Data processing: generic control systems or specific application – Generic control system – apparatus or process – Optimization or adaptive control
Reexamination Certificate
1998-10-19
2001-04-10
Grant, William (Department: 2121)
Data processing: generic control systems or specific application
Generic control system, apparatus or process
Optimization or adaptive control
C700S035000, C700S052000
Reexamination Certificate
active
06216047
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention belongs to a technical field of active suppression engineering. For instance, it belongs to a technical field of active damping when a cyclic signal is a vibration, and to a field of active noise suppression when a cyclic signal is a noise. Thus, depending on the types of the cyclic signal, its application field can be expanded widely.
2. Description of the Related Art
Japanese Unexamined Patent Publication (KOKAI) No. 8-44,377 is derived from Japanese Patent Application No. 6-201,384, and discloses a DXHS-LMS algorithm. Compared to a previous FX-LMS algorithm, the DXHS-LMS algorithm produces an advantage in that, although the calculation steps are reduced, the convergence speed can be improved. The FX-LMS algorithm is referred to in the publication and Japanese Unexamined Patent Publication (KOKAI) No. 8-272,378.
However, even the DXHS algorithm cannot necessarily exhibit an appropriate following characteristic when a transfer function of a controlled system is a resonance system whose gain shows a sharp peak. For example, when angular frequencies &ohgr;
k
to be suppressed varies rapidly in a cyclic signal f(n), the adaptation, effected by the adaptive control system according to the DXHS algorithm, cannot fully follow the rapid variation. As a result, an error signal e (n) may sometimes enlarge to a non-negligible extent.
There is a data tabulation method, one of the countermeasures for coping with the rapid variation of the specific components of the angular frequencies &ohgr;
k
to be suppressed in the cyclic signal f(n). In the data tabulation method, the amplitudes and phases of the adaptive signal y(n) are converted into a tabulated data for each range of the angular frequencies &ohgr;
k
, and the amplitudes and phases of the adaptive signal y(n) are read out from the tabulated data to renew the components of the adaptive coefficient vector W(n) when the angular frequencies &ohgr;
k
have shifted. Thus, the convergence speed can be improved.
Whilst, in the method employing the tabulated data, the amplitudes and phases of the adaptive signal y(n) vary discontinuously upon reading out the data from the tabulated data in accordance with the variation of the angular frequency &ohgr;
k
. Accordingly, there arises inconvenience in that the user feels uneasiness. In addition, the method requires a memory capacity for storing the tabulated data. Consequently, there also arises other inconvenience in terms of the memory capacity. Thus, although the method employing the tabulated data can compensate for the lack of the following characteristic in the DXHS algorithm, it results in the new inconveniences. Therefore, the method cannot be smart and reasonable measures for solving the problem associated with the DXHS algorithm.
Hence, the inventor of the present invention returned to the square one. He then studied into the cause of the delayed adaptation which results in the lack of the convergence speed in the DXHS algorithm when the controlled system is the resonance system. As a result, he thought of the following facts: the maximum value of the renewing coefficient (or step size parameter) is designed so that it is stable in the high-gain frequency where it is highly probable to diverge; and accordingly the renewing coefficient is extremely small in the other frequency regions. In other words, the renewing coefficient is designed so that the adaptive control system does not diverge even in the high-gain frequency range. Hence, the renewing coefficient cannot be set at such a sufficiently large value that the convergence speed is sufficiently fast in the other frequency regions.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide a novel adaptive control method for a cyclic signal. In the novel adaptive control method, the stability of adaptive convergence and the characteristic following a specific angular frequency to be suppressed are compatible with each other even when an adaptive signal y(n) is added at a measurement point by way of a transfer function having a resonance frequency.
The inventor of the present invention invented the following measures in order to carry out the object.
A first aspect of the present invention is an adaptive control method for a cyclic signal, and comprises:
adding an adaptive signal y(n) to a cyclic signal f(n) in an inverted phase at a measurement point by way of a transfer system having a predetermined transfer characteristic, thereby actively eliminating an influence of specific components of the cyclic signal f(n) to the measurement point, and suppressing an error signal e(n) detected at the measurement point to which the cyclic signal f(n) is input;
the cyclic signal f(n) including at least one angular frequency &ohgr;
k
* (1≦k≦K′, k and K′ are natural numbers.);
the adaptive signal y(n) being a linear combination of at least one sinusoidal signal whose angular frequencies &ohgr;
k
(1≦k≦K≦K′, K is also a natural number.) are K pieces of measurements or estimations of the angular frequencies &ohgr;
k
*;
wherein the adaptive control method employing:
an adaptive signal generation algorithm for generating the adaptive signal y(n) at each time n in a discrete time; and
an adaptive coefficient vector renewing algorithm for carrying out a quasi-normalized gradient method;
the quasi-normalized gradient method comprising the step of:
subtracting a vector from an adaptive coefficient vector W(n), thereby renewing the adaptive coefficient vector W(n);
the adaptive coefficient vector W(n) including components defining at least amplitudes and phases of the sinusoidal components of the adaptive signal y(n);
the vector being prepared by multiplying components of a gradient vector ∇(n)=∂e
2
(n)/∂W(n) with appropriate step size parameters, and by dividing the resulting products with a sum (A
k
+&ggr;
k
);
A
k
being gain measurements or gain estimations of the transfer characteristic corresponding to the angular frequencies &ohgr;
k
;
&ggr;
k
(0≦&ggr;
k
) being appropriate divergence prevention constants;
whereby at least the amplitudes and phases of the sinusoidal components of the adaptive signal y(n) are replaced with components of the renewed adaptive coefficient vector W(n).
The first aspect of the present cyclic-signal adaptive control method is applicable to cases even where the specific component to be suppressed in the cyclic signal f(n) is a sinusoidal function which includes a single angular frequency &ohgr; alone, where it is a sinusoidal function which includes a plurality of angular frequencies &ohgr;
k
being independent of each other, or where it is a combination of a fundamental frequency and harmonic components of the fundamental frequency (i.e., &ohgr;
k
=k&ohgr;
0
).
In the first aspect of the present cyclic-signal adaptive control method, the quasi-normalized gradient method is applied to the adaptive coefficient vector renewing algorithm, a renewing equation of the adaptive coefficient vector W(n). For instance, in the quasi-normalized gradient method, the renewing vector is subtracted from the adaptive coefficient vector W(n). The renewing vector is prepared by multiplying components of the gradient vector ∇(n)=∂e
2
(n)/∂W(n) with an appropriate step size parameter, and by dividing the resulting products with the sum (A
k
+&ggr;
k
). Note that the A
k
is herein gain measurements or gain estimations of the transfer characteristic corresponding to the angular frequencies &ohgr;
k
at a time n; and that the &ggr;
k
(0≦&ggr;
k
) is herein an appropriate divergence prevention constant. Specifically, when the gain A
k
is large at the time n, the step size of the adaptive coefficient vector W(n) decreases. On the contrary, when the gain A
k
is small at the time n, the step size of the adaptive coefficient vector W(n) increases.
For example, the angular frequencies &ohgr;
k
correspond to resonance frequencies at the time n. Hence, i
Grant William
Jacobson Price Holman & Stern PLLC
Rodriguez Paul
Tokai Rubber Industries Ltd.
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