JP2016003933A - Absolute displacement sensor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an absolute displacement sensor capable of lowering a characteristic frequency, even if a feedback gain is increased in relative acceleration, and detecting absolute displacement even in a long periodic vibration.SOLUTION: An absolute displacement sensor 1 includes: a mass body 2; a sensor housing 4 which supports the mass body 2 through a spring 3; detection means 5 for detecting relative speed during the displacement of the sensor housing 4 to the mass body 2; a low pass filter 8 which suppresses high frequency components higher than a characteristic frequency determined by the mass body 2 and the spring 3, and transmits low frequency components lower than the characteristic frequency; feedback control means 9 which suppresses and controls the absolute displacement of the mass body 2 by positively feeding back relative displacement outputted from the low pass filter 8 and negatively feeding back relative speed and relative acceleration; and phase delay compensation means 10 for performing tertiary phase delay compensation on the relative displacement obtained by integrating from the feedback control means 9 in a required frequency area.

Description

  The present invention relates to an absolute displacement sensor for detecting an absolute displacement of a vibrating body (detected body) necessary for observing or controlling vibrations of a skyscraper due to earthquake or wind vortex excitation, and in particular, a period of 10 seconds. The present invention relates to an absolute displacement sensor for detecting long-period and large-amplitude vibrations that enables detection of long-period vibrations up to 1 m and large-amplitude vibrations exceeding 1 meter.

  In the Great East Japan Earthquake that occurred on March 11, 2011, major earthquakes with long-period large-amplitude vibration occurred mainly in Iwate, Miyagi, and Fukushima prefectures. And many lives were lost. In Tokyo, a 200-meter-class skyscraper caused a long-period, large-amplitude vibration that exceeded 1 meter in a long period of more than 10 minutes, causing tremendous anxiety and damage to the residents. Even the Tonankai earthquake predicted in the near future is concerned about a huge earthquake with long period and large amplitude oscillation. In order to prevent the damage of the building due to such a huge earthquake, it is necessary to incorporate a vibration control technique in the building. First, means for detecting the ground motion of the building, that is, an absolute displacement sensor is indispensable.

  Such an absolute displacement sensor is used to detect the displacement of a skyscraper when controlling a skyscraper that generates long-period vibrations due to vortex excitation by the wind. The seismic isolation device has been introduced not only in low-rise buildings but also in middle and high-rise buildings, but in order to monitor the earthquake motion in each layer of the building where the seismic isolation device was introduced, In addition, it is indispensable to perform feedback control of the active vibration isolation device of the vibration isolation table when utilizing vibration isolation technology such as skyhook damping and skyhook spring technology.

JP 2009-41954 A

  By the way, a seismo type displacement sensor has been conventionally used for detection of absolute displacement vibration, and this seismo type displacement sensor includes a mass body and a spring that supports the mass body on a detection surface. The vibration of the natural frequency of the body and the spring makes use of the fact that the vibration of the detection surface matches the relative displacement of the mass body with respect to the detection surface. Since it is in the above frequency range, it is necessary to lower the natural frequency in order to expand the frequency range to be detected to a low frequency, but this is limited to reducing the natural frequency to about 1 Hz at most. Therefore, seismo type displacement sensors are not suitable for detecting vibrations at low frequencies.

  On the other hand, seismo type acceleration sensors and speed sensors are used as sensors for seismic observation and building vibration control. This acceleration sensor can detect vibrations below the natural frequency, and the speed sensor is near the natural frequency. Can be detected, and is widely used to control the vibration of the main towers of high-rise buildings and long suspension bridges. However, the current most common control theory is linear quadratic optimal control theory (LQ optimal control). In theory, since the control variables to be controlled are displacement and speed, detection of absolute displacement and absolute speed is indispensable for building vibration control. However, acceleration sensors and speed sensors directly detect absolute displacement. Cannot be detected.

  In the case of an acceleration sensor to directly detect this absolute displacement, two stages of integrators are used. However, such an integrator also integrates a small DC signal and varies with the passage of time regardless of the input. An integrated signal, a so-called drift signal, is output and the mass body is moved by the drift signal to make it uncontrollable, and a sensor having an integrator without this drift becomes extremely expensive.

  On the other hand, since the speed sensor has only one stage of integration, it is relatively insensitive to drift, but the natural frequency must be lowered, so that the mass body becomes large and a weak spring must be used. Therefore, downsizing is difficult and handling is difficult.

  In order to solve such a problem, an absolute displacement / velocity sensor using a relative displacement sensor disposed between the mass body and the housing has been proposed. A method using a gap sensor or a strain gauge or a method using an optical signal is used, but it is difficult to stably obtain a relative displacement signal in a narrow space, and the absolute displacement / speed sensor itself is expensive. When installing the sensor, if it is attached to the installation surface even if it is tilted slightly, the position of the mass body changes due to its own weight, so that the displacement signal will be biased, and that bias will appear as a relative displacement DC signal, This has a bad influence on the control signal, and every time an absolute displacement / speed sensor is installed, its DC component must be removed.

  Patent Document 1 proposes an absolute displacement sensor that solves the generation of a DC signal caused by bias by using a relative speed sensor instead of a relative displacement sensor disposed between a mass body and a housing. .

  By the way, in the absolute displacement sensor proposed in Patent Document 1, the natural frequency can be lowered by increasing the feedback gain of the relative acceleration, and the frequency range to be detected can be expanded to a low frequency. However, when the feedback gain of this relative acceleration is increased, a split vibration peculiar to the distributed constant system that occurs in the high frequency region of the spring supporting the mass body is generated, and the natural frequency is reduced due to resonance caused by this split vibration. There is a limit to doing it.

  The present invention has been made in view of the above-mentioned points, and the object of the present invention is to divide vibrations peculiar to a distributed constant system generated in a high frequency region of a spring even if the feedback gain of relative acceleration is increased. It is an object of the present invention to provide an absolute displacement sensor that can reduce the natural frequency without being influenced by the above-described phenomenon, and can detect the absolute displacement even with a long-period vibration of, for example, a period of 10 seconds.

  An absolute displacement sensor according to the present invention includes a mass body, a detected body that elastically displaces the mass body via a spring, and a displacement in one direction of the detected body with respect to the mass body. The detection means for detecting the relative speed, and a transmission characteristic for passing a low frequency component lower than the natural frequency while suppressing a high frequency component higher than the natural frequency determined by the mass body and the spring. With this transfer characteristic, the low frequency component passing means that transmits the relative speed input from the detecting means to the output, and the relative displacement obtained by integrating the relative speed output from the low frequency component passing means are positive, The relative velocity and the relative acceleration obtained by first-order differentiation of the relative velocity are fed back negatively, respectively, so that the absolute displacement of the detected mass in one direction is eliminated. Displacement has and a feedback control means for inhibiting control, and outputs as one direction of the absolute displacement of the detection object relative displacement obtained by the integration in the feedback control means.

  According to the present invention, in the feedback loop, a transfer characteristic that suppresses a high frequency component higher than the natural frequency determined by the mass body and the spring while allowing a low frequency component lower than the natural frequency to pass therethrough. And the low frequency component passing means for transmitting the relative speed input from the detection means to the output with this transmission characteristic is arranged, so that the spring element and the mass element are distributed infinitely in the high frequency range. As a result of suppressing the high frequency component caused by the spring that can be regarded as an elastic body of a distributed parameter system, the vibration of the mass body at the higher natural frequency specific to the distributed parameter system generated in the high frequency region of the spring The natural frequency can be reduced by increasing the feedback gain of the relative acceleration without being influenced by the absolute acceleration. For example, even in the case of a long-period vibration of a period of 10 seconds, an absolute displacement in one direction can be detected. .

  In a preferred example of the present invention, the low frequency component passing means has a transmission characteristic that suppresses the vibration of the mass body having a higher order natural frequency generated due to the spring in the displacement in one direction of the mass body. doing.

In the present invention, the low frequency component passing means includes the transfer function G _P (s) = (R _f / R) · {1 / (1 + R _f · C · s)} (where R _f and R are electric An electric circuit having a resistance value, C is a capacitance value, and s is a differential operator). In this case, the transfer function G _P (s) = (R _f / R) · {1 / The electrical circuit having (1 + R _f · C · s)} may have a cutoff frequency f = 1 / (2πR _f · C) equal to or higher than the natural frequency of the mass body, where the cut The off frequency f = 1 / (2πR _f · C) may be the upper limit value of the frequency region of the absolute displacement in one direction of the detected object to be detected.

  In a preferable example of the present invention, the feedback control means includes a relative displacement in which the high frequency component is suppressed and positively fed back, a relative speed in which the high frequency component is suppressed and negatively fed back, and the high frequency. An actuator is provided for displacing the mass body with respect to the direction of displacement applied to the detected object based on the relative acceleration obtained by first-order differentiation of the relative velocity with suppressed frequency components and fed back negatively. .

  According to the present invention, even if the feedback gain of the relative acceleration is increased, the natural frequency can be lowered without being affected by the divided vibration unique to the distributed constant system generated in the high frequency region of the spring. Thus, for example, it is possible to provide an absolute displacement sensor that can detect an absolute displacement even with a long-period vibration having a period of 10 seconds.

  That is, according to the present invention, by introducing a low frequency component passing means that suppresses an infinite number of higher-order frequencies generated by a spring supporting the mass body, a so-called low-pass filter, the state quantity of the mass body ( By stably feeding back (displacement, velocity, acceleration), the natural frequency can be lowered without causing structural defects, and the detectable amplitude can be greatly increased.

FIG. 1 is an explanatory diagram of a preferred example of an embodiment of the present invention. FIG. 2 is a detailed explanatory view of the sensor housing, the mass body, the detection means, and the actuator of the example shown in FIG. FIG. 3 is a detailed explanatory diagram of the low-pass filter of the example shown in FIG. FIG. 4 is an explanatory diagram of the frequency response characteristics of the low-pass filter shown in FIG. FIG. 5 is a detailed explanatory diagram of the phase lag compensation means of the example shown in FIG. FIG. 6 is an explanatory diagram of the frequency response characteristics of the phase lag compensation means of the example shown in FIG. FIG. 7 is an explanatory diagram of the effect of the low-pass filter of the example shown in FIG. FIG. 8 shows frequency response characteristics (curve 142) without acceleration / velocity / displacement feedback in the example shown in FIG. 1, frequency response characteristics (curve 141) when acceleration / velocity / displacement feedback is applied, and acceleration / velocity.・ Frequency response characteristics when second-order phase delay compensation is applied in addition to displacement feedback (curve 144), and frequency response characteristics when third-order phase delay compensation is performed in addition to acceleration, velocity, and displacement feedback It is explanatory drawing of four types of frequency response characteristics of (curve 145). FIG. 9 is a comparative explanatory diagram of the frequency response characteristic (curve 143) of the second-order phase lag compensation circuit of the example shown in FIG. 1 and the frequency response characteristic (curve 146) of the third-order phase lag compensation means. . FIG. 10 is an explanatory diagram of frequency response characteristics of the first-order phase lag compensation circuit of the example shown in FIG.

  Next, an example of an embodiment of the present invention will be described in more detail based on an example shown in the figure. The present invention is not limited to these examples.

1 to 9, an absolute displacement sensor 1 of this example includes a mass body 2 having a mass m (kg), a spring coefficient k (N / m), and a damping coefficient c (N · sec / m) (sec. In the direction H of the sensor housing 4 with respect to the mass body 2, and a sensor housing 4 as a detected body that elastically supports the mass body 2 movably in one direction H via the spring 3 in seconds. the relative velocity _{v (= v U -v X)} (m / sec) ( _wherein, v X (m / sec), the mass body attributable to the absolute velocity _v U direction H of the sensor housing 4 (m / sec) 2 which suppresses high frequency components higher than the natural frequency ω _n / 2π determined by the mass body 2 and the spring 3, Den passing a low frequency component lower than the natural frequency omega _{n /} 2 [pi Characteristics (transfer function = GP (s)) the relative velocity voltage signal e _{r (V)} relative to the output terminal 7 from the detection means 5 has a transfer characteristic as the relative velocity v which is input through the input terminal 6 and having a a low-pass filter 8 as a low frequency component passing means for outputting to transmit the relative velocity voltage signal ev (V) as the speed v _Lp, the relative velocity v _Lp output from the low pass filter 8 via the output 7 relative displacement obtained by integrating the relative velocity voltage signal eV the (u-x) relative displacement voltage signal as e _{D (V)} to the positive, the relative velocity voltage as the relative velocity v _Lp signal eV and the relative velocity v _Lp Each of the relative acceleration voltage signals eA _(V) as the relative acceleration a (m / sec ² ) obtained by first-order differentiation of the relative velocity voltage signal eV is negatively fed back. The feedback control means 9 for suppressing and controlling the absolute displacement x of the mass body 2 caused by the absolute displacement u in the direction H of the sensor housing 4 and the relative displacement (ux) obtained by integrating from the feedback control means 9 And a phase lag compensation means 10 for performing third-order phase lag compensation in the required frequency range on the electric signal e _{D of (1} ).

  The mass body 2 includes a pair of cylindrical portions 21 and 22 arranged concentrically, a pair of disk-like portions 23 and 24 formed integrally with each of the pair of cylindrical portions 21 and 22, and A shaft member 25 that connects the pair of disk-like portions 23 and 24 to each other is provided.

  The sensor housing 4 includes a hollow main body member 31, lid members 32 and 33 attached to both end surfaces of the hollow main body member 31, an annular attachment 34 fitted to both ends of the inner peripheral surface of the hollow main body member 31, and 35, and the mass body 2 is attached to the annular attachments 34 and 35 via the spring 3 in the disk-like portions 23 and 24 so that the mass 2 can vibrate in the direction H by elastic deformation of the spring 3. The sensor housing 4 is supported so as to be displaceable in the direction H.

  A spring 3 having a spring constant k (N / m) is formed of spider web-like (annular) spring portions 37 and 38 around the disc-like portions 23 and 24, and the spring portion 37 is a disc-like portion. At the same angular interval of 120 degrees around 23, one end is fixed to the inner peripheral surface of the annular fixture 34, and the other end is fixed to the outer peripheral surface of the disk-shaped portion 23. Similarly to the portion 37, at an equal angular interval of 120 degrees around the disk-shaped portion 24, one end is fixed to the inner peripheral surface of the annular fixture 35, and the other end is fixed to the outer peripheral surface of the disk-shaped portion 24. The spring 3 composed of the spring portions 37 and 38 can be largely deformed in the direction H.

The detecting means 5 includes a coil 41 wound around the cylindrical portion 21 and a magnetic circuit forming means 42, and the magnetic circuit forming means 42 is an annular shape fixed to the inner peripheral surface of the hollow body member 31. Permanent magnet 43, one magnetic circuit forming member 44 that is fixed to the inner peripheral surface of the hollow body member 31 and made of an annular magnetic material, and in cooperation with the magnetic circuit forming member 44 is permanent in the direction H. A cylindrical space 45 that sandwiches the magnet 83 and in which the cylindrical portion 21 and the coil 41 are arranged to be displaceable in the direction H is formed in cooperation with the magnetic circuit forming member 44 and the shaft member 25 is Amplification degree (current-voltage conversion coefficient = conversion feedback gain) K _a (the current signal i indicating the relative velocity v from the other magnetic circuit forming member 46 made of a magnetic material penetrating through the direction H in a freely displaceable manner and the coil 41) V / A) And comprises an amplifier 47 for converting the relative velocity v _r as the relative velocity voltage signal e _{r (V),} the coil 41 is displaced in the direction H due to the displacement of the direction H of the cylindrical portion 21 relative to the sensor housing 4 Thus, the relative velocity v in the displacement in the direction H of the mass body 2 with respect to the sensor housing 4 is electrically detected by traversing the magnetic flux from the permanent magnet 43 in the cylindrical space 45, and this electricity generated at the output terminal 48 is detected. specific detection result of the relative speed electric signal e _{r (V) is} adapted to output to the input terminal 6 via the amplifier 47, the eddy current loss in the electrical detection of the magnetic flux of the permanent magnet 43 of the coil 41 is This contributes to the damping coefficient c.

In the high frequency region, a high frequency component higher than the natural frequency ω _n / 2π due to the spring portions 37 and 38 that can be regarded as an elastic body of a distributed constant system in which the spring elements and the mass elements are distributed infinitely. The suppression low-pass filter 8 is connected to the operational amplifier 51, on the one hand, to the input terminal 6 and on the other hand to the inverting input terminal of the operational amplifier 51, and has an input resistance 52 having a resistance value R _f1 (Ω). On the one hand, the resistance value R _f2 (Ω) and the capacitance value C _f (F) are connected to the inverting input terminal of the operational amplifier 51 and on the other hand to the output terminal of the operational amplifier 51, respectively. and comprising a feedback resistor 53 and feedback capacitor 54, a low pass filter 8 for outputting the relative speed voltage signal e _r from the amplifier 47 and _(V) as the relative velocity voltage signal e _{V (V),} the cut-off frequency f _c = 1 / (2 An electric circuit having a transfer function _GP (s) = e _V / _er = (R _f2 / R _f1 ) · {1 / (1 + R _f2 · C _f2 · s)} having π · R _f2 · C _f ) have.

For example, the resistance value _R f1 = 1 k [Omega input resistor 52, having a capacitance value _C f = 10uF and cutoff frequency _f c = 1.59 Hz of the resistance value _R f2 = 1 k [Omega and the feedback capacitor 54 of the feedback resistor 53 The frequency response characteristic (Bode diagram) of the transfer function G _P (s) in the low-pass filter 8 is as shown by a curve 55 in FIG. 4, and such cutoff frequency f _c = 1 / (2π · R _f2 If C _f ) is too high, the divided frequency cannot be suppressed, but if it is too low, the stability of the feedback loop is hindered. Preferably, the natural frequency ω _n / determined by the mass body 2 and the spring 3 is reduced. The upper limit of the frequency region to be detected by the absolute displacement sensor 1 is 2π or more, in other words, the upper limit value of the frequency region of the absolute displacement u in the direction H of the sensor housing 4 to be detected. To.

Feedback control means 9 includes an integration circuit 61 which outputs a relative displacement voltage signal e _D as integrating the relative displacement of the relative velocity voltage signal e _v from the low-pass filter 8 (u-x), relative to the low-pass filter 8 a differentiating circuit 62 which outputs a relative acceleration voltage signal e _a as the relative acceleration a velocity voltage signal e _V primary differentiation on the relative displacement voltage obtained by integrating the relative velocity voltage signal e _v from the low-pass filter 8 a multiplier 63 which outputs a voltage signal by multiplying the displacement feedback gain _{K D} to the signal _{e D K D · e D (} V), multiplied by the velocity feedback gain _{K V} the relative velocity voltage signal _{e v} from the low-pass filter 8 Then, a multiplier 64 that outputs a voltage signal K _V · e _v (V) and an acceleration to a relative acceleration voltage signal e _A through a differentiation circuit 62 from the low-pass filter 8 _A multiplier 65 that multiplies the feedback gain K _A and outputs a voltage signal K _A · e _A (V), and voltage signals K _D · e _D , K _V · e _v, and K from the multipliers 63, 64, and 65 subtractor 66 for outputting by subtracting the _a · _{e a} subtraction voltage signal _{e C (= K D · e} D -K V · e v -K a · e a), converting the feedback gain subtraction voltage signal _{e C} a converter 67 which converts the current signal f _c with K f a _(a / V), which comprises an electromagnetic actuator 68 for actuating the current signal f _c from the converter 67 as a coil drive current.

The integrating circuit 61 includes a resistor 71 having a resistance value R _D (Ω) and a capacitor 72 having a capacitance value C _D (F), and the differentiating circuit 62 includes a capacitance value C _A (F ) And a resistor 74 having a resistance value R _A (Ω).

Voltage signal K _D · e _D corresponding to the relative displacement (ux) fed back positively while the high frequency component is suppressed, and the relative speed fed back negatively while the high frequency component is suppressed The voltage signal −K _A · e corresponding to the relative acceleration a obtained by first-order differentiation of the voltage signal −K _V e _V corresponding to v and the relative velocity v in which the high frequency component is also suppressed is negatively fed back. The electromagnetic actuator 68 as an actuator for displacing the mass body 2 with respect to the sensor housing 4 with respect to the direction H based on _A includes a coil 81 wound around the cylindrical portion 22 and a magnetic circuit forming means 82. The magnetic circuit forming means 82 includes an annular permanent magnet 83 fixed to the inner peripheral surface of the hollow body member 31, and the inner periphery of the hollow body member 31. The magnetic circuit forming member 84 made of an annular magnetic material and the permanent magnet 83 in the direction H in cooperation with the magnetic circuit forming member 84, and the cylindrical portion 22 and A cylindrical space 85 in which the coil 81 is displaceably displaceable in the direction H is formed in cooperation with the magnetic circuit forming member 84 and the shaft member 25 is formed of a magnetic material penetrating displaceably in the direction H. and comprising a magnetic circuit forming member 86, the driving force F (N) is an electromagnetic force in the direction H by a current flowing in the coil 81 (a) based on the current signal f _c which is input to the input terminal 87 And generating a driving force F relative to the sensor housing 4 relative to the cylindrical portion 22 to displace the mass body 2 relative to the sensor housing 4 in the direction H. the gain _{K f} , It is assumed to include the conversion gain of the driving force F with respect to the current signal f _c.

  In the case of having the detection means 5 and the electromagnetic actuator 68 described above, the mass m of the mass body 2 is such that the pair of cylindrical portions 21 and 22, the pair of disk-like portions 23 and 24, the coils 41 and 81, and the shaft member 25. The damping coefficient c (N · sec / m) is the sum of the mass of each of the eddy current loss in the elastic detection of the spring 3 itself, the eddy current loss in the electrical detection of the magnetic flux of the permanent magnet 43 by the coil 41, and the coil. 81 based on the eddy current loss in the displacement of the mass body 2 in the direction H relative to the sensor housing 4.

  The phase delay compensation means 10 for performing the third-order phase delay compensation comprises a combination of a second-order phase delay compensation circuit 91 and a first-order phase delay compensation circuit 92.

The second-order phase delay compensation circuit 91 has input resistors 101, 102, and 103 having resistance values R ₁ (Ω), R ₂ (Ω), and R ₃ (Ω), respectively, and a resistance value R ₄ (Ω). Feedback circuit 104, feedback capacitor 105 having capacitance value C ₁ (F), and operational amplifier 106, and an integration circuit that adds and integrates electric signals input through input resistors 101, 102, and 103. 107, an input resistor 108 having a resistance value R ₅ (Ω), a feedback resistor 109 having a resistance value R ₆ (Ω), a feedback capacitor 110 having an electrostatic capacitance value C ₂ (F), and an operational amplifier 111 And an integration circuit 112 for integrating an electric signal input via the input resistor 108, an input resistor 113 having a resistance value R ₇ (Ω), a feedback resistor 114 having a resistance value R ₈ (Ω), and Operational amplifier Electric signal input via an input resistor 113 and sign inversion circuit 116 inverts the with of 15, the resistance value R ₉ input resistor 117 having a _(Omega), a feedback resistor having the resistance value R _{10 (Ω)} 118, an operational amplifier 119, and a sign inversion circuit 120 for inverting an electric signal input via the input resistor 117, a resistance value R ₁₁ (Ω), a resistance value R ₁₂ (Ω), and a resistance value R ₁₃ (Ω ), Input resistors 121, 122, and 123, a feedback resistor 124 having a resistance value R ₁₄ (Ω), and an operational amplifier 125, and an electric signal input through the input resistors 121, 122, and 123 is added. The first-order phase lag compensation circuit 92 includes an input resistor 127 having a resistance value R ₁₅ (Ω) and a feedback having a resistance value R ₁₇ (Ω). The integrating circuit 107 includes a resistor 128, a feedback resistor 129 having a resistance value R ₁₆ (Ω), a feedback capacitor 130 having a capacitance value C ₃ and an operational amplifier 131 connected in series to the feedback resistor 129. Includes a relative displacement voltage signal e _D via the input resistor 101, an output voltage signal of the sign inverting circuit 120 via the input resistor 102, and an output voltage signal of the integrating circuit 107 itself via the input resistor 103. The output voltage signal of the integrating circuit 107 is input to the integrating circuit 112 via the input resistor 108, and the output voltage of the integrating circuit 107 is input to the sign inverting circuit 116 via the input resistor 113. The signal is input, and the output voltage signal of the integration circuit 112 is input to the sign inversion circuit 120 via the input resistor 117, and the addition circuit The 26, the relative displacement voltage signal e _D via an input resistor 121, the output voltage signal of the integrating circuit 112 via an input resistor 122, and the output voltage signal of the sign inversion circuit 116 via the input resistor 123 The output voltage signal of the adder circuit 126 is input to the primary phase delay compensation circuit 92 via the input resistor 127, and the output terminal 135 of the primary phase delay compensation circuit 92 is input to the primary phase delay compensation circuit 92. A relative displacement voltage signal e _{OUT in} which third-order phase delay compensation is applied to the relative displacement voltage signal e _D with the transfer function G _lag3 (s) represented by the equation (1) is output.

In equation (1), (s ² + 2ζ ₂ ω ₂ s + ω ₂ ² ) / (s ² + 2ζ ₁ ω ₁ s + ω ₁ ² ) (where ω ₂ > ω ₁ ) is the transfer function of the second-order phase delay compensation circuit 91 {S + (1 / T)} / [s + {1 / (α · T)}] is a transfer function of the first-order phase delay compensation circuit 92, and ω ₁ , ω ₂ , ζ ₁ , ζ ₂ , Α and T, and the resistance values R ₁ to R ₁₇ and the capacitance values C ₁ to C ₃ in FIG. 5 are C ₁ R ₁ = 1, C ₂ R ₅ = 1, R ₂ = ω _{1. ^{2, R 3 = 2ζ 1 ω}} 1, R 14 / R 11 = 1, R 14 / R 12 = ω 2 2 -ω 1 2, R 14 / R 13 = 2ζ 2 ω 2 -2ζ 1 ω 1, R 7 _{= R 8, R 10 / R} 9 = 1/10, T = R 16 C 3, α = (R 17 + R 15) is _{/ R 15, R 4} and _{R 6,} other resistor Sufficiently large as compared with R ₁ and the like, negligible.

For example, ω ₁ = 0.05 × 2π (rad / sec), ζ ₁ = 0.8, ω ₂ = 0.23 × 2π (rad / sec), ζ ₂ = 0.45, T = 1 (sec) When α = 4, the frequency response characteristic of the transfer function G _lag3 (s) of the phase lag compensation means 10 is as shown by a curve 136 in FIG.

In the absolute displacement sensor 1 described above, if all of the relative displacement voltage signal e _D , the relative velocity voltage signal e _V and the relative acceleration voltage signal e _A are negatively fed back, the absolute displacement u of the sensor housing 4 as the detection object is detected. The transfer function e / u of the relative displacement voltage signal e _D with respect to is given by the following equation (2).

In the equation (2), the coefficients a ₀ , a ₁ , a ₂ , a ₃ and a ₄ are expressed by the following equations (3) to (7).

Here, T _D (= C _D R _D ) is a time constant of the integrating circuit 61, and T _A (= C _A R _A ) is a time constant of the differentiating circuit 62.

The transfer function G _D (s) of the integration circuit 61 is G _D (s) = 1 / (T _D · s + 1). If T _D is large, T _{D s} >> 1, so the transfer function G _D (s) _is the transfer function _G a (s) of G D (s) = 1 / (T D · s) , and the differentiating circuit _{62, G a (s) = T} a · s / (T a · s + 1) , and the Since T _{A s} << 1 in a range where s is small, the transfer function G _A (s) is G _A (s) = T _A · s.

Then, the transfer function e _D / u of the relative displacement voltage signal e _D with respect to the absolute displacement u in Expression (2) is expressed by the following Expression (8).

From the equation (8), the coefficient K, the natural angular frequency ω _n and the damping ratio ζ of the equation (9) are expressed by the following equations (10), (11), and (12).

If only the relative displacement voltage signal e _D is positively fed back, the sign of the displacement feedback gain K _D turns negative, so that the natural angular frequency ω _n and the damping ratio ζ are expressed by the following equations (13) and (14): Become.

From these equations (13) and (14), the natural angular frequency ω _n is related to the acceleration feedback gain K _A and the displacement feedback gain K _D, and if the acceleration feedback gain K _A is increased negatively, the natural angular vibration is obtained. The number ω _n can be reduced, and thereby the mass m of the mass body 2 can be increased. Also, if positively increase the displacement feedback gain K _D, is a possible reduction in the natural angular frequency omega _n, for transferring the direction of destabilizing feedback loop, this is limited.

Therefore, the denominator of equation (2) is an n-order polynomial (P (s) = a ₀ s ⁿ + a ₁ s ^n-1 + a ₂ s ^n-2 + a ₃ s ^n-3 +... a _n−1 s + a _n ), the limit of increasing the acceleration feedback gain K _A by the Rous's stability determination method that algebraically solves whether it is stable or unstable is defined as the acceleration feedback gain K _A and the speed feedback gain. negatively and K _V, positively respectively set displacement feedback gain K _V, determined.

  Expression (15) shows a Rous table of the polynomial of the variable s in the denominator of Expression (1).

According to such Rous's stability discrimination method, if the signs of a ₀ , a ₁ , A ₃ , A ₄ , a _{4 in} the first row are all the same sign, the feedback loop is stable, but a ₀ , a _{Since 4} takes a positive sign, all of a ₁ , A ₃ , and A ₄ must take a positive sign. Substituting the denominator coefficients of equation (2) into equation (15) yields equations (16) through (19).

Thus, all of a ₁ and A ₃ can have a positive sign by making the value of the displacement feedback gain K _D equal to or less than the values of the acceleration feedback gain K _A and the speed feedback gain K _V. The same is true for A _4.

In conclusion, in the absolute displacement sensor 1, the acceleration feedback gain K _A of the relative acceleration _ap does not destabilize the feedback loop, and this value must be increased to reduce the natural angular frequency ω _n. Is possible.

Further, in the absolute displacement sensor 1, the ratio between the relative displacement (ux) and the absolute displacement u is expressed by the equation (20), and the vibration detection area is _{equal to} or greater than the natural angular frequency ω _n. the ratio of the (u-x) and the absolute displacement u is by increasing expression (21), and the acceleration feedback gain _{K a} of the relative acceleration _{a p,} decreases the value of the expression (21), relative displacement (u Even if -x) is small, it is possible to detect a large displacement amplitude.

Incidentally, in the absolute displacement sensor 1, in principle, since the acceleration feedback gain K _A of the relative acceleration a _p does not destabilize the feedback loop, to define a large acceleration feedback gain K _A of the relative acceleration a _p Thus, the natural angular frequency ω _n can be reduced, but the spring 3 supporting the mass body 2 is substantially a distributed constant system in which the spring elements and the mass elements are distributed infinitely. Strictly speaking, it has an infinite number of higher-order natural angular frequencies ω _n than the natural angular frequency ω _n , and this innumerable higher-order natural angular frequency ω _n Based on, for example, mass m = 25.2 × 10 ⁻³ (kg), spring coefficient k = 30.1 (N / m), damping coefficient c = 0.87 (N · sec / m), conversion feedback gain K _a = 35, displacement feedback C gain K _D = 0, velocity feedback gain K _V = 0, acceleration feedback gain K _A = 0, time constant T _D (sec) of integrating circuit 61 = 3.3, time constant T _A (sec) of differentiating circuit 62 0.001, the resistance value _R f1 = 1 k [Omega input resistor 52, without the function of the resistance _R f2 = 1 k [Omega and when the capacitance value _C f = _0μF the feedback capacitor 54 (low-pass filter 8 of the feedback resistor 53, feedback In the case of no), the transfer function e _D / u of the relative displacement voltage signal e _D with respect to the absolute displacement u in the equation (2) has a characteristic frequency with a phase of 90 degrees as shown by the curve 137 in FIG. If defined as the angular frequency ω _n , the divided vibration (resonance peak) 138 in the vicinity of 240 Hz, 380 Hz, and 480 Hz in the frequency range higher than the natural frequency ω _n /2π=5.5 Hz, that is, high An infinite number of natural vibrations (divided resonance phenomenon) occur.

In the absolute displacement sensor 1, the expression (2) is a transfer function e _D / u using the spring 3 as a simple elastic body, but when the acceleration feedback gain K _A of the relative acceleration _ap is increased, the natural vibration is obtained. The divided vibration 138 in the frequency region higher than the number ω _n /2π=5.5 Hz is also increased, and there is a possibility of oscillation in the feedback loop. As a result, the relative acceleration a _p is decreased in order to reduce the natural angular frequency ω _n. of to increase the acceleration feedback gain K _a is limited, it is not possible to increase the acceleration feedback gain K _a of the relative acceleration a _p unless suppressed divided vibration 138, for example, the capacitance value C _f Instead of = 0 μF, the feedback capacitor 54 having a capacitance value C _f = 10 μF is used, and the cut-off frequency fc = 1.5 shown by the curve 55 of the frequency response characteristic of FIG. By using a low-pass filter 8 with a transfer function G _p (s) = e _V / e _Lr = (R _f / R) · {1 / (1 + R _f · C · s)} having 9 Hz, the expression (2) When there is no feedback, the transfer function e _D / u of the relative displacement voltage signal e _D with respect to the absolute displacement u is a divided vibration having a natural frequency ω _n /2π=5.5 Hz or more as shown by a curve 139 in FIG. 138 can be suppressed, and the oscillation phenomenon caused by the divided vibration 138 can be avoided without being influenced by the vibration of the mass body 2 at the high-order natural angular frequency specific to the distributed constant system generated in the high frequency region of the spring 3. by increasing the acceleration feedback gain K _a of the acceleration a _p, it is possible to lower the natural angular frequency omega _n, then Thus, for example, detect the absolute displacement u of the direction H in the long-period oscillations leading to cycle 10 seconds Can do.

Further, in the absolute displacement sensor 1, by setting the acceleration feedback gain _{K A} such that h ≦ 1/500 In the formula (21), very over total displacement 1000mm of the sensor housing 4 in displacement ± 1mm of the mass 2 Position can be detected. For example, the mass m of the mass body 2 = 25.2 × 10 ⁻³ (kg), the spring constant k = 30.1 (N / m), the damping coefficient c = 0.87 (N · sec / m), conversion feedback gain K _a = 35, displacement feedback gain K _D = 0.5, speed feedback gain K _V = 0.75, conversion feedback gain K _f (A / V) = 0.6, integration circuit 61 time constant T _D = 3.3 (sec), differentiation circuit 62 time constant T _A = 0.001 (sec), input resistance 52 resistance value R _f1 = 1 kΩ, feedback resistance 53 resistance value R _f2 = 1 When the acceleration feedback gain K _{A is set} to K _A = 550 at kΩ and the capacitance value C _f = 10 μF of the feedback capacitor 54 and the phase delay compensation means 10 is not provided, e _D = e _OUT 8 when the acceleration feedback gain K _A = 0, the speed feedback gain K _A = 0, and the displacement feedback gain K _D = 0 shown by the curve 142 in FIG. 8 (when there is no feedback). Compared with the case of e _D = e _OUT where the phase delay compensation means 10 is not provided, the natural frequency ω _n /2π=5.5 Hz to 0.23 Hz and the natural frequency ω _n / 2π = 0. above 23 Hz, to the sensor housing 4 of the displacement at the natural frequency ω _n /2π=5.5Hz, it can be compressed to -55 dB = 1/570, therefore, the absolute In position sensor 1, the displacement of the mass member 2 relative to the total displacement of the sensor housing 4, can be compressed to -55 dB = 1/570, such compression effect than natural frequency ω _n /2π=0.23Hz The same can be obtained when the low-pass filter 8 has a sufficiently high cutoff frequency f _c , for example, the cutoff frequency f _c = 1.59 Hz.

Thus, in the absolute displacement sensor 1, in one example, the displacement of the mass body 2 can be compressed to −55 dB = 1/570 with respect to the total displacement of the sensor housing 4, but the equation (2) or (20) In the feedback loop having the transfer function, the natural frequency ω _n / 2π is 0.23 Hz, and the phase is also advanced by 90 degrees at the natural frequency ω _n /2π=0.23 Hz. In the absolute displacement sensor 1, for example, the second-order phase lag in the equation (1) is further advanced toward 270 degrees at a frequency of less than the natural frequency ω _n / 2π. In the transfer function (s ² + 2ζ ₂ ω ₂ s + ω ₂ ² ) / (s ² + 2ζ ₁ ω ₁ s + ω ₁ ² ) of the compensation circuit 91, the natural angular frequency ω ₂ and the damping ratio ζ ₂ are expressed as the natural angular frequency of the feedback loop. ω _n and reduced In the same value of the ratio zeta, by offsetting the natural angular frequency omega _n and damping ratio of the feedback loop zeta, the output electrical signal e _D1 of secondary phase delay with respect to the absolute displacement u compensating circuit 91 transfer function e _D1 When / u is expressed by the equation (22), the transfer function (s ² + 2ζ ₂ ω ₂ s + ω ₂ ² ) / (s ² + 2ζ ₁ ω ₁ s + ω ₁ ² ) of the second-order phase lag compensation circuit 91 9 is a frequency response characteristic indicated by a curve 143 in FIG. 9, and the transfer function e _D1 / u in the equation (22) is a natural vibration of about 0.075 Hz as indicated by a curve 144 in FIG. A frequency response characteristic having a number ω _n / 2π can be obtained.

Even in the absolute displacement sensor 1 in which the new transfer function e _D1 / u is determined by (s ² + 2ζ ₁ ω ₁ s + ω ₁ ² ) of the transfer function G _lag3 (s) of the formula (1), the phase becomes 90 degrees. The natural frequency ω _n / 2π can only be reduced to about 0.075 Hz. In addition, as a result of actually including the inductance of the coil 81 and the like, strictly speaking, the denominator of the equation (22) is a quartic equation with respect to s. The phase advances up to 270 degrees in the extremely low frequency region, so that such a phase advance can be offset and the target natural frequency ω _n / 2π of the ultra-low frequency can be obtained. That is, for example, in the transfer function e _OUT / u of the relative displacement voltage signal e _OUT with respect to the absolute displacement u, the natural frequency ω _n / 2π is reduced to 0.060 Hz, and the leading phase is 45 degrees at the frequency of 0.1 Hz. Figure held down The first-order phase that becomes the phase delay compensation means 10 having the vibration response characteristic of the curve 146 of FIG. 9 (same as the curve 136 of FIG. 6) in the transfer function G _lag3 (s) so that the curve 145 shown in FIG. Α and T in the transfer function {s + (1 / T)} / [s + {1 / (α · T)}] of the delay compensation circuit 92 have been determined, and the first order having α and T thus determined. The vibration response characteristic of the phase lag compensation circuit 92 is, for example, a curve 147 shown in FIG.

As described above, in the absolute displacement sensor 1, the absolute displacement sensor 1 having the frequency response characteristic of the curve 145 in FIG. 8 is obtained by the phase delay compensation means 10 having the vibration response characteristic indicated by the curve 146 in FIG. The natural frequency ω _n / 2π can be reduced to 0.060 Hz, and the phase can be stopped at 45 ° at 0.1 Hz, and an extremely low frequency with a period T = 10 seconds can be detected. That is, in the absolute displacement sensor 1, in addition to the second-order phase delay compensation circuit 91, the phase advance in the detection range for detecting the absolute displacement u of the sensor housing 4 as the detected object becomes zero as much as possible. the phase lag compensation means 10 having a first-order phase lag compensation circuit 92, into an electric signal e _D relative displacement (u-x), at the required frequency region including the natural frequency omega _{n / 2 [pi} feedback loop Third-order phase delay compensation is performed.

Therefore, in the absolute displacement sensor 1 configured to output the relative displacement ux obtained by integration in the feedback control means 9 via the phase delay compensation means 10 as the absolute displacement x in the direction H of the sensor housing 4. The relative displacement ux can be compressed by the feedback control means 9, and the vibration of the mass body 2 having a higher natural frequency caused by the spring 3 at the displacement x in the direction H of the mass body 2 can be reduced by the low-pass filter 8. As a result, the natural frequency ω _{n / 2π} of the feedback control means 9 can be reduced by the third-order phase lag compensation means 10 and the detection range can be expanded to an extremely low frequency of 0.1 Hz or less. Even if the relative displacement ux in the direction H between the mass 4 and the mass body 2 is ± 1 mm, the displacement u in the direction H of ± 570 mm can be detected, and more than 10 seconds of long-period vibration is detected. Therefore, even with this small absolute displacement sensor 1 that can only have a relative displacement ux in the direction H of ± 1 mm, it is possible to detect a displacement of a long period and large amplitude vibration of 10 seconds or more with a total amplitude of 1 meter or more. become.

  In the absolute displacement sensor 1 described above, the absolute displacement u in the direction H of the sensor housing 4 as a detected object is obtained by using the relative displacement (ux) obtained by integrating the feedback control means 9 via the phase delay compensation means 10. However, in the present invention, instead of this, for example, the absolute displacement sensor 1 uses the relative displacement (ux) itself obtained by integrating the feedback control means 10 as the detected object. The absolute displacement in the direction H of the housing 4 may be output.

  In addition, in the absolute displacement sensor 1, the low-pass filter 8, the feedback control unit 9, and the phase lag compensation unit 10 are configured by an electric circuit using a resistor, a capacitor, an operational amplifier, and the like. For example, the low-pass filter 8, the feedback control means 9, and the phase delay compensation means 10 may be embodied by a computer using a program.

DESCRIPTION OF SYMBOLS 1 Absolute displacement sensor 2 Mass body 3 Spring 4 Sensor housing 5 Detection means 6 Input end 7 Output end 8 Low pass filter 9 Feedback control means 10 Phase delay compensation means

Claims (6)

  A mass body, a detected body that elastically supports the mass body via a spring so as to be freely displaceable in one direction, and a detection means that detects a relative speed of the detected body relative to the mass body in one direction. The high frequency component higher than the natural frequency determined by the mass body and the spring is suppressed, while the low frequency component lower than the natural frequency is allowed to pass and the transfer characteristic is input from the detection means. The low frequency component passing means for transmitting the relative speed to the output and the relative displacement obtained by integrating the relative speed output from the low frequency component passing means are positive, and the relative speed and the relative speed are Feeders that control the absolute displacement in one direction of the mass body caused by the absolute displacement in one direction of the detected object by negatively feeding back each of the relative accelerations obtained by the first differentiation. It has and a click control means, absolute displacement sensor which is a relative displacement obtained by the integration in the feedback control means is outputted as the absolute displacement of one direction of the object to be detected.   2. The low frequency component passing means has a transmission characteristic for suppressing vibration of the mass body at a high-order natural frequency generated due to a spring in a displacement in one direction of the mass body. Absolute displacement sensor described in 1. The low frequency component passing means has a transfer function G _P (s) = (R _f / R) · {1 / (1 + R _f · C · s)} (where R _f and R are electric resistance values, C 3. An absolute displacement sensor according to claim 1, further comprising an electric circuit having a capacitance value and s being a differential operator. An electric circuit having a transfer function G _P (s) = (R _f / R) · {1 / (1 + R _f · C · s)} has a cutoff frequency f = 1 / greater than the natural frequency of the mass body. The absolute displacement sensor according to claim 3, having (2πR _f · C). 5. The absolute displacement sensor according to claim 4, wherein the cutoff frequency f = 1 / (2πR _f · C) has an upper limit value in a frequency region of absolute displacement in one direction of the detected object to be detected.   In the feedback control means, the high frequency component is suppressed, the relative displacement fed back positively, the high frequency component is suppressed, the relative speed fed back negatively, and the high frequency component are suppressed. 6. The actuator according to claim 1, further comprising an actuator for displacing the mass body with respect to a direction of displacement applied to the detected object based on a relative acceleration obtained by first-order differentiation of the relative velocity and fed back negatively. An absolute displacement sensor according to claim 1.

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