WO2009050408A2 - Method for qualifying the stability of a controlled system - Google Patents

Method for qualifying the stability of a controlled system Download PDF

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WO2009050408A2
WO2009050408A2 PCT/FR2008/051761 FR2008051761W WO2009050408A2 WO 2009050408 A2 WO2009050408 A2 WO 2009050408A2 FR 2008051761 W FR2008051761 W FR 2008051761W WO 2009050408 A2 WO2009050408 A2 WO 2009050408A2
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signal
dsp
mod
regulated
stability
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PCT/FR2008/051761
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French (fr)
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WO2009050408A3 (en
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Laurent Jacquot
Grégory LAUNAY
Yves Le Vourch
Didier Martinez
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Renault S.A.S.
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Publication of WO2009050408A2 publication Critical patent/WO2009050408A2/en
Publication of WO2009050408A3 publication Critical patent/WO2009050408A3/en

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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B5/00—Anti-hunting arrangements
    • G05B5/01—Anti-hunting arrangements electric
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/42—Servomotor, servo controller kind till VSS
    • G05B2219/42267—Stability analysis

Definitions

  • the present invention relates to a method of qualifying the stability of a slave system for evaluating this stability and comparing the respective stabilities of different slave systems.
  • the stability of a slave system is defined as follows: when a finite and bounded input signal is applied to a slave system, the output signal, or response signal of the slave system subjected to this input signal is not diverge. The output signal may exhibit damping oscillations. The output signal then converges to a final stationary value.
  • a slave system is said to be asymptotically stable if, when a finite input signal is applied to it, the output signal does not diverge and when a step input signal is applied thereto, all oscillations are damped. The output signal thus tends asymptotically towards a final stationary value.
  • the application of a Dirac pulse input signal produces a rapid attenuation of the observable oscillations on the output signal. The system then returning to its previous stationary state.
  • stability of a slave system is an estimate of the quality of its adjustment.
  • a first method detects the maxima, the minima and the average value of a signal. The further away the extrema are from the average value, the more unstable the slave system is.
  • Such a device is for example used in the device described in US 4806848. This method is not however applicable only for a stabilized signal. It is therefore impossible to use it to qualify the stability in transient mode.
  • a second analytical method is based on a quality factor Q.
  • a slave system can be defined by means of an electrical diagram, and can be written as a product of
  • T ⁇ second-order transfer function - -, with pp + 2 ⁇ 0 p + ⁇ 0 Laplace operator, K gain, C ⁇ O own pulsation and ⁇ damping coefficient.
  • the adjustment of a slave system is most often a compromise between speed and stability.
  • the regulatory constraints on pollution are becoming more and more demanding.
  • Optimum adjustment of the performance of a slave system is always sought, both in dynamics and in steady state phases.
  • An objective tool is thus necessary to qualify the stability of a system, in steady state or in transient, and preferably on the basis of the setpoint signal and the regulated signal in order to be able to also consider the nonlinear systems, and thus be able to compare the stabilities of two slave systems.
  • the invention meets these needs without the disadvantages of the prior art.
  • the subject of the invention is a method for qualifying the stability of a controlled system producing at output a regulated temporal signal as a function of a set input time signal, comprising the following steps: : selection of an evaluation time window, centering of the regulated time signal and of the target time signal, calculation of the loop difference signal, on the evaluation time window, calculation of the power spectral density signal, DSP, of said loop difference signal, modeling of the power spectral density signal by a polynomial function, DSP Mod, as a function of frequency, calculation of the area for which the power spectral density signal, DSP, is greater than the modeled signal , DSP_mod, determination of a stability criterion, between 0 and
  • the method further comprises, between the step of calculating the signal
  • the filtered signal DSP_Flt is calculated from the DSP signal by determination of a sliding average, according to the formula
  • the polynomial function used in the modeling step is
  • Another advantage of the process according to the invention is that it can be applied both to the stabilized phases and to the transient phases.
  • Another advantage of the method according to the invention is to require only recordings of the regulated signal and, if appropriate, of the reference signal.
  • FIG. 1 shows a slave system
  • FIG. 2 presents on a timing diagram, a setpoint signal and a regulated signal
  • FIG. 3 presents on the same time diagram, a corresponding difference signal
  • FIG. frequency diagram the signals DSP, DSP_Flt and DSP_Mod
  • - figure 5 presents on the same frequency diagram, the signals DSP_Flt and DSP_Mod, as well as the area determining the criterion of stability.
  • a typical slave system 1 receives as input a setpoint signal 2.
  • the slave system regulates said signal 2 to output a regulated signal 3.
  • the setpoint signal 2 is absent.
  • the subject of the present invention is a method for qualifying the stability of such a controlled system 1 producing as output a regulated temporal signal 3 as a function of a setpoint time signal 2 input.
  • the method includes a first step of selecting an evaluation time window.
  • an evaluation time window can be chosen both in a transient phase and in a steady state phase, or both.
  • On this window are sampled the input signal 2 or reference signal and the output signal 3 or response signal or regulated signal.
  • said signals 2, 3 are centered along the ordinate axis, in amplitude. It is considered that the setpoint 2 and regulated 3 compared signals are available in the same unit.
  • a preliminary processing applying a gain, on one or two of the signals 2, 3, is performed, so that the two signals appear in the same unit, in order to be compared.
  • a comparison signal or loop gap signal 4 is then calculated by subtracting the regulated signal 3 from the setpoint signal 2 on the evaluation time window.
  • FIG. 2 illustrates an example, on a time diagram, of setpoint 2 and regulated signals 3 over a given evaluation time window.
  • the setpoint signal 2 is here constant.
  • FIG. 3 illustrates, for the signals of the example of FIG. 2, the loop difference signal 4 obtained by difference, regulated signal - reference signal.
  • FIG. 4 presents a frequency diagram showing the power spectral density signal, DSP, obtained for the difference signal 4 illustrated previously in FIG. 3.
  • said power spectral density signal, DSP is modeled by a polynomial function of the frequency variable.
  • the modeling can be carried out by any polynomial interpolation method known to the man of the job.
  • FIGS. 4 and 5 show, on a frequency diagram, said modeled signal DSP_Mod corresponding to the signal DSP shown in the diagram of FIG. 4.
  • the comparison of the signal 8 modeled DSP_Mod with the signal DSP 5 reveals portions where the signal DSP is greater than the signal 8 modeled DSP_Mod.
  • the modulated signal DSP Mod represents a "perfect” or “ideal” DSP, as it should be on the evaluation window considered in the absence of noise or resonance.
  • the method evaluates a resonance in the loop. Area 7 is indicative of this resonance. This area 7 represents a percentage of resonance energy. The larger the area 7, the more resonant and therefore unstable the system. The stability criterion is thus even lower than the slave system 1 is stable.
  • the DSP signal is advantageously filtered.
  • a filtering step is then inserted between the step of calculating the signal DSP and the modeling step producing the signal DSP_Mod.
  • This step produces a filtered signal DSP_Flt.
  • This signal is illustrated in FIGS. 4 and 5 which show, on a frequency diagram, said filtered signal DSP_Flt corresponding to the signal DSP shown in the diagram of FIG. 4.
  • the filtered signal DSP Fit then replaces the power spectral density signal, DSP in the later stages.
  • the area 7 is determined between the filtered signal 9 and the signal 8 modeled, when the first is greater than the second.
  • the filtered signal DSP_Flt 9 can be determined by any type of filtering. According to a particular embodiment, the filtered signal DSP_Flt 9 is calculated from the signal 5
  • DSP for example by determining a sliding average
  • Criterion where Pts_Sup represents the set of points where the signal DSP, respectively the filtered signal 9 DSP_Flt is greater than the signal 8 modeled DSP Mod.
  • the polynomial function used for the modeling producing the modulated DSP modulated signal 8 can be any function of the frequency variable f.
  • this function is a function of order 4 of the form:

Abstract

The invention relates to a method for qualifying a controlled system (1) generating at the output a time signal (3) adjusted on the basis of a setpoint time signal (2) fed at the input, wherein said method comprises: selecting an evaluation time slot; centring the adjusted time signal (3) and the setpoint time signal (2); calculating the loop deviation signal (4), deviation signal, setpoint signal, adjusted signal, in the evaluation time slot; calculating the power spectral density signal (5), PSD, of said loop deviation signal (4); modelling the power spectral density signal (5), PSD, by a polynomial function PSD Mod based on the frequency; calculating the area (7) for which the power spectral density signal (5), PSD, is higher than the modelled signal (8) PSD_mod; determining a stability criterion between 0 and 100 equal to one hundred times said area (7) weighed by the signal PSD (5), wherein the lower said stability criterion is, the more stable the controlled system (1) is.

Description

PROCEDE DE QUALIFICATION DE LA STABILITE D'UN SYSTEME METHOD FOR QUALIFYING THE STABILITY OF A SYSTEM
ASSERVISLAVE
La présente invention concerne un procédé de qualification de la stabilité d'un système asservi afin d'évaluation de cette stabilité et de comparaison des stabilités respectives de différents systèmes asservis.The present invention relates to a method of qualifying the stability of a slave system for evaluating this stability and comparing the respective stabilities of different slave systems.
La stabilité d'un système asservi est définie ainsi : lorsqu'est appliqué à un système asservi un signal d'entrée fini et borné, le signal de sortie, ou signal de réponse du système asservi soumis à ce signal d'entrée ne va pas diverger. Le signal de sortie peut présenter des oscillations s' amortissant . Le signal de sortie converge alors vers une valeur stationnaire finale. Un système asservi est dit asymptotiquement stable si lorsqu'on lui applique un signal d'entrée fini, le signal de sortie ne diverge pas et que lorsqu'on lui applique un signal d'entrée en échelon, toutes les oscillations sont amorties. Le signal de sortie tend ainsi de manière asymptotique vers une valeur stationnaire finale. Enfin l'application d'un signal d'entrée impulsion de Dirac produit une atténuation rapide des oscillations observables sur le signal de sortie. Le système retrouvant alors son état stationnaire précédent. De manière générale la stabilité qualifie l'absence de caractère oscillatoire de la réponse d'un système en dynamique. La stabilité d'un système asservi est une estimation de la qualité de son réglage.The stability of a slave system is defined as follows: when a finite and bounded input signal is applied to a slave system, the output signal, or response signal of the slave system subjected to this input signal is not diverge. The output signal may exhibit damping oscillations. The output signal then converges to a final stationary value. A slave system is said to be asymptotically stable if, when a finite input signal is applied to it, the output signal does not diverge and when a step input signal is applied thereto, all oscillations are damped. The output signal thus tends asymptotically towards a final stationary value. Finally, the application of a Dirac pulse input signal produces a rapid attenuation of the observable oscillations on the output signal. The system then returning to its previous stationary state. In a general way stability qualifies the absence of oscillatory character of the response of a system in dynamics. The stability of a slave system is an estimate of the quality of its adjustment.
Dans le domaine de la qualification de la stabilité d'un système asservi, il est connu deux méthodes.In the field of qualification of the stability of a slave system, two methods are known.
Une première méthode détecte les maxima, les minima et la valeur moyenne d'un signal. Plus les extrema sont éloignés de la valeur moyenne et plus le système asservi est instable. Un tel dispositif est par exemple utilisé dans le dispositif décrit dans le document US 4806848. Cette méthode n'est cependant applicable que pour un signal stabilisé. Il est donc impossible de l'utiliser pour qualifier la stabilité en mode transitoire.A first method detects the maxima, the minima and the average value of a signal. The further away the extrema are from the average value, the more unstable the slave system is. Such a device is for example used in the device described in US 4806848. This method is not however applicable only for a stabilized signal. It is therefore impossible to use it to qualify the stability in transient mode.
Une seconde méthode analytique se base sur un facteur de qualité Q. Un système asservi peut être défini à l'aide d'un schéma électrique, et peut s'écrire sous forme de produit deA second analytical method is based on a quality factor Q. A slave system can be defined by means of an electrical diagram, and can be written as a product of
Tζ fonction de transfert du second ordre : — -, avec p p +2εω0p + ω0 opérateur de Laplace, K gain, CÙO pulsation propre et ε coefficient d'amortissement. Le facteur de qualité s'écrit alors Q= , Une telle méthode est mise en œuvre parTζ second-order transfer function: - -, with pp + 2εω 0 p + ω 0 Laplace operator, K gain, CÙ O own pulsation and ε damping coefficient. The quality factor is then written Q =, Such a method is implemented by
2Wl-£2 exemple par EP 1030815. Cette méthode n'est cependant applicable que pour des systèmes identifiés par une telle fonction de transfert analytique.£ 2 2Wl- example EP 1030815. However, this method is only applicable to systems identified by such analytical transfer function.
Le réglage d'un système asservi est le plus souvent un compromis entre rapidité et stabilité. Ainsi par exemple dans le domaine du contrôle moteur, les contraintes réglementaires en matière de pollution deviennent de plus en plus exigeantes. Un réglage optimum des performances d'un système asservi est toujours recherché, tant en dynamique que dans les phases de régime établi. Un outil objectif est ainsi nécessaire pour qualifier la stabilité d'un système, en régime établi ou en transitoire, et de préférence à partir du signal de consigne et du signal régulé afin de pouvoir considérer aussi les systèmes non linéaires, et ainsi pouvoir comparer les stabilités de deux systèmes asservis.The adjustment of a slave system is most often a compromise between speed and stability. For example, in the field of engine control, the regulatory constraints on pollution are becoming more and more demanding. Optimum adjustment of the performance of a slave system is always sought, both in dynamics and in steady state phases. An objective tool is thus necessary to qualify the stability of a system, in steady state or in transient, and preferably on the basis of the setpoint signal and the regulated signal in order to be able to also consider the nonlinear systems, and thus be able to compare the stabilities of two slave systems.
L' invention répond à ces besoins sans présenter les inconvénients de l'art antérieur.The invention meets these needs without the disadvantages of the prior art.
L'invention a pour objet un procédé de qualification de la stabilité d'un système asservi produisant en sortie un signal temporel régulé en fonction d'un signal temporel de consigne introduit en entrée, comprenant les étapes suivantes : sélection d'une fenêtre temporelle d'évaluation, centrage du signal temporel régulé et du signal temporel de consigne, calcul du signal d'écart de boucle, sur la fenêtre temporelle d'évaluation, calcul du signal densité spectrale de puissance, DSP, dudit signal d'écart de boucle, modélisation du signal densité spectrale de puissance par une fonction polynomiale, DSP Mod, en fonction de la fréquence, calcul de l'aire pour laquelle le signal densité spectrale de puissance, DSP, est supérieur au signal modélisé, DSP_mod, détermination d'un critère de stabilité, compris entre 0 etThe subject of the invention is a method for qualifying the stability of a controlled system producing at output a regulated temporal signal as a function of a set input time signal, comprising the following steps: : selection of an evaluation time window, centering of the regulated time signal and of the target time signal, calculation of the loop difference signal, on the evaluation time window, calculation of the power spectral density signal, DSP, of said loop difference signal, modeling of the power spectral density signal by a polynomial function, DSP Mod, as a function of frequency, calculation of the area for which the power spectral density signal, DSP, is greater than the modeled signal , DSP_mod, determination of a stability criterion, between 0 and
100, égal à 100 fois ladite aire moyennée par le signal densité spectrale de puissance, DSP, ce critère de stabilité étant d'autant plus faible que le système asservi est stable.100, equal to 100 times said area averaged by the power spectral density signal, DSP, this stability criterion being all the lower as the slave system is stable.
Selon une autre caractéristique de l'invention, le procédé comprend encore, entre l'étape de calcul du signalAccording to another characteristic of the invention, the method further comprises, between the step of calculating the signal
DSP et l'étape de modélisation, une étape de filtrage remplaçant le signal densité spectrale de puissance, DSP, dudit signal d'écart de boucle, par un signal filtré DSP_Flt.DSP and the modeling step, a filtering step replacing the power spectral density signal, DSP, of said loop difference signal by a filtered signal DSP_Flt.
Selon une autre caractéristique de l'invention, le signal filtré DSP_Flt est calculé à partir du signal DSP par détermination d'une moyenne glissante, selon la formuleAccording to another characteristic of the invention, the filtered signal DSP_Flt is calculated from the DSP signal by determination of a sliding average, according to the formula
∑DSP(k-i)ΣDSP (k-i)
DSP_Flt(k) = ^ . nDSP_Flt (k) = ^. not
Selon une autre caractéristique de l'invention, la fonction polynomiale employée à l'étape de modélisation estAccording to another characteristic of the invention, the polynomial function used in the modeling step is
R C D F une fonction d'ordre 4, DSP Λfo<i(/) = A +— +— + — +—. f f f f4 RCDF a function of order 4, DSP Λfo <i (/) = A + - + - + - + -. ffff 4
Selon un mode de réalisation alternatif, appliqué à un système asservi ne comportant pas de signal temporel de consigne, le signal d'écart de boucle, est calculé selon la formule : signal d'écart = signal régulé. Un avantage du procédé selon 1 ' invention est de produire un critère objectif pour tout système asservi.According to an alternative embodiment, applied to a slave system having no set time signal, the loop difference signal is calculated according to the formula: deviation signal = regulated signal. An advantage of the method according to the invention is to produce an objective criterion for any slave system.
Un autre avantage du procédé selon l'invention est de pouvoir être appliqué aussi bien aux phases stabilisées, qu'aux phases transitoires.Another advantage of the process according to the invention is that it can be applied both to the stabilized phases and to the transient phases.
Un autre avantage du procédé selon l'invention est de ne nécessiter que des enregistrements du signal régulé et le cas échéant du signal de consigne.Another advantage of the method according to the invention is to require only recordings of the regulated signal and, if appropriate, of the reference signal.
D'autres caractéristiques, détails et avantages de l'invention ressortiront plus clairement de la description détaillée donnée ci-après à titre indicatif en relation avec des dessins sur lesquels :Other characteristics, details and advantages of the invention will emerge more clearly from the detailed description given below as an indication in relation to drawings in which:
- la figure 1 présente un système asservi, la figure 2 présente sur un diagramme temporel, un signal de consigne et un signal régulé, la figure 3 présente sur le même diagramme temporel, un signal d'écart correspondant, la figure 4 présente sur un diagramme fréquentiel, les signaux DSP, DSP_Flt et DSP_Mod, - la figure 5 présente sur le même diagramme fréquentiel, les signaux DSP_Flt et DSP_Mod, ainsi que l'aire déterminant le critère de stabilité. Selon la figure 1, un système asservi 1 typique reçoit en entrée un signal de consigne 2. Le système asservi régule ledit signal 2 pour produire en sortie un signal régulé 3. Dans certains modes de réalisation le signal de consigne 2 est absent.FIG. 1 shows a slave system, FIG. 2 presents on a timing diagram, a setpoint signal and a regulated signal, FIG. 3 presents on the same time diagram, a corresponding difference signal, FIG. frequency diagram, the signals DSP, DSP_Flt and DSP_Mod, - figure 5 presents on the same frequency diagram, the signals DSP_Flt and DSP_Mod, as well as the area determining the criterion of stability. According to FIG. 1, a typical slave system 1 receives as input a setpoint signal 2. The slave system regulates said signal 2 to output a regulated signal 3. In some embodiments, the setpoint signal 2 is absent.
La présente invention a pour objet un procédé de qualification de la stabilité d'un tel système asservi 1 produisant en sortie un signal 3 temporel régulé en fonction d'un signal 2 temporel de consigne introduit en entrée. Ledit procédé comprend une première étape de sélection d'une fenêtre temporelle d'évaluation. A noter que selon l'invention, une telle fenêtre d'évaluation peut être choisie aussi bien dans une phase transitoire que dans une phase de régime établi, ou les deux. Sur cette fenêtre sont échantillonnés le signal 2 d'entrée ou signal de consigne et le signal 3 de sortie ou signal de réponse ou signal régulé. Afin de permettre une comparaison, lesdits signaux 2, 3 sont centrés selon l'axe des ordonnées, en amplitude. Il est considéré que les signaux de consigne 2 et régulé 3 comparés sont disponibles dans la même unité. Dans le cas contraire un traitement préalable, appliquant un gain, sur un ou deux des signaux 2, 3, est effectué, afin que les deux signaux apparaissent dans même unité, afin de pouvoir être comparés. Un signal comparatif ou signal 4 d'écart de boucle est ensuite calculé en soustrayant le signal 3 régulé au signal 2 de consigne, sur la fenêtre temporelle d'évaluation.The subject of the present invention is a method for qualifying the stability of such a controlled system 1 producing as output a regulated temporal signal 3 as a function of a setpoint time signal 2 input. The method includes a first step of selecting an evaluation time window. Note that according to In the invention, such an evaluation window can be chosen both in a transient phase and in a steady state phase, or both. On this window are sampled the input signal 2 or reference signal and the output signal 3 or response signal or regulated signal. In order to allow a comparison, said signals 2, 3 are centered along the ordinate axis, in amplitude. It is considered that the setpoint 2 and regulated 3 compared signals are available in the same unit. In the opposite case, a preliminary processing, applying a gain, on one or two of the signals 2, 3, is performed, so that the two signals appear in the same unit, in order to be compared. A comparison signal or loop gap signal 4 is then calculated by subtracting the regulated signal 3 from the setpoint signal 2 on the evaluation time window.
La figure 2 illustre un exemple, sur un diagramme temporel, de signaux de consigne 2 et régulé 3 sur une fenêtre temporelle d'évaluation donnée. Le signal de consigne 2 est ici constant. La figure 3 illustre pour les signaux de l'exemple de la figure 2, le signal 4 d'écart de boucle obtenu par différence, signal régulé - signal de consigne.FIG. 2 illustrates an example, on a time diagram, of setpoint 2 and regulated signals 3 over a given evaluation time window. The setpoint signal 2 is here constant. FIG. 3 illustrates, for the signals of the example of FIG. 2, the loop difference signal 4 obtained by difference, regulated signal - reference signal.
Dans une étape ultérieure du procédé selon l'invention, une analyse fréquentielle est appliquée audit signal 4 d'écart de boucle. La figure 4 présente un diagramme fréquentiel figurant le signal 5 densité spectrale de puissance, DSP, obtenu pour le signal 4 d'écart illustré précédemment à la figure 3.In a subsequent step of the method according to the invention, a frequency analysis is applied to said loop difference signal 4. FIG. 4 presents a frequency diagram showing the power spectral density signal, DSP, obtained for the difference signal 4 illustrated previously in FIG. 3.
Dans une étape ultérieure du procédé selon l'invention, ledit signal 5 densité spectrale de puissance, DSP, est modélisé, par une fonction polynomiale de la variable fréquence. La modélisation peut être effectuée par toute méthode d'interpolation polynomiale connue de l'homme du métier. Les figures 4 et 5 présentent sur un diagramme fréquentiel ledit signal 8 modélisé DSP_Mod correspondant au signal 5 DSP figuré sur le diagramme de la figure 4.In a subsequent step of the method according to the invention, said power spectral density signal, DSP, is modeled by a polynomial function of the frequency variable. The modeling can be carried out by any polynomial interpolation method known to the man of the job. FIGS. 4 and 5 show, on a frequency diagram, said modeled signal DSP_Mod corresponding to the signal DSP shown in the diagram of FIG. 4.
La comparaison du signal 8 modélisé DSP_Mod avec le signal 5 DSP, fait apparaître des portions où le signal 5 DSP est supérieur au signal 8 modélisé DSP_Mod. Un calcul de l'aire 7 ainsi délimitée par la courbe du signal 5 DSP, lorsqu'elle est supérieure à la courbe du signal 8 DSP_Mod, divisé par le signal DSP, fournit un nombre compris entre 0 et 1. Ce nombre, multiplié par 100 fournit un critère de stabilité, compris entre 0 et 100.The comparison of the signal 8 modeled DSP_Mod with the signal DSP 5, reveals portions where the signal DSP is greater than the signal 8 modeled DSP_Mod. A calculation of the area 7 thus delimited by the curve of the signal DSP, when it is greater than the curve of the signal 8 DSP_Mod, divided by the signal DSP, gives a number between 0 and 1. This number, multiplied by 100 provides a stability criterion, between 0 and 100.
Le signal 8 modélisé DSP Mod représente une DSP « parfaite » ou « idéale », telle qu'elle devrait être sur la fenêtre d'évaluation considérée en l'absence de bruit ou de résonance. Le procédé évalue une résonance dans la boucle. L'aire 7 est indicative de cette résonance. Cette aire 7 représente un pourcentage d'énergie de résonance. Plus cette aire 7 est grande et plus le système est résonant et donc instable. Le critère de stabilité est ainsi d'autant plus faible que le système asservi 1 est stable.The modulated signal DSP Mod represents a "perfect" or "ideal" DSP, as it should be on the evaluation window considered in the absence of noise or resonance. The method evaluates a resonance in the loop. Area 7 is indicative of this resonance. This area 7 represents a percentage of resonance energy. The larger the area 7, the more resonant and therefore unstable the system. The stability criterion is thus even lower than the slave system 1 is stable.
Avantageusement, avant de procéder au calcul de l'aire 7, le signal 5 DSP est avantageusement filtré. Une étape de filtrage est alors insérée entre l'étape de calcul du signal 5 DSP et l'étape de modélisation produisant le signal 8 DSP_Mod. Cette étape produit un signal 9 filtré DSP_Flt. Ce signal est illustré aux figures 4 et 5 qui présentent sur un diagramme fréquentiel ledit signal 9 filtré DSP_Flt correspondant au signal 5 DSP figuré sur le diagramme de la figure 4. Le signal 9 filtré DSP Fit remplace ensuite le signal 5 densité spectrale de puissance, DSP dans les étapes ultérieures. Ainsi tel qu'illustré à la figure 5, l'aire 7 est déterminée entre le signal 9 filtré et le signal 8 modélisé, lorsque le premier est supérieur au second.Advantageously, before proceeding with the calculation of the area 7, the DSP signal is advantageously filtered. A filtering step is then inserted between the step of calculating the signal DSP and the modeling step producing the signal DSP_Mod. This step produces a filtered signal DSP_Flt. This signal is illustrated in FIGS. 4 and 5 which show, on a frequency diagram, said filtered signal DSP_Flt corresponding to the signal DSP shown in the diagram of FIG. 4. The filtered signal DSP Fit then replaces the power spectral density signal, DSP in the later stages. As shown in Figure 5, the area 7 is determined between the filtered signal 9 and the signal 8 modeled, when the first is greater than the second.
Le signal 9 filtré DSP_Flt peut être déterminé par tout type de filtrage. Selon un mode de réalisation particulier, le signal 9 filtré DSP_Flt est calculé à partir du signal 5The filtered signal DSP_Flt 9 can be determined by any type of filtering. According to a particular embodiment, the filtered signal DSP_Flt 9 is calculated from the signal 5
DSP, par exemple par détermination d'une moyenne glissante,DSP, for example by determining a sliding average,
∑DSP(k - i) selon la formule DSP_Flt{k) = — . Un tel filtrage n permet de s'affranchir d'une partie du bruit pouvant être présent dans le signal 5 DSP. Le calcul du critère de stabilité peut encore s'exprimer selon la formule suivante :ΣDSP (k - i) according to the formula DSP_Flt {k) = -. Such a filtering makes it possible to overcome some of the noise that may be present in the DSP signal. The calculation of the stability criterion can still be expressed according to the following formula:
Critère =
Figure imgf000009_0001
où Pts_Sup représente l'ensemble des points où le signal 5 DSP, respectivement le signal 9 filtré DSP_Flt est supérieur au signal 8 modélisé DSP Mod.Criterion =
Figure imgf000009_0001
where Pts_Sup represents the set of points where the signal DSP, respectively the filtered signal 9 DSP_Flt is greater than the signal 8 modeled DSP Mod.
La fonction polynomiale utilisée pour la modélisation produisant le signal 8 modélisé DSP Mod peut être une fonction quelconque de la variable fréquence f. Avantageusement cette fonction est une fonction d' ordre 4 de la forme :
Figure imgf000009_0002
The polynomial function used for the modeling producing the modulated DSP modulated signal 8 can be any function of the frequency variable f. Advantageously this function is a function of order 4 of the form:
Figure imgf000009_0002
Dans le cas particulier d'un système asservi 1 ne comportant pas de signal 2 temporel de consigne, il est néanmoins possible de déterminer un critère de stabilité en utilisant une variante du procédé selon l'invention. Pour cela le signal 4 d'écart de boucle est calculé d'après la formule : signal 4 d'écart = signal 3 régulé, sur la fenêtre temporelle d'évaluation. Les autres étapes du procédé restant identiques . In the particular case of a slave system 1 having no setpoint time signal 2, it is nevertheless possible to determine a stability criterion by using a variant of the method according to the invention. For this purpose, the loop difference signal 4 is calculated according to the formula: deviation signal 4 = regulated signal 3, on the evaluation time window. The other steps of the process remain identical.

Claims

REVENDICATIONS
1. Procédé de qualification de la stabilité d'un système asservi (1) produisant en sortie un signal (3) temporel régulé en fonction d'un signal (2) temporel de consigne introduit en entrée, caractérisé en ce qu'il comprend les étapes suivantes:1. A method for qualifying the stability of a slave system (1) producing as output a regulated time signal (3) as a function of a reference time signal (2) introduced at input, characterized in that it comprises the following steps:
- sélection d'une fenêtre temporelle d'évaluation,- selection of an evaluation time window,
- centrage du signal (3) temporel régulé et du signal temporel de consigne (2),centering of the regulated time signal (3) and the set time signal (2),
- calcul du signal (4) d'écart de boucle, signal d'écart = signal de consigne - signal régulé, sur la fenêtre temporelle d'évaluation,calculation of the loop difference signal (4), deviation signal = setpoint signal-regulated signal, on the evaluation time window,
- calcul du signal (5) densité spectrale de puissance, DSP, dudit signal (4) d'écart de boucle, modélisation du signal (5) densité spectrale de puissance, DSP, par une fonction polynomiale, DSP_Mod, en fonction de la fréquence, calcul de l'aire (7) pour laquelle le signal (5) densité spectrale de puissance, DSP, est supérieur au signal (8) modélisé, DSP_mod,- calculation of the signal (5) power spectral density, DSP, of said loop difference signal (4), modeling of the signal (5) power spectral density, DSP, by a polynomial function, DSP_Mod, as a function of the frequency , calculating the area (7) for which the signal (5) power spectral density, DSP, is greater than the signal (8) modeled, DSP_mod,
- détermination d'un critère de stabilité, compris entre 0 et 100, égal à 100 fois ladite aire (7) moyennée par le signal (5) DSP, ce critère de stabilité étant d'autant plus faible que le système asservi (1) est stable.determination of a stability criterion, between 0 and 100, equal to 100 times said area (7) averaged by the DSP signal (5), this stability criterion being even lower than the slave system (1) is stable.
2. Procédé selon la revendication 1, caractérisé en ce qu'il comprend encore, entre l'étape de calcul du signal (5) DSP et l'étape de modélisation, une étape de filtrage remplaçant le signal (5) densité spectrale de puissance, DSP, dudit signal (4) d'écart de boucle, par le signal (9) filtré DSP Fit, ce signal (9) DSP_Flt étant ensuite utilisé en lieu et place du signal (5) DSP, dans les étapes ultérieures.2. Method according to claim 1, characterized in that it further comprises, between the step of calculating the signal (5) DSP and the modeling step, a filtering step replacing the signal (5) spectral power density , DSP, of said loop difference signal (4), by the signal (9) filtered DSP Fit, this signal (9) DSP_Flt being then used in place of the signal (5) DSP, in the subsequent steps.
3. Procédé selon la revendication 2, caractérisé en ce que le signal (9) filtré DSP_Flt est calculé à partir du signal (5)3. Method according to claim 2, characterized in that the signal (9) filtered DSP_Flt is calculated from the signal (5)
DSP par détermination d'une moyenne glissante, selon laDSP by determining a sliding average, according to the
∑DSP(k-i) formule DSP_Flt(k) = J≤ . nΣDSP (ki) formula DSP_Flt (k) = J≤ . not
4. Procédé selon l'une quelconque des revendications 1 à 3, caractérisé en ce que la fonction polynomiale employée à l'étape de modélisation est une fonction d'ordre 4,4. Method according to any one of claims 1 to 3, characterized in that the polynomial function used in the modeling step is a function of order 4,
DSP Mod(f) = A +—+-^-+-^+-^. f f2 /3 rDSP Mod (f) = A + - + - ^ - + - ^ + - ^. ff 2/3 r
5. Procédé selon l'une quelconque des revendications 1 à 4, appliqué à un système asservi (1) ne comportant pas de signal5. Method according to any one of claims 1 to 4, applied to a slave system (1) having no signal
(2) temporel de consigne, caractérisé en ce que le signal (4) d'écart de boucle est calculé selon la formule : signal (4) d'écart = signal (3) régulé, sur la fenêtre temporelle d' évaluation . (2) time setpoint, characterized in that the loop difference signal (4) is calculated according to the formula: signal (4) deviation = signal (3) regulated, on the time window evaluation.
PCT/FR2008/051761 2007-10-04 2008-09-30 Method for qualifying the stability of a controlled system WO2009050408A2 (en)

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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4806848A (en) * 1987-03-11 1989-02-21 The United States Of America As Represented By The Secretary Of The Air Force Compressor blade clearance measurement system
WO1996018110A1 (en) * 1994-12-09 1996-06-13 Exxon Chemical Patents Inc. Plant parameter detection by monitoring of power spectral densities
US20040088058A1 (en) * 2002-10-25 2004-05-06 Lahoucine Ettaleb Diagnostic for poorly tuned control loops

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4806848A (en) * 1987-03-11 1989-02-21 The United States Of America As Represented By The Secretary Of The Air Force Compressor blade clearance measurement system
WO1996018110A1 (en) * 1994-12-09 1996-06-13 Exxon Chemical Patents Inc. Plant parameter detection by monitoring of power spectral densities
US20040088058A1 (en) * 2002-10-25 2004-05-06 Lahoucine Ettaleb Diagnostic for poorly tuned control loops

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