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This paper presents a method of reducing a sinusoidal disturbance through a periodic transfer function. First, a precise definition of the problem (transfer function and disturbance characteristics) is made. A control strategy that minimizes a quadratic cost function is next elaborated. Its good performances are then compared with a classical adapt...
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... globally transfer function is then periodic, with period T m = 1 νm , and is supposed to be perfectly known in the rest of this paper. Its structure is shown on figure 1. Figure 2 represents an example of the alternator's natural vibration power spectrum in dB, with a fixed machine ro- tating frequency ν m = 47.6 Hz. Most part of this signal power is due to a set of spectral lines, located at harmonic frequencies of ν m . ...
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... As shown in Fig. 1, m j (t) followed by G j (t) can be seen as a single LPTV transfer function. Unfortunately, classical active control methods are developed for LTI or slowly time-varying systems [2,3,4], and have middling performance in this strong time-varying case [5]. The multiple input multiple output (MIMO) control strategy proposed in this paper locally reduces the stator vibrations power, although the system is LPTV. ...
... Disturbances d j (t) being due to the machine rotation, their spectra mostly consist of spectral lines located at harmonic frequencies of ν 0 [5]. Now, to reach good attenuation rates, "antivibrations" yj(t) have to be strongly correlated with signals to cancel [4]. ...
... Therefore, their spectra must have the same property and be also made up of spectral lines. Next, LPTV systems formed by the association of m j (t) and G j (ν) imply only pν 0 frequency shifts [5,6]. Therefore, input signals also should be modelized as a set of sine waves with frequencies nν0 (n ∈ N). ...
This paper deals with a new multiple input multiple output active
control algorithm applied to reduce synchronous machine vibrations.
Usually, this kind of algorithm has good performance on linear
time-invariant, or slowly time-varying systems. The present system has
been developed taking into account the presence of a linear periodically
time-varying transfer function. Signals are first shown periodic with
the same fundamental frequency. Next, Fourier coefficients of the
signals measured by sensors are linked to the input ones thanks to a
linear matrix equation. Classical least mean square minimization can
then be used to find the optimal input Fourier coefficients. Finally, a
simple adaptive algorithm updating these coefficients is elaborated, in
order to converge to the optimal solution and to follow the disturbances
fluctuations. Results on real vibration signals show good attenuation
performance with one or several sensors
... fonction de transfertFigure 1: Fonction de transfert globale du système. imiser la puissance du signal d'erreur et utilisant des algorithmes adaptatifs temporels tels que le FxLMS [2, 3], ont des performances très limitées pour cette application du fait de la non-stationnarité de la fonction de tranfert [4]. Dans ce papier, cet inconvénient est contourné en faisant agir l'algorithme sur les coecients de Fourier de la commande, préalablement montrée périodique. ...
Nous proposons une méthode de compensation active des vibrations d'une machine synchrone. Ceci revient à annuler un signal périodique à travers une fonction de transfert linéaire non-stationnaire périodique. Nous exprimons les coefficients de Fourier du signal de commande, préalablement montré périodique. Ces coefficients convergent vers des valeurs optimales stationnaires, malgré la non-stationnarité du transfert. Un algorithme du gradient est ensuite proposé et testé sur des signaux de vibration.
... As shown in Fig. 1, m j (t) followed by G j (t) can be seen as a single LPTV transfer function. Unfortunately, classical active control methods are developed for LTI or slowly time-varying systems [2,3,4], and have middling performance in this strong time-varying case [5]. The multiple input multiple output (MIMO) control strategy proposed in this paper locally reduces the stator vibrations power, although the system is LPTV. ...
... Disturbances d j (t) being due to the machine rotation, their spectra mostly consist of spectral lines located at harmonic frequencies of ν 0 [5]. Now, to reach good attenuation rates, "antivibrations" yj(t) have to be strongly correlated with signals to cancel [4]. ...
... Therefore, their spectra must have the same property and be also made up of spectral lines. Next, LPTV systems formed by the association of m j (t) and G j (ν) imply only pν 0 frequency shifts [5,6]. Therefore, input signals also should be modelized as a set of sine waves with frequencies nν0 (n ∈ N). ...
For most of mechanical systems, vibrations are damaging. This article deals with an active control system of synchronous alternator vibrations. It is based on auxilliary coils located in the stator, and named compensation coils. Supplied with a current, they generate an additional vibration, which interacts destructively with the engine's natural one. Higher ordre statistics (bicoherence) allow the full non linear vibration/control transfer model, although the spectrum is enough to validate its approximation. A feedforward control method is developped, and then simulated. It uses a priori knowledge of the transfer, i.e. the form of non linearity. Vibration power has been reduced by 80% during simulation.
Frequency methods only are used here for the study and control of continuous linear time periodic systems. Using time varying frequency responses defined by L. A. Zadeh in the 1950s, the second generation CRONE control is extended to the control of linear time periodic systems. This control strategy ensures, for the closed-loop system, a near stationary behavior, performances set by the designer, and robustness of performances to gain variations of the plant. An application of the proposed control strategy to a testing bench shows its efficiency.
