JP3442637B2 - Vibration reduction method - Google Patents

Description

Detailed Description of the Invention

[0001]

FIELD OF THE INVENTION The present invention is an improved modified L
The present invention relates to a vibration reduction method that actively reduces engine vibration and the like using an MS algorithm.

[0002]

2. Description of the Related Art When an unknown system can be approximated by a FIR (finite response) filter, that is, a non-recursive filter, adaptive parameter processing attempts to estimate its parameter, that is, impulse response, and obtain the same output as that of the unknown system. Is. That is, the adaptive signal processing is to estimate the parameters of the unknown system. For example, if the engine vibration system is analyzed as an unknown system, a vibration reduction device that actively cancels the engine vibration by generating pseudo vibration is configured. can do.

A vibration reduction device 1 shown in FIG. 5 reduces vibrations of an engine 3 transmitted to a seat 2 such as a driver's seat by vibrating an actuator 4 mounted on an engine mount, and is a center of vibration reduction. An adaptive algorithm calculator 6 is incorporated in the controller 5. The vibration frequency of the engine 3 is taken into the controller 5 by the frequency sensor 7, and the acceleration applied to the seat 2 is taken into the controller 5 by the acceleration sensor 8. The controller 5 supplies a vibration output that cancels the vibration of the vibration system estimated by the adaptive algorithm calculator 6 to the actuator 4 via the power amplifier 9 to actively suppress the engine vibration.

The conventional vibration reducing apparatus 1 uses, for example, a synchronous LMS (Least Mean Square) algorithm, a so-called SFX algorithm, as an adaptive algorithm. This SFX algorithm is one in which an impulse train synchronized with a fundamental period of a periodic signal or a quasi-periodic signal is generated inside a processor, and the filtered XLMS algorithm can be applied with this as an imaginary input. Since the signals and the reference signals can be generated only in the necessary ones, the convolution calculation is unnecessary and the calculation amount is small, and it is possible to improve the control capability by increasing the sampling frequency. It was
However, since this SFX algorithm processes a periodic signal such as engine vibration, the sampling frequency also rises in accordance with the upper limit of the frequency, and it is necessary to increase the order of the tap number of the impulse response. There is a problem that the sampling cycle becomes longer as the time increases, and the calculation accuracy also decreases.

Therefore, in order to remove the specific frequency component of the periodic signal, for example, as disclosed in Japanese Patent Application Laid-Open No. 8-44377, "Adaptive Control Method for Periodic Signal", a square of a function including a sine wave output signal is used. A gradient vector is obtained by partially differentiating the evaluation function represented by the filter coefficient of the estimation system, which is a function of the amplitude and phase of the output signal, and the gradient vector is multiplied by a certain number and subtracted from the filter coefficient. By doing so, an adaptive algorithm has been proposed which updates the filter coefficient for each lapse of time, and updates the amplitude and phase of the sine wave output signal based on the updated filter coefficient amplitude and phase. This adaptive algorithm can be calculated only from the fundamental period of the periodic signal, and the convolution calculation for generating the filter coefficient and the reference signal is also unnecessary. Also,
Since the sampling cycle is constant, it has the advantage that the calculation time is not sacrificed due to the increase in the frequency.

[0006]

However, since the conventional LMS algorithm according to the above proposal uses the LMS algorithm that follows the evaluation function represented by the square of the function including the sine wave output signal, the estimated value The convergence speed is slow, 200 to 300 sample points are required for the estimation error to converge, and the calculation takes too much time. Therefore, it is difficult to apply it to a system that requires responsiveness. It was

SUMMARY OF THE INVENTION The present invention has been made to solve the above problems, and an object of the present invention is to improve the response characteristic by accelerating the convergence speed of estimated values.

[0008]

In order to achieve the above object, an unknown vibration system is estimated using an adaptive algorithm by the least squares method using the steepest descent method, and the vibration system is activated based on the estimated value. In the method of dynamically controlling vibrations, the adaptive algorithm uses an improved correction algorithm that minimizes the sum of even powers having different orders of estimation error.
Then, the evaluation function of the adaptive algorithm is converged .

In the present invention, the improvement / correction algorithm minimizes the sum of the squared value of the estimation error and a specific even-powered value of a fourth or higher order , and evaluates the adaptive algorithm.
It is characterized by converging numbers .

[0010]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to FIGS. FIG. 1 is a schematic configuration diagram showing an embodiment of a controller to which the vibration reduction method of the present invention is applied, and FIGS. 2 to 4 are an LMS algorithm, a modified LMS algorithm, and an improved modified LMS, respectively.
It is a figure which shows an example of the convergence characteristic by an algorithm.

The controller 11 shown in FIG. 1 is the above-described vibration reduction device 1 for actively controlling the engine vibration of an automobile.
It has been applied to the
A feature is that an MS (Modified Least Mean Square = M-LMS) algorithm is used to accelerate the convergence speed without deteriorating the estimation accuracy. The target of vibration reduction is the vibration system from the engine that is the vibration source to the seat that is the vibration end, and this vibration system is unknown system 12
Is. Input x of unknown system 12 at time t = j
(T), noise n (t) included in the output, and observed signal d
(T) is represented by xj, nj, and dj, respectively. H (z)
Is the z-transform transfer function of the unknown system 12, and if its impulse response sequence is h0, h1, ... hn, It is represented by.

The input x (t) to the unknown system 12 is taken in by the adaptive digital filter 13 which is a non-recursive type filter in the controller 11, and the LMS algorithm calculator 14 causes the impulse response sequence w0, w1, ...
wn, that is, the filter coefficient vector is variably set.
Z-transform transfer function W (z) of the adaptive digital filter 13
Is And the value y of the output y (t) at time t = j
The difference between j and observed value dj is LMS as error ej.
It is supplied to the algorithm calculator 14.

The LMS algorithm calculator 14 uses the filter coefficient vector wj before adaptation, that is, the old estimation value, and performs the calculation for obtaining the updated estimation value, that is, the filter coefficient vector wj + 1 after adaptation. This operation is performed, for example, according to the improved modified LMS algorithm exemplified below. wj + 1 = wj + (2μ2εj + 4μ4εj3) xj where μ is a step size parameter and μ2,
An appropriate value is used for μ4. Before describing the improved modified LMS algorithm, the modified LMS (M-LMS)
The algorithm will be described.

The modified LMS algorithm uses the squared error estimate (E) as the evaluation function J of the adaptive digital filter.
Probability gradient algorithm obtained when εj2 is adopted as [εj2]) wj + 1 = wj + 2μεjxj
The LMS algorithm that uses j = 0, 1, ... As it is is modified to use a stochastic gradient algorithm obtained under the extended evaluation function J. Specifically, when K is an appropriate positive integer, εjK2 (eg, εj4, εj6, εj8, etc.) is used as the extended evaluation function J instead of εj2. That is,
When εjK2 is used as the estimated value of J (= E [εjK2]), the estimated partial differential value of the steepest descent method is ∂εjK2 / ∂w.
j = 2KεjK2-1 ∂εj / ∂wj = -2KεjK2
−1xj, and wj + 1 = wj + 2 μKεj2K−1
xj j = 0, 1, ...

As an example, when K = 2, that is, εj4
In the correction algorithm focusing on, wj + 1 = wj + 4
μ4εj3xj j = 0,
1, ... is obtained. Here, comparing the performances of the modified LMS algorithm and the LMS algorithm, as shown in FIGS. 2 and 3, since | εj | is large in the initial stage of estimation, the modified algorithm focusing on εj4 converges faster. However, when viewed in the steady state, | εj
Since | becomes small, | εj3 | becomes a very small value, and the estimated value is hardly updated.
It can be seen that the uncorrected LMS algorithm focusing on (1) converges faster.

Therefore, in the present embodiment, an improved correction algorithm focusing on εj2 + εj4 is adopted by making a compromise between K = 1 (non-modified LMS algorithm) and K = 2 (modified LMS algorithm). In this improved correction algorithm, wj + 1 = wj + 2μ2εjxj + 4μ4εj
3xj j = 0, 1, ... In this case, the subscripts added to μ2 and μ4 are numerical values indicating that the LMS algorithm corresponds to the order of the estimation error εj of interest, and indicate that both are step size parameters that can be set arbitrarily. ing.

2 to 4 show μ = μ2 = μ4 = 0.
As 0005, unmodified LMS algorithm and modified LM
It shows the result of performance comparison between the S algorithm and the improved modified LMS algorithm. As can be seen from the figure, the improved modified LMS algorithm has a high convergence speed of the estimated value,
Moreover, it is clear that the error in the steady state is very small. This is because εj3 is large in the initial stage of estimation when | εj |
Is present, and the presence of εj is effective in the steady state where | εj | is small.
200 required for the estimation error of the algorithm to converge
With the improved modified LMS algorithm, 300 sample points can be reduced to about 1/10, which is 20 to 30 sample points.

As described above, the controller 11 uses the improved correction algorithm in which a plurality of even power values of the error are combined as the estimation error, so that the estimation error having a large absolute value of the estimation error has a higher correction term of the estimation error. Is effective, and in the steady state where the absolute value of the estimation error is small, the existence of the first-order estimation error is effective, the convergence speed of the estimated value is fast, and the error in the steady state is very small. System estimation is possible, and high-quality vibration reduction is possible based on this excellent vibration estimation system.

In the improved correction algorithm, wj + is used as a recurrence formula for the filter coefficient vector wj.
1 = wj + (2μ2εj + 4μ4εj3) xj
Although j = 0, 1, ... Is used, it is also possible to adopt an improved correction algorithm focusing on, for example, εj2 + εj6. In this case, the recurrence formula for the filter coefficient vector wj of the improved correction algorithm is wj
+ 1 = wj + (2μ2εj + 6μ6εj5) xj
j = 0, 1, ... Again, | ε
The existence of εj5 is effective in the initial stage of estimation when j | is large,
In the steady state where | εj | is small, the presence of εj is effective, the convergence speed of the estimated value is fast, and the error in the steady state is very small.

Furthermore, it is also possible to adopt an improved correction algorithm focusing on εj2 + εj4 + εj6. In this case, the recurrence formula for the filter coefficient vector wj of the improvement correction algorithm is wj + 1 = wj + (2μ
2εj + 4μ4εj3 + 6μ6εj5) xj j = 0,
1, ... Also here, the presence of εj3 and εj5 exerts an effect in the initial stage of estimation with a large | εj |, and the presence of εj exerts an effect in the steady state with a small | εj |. The effect is that the error in is very small.

[0021]

As described above, according to the present invention,
In the LMS algorithm using the steepest descent method, an improved correction algorithm that combines multiple even-valued errors is used as the estimation error. The existence of the primary estimation error is effective in the steady state where the existence of the estimation error is small and the absolute value of the estimation error is small.
Moreover, it is possible to perform an excellent vibration system estimation in which the error in the steady state is very small, and it is possible to achieve high-quality vibration reduction based on the excellent vibration estimation system.

Further, according to the present invention, since the improvement correction algorithm minimizes the sum of the squared value of the estimation error and the specific even-powered value of the fourth or higher order, for example, the gradual correction of the filter coefficient vector wj is performed. As a chemical formula, wj + 1 = wj
+2 (μ2εj + 4μ4εj3) xj j =
By using 0, 1, ..., the existence of εj3 exerts an effect in the estimated initial stage where | εj | is large, and the presence of εj exerts an effect in the steady state in which | εj | is small. It is possible to perform an excellent vibration system estimation with a fast convergence speed of and a very small error in the steady state. Based on this excellent vibration estimation system, it is possible to reduce vibration of high quality, and also filter coefficient vector As a recurrence formula of the recurrence formula regarding wj, wj + 1 = wj + (2μ
2εj + 6μ6εj5) xj j = 0,1,
, The existence of εj5 is effective in the initial stage of estimation where | εj | is large, and the existence of εj is effective in the steady state where | εj | is small, and the convergence speed of the estimated value is high. Moreover, there are effects such as an extremely small error in the steady state.

[Brief description of drawings]

FIG. 1 is a schematic configuration diagram showing an embodiment of a controller to which a vibration reduction method of the present invention is applied.

FIG. 2 is a diagram showing an example of a convergence characteristic according to a conventional LMS algorithm.

FIG. 3 is a diagram showing an example of a convergence characteristic by a conventional modified LMS algorithm.

FIG. 4 is a diagram showing an example of a convergence characteristic by an improved modified LMS algorithm.

FIG. 5 is a schematic configuration diagram showing an example of a conventional vibration reduction device.

[Explanation of symbols]

1 Vibration reduction device 2 sheets 3 actuators 5,11 controller 7 Frequency sensor 8 Accelerometer 9 power amplifier 12 unknown system 13 Adaptive digital filter 14 LMS algorithm calculator

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Claims (2)

(57) [Claims] 1. A vibration reduction method for estimating an unknown vibration system by using an adaptive algorithm based on a least squares method using a steepest descent method, and actively controlling the vibration system based on the estimated value. The algorithm uses an improved modified algorithm that minimizes the sum of even powers with different orders of estimation error .
A vibration reducing method comprising converging an evaluation function of the adaptive algorithm . 2. The improved correction algorithm minimizes the sum of the squared value of the estimation error and a specific even-powered value of the fourth or higher order to converge the evaluation function of the adaptive algorithm.
Vibration reduction method according to claim 1, wherein the that.