JPH10163812A - Filter circuit for communication/control - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a filter circuit which uses an excellent characteristic of a complex coefficient filter circuit of a two-input two-output system and applies it to general communication and control use of a one-input one-output system. SOLUTION: A one-input signal Ux of a complex filter circuit of a two-input/ two-output system is branched into two, one of them is inputted to one of an inputting part of the filter, the other one is passed through a circuit (j circuit) which generates a signal whose phase is different by 90 deg. from the one and inputted to the other inputting part (Uy), F'(s-jω) which replaces the Laplacian operator s of the transfer faction F(s) of a complex filter that makes these two input signals inputs by (s-jω) is a complex transfer function of the filter, both sides of a relational expression are multiplied by a denominator of F'(s-jω) in a transfer function expression U'.F'(s-jω)=V' between U' and an output V' that passes through the complex transfer expression F'(s-jω), and a real part and an imaginary part of the transfer function expression are connected by a transfer element of a real coefficient so that they may be equal to each other.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a filter circuit using complex coefficients, and more particularly, to a bandpass / stop filter having a high steepness or an arbitrary frequency range limited by using a low-pass filter or a high-pass filter having real coefficients. The present invention relates to a one-input / one-output communication / control filter circuit capable of performing phase shift of a phase angle and the like.

[0002]

2. Description of the Related Art Conventionally, filter circuits used for various kinds of communication control and the like have been designed and constructed based on a transfer function of a real number coefficient. The conventional low-pass or high-pass filter has no distinction between the positive and negative angular frequencies Ω of the signal, and has a symmetrical gain characteristic with respect to the origin, that is, zero frequency, if a negative frequency region is included. This means that the filter is used as a bandpass or band rejection filter having zero as a center frequency. Therefore, as shown in FIG. 1, the higher the breakpoint angular frequency (a, b), the wider the bandwidth, and the steep gain when the abscissa is not a logarithmic scale logΩ of angular frequency but a linear scale. It was difficult to obtain the characteristics.

[0003] This implies that in the gain characteristics of a normal Bode diagram, the slope (dB / dec) of the broken line approximation is apparently the same in any frequency region, but the higher the break point, the higher the frequency, the logarithm of the abscissa. It is easily understood from the fact that the change (increment) of the frequency that does not occur becomes much larger. For example, at break frequencies of 10 and 1000, the change per dec is 100-10 = 90 for the former and 10000-1000 = 9000 for the latter,
Even with the same slope, the former has a steep slope of 100 times on the linear scale.

A biquad filter is known as a conventional filter using a real-number-coefficient resonance circuit. This is one in which two integration circuits are connected to provide a feedback loop. According to such a circuit, a bandpass filter having a relatively narrow band can be obtained. However, when the resonance frequency ω is variable, it is difficult to control the steepness of the filter. I was

In controlling the high-speed rotating body, a filter circuit for passing or blocking only a narrow bandwidth near the rotating speed of the rotating body is required. The conventional method of such a narrow band filter obtains a steep characteristic by converting the coordinates from the stationary coordinates to the coordinates of the rotating body and replacing the rotation speed with zero. To do so, the input signal of the stationary coordinate system is multiplied by a sine or cosine function to convert the coordinate to the rotating coordinate system. Then, it is necessary to take out the rotation synchronizing signal component with a low-pass filter, convert only the narrow-band frequency component, and then perform an inverse transformation to a stationary coordinate system. Therefore, in addition to the low-pass filter, it is necessary to configure two sets of coordinate conversion circuits configured to generate a positive cosine function corresponding to the rotation angle of the rotating body.

Further, in the above-mentioned conventional method, it has been impossible to adjust the phase to an arbitrary value irrespective of the frequency similarly to the gain.

[0007]

In the control of the rotating body, since the control is performed from two orthogonal radial axes, a signal relating to the x-axis is a real number, and a signal relating to the y-axis is a complex variable using an imaginary number multiplied by j. Is often used. A transfer function including complex coefficients is an extremely effective analysis means in that case. In such a transfer function of the complex coefficient, the sign of the frequency should be distinguished sharply, and the characteristic root of the system is not necessarily a conjugate root.

For example, a first-order low-pass filter k / (a +
In s), it may be considered that a is a corner angular frequency and zero is a central angular frequency. Therefore, in a complex system, the central angular frequency is not limited to zero, and if, for example, ω, k / ｛a +
(s-jω)｝ changes to a complex coefficient transfer function with the symmetry point as ω. At the same time, a is not from zero, but a distance from ω or half the passband. Even if ω is a high value, it is returned to the origin, so in the above example, ω is 1000 and a is
If a value of 10 is selected, the slope of the polygonal line will be about 100 times sharp on a logarithmic scale, and of course, (ω-a) on the opposite side of ω will also be a break point, and a narrow steep bandpass characteristic will be obtained.

However, the two-input two-output complex coefficient filter circuit treats the spatially orthogonal x-axis and y-axis variables as complex numbers, and is used for one-input one-output communication / control. Cannot be applied as is.

The present invention has been made in view of the above-mentioned circumstances, and utilizes the excellent characteristics of a 2-input 2-output complex coefficient filter circuit to convert it into a 1-input 1-output general-purpose communication / communication system.
An object of the present invention is to provide a filter circuit which can be applied to control applications.

[0011]

According to the first aspect of the present invention, one input signal (its Laplace conversion amount is Ux) of a two-input / two-output filter circuit is branched into two, and one of them is divided into two. Input to one input of the filter, and 9 for Ux
Ux is added to the circuit (j circuit) that generates a signal that is 0 degrees out of phase.
And input it to the other input part of the filter as an imaginary input part signal (Uy). The output of the filter which receives two input signals Ux and Uy is also a two output signal of Vx and Vy. , And the two inputs and the two outputs are converted into one complex variable ( U = Ux + jU) using an imaginary unit j.
y, V = Vx + jVy), the transfer function of a low-pass or high-pass filter with real coefficients is F (s), the central angular frequency to be passed or blocked is ω, and the transfer function F
Laplace operator s of (s) was replaced with (s-jω)
F (s-jω) is the complex transfer function of the filter, and the input U is the output of the filter passing through the complex transfer function F (s-jω)
In the transfer relation U · F (s−jω) = V between V and V , the denominator of F (s−jω) is multiplied by both sides of the relation, and the real part and the imaginary part of the transfer relation are equal. It is characterized by being connected by a transmission element of a real number coefficient.

According to a second aspect of the present invention, the central angular frequencies to be passed and blocked are ω ₁ and ω ₂ , respectively, and ω ₁ ≠ ω ₂ , and the bandwidth (2a) before and after ω ₁ is set as the center. In order to pass the included components and block components including the bandwidth (2b) before and after ω ₂ as a center, k is an arbitrary gain or coefficient, z is an arbitrary dimensionless number, and the complex coefficient The transfer function is k (s + b−jω ₂ ) / (s + a−jω ₁ )
Or k (s + b−jω ₂ ) / {(s−jω ₁ ) ² + 2za (s−
jω ₁ ) + a ² }.

According to a third aspect of the present invention, in the numerator and / or denominator of the transfer function F (s) in the first aspect, k is an arbitrary gain or coefficient, and 2a is the center of the central angular frequency. K (s ² + 2z) to be the pass or stop bandwidth
as + a ² ), where s is replaced by (s−jω), and dimensionless number z is arbitrarily selected to obtain the vicinity of a break point at both ends of the bandwidth in the gain characteristic of the frequency characteristic of the filter. Is brought closer to an ideal filter.

According to a fourth aspect of the present invention, a plurality of communication / control filter circuits according to any one of the first to third aspects are combined to pass or block a specific band in the entire frequency band. It is characterized by doing so. Of course, not only the passing or blocking of the gain characteristic, but also the phase characteristic can be used.

According to a fifth aspect of the present invention, in the communication / control filter circuit according to any one of the first to fourth aspects, each instantaneous value is set as a variable without using ω, ω ₁ and ω ₂ as constants. It is a tracking filter to be input.

According to a sixth aspect of the present invention, there is provided a filter section for extracting necessary frequency components or band components from an input signal using the two-input / two-output complex coefficient transfer function according to the first to fifth aspects. And constructing a complex gain part that gives a necessary phase angle to the extracted component, and using the output passing through both parts to estimate other state quantities necessary for control, or by feeding back the output a communication / control filter circuit for stabilizing the mode of extraction components, complex-gain portion is an complex gain circuits represented by a + jB≡ F c which a, B and a real constant , F c
Between the input (Ux, Uy) and the output (Vx, Vy) to the x, y axis portion of Vx = AUx−BUy, Vy = BUx + AUy, and A and B are arbitrarily set. By selecting, it is possible to give not only an arbitrary gain but also a phase angle to the extracted component, and to give an arbitrary necessary phase angle only to a frequency region necessary for estimating a communication or control-related signal. Features.

According to a seventh aspect of the present invention, as the j-circuit, the numerator of the integrator 1 / s is provided with a central angular frequency in the case of one pass or stop band, or one tenth to tenth of the center angular frequency. In the case where there are a plurality of pass or stop bands, an integrator multiplied by a value of about one-tenth to ten-fold times as a gain, or a denominator s of the integrator, The gain is an incomplete integrator to which a constant less than about one tenth of the gain is added.

[0018]

BEST MODE FOR CARRYING OUT THE INVENTION For example, as in an axially symmetric magnetic bearing, a radial orthogonal 2 which is orthogonal to the rotation axis (z axis) of the rotor.
In a system where the axes (x, y axes) are controlled by electromagnetic force, etc., the position and velocity of the center of gravity are used for translational motion, and the tilt angle and angular velocity are used for posture motion. In many cases, both are combined into one vector and expressed as one complex number as an imaginary number. For example, if it is the position of the center of gravity, r = x + yy (1) If the inclination angle is, it is expressed as θ = θx + jθy (2). θx and θy are inclination angles about the x-axis and the y-axis of the z-axis, respectively. Note that the imaginary component is different from the imaginary part in the vector calculation of the AC circuit.
This is a physical quantity related to the y-axis (sensor signal, control torque) that can be detected or generated by a sensor or an actuator.

In such a notation system (here, complex quantities are represented by underscores), a two-input two-output system can be treated like a one-input one-output system, so that the expression is simple, intuitive, easy to understand, and differentiated. When expressed by an equation, the order is halved, so the eigenvalue is also halved, and there is no nonexistent eigenvalue from the beginning. In such a complex variable system, a complex coefficient transfer function often appears. For example, look at the frequency characteristic of the complex coefficient transfer function expressed by the Laplace transform including the Laplace operator s of F (s) = a / (s + a−jω) (a and ω are positive real constants). Has s = jΩ
It is not enough to change Ω from zero to infinity. This is because, in a complex system, the frequency is in the positive / negative region and the characteristic is generally not symmetric with respect to zero, so it is necessary to examine not only the positive region of Ω but also the negative region.

Now, in the above formula: F (s), the denominator becomes minimum when Ω = ω (4), so that it is clear that the resonance frequency is obtained. If ω = 0 in equation (3), F (s) is a first-order delay of the real number system, and it is considered that F (jΩ) = a / {j (Ω−0) + a} (5), where s = jΩ. This makes it easier to understand the extension of the real number system transfer function to a complex system. That is, if ω ≠ 0, only F (jΩ) = a / {j (Ω−ω) + a} (6), and the symmetry point has just moved from zero to ω.

By the way, the gain characteristic of the Bode diagram of the equation (5) is obtained by using a horizontal zero dB straight line and Ω-0 = a as a break point.
It is well known that this is an approximation characteristic of a broken line of 20 dB / dec. On the other hand, the same can be obtained from equation (6), but note that Ω = ω at the symmetry point, and Ω = ω ± a (7) is a break point, and 2a is the pass band width. If the origin is Ω = ω, the slope of the polygonal line is ± 20 dB / dec. That is, assuming that Ω−ω = x (8), the gain of the Bode diagram is obtained by substituting into equation (6), and G = 20 loga + 20 log [x ² + a ² ] ^−1/2 (9) High frequency x ² ≫a ² Since G 20 loga−20 logx (10), the gradient of the polygonal line in the high frequency region with Ω = ω as the origin is dG / d (logx) = − 20 [dB / dec] (11) That is, −20 dB / dec Is as described above.

However, in a normal Bode diagram expression with Ω = 0 as the origin, the gradient is completely different. That is, since the gradient in this case is d (logΩ) in the denominator of equation (11), dG / dlogΩ = (dG / dlogx) · (dlogx / dlogΩ) (dG / dlogx) · {Ω / (Ω + ω)} [dB / dec] (12) Therefore, when Ω ≒ 0, the slope of the polygonal line approaches zero, but near the break point, that is, Ω + ω is a frequency slightly larger than a. Ω + ω ≧ a (13) Steeply, and this tendency is
≒ 0, that is, the narrower the bandwidth, the more noticeable. For example, if the break point frequency is Ω = a + ω = 1000 and a = 10 (if the center frequency ω is moved from zero to 1000−10 = 990), the gradient near the break point is Ω = ω from equation (12). 10 when the origin is
It changes to steepness of 0 times (= Ω / a). However, this steepness gradually becomes loose, and the hem far from the break point is -20 dB /
The shape approaches dec.

The steep gain characteristic described above is derived from a primary low-pass filter (LPF) instead of utilizing the resonance characteristic of a secondary system as in a biquad filter in normal communication.

In the complex primary filter, a primary filter is provided in both the x and y paths, and a substantial secondary filter is formed by cross-connecting the two. However, a general-purpose filter for communication and control needs to be a one-input one-output system that can obtain one output for one input. For this purpose, the input is, for example, the input to the x-axis, and the phase is
By generating a signal that differs by 90 degrees by some means and using it as an input to the y-axis, it is possible to convert from a one-input system to a two-input system.

FIG. 2 shows a connection for converting a two-input / two-output complex filter circuit into a one-input one-output system versatile communication / control filter circuit. A signal having a phase difference of 90 ° from one input signal of a two-input two-output complex filter circuit is formed, and this is input as the other input signal. A circuit that forms a signal having a phase difference of 90 ° is referred to as a j circuit. Specifically, 1. Use an observer. 2. Assuming that the filter center frequency is ω, an integrator having a gain (−ω) of (−ω / s) or an incomplete integrator is used. If s = jΩ, if the bandwidth is narrow, Ω ≒ ω, so −ω / (jΩ) ≒ j, and a signal having a phase difference of 90 ° can be formed.

In a control system in which the communication system and the control target are relatively simple, or in which the observer is already incorporated,
It is considered that the method 1 is effective as the j circuit. On the other hand, the second method is considered to be extremely effective when the bandwidth of the filter is narrow. It is also considered that an incomplete integration circuit in which a small attenuation is added to the denominator is more practical. Some Bode diagrams given below are obtained by the method of 2. If the input and output to and from the imaginary axis of the complex filter are imaginary input and imaginary output by the above method, the complex filter is represented by a block diagram as shown in FIG.

It is to be noted that 1 /
In the case where the s numerator has one pass or stop band, the central angular frequency ω, or a value that is about 1/10 to 10 times the central angular frequency ω is preferable. That is, when there are a plurality of passing or stop bands at ω / (10 s) to 10 ω / s, the average value ω ₀ , or 1/10 to 10 times the average value, is preferable. That is, in the case where the integrator is configured as ω ₀ / (10 s) to 10ω ₀ / s, it is preferable that δ be a small constant of 1/10 or less of the gain kω in kω / (s + δ). is there.

FIG. 3 is a diagram showing a filter circuit according to the first embodiment of the present invention. In the following, a specific circuit configuration method of an active filter will be described in consideration of the use of a general-purpose operational amplifier (operational amplifier). This circuit has the following 1
It is created based on the transfer function F ₁ (s) of a low-pass filter having the following real coefficients. F ₁ (s) ≡k / (s + a) (14)

The Laplace operator s of this transfer function F ₁ (s)
Is replaced by (s−jω), and the complex coefficient transfer function is represented by F (s−
jω), the input U is the complex coefficient transfer function F (s−j)
ω), the output signals related to the x and y axes (the Laplace transform amounts thereof are Vx and Vy, respectively) are converted into one complex variable ( V = V
x + jVy) transfer expression U · obtained expressed by F (s-jω) = V (15) becomes _{k (U x + jU y)} / (s + a-jω) = V x + jV y (16). Multiply both sides of the above equation by (s + a-jω) and expand
Made to correspond to real and imaginary _{parts, U x -aV x -ωV y =} sV x / k (17) U y -aV y + ωV x = sV y / k (18)

When this is materialized, a filter circuit as shown in FIG. 3 is obtained. That is, an integrator 1 / s is provided in a signal path of each of the x and y axes, and a negative feedback 1 is given to each of the signal paths for a, which is a half of the pass bandwidth, with a being a gain.
The following low-pass filter is configured. Then, feedback is performed from each integrator so as to cross the x and y axes so that the feedback from the x axis to the y axis is positive and the feedback from the y axis to the x axis is negative. In these feedback paths, the angular frequency ω to be passed is inserted as a gain, thereby selectively passing the angular frequency component.

In this embodiment, ω = 3750 [rad /
FIG. 4 shows a Bode diagram when s] and a = 7.5 [rad / s]. As a result, the effect of passing the band including the central angular frequency with the characteristic having sharp selectivity is shown.

Incidentally, in the conventional biquad filter corresponding to the filter having the configuration shown in FIG. 3, V = {2zωs / (s ² + 2zωs + ω ² )} U (19) z is a dimensionless number that gives the steepness of the filter, and corresponds to an attenuation ratio or a reciprocal of selectivity.
Equation (19) is a real number system and should be provided separately for the two axes x and y. FIG. 15 shows a specific block diagram. Integrators require a total of four for each two axes. Further, when z is fixed, the slope of attenuation is constant in the Bode diagram, but when the horizontal axis is set to a linear scale, the steepness decreases in a high frequency region, and the bandwidth increases equivalently.

For this reason, in a use such as a tracking filter, an operation for reducing z in accordance with an increase in ω is required. In addition, since ω is a variable, ω in the figure needs to be a multiplier, and four of them are required, which increases cost or calculation time. On the other hand, in the complex filter shown in FIG. 3, since the bandwidth remains unchanged at a and the z remains unchanged, it is simple and clear and requires about half the hardware, and the digital control has the advantage that the calculation time is short. .

FIG. 5 (a) shows a second embodiment of the present invention, which is a so-called notch filter for blocking only a specific frequency signal. The real coefficient transfer function that is the basis of this notch filter is: F ₂ (s) ≡k (s + b) / (s + a), a, b> 0 (20) The complex coefficient transfer function calculates s of this denominator and (s−j
ω) is replaced by F ₂ (s−jω). The specific connection method is omitted because it is a special case where ω ₁ = ω ₂ = ω in F ₃ described later.

When this is materialized, a filter circuit as shown in FIG. That is, in the signal path of each axis,
A direct connection path having a gain of k is provided, and a low-pass filter (LPF) is provided in parallel with a branch therefrom. On the output side, 1/1 of the rejection bandwidth is obtained from the corner frequency a of the low-pass filter. Value obtained by subtracting b that is 2
There are provided a path for multiplying (ab) as a gain and returning to the direct connection path for subtraction coupling, and a crossing path for crossing the axes from the output of each low-pass filter and feeding back to the low-pass filter. . The low-pass filter includes an integrator and a feedback of a gain a as shown in FIG. In this crossing path, the angular frequency to be blocked is inserted as a gain, and at the connection point, the path from the x-axis to the y-axis is added, and the path from the y-axis to the x-axis is subtracted. I have. Thereby, as a result, the signal of the angular frequency component is canceled and the passage is prevented. This filter circuit can compensate for maintaining stable operation by preventing passage of only the angular frequency ω and giving an appropriate phase to the remaining signal. If b>a> 0, the filter becomes a pass filter and k
= A / b, the bottom of the skirt of the passage characteristic is 0 dB.
Since there is only a phase change with little change in gain near the rejection or out of the pass band (see FIG. 6), this feature can be used for control.

FIG. 7 shows a third embodiment of the present invention, in which the first and second embodiments are combined. Functionally, the above two filter circuits are connected in series. Works the same as if you let it. That is, passed through the angular frequency components omega ₁ required to configure two axial directions of the control signal, a filter circuit for blocking other angular frequency components omega _2.

From the transfer function F ₃ ≡k (s + b) / (s + a) (21) when both the denominator and the denominator are of the first order, the s of the denominator and the denominator are (s−jω ₁ ) and (s−jω ₁ ), respectively. jω
_The complex coefficient transfer function F ₃ ≡k (s + b−jω ₂ ) / (s + a−jω ₁ ) obtained by replacing with ( ₂ ) is expressed by (22). First, measure the dimension reduction of the molecule _{F 3 = k {s + a} -jω 1 -a + b + j (ω 1 -ω 2)} / (s + a-jω 1) = k + k [{b-a + j (ω 1 -ω 2) } / (S + a−jω ₁ )] (23). Therefore, multiplying the input by k and passing it through,
It can be decomposed into a first-order lag element including the complex constant of the second term or a low-pass filter. Here, the configuration method of only the second term will be described.

[{B−a + j (ω ₁ −
ω ₂ )} / (s + a−jω ₁ )] and U ₂ = (U ₂ x + jU ₂ y)
Is the output V ₂ = V ₂ x + jV ₂ y, the real part and the imaginary part of the complex equation after multiplying both sides by the denominator are equal, so that U ₂ x (b−a) −U ₂ y (ω ₁ −ω ₂ ) = V ₂ x (s + a) + V ₂ yω ₁ (24) U ₂ x (ω ₁ −ω ₂ ) + U ₂ y (ba) = V ₂ y (s + a) −V ₂ xω ₁ (25) is obtained, and from equation (12), V ₂ x = [U ₂ x (ba) −U ₂ y (ω ₁ −ω ₂ ) −V ₂ yω ₁ ] / ( s + a) (26) Similarly _{(13) V 2 y = [} U 2 x (ω 1 -ω 2) + U 2 y (b-a) + V 2 xω 1] from equation / (s + a) (27 ) is obtained . Multiplying the denominator by the conjugate of the denominator in equation (22) to make the denominator a real number is not desirable because it increases the number of components, increases the order of the system, and increases the calculation time in digital control. The connection according to the equations (26) and (27) is shown in FIG.
Is shown in the part other than the passage.

A signal path for each of the x and y axes is provided with a direct connection path having a gain of 1 and two parallel circuits branched from each of the paths. One of the parallel circuits includes a low-pass filter LP connected to a half of the stop band and a rear part thereof.
An amount (ba) obtained by subtracting the corner frequency a of F is given as a gain, and this is input to the low-pass filter LPF. On the other hand, (ω ₁ −ω ₂ ) is given as a gain and connected to the input of the low-pass filter LPF crosswise. This connection is such that the path from the first axis to the second axis is added and the path from the second axis to the first axis is subtracted.

The circuit including the intersection feedback shown in FIG. 5 (b) and the same low-pass filter LPF omega ₁ constitutes a band-pass filter, the same as that described in FIG. 3, in this figure, the omega in omega ₁ It has been replaced. That is, an integrator is provided in the signal path of each axis, and a negative feedback accompanied by a which is の of the pass bandwidth is applied to each of the integrators. Feedback from each integrator crossing between the x and y axes is applied so that the feedback from the x axis to the y axis is positive, and the feedback from the y axis to the x axis is negative. It is inserted the angular frequency omega ₁ to be passed as the gain. The output of the bandpass filter as a whole is summed and connected to a direct connection path.

This example is particularly effective when ω ₁ ≒ ω ₂ . In other words, only the mode of ω ₁ is selected and ω ₂
This is the case when you do not want to touch the mode. a = b = 10 [r
ad / s], ω ₁ = 5000 [rad / s] and ω ₂ = 5100 [rad / s] are Bode diagrams in FIG. In spite of such close frequencies and considerable bandwidth, the gain difference between passing and blocking is about 40 [dB], demonstrating the effectiveness of this filter circuit.

FIG. 9 shows an example in which the phase angle of only a certain angular frequency band is delayed by 180 degrees in the circuit of FIG. 7 and the phase in other angular frequency regions is not affected. ω ₁ = 10000 [rad / s], ω ₂ = 40000 [rad / s
s], b = 0, a = 1 [rad / s], and a is sharply reversed over the bandwidth between the two angular frequencies by setting a so small that a does not oscillate. However, the gain characteristics are not completely flat. ω
_{If 1} and ω ₂ are reversed, the phase between them will be reversed by 180 degrees, and the slope of the gain will also be reversed.

Next, an example will be described in which a transfer function is a real number coefficient and a second-order low-pass filter represented by the following equation is used as a band-pass filter having a steep gain characteristic. F ₄ ≡ka ² / (s ² + 2zas + a ² ) (28) z of this filter is usually called an attenuation ratio, and z <
Normally, it is set to 1 to make the bump near the break point thinner and higher to give resonance characteristics. However, in such a usage, the high-frequency side of the bump has a somewhat steep characteristic,
Since the low-frequency side has a disadvantage that the bottom is shallow, it is common to multiply the numerator of equation (28) by s, but the shape design of the bump was complicated (see FIG. 16).

According to the present invention, steep characteristics can be obtained even with the secondary filter, and not only the bandwidth but also the shape of the bump can be freely selected. If s in equation (28) is replaced with (s−jω) in order to take the arbitrary center angular frequency ω as a reference, the relationship with inputs U and V is obtained by multiplying both sides by a denominator including a complex number, and ka ² U = {(S−jω) ² + 2za (s−jω) + a ² } V = {(s ² + 2zas + a ² −ω ² ) −j ² (ωs + zaω)} (Vx + jVy) (29) Real part and imaginary part of this equation {Ka ² Ux−2 (ωs + zaω) Vy} / (s ² + 2zas + a ² −ω ² ) = Vx (30) {ka ² Uy + 2 (ωs + zaω) Vx} / (s ² + 2zas + a ² −ω ² ) = Vy (31) FIG. 10 shows a circuit obtained by dividing the denominator and the child in the equations (30) and (31) by a ² . However, k is omitted.

Both x and y axes are secondary circuits.
It has extremely advanced functions and performance by crossing between them. Numerical examples are a = 250 [rad / s], ω = 5000 [rad /
FIG. 11 shows three Bode diagrams where z = 0.5, 0.707, and 1.0 in the case of [s]. However, the abscissa was a linear scale of angular frequency. The bandwidth can be given by 2a,
Appropriate choice of z helps to improve the corners of the bandwidth. The gain characteristic becomes steeper as the bandwidth is smaller.

FIG. 12 shows an example in which the present invention is applied to a tracking filter. The tracking filter is used, for example, to extract a rotation synchronization component and remove a vibration component near the rotation speed including the rotation speed component, or to increase a gain only near the rotation speed. In the tracking filter of the present invention, in the band-pass filter described with reference to FIG. 3, the cross feedback ω is not a constant but a variable. That is, the output of the integrator is multiplied by a signal from the sensor or a voltage signal corresponding to the rotation speed generated from a sensor dedicated to rotation speed detection as a variable.
Further, a fed back from the output of the integrator is 1/2 of the pass band width, and at the same time as the operation of the low-pass filter, plays a role of preventing oscillation of the selection path. a
Is small enough to include a voltage generation error corresponding to the rotation speed, unnecessary signals such as noise other than the rotation synchronization signal are reduced.

FIG. 13 shows a filter section for extracting a required angular frequency component or band component from an input signal using the above-described various 2-input / 2-output complex coefficient transfer functions, and a filter section necessary for the extracted component. And a complex gain part that provides a large phase angle. The complex gain circuit has the following characteristics: A = g cos θ B = g sin θ, and the gain and phase can be independently adjusted. In FIG. 13, the rightmost circuit 1 / (s + a
−jω) is the bandpass filter circuit shown in FIG. In the figure, the j circuit on the left end is a circuit of an incomplete integration type, and is composed of kω / (s + δ), where k is about 1/10 and δ is 1/10 of ω
00 is preferred.

FIG. 14 is a circuit diagram of FIG. 10 using the above-described approximate j circuit.
13 is an example of gain characteristics in the case of FIG. As shown at the left end of the figure, a newly derived resonance mode P is generated at a low frequency. In order to avoid the influence of this, the peak is selected to be lowered. If a is reduced, the steepness increases, and the influence of the derived low-frequency mode can be reduced.

[0049]

According to the communication / control filter circuit of the present invention, a one-input one-output general-purpose communication / control filter is used by using the excellent characteristics of a two-input two-output complex transfer function filter. Can be configured. Thereby, a steep band-pass filter characteristic or a notch filter characteristic,
Alternatively, a one-input one-output filter circuit having a phase shift characteristic can be easily configured from a low-pass filter or a high-pass filter having real coefficients, an integrator, and the like.

[Brief description of the drawings]

FIG. 1 is a graph showing characteristics of a low-pass or high-pass filter circuit.

FIG. 2 is a block diagram showing a basic configuration of a one-input one-output filter circuit of the present invention.

FIG. 3 is a block diagram showing the first embodiment of the present invention.

FIG. 4 is a graph showing characteristics of the circuit according to the embodiment of FIG. 3;

FIG. 5 is a block diagram showing a second embodiment of the present invention.

FIG. 6 is a graph showing characteristics of the circuit according to the embodiment of FIG. 5;

FIG. 7 is a block diagram showing a third embodiment of the present invention.

FIG. 8 is a graph showing characteristics of the circuit of the embodiment of FIG. 7;

FIG. 9 is a graph showing characteristics of another example in which constants are changed in the circuit of the embodiment of FIG. 7;

FIG. 10 is a block diagram showing a fourth embodiment of the present invention.

FIG. 11 is a graph showing characteristics of the circuit according to the embodiment of FIG. 10;

FIG. 12 is a block diagram of a tracking filter according to the present invention.

FIG. 13 is a block diagram showing a fifth embodiment of the present invention.

FIG. 14 is a graph showing characteristics of the circuit of the embodiment shown in FIG. 10;

FIG. 15 is a diagram showing a conventional filter circuit.

FIG. 16 is a graph showing characteristics of a conventional secondary filter circuit.

Claims (7)

[Claims] 1. An input signal of a 2-input / 2-output filter circuit (its Laplace conversion amount is Ux) is branched into two,
One of them is input to one input of the filter, and Ux
Ux is passed through a circuit (j circuit) that generates a signal having a phase difference of 90 degrees to the other input of the filter as an imaginary input signal (Uy), and Ux and Uy
Similarly, the output of the filter which receives the two input signals
Two output signals x and Vy are output, and each of the two inputs and the two outputs is a complex variable ( U = U) using an imaginary unit j.
x + jUy, V = Vx + jVy), the transfer function of a low-pass or high-pass filter with real coefficients is F (s), the central angular frequency to be passed or blocked is ω,
The Laplace operator s of the transfer function F (s) is expressed as (s-jω)
The F (s-jω) is replaced with a complex coefficient transfer function of the filter, transmitting relation U · F between the output V of the input U has passed the complex-coefficient transfer function F (s-jω) At (s−jω) = V , the denominator of F (s−jω) is multiplied on both sides of the relational expression, and connected by a transmission element of a real number coefficient such that the real part and the imaginary part of the transmission relational expression are equal to each other. A communication / control filter circuit, characterized in that: 2. The center angular frequencies to be passed and blocked are ω ₁ and ω ₂ , respectively, and ω ₁ ≠ ω ₂ , and components including a bandwidth (2a) before and after ω ₁ are passed around the center. In order to block components including the bandwidth (2b) before and after ω ₂ , k is set to an arbitrary gain or coefficient, z
Is an arbitrary dimensionless number, the complex coefficient transfer function is k (s + b−jω ₂ ) / (s + a−jω ₁ ) or k (s + b−jω ₂ ) / {(s−jω ₁ ) ² + 2za ( s−jω ₁ ) +
The communication / control filter circuit according to claim 1, wherein the filter circuit is provided in the form of a ² }. 3. In the numerator and / or denominator of the transfer function F (s) according to claim 1, k is an arbitrary gain or coefficient, and 2a is a passing or blocking bandwidth centered on the central angular frequency. Including a quadratic system represented by k (s ² + 2zas + a ² ), replacing s with (s−jω), and arbitrarily selecting a dimensionless number z to obtain a bandwidth in a gain characteristic of a frequency characteristic of the filter. 3. The communication / control filter circuit according to claim 1, wherein the vicinity of the break points at both ends of the filter is made closer to the ideal filter. 4. A communication / control filter circuit according to claim 1, wherein a plurality of communication / control filter circuits are combined so as to pass or block a specific band among all frequency bands. Communication / control filter circuit. 5. The communication / control filter circuit according to claim 1, wherein each instantaneous value is input as a variable without using ω, ω ₁ , ω ₂ as constants. Tracking filter to be characterized. 6. A filter part for extracting a required angular frequency component or band component from an input signal using the two-input / two-output complex coefficient transfer function according to claim 1;
A complex gain part that gives a necessary phase angle to the extracted component, and an output that has passed through both parts is used to estimate another state quantity necessary for control or the like, or a communication / control filter circuit for stabilizing mode, the complex-gain portion, a, and B is a real constant a + jB≡ F
is the complex gain circuit represented by c, the x of F c, the input to the y-axis portion (Ux, Uy) and output (Vx, Vy) Vx = AUx -BUy between, Vy = BUx + AUy By selecting A and B arbitrarily, it is possible to give not only an arbitrary gain but also a phase angle to the extracted component, and a frequency necessary for estimating a communication or control-related signal. A communication / control filter circuit which provides an arbitrary necessary phase angle only to a region. 7. The j-circuit includes, in the numerator of the integrator 1 / s, a central angular frequency in the case of one pass band or stop band, or a value about one tenth to ten times as large as the pass or stop band. When there are a plurality of pass or stop bands, an integrator obtained by multiplying the average value or a tenth to ten-fold value thereof as a gain or a denominator s of the integrator is approximately one tenth of the gain. 7. The communication / control filter circuit according to claim 1, wherein an incomplete integrator is added with the following constants.