustrated in FIG .

Filter H is in the form presented in FIG . The equation of the filter H is therefore the following:

with

The filter parameters are: Ts the sampling period, ω _n the cut-off pulsation (this cut-off pulsation is taken such that ω _n =2π/60×Ω), ξ _d and ξ _n two filter adjustment parameters which allow it to be adjusted through the width of its rejection band and its attenuation.

Thus for each new sampling period, i.e. every Ts seconds (the following time sample), it is possible to recalculate the values of the coefficients of the filter H with the new frequency of the disturbance. In this way, it is possible to maintain filtering adapted to the disturbance at all times.

The adjustment parameters ξ _d and ξ _n are always explicit in the discrete implementation presented above, which makes it possible to carry out the adjustment of these two parameters in the continuous domain (where the expression of the filter is simple), then to use them in the discrete domain.

These two parameters can be directly linked to the filter characteristics from the expression of the continuous filter. So they can be set as follows:

where x' is the bandwidth at -3 dB in rad/s and t is the attenuation at ω _n in dB (with t < 0).

Figures 3 to 5 represent simulation results obtained for the filter presented above.

Consider a rotating element 12 having speeds varying from 500 to 1000 rpm. This rotation then causes oscillations at the rotation frequency of the system (from about 8Hz to 17Hz) on the sensor 22 of the LVDT type.

The parameters ξ _n and ξ _{d are then} adjusted so as to obtain an H filter with a bandwidth of 0.5 Hz at -3 dB and an attenuation of 40 dB at ω _n .

For a cutoff frequency ω _n of 10 Hz (i.e. 62 rad/s), the synthesized discrete H filter is represented in figure 3.

Figure 4a illustrates the three signals of setpoint x_cons, measurement x_m (therefore disturbed) and filtered measurement x_mf (which appear to be merged on this scale), as a function of time T.

Figure 4b illustrates the error x_e with H filter and without ØH filter, as a function of time T.

Figure 4c illustrates the x_com command signal to system 10 (an actuator here) with H filter and without ØH filter, as a function of time T.

Figure 4d illustrates the variations of the rotation speed Ω, as a function of time T.

It is observed that in the absence of filtering, the error signal x_e is very noisy and that and that the amplitude of the oscillations is of the order of the error signal x_e, which represents the tracking error of the signal setpoint x_cons. This noise on the error signal x_e then causes significant oscillations on the control signal x_com, which can harm the actuator 10 (unnecessary strokes, rapid control variations, unwanted stresses, etc.).

On the contrary, when the measurement x_m is filtered, that is to say that the error signal x_e takes into account the filtered measurement signal x_mf, the servo error signal x_e is smoothed just like the current of control independent of rotational speed. In addition, the regulation performance is not affected due to the shape of the filter.

We also see that the filtering is effective at any engine speed value, which shows the efficiency of the H filter whose cut-off frequency takes into account the engine speed in its implementation.

Figures 5a to 5d represent a portion zoom of previous Figures 4a to 4d (from about 36s to 37.5s). We see a strong attenuation of the oscillations.

Note for example that the control signal x_com (control current here) changes from a variation of 10% of the full scale without ØH filtering to variations of 0.2% of the full scale when the H filtering is active.

Finally, to validate the interest of an H filter with a variable cut-off frequency ω _n , we compare two simulations, one made with an H0 filter at a fixed cut-off frequency (at 10 Hz which corresponds to Ω=600 tr /min), the other with the H filter with variable cutoff frequency . The setting parameters ξn and ξd are identical in both cases.

The results are given in Figures 6a to 6d .

We then observe that when the speed is different from Ω=600 rpm (ie the cutoff frequency of the fixed filter) the H0 filter with a fixed cutoff frequency does not attenuate the oscillations, just like when there is no filter. . However, when we are at Ω=600 rpm, the two filters H0 and H (fixed and variable cut-off frequency ω _n ) behave in the same way and attenuate the oscillations.

Two lessons can be drawn from this simulation:
- the H filter with variable cut-off frequency ω _n attenuates the signal only near the cut-off frequency ω _n (ie the measured rotation speed Ω) and leaves the rest of the spectrum unchanged,
- with fixed cutoff frequency, the H filter with variable cutoff frequency has the same performance as an H0 filter synthesized specifically for this operating point.

The proposed filter H makes it possible to filter disturbances with a cut-off frequency ω _n measured in a relatively simple way since the filter H is simply of the second order. This solution makes it possible in particular to limit the impact of the filtering to the only signals to be filtered and not to disturb the behavior of the system unduly. Indeed, the fact of having a variable cutoff frequency makes it possible to use a filter with a very narrow rejection band to limit as much as possible the impact of the filtering on the frequencies that one wishes to keep.

Another advantage of this solution is that the most restrictive performances are required for high rotation speeds Ω. However, the cutoff frequency ω _n is greater at high speed and the filter therefore has a lesser impact on the bandwidth of the system.

Finally, the form given to the discrete filter means that the adjustment parameters remain accessible and are explicit. Thus, it is not necessary to calculate new coefficients if one wishes to modify the filtering parameters. The solution is therefore easily adaptable to other applications as long as the disturbance frequency is measured or estimated, the only constraint being to adjust the two filter parameters again to adapt them to the new system.

One difficulty was to find a way to explicitly express the cutoff frequency of a discrete notch filter. This choice of a discreet filter is explained in particular by the desire to facilitate the implementation of the filter on the engine computer. Different tools therefore had to be implemented (Notch filter and bilinear transformation) to obtain it.

Obtaining the cutoff frequency explicitly was not the only constraint, however. Indeed, it was also important to be able to tune this filter since unlike a filter defined for a known cutoff frequency, this filter must be tuned over a wide spectral range. Fortunately, the method used to preserve the cutoff frequency is also valid with respect to the notch filter adjustment parameters.

The bilinear transformation used to obtain the discrete expression of the Notch filter induces a frequency shift which causes the calculated cutoff frequency of the filter ω _{n to be} different from the actual cutoff frequency. This offset is greater the closer the cut-off frequency is to the sampling frequency. If this shift is too large, it is necessary to adjust the cutoff frequency by the Tustin transformation, which makes it possible to obtain the exact cutoff frequency but complicates the expression of the filter.

As a note, the offset of the cutoff frequency is less than 1% if the cutoff frequency is less than 10 times the sampling frequency and less than 0.1% if the cutoff frequency is less than 20 times the sampling frequency. 'sampling.

Finally, if the rotation speed becomes too low, the filtering cuts too much at low frequencies, which will greatly degrade the useful signal.

It is therefore necessary to activate this filtering only from a certain rotation speed.

Claims (11)

Method for filtering a measurement signal (x_m) disturbed by electromagnetic disturbances generated by at least one metallic mass (14), in rotation, of a rotating element (12) of a turbomachine, said rotating element (12) being driven at a known rotational speed (Ω), said method of filtering using a filter (H) having a variable cutoff frequency (ω _n ), said cutoff frequency (ω _n ) being a function of the rotational speed (Ω ) of the rotating element (12). Filtering method according to Claim 1, in which the filter (H) receives as input the measurement signal (x_m) and a signal relating to the speed of rotation (Ω). Filtering method according to Claim 1 or 2, in which the variable cut-off frequency ω _n is _{equal to ω n} =2П/60×Ω, where Ω is the speed of rotation expressed in revolutions per minute Filtering method according to any one of Claims 1 to 3, in which the filter (F) is defined in a continuous domain according to a Notch filter of order 2. Filtering method according to Claim 4, in which the Notch filter (H) of order 2 is in the following form:


where ω _n is the cutoff frequency and ξ _n , ξ _d tuning parameters. Filtering method according to claim 5, in which a change of variable has been carried out using the following bilinear transformation:

where T _s is the system sampling frequency, s is the Laplace variable, and z is the discrete operator. Filtering method according to any one of Claims 1 to 6, in which the rotating element (12) of the turbine engine is a propulsion rotor comprising blades or vanes. Filtering method according to claim 7, in which the turbine engine is of the unducted fan type comprising at least one propulsion rotor with blades, and the speed of rotation of each rotor is for example between 300 rpm and 1300 rpm. min. Filter (F) for filtering a measurement signal (x_mes) disturbed by electromagnetic disturbances generated by at least one metal mass (14), in rotation, of a rotating element (10, 12, 14) of a turbomachine, said rotating element being driven at a known rotational speed (Ω), said filter (F) comprising an input receiving the measurement signal (x_mes) and a value relating to the rotational speed (Ω), and in which the cut-off frequency (ω _n ) of the filter (F) depends on the value relative to the rotation speed (Ω). Control unit (A) for controlling a device, the control unit receiving a setpoint (x_cons) as input, the control unit comprising
- a filter (H) according to claim 8 for generating a filtered measurement signal (x_mesf) and
- a corrector receiving at input an error signal (x_e) taking into account the setpoint signal (x_cons) and the filtered measurement signal (x_mesf), the corrector generating at output a command (x_com) intended for the device. Driver unit (A) comprising a filter (H) configured to implement the method of claim 1.