FR2706559A1 - Method for actively damping out vibration - Google Patents

Abstract

Actuators (16) are made to operate in order to generate a secondary field of vibration designed to interfere with a primary field to be damped out. The output signal from sensors (14) is picked up, and optimum parameters for operating the actuators are determined recursively (iteratively) by estimating components of the primary field and a transfer matrix relating the actuators and the sensors, on the basis of the output signals from the sensors. The actuators (16) are operated by applying to them control parameters (Ui) obtained by adding a random noise (Bi) to the determined optimum parameters (Uopt'i).

Description

METHOD FOR ACTIVE DAMPING OF VIBRATIONS

  The invention relates to methods of actively damping vibrations, intended to reduce and if possible to cancel the amplitude of the vibrations of a mechanical member or

of a medium.

  The term "vibrations" is to be interpreted in a general sense and as defining periodic or random phenomena of very diverse nature and origin, such as the vibration of a mechanical organ or the vibration of a fluid in the form of waves. sound with free propagation or

  guided, in any frequency range.

  In order to damp a primary vibration field, it is conventional to control one or more actuators to produce a secondary field of vibration to interfere with the primary field, and to measure the residual amplitude of the vibrations by means of one or more sensors. The output signals of the sensors are taken into account to calculate the control parameters of the

  actuators so as to obtain the desired damping.

  The invention relates more precisely to the case where a recursive algorithm is applied to calculate the control parameters (see for example EP-A-0 425 352). An example of such an algorithm is the Recursive Least Squares (RLS) algorithm in which the system is modeled by a relation such that:

Y = HU + E (1)

  Y is the C component measurement vector (C = number of sensors), H is the actuator / sensor transfer matrix, U is the A component control vector (A = number of actuators) and E is the vector to C components representing the values of the primary field at the level of the sensors. The algorithm consists in statistically estimating H and E, U being known and Y being measured. The optimal command to be applied, according to the criterion of minimization of the vector Y, is then given by:

U = - (H'H) - 'H * E (2)

  The application of the optimal command according to relation (2) leads to divergence problems in the H and E estimates, which can be explained by the fact that the relation (1) has C equations for (A + 1 ) xC unknowns to estimate (the AxC terms of the matrix H and the C components of the vector E). If we suppose that the algorithm has converged, that is to say that the estimates of H and E are constant, the successive observations of the relation (1) become redundant and therefore insufficient to inform on the values of H and E In other words, the linear system (1) becomes unobservable, the algorithm being no longer able to identify the true values of H and E. An object of the invention is to eliminate, or at least of

  master these divergence issues.

  The invention thus proposes a method of active damping of vibrations in at least one location subjected to a primary vibration field, in which at least one actuator is controlled to generate a secondary vibration field intended to interfere with the primary field. collects the output signal from at least one sensor located at said location, and recursively determines optimal control parameters of the actuator (s) by estimating primary field components and a transfer matrix between the actuator (s) and the the sensors, from the output signals of the sensor or sensors, characterized in that the actuator or each actuator is controlled by applying to it control parameters obtained by adding a random noise to the parameters

determined optimal.

  The introduction of noise reduces the problems of unobservability encountered with conventionally applied recursive algorithms. This results in better convergence in the transfer matrix and primary field estimates. The amplitude of the noise can be controlled to limit the degradation of damping

resulting.

  The invention applies particularly, but not exclusively, whenever the vibration energy is concentrated at a few frequencies comprising a fundamental

  and harmonics that remain in a constant relationship.

  The invention finds application in all industrial systems where it is desirable to damp the vibrations occurring at identifiable frequencies, possibly because they are directly related to a

measurable frequency.

  These include rotating machinery,

  pumps, fans, internal combustion engines.

  The aim may be to increase the reliability of the system, reduce noise and / or obtain

acoustic stealth.

  The invention will be better understood on reading the

  following description of a particular embodiment,

  given by way of non-limiting example. The description is

  refers to the drawings which accompany it, in which: - Figure 1 is a block diagram of a device for implementing the invention; FIG. 2 is a block diagram of a computing unit that can be used in the device of FIG. 1; FIG. 3 is a block diagram showing a constitution of a signal mixer that can be used in the

device of Figure 1.

  The method will be described in its application to the active dynamic damping of periodic vibrations

  a vibrating structure constituted by a rotating member.

  FIG. 1 shows such a rotating member constituted by a

tree 11.

  The input signals of the device embodying the invention comprise, on the one hand, a synchronization signal supplied by a sensor 12, for example providing a pulse whenever it is facing given locations of the shaft 11 on the other hand C electrical signals each provided by a sensor 14 and representing the displacements due to vibrations at

  the location o is located the sensor on the stator 10.

  The output signals of the device are applied to electrodynamic actuators 16, which may for example be constituted by vibrating pots acting on the vibrating structure at points which can in general be defined by calculation and then adjusted by

  experimentation, so as to obtain an optimal result.

  For simplicity, only the connections of a single actuator and a single sensor are shown in FIG. The damping device further comprises an actuator signal processing and control assembly 18 which receives the input signals through charge amplifiers 19 and provides the output signals. This assembly 18 is designed to reduce the vibrations at particular frequencies, by a closed-loop servocontrol. These particular frequencies are as a rule harmonic f0, f1, ..., fp-1 of a fundamental frequency f0 that the sensor of

  12 synchronization helps to get.

  The assembly 18 can be regarded as providing three functions: the extraction of the components Y0 (1), ..., Yp1 (l); ; Y0 (C), ..., Yp1 (C) of the signal spectrum of each of the sensors 14, at each of the frequencies f, f, ..., fp-1 to be controlled, - the calculation of weighting parameters for the control of the actuators, and - the generation, by mixing analog signals, of the output signals applied to each actuator 16 by

  via power amplifiers 20.

  To perform these functions, the assembly 18 must realize the synthesis 24 of periodic signals, generally sinusoidal, synchronous with the periodic signal supplied by the sensor 12. A synthesizer 24 that can be used to generate periodic waves of any shape at a frequency (n / m) f 0

is described in EP-A-0425352.

  The extraction of the components is carried out by subjecting the output signal of each sensor 14, brought to a sufficient level by the corresponding amplifier 19, to an anti-aliasing low-pass filtering 21 and to an analog-digital conversion sampling. 22 at a sufficiently high rate with respect to each of the synthesized frequencies. The samples are subjected to a synchronous demodulation which involves a digital multiplication 26 and a low-pass filtering 28 for each

frequency retained.

  The amplitude and the phase of the spectrum of each sensor are thus extracted, each time for a respective synthesized frequency. Often, except for very complex systems, a control for p = 4 synthesized frequencies

is enough.

  In the notations used in the drawings, Yi (j) denotes the component derived from the output signal of the jth sensor (1 <j <c) by synchronous demodulation according to the frequency f 1 (0 <i <p-1), Ui (k) denotes the weighting coefficient of the synthesized wave of frequency fi for the control of the kth actuator, Ui denotes the column vector (control vector) constituted by the Ui (k) for 1 <k <A, and U (k) denotes the column vector constituted by

the Ui (k) for 0 <i <p-1.

  The calculation unit 30 shown in FIG. 2 separately calculates each control vector U i as a function of the components Y i (I),..., Y i (C) relating to the frequency f 1. The weighting coefficients Ui (k) are then reordered according to the vectors U (k). The computing unit 30 thus provides, at the output, for each of the A actuators, weighting coefficients in a number equal to that of the frequencies for which the damping must be realized (that is to say in number equal to that of the waves provided by the synthesizer 24). These coefficients are applied to the mixer 32, comprising a number of outputs

equal to that of the actuators.

  The mixer 32 may have the constitution of principle shown in FIG. 3. It comprises blocks 46 of digital-to-analog converters each comprising a number of converters equal to that of the waveforms generated by the synthesizer 24. Each block 46 is assigned to a particular actuator 16. Each converter of the same block 46 receives one of the waveforms generated by the synthesizer 24 and supplies, on its output, an analog signal which is the product of the waveform by the respective weighting coefficient, provided by the calculation unit 30. The outputs of a block 46, which consist of the contributions of the damping signal for the same frequency, are applied to a summator 48 whose output drives a filter amplifier 50. The signal thus generated is applied to the power amplifier of

the appropriate actuator.

  Figure 2 illustrates how to obtain

  weights at each sampling step.

  For each frequency fi, the block 52 first estimates the A x C terms of the transfer matrix Hi between the actuators 16 and the sensors 14, and the C components Ei of the primary vibration field at the sensors. At each sampling step, a vector Yi is measured which constitutes the response to the frequency f 1 of the system to the stresses caused by the components E 1 of the primary field and by the components U 1 of the control of the actuators 16. By accumulating these measurements, can make a statistical estimate of Hi and Ei given the relation Yi = HiUi + Ei which models the response. The estimation is for example carried out by applying the least squares algorithm. Then block 53 determines the optimal weighting coefficients Uopt, i for each frequency synthesized by the estimates of the matrix Hi and the vector Ei: Uopt, i = - (HiHi) -Hi * Ei. control Ui, composed of the weighting coefficients that will be used to control the actuators 16 at the next sampling rate, a random noise Bi is added to each vector of optimal coefficients Uopti determined at 53. The noise Bi, generated at 54, consists of by a sequence of decorrelated random vectors, of zero average, whose components are independent. Each component of Bi is added at 55 to the corresponding optimal weighting coefficient to obtain the coefficient Ui (k) addressed to

mixer 32.

  The introduction of the noise causes a certain degradation of the attenuation provided by the device, but it makes it possible to very significantly improve the

  estimates of primary field and transfer matrix.

  We can also adapt the noise generator 54 so as to maintain the degradation of the attenuation within predetermined limits. In this respect, the method explained below can be applied to calculate each noise vector Bi (in the following, the indices are left out

frequency i).

  We reason in the case where the identification process has converged, and it is assumed that the estimated values of the transfer matrix H and the primary field E coincide with the true values. Let Uopt be the calculated optimal control vector and Yopt the corresponding sensor output. Let V be a random complex vector of the same size as the control vector U. For X scalar, we consider the disturbed control by the noise B = XV: U = Uopt + XV The square of the standard of the sensor output is then: i Y2 = 11H (U + XV) + EB2 = IYI2 + H12 Let X0 be the value of X corresponding to a loss of attenuation of a dB. We have: 10. loglo (112) = .X loglo (+2 YoTII2) = a of o: 0-IY J2 (1 0 / -l) - a ln (10) YoF

IHV2 10! IHV2

  this last approximation being valid for a << 10. One places oneself in the case where the degradation of gain is weak, and one makes the assumption that X0 is small in front of 1. A development with the first order gives the following expression of the loss of attenuation corresponding to the disturbed command: t1 0gl (il 1l 10 2 IIHxjl = 12 This expression makes it possible to select X following This expression makes it possible to select X according to a law of probability chosen and to use the perturbed command U = Uopt + XV so as to obtain a random command leading to a controlled degradation of the performance A random choice of X is considered according to a normalized probability law centered, of standard deviation o If one wishes that the degradation is lower than 1 dB at 99%, it is necessary to realize: Probability t 2-- = 0.99 (X2 / a2) being a variable of x2 with a degree of freedom, a statistical table indicates: - = 6.63 o / 6.63

  the average of the degradation is then 0.15 dB.

  A uniform draw of X in the interval [0, X0] leads to a maximum degradation of 1 dB, with a

average of 0.33 dB.

  Although the invention has been described with reference to a particular embodiment, it will be understood that various modifications can be made to this example without departing from the scope of the invention. Thus, the invention is not limited to the case where the different frequency components of the control of the actuators are

  independent recursive calculations.

Claims (1)

CLAIM   A method of actively damping vibrations in at least one location subject to a primary vibration field, in which at least one actuator (16) is controlled to generate a secondary vibration field for interfering with the primary field, the signal is collected for outputting at least one sensor (14) located at said location, and recursively determining optimal control parameters (Uopt, i) of the actuator (s) by estimating components (E) of the primary field and a matrix of transfer (Hi) between the actuator (s) and the sensor (s), from the output signals of the at least one sensor, characterized in that the actuator or each actuator (16) is controlled by applying to it control parameters ( Ui) obtained by adding a random noise (Bi) to   determined optimal parameters (Uopt, i).