CN107560717A - Motor oscillating measuring instrument based on MEMS sensor - Google Patents
Motor oscillating measuring instrument based on MEMS sensor Download PDFInfo
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Abstract
Motor oscillating measuring instrument based on MEMS sensor, digital micro-acceleration gauge FXLS8471Q is used as measuring cell, high-performance low-power-consumption single-chip microcomputer MSP430F5638 is as controller, with reference to Kalman filtering algorithm and cumulative summation displacement algorithm, realizes the high-acruracy survey of mechanical vibration displacement.
Description
Technical field
The present invention relates to a kind of measuring instrument, particularly relates to the motor oscillating measuring instrument based on MEMS sensor.
Background technology
By the rotary grinding equipment of motor driven at work due to the fit-up gap of machine tool, the pine of gear engagement
Tightly, the reasons such as bearing eccentric wear, the bending of shafting, the abrasion of fixture can all cause mechanical oscillation.This vibration is for production
The harmfulness of equipment is more and more prominent.Such as vibration displacement caused by the emery wheel rotation of grinding machine, polishing can be caused excessive so that
The mismachining tolerance of workpiece increases.The whirling vibration of lathe can make workpiece and cutter produce movement, influence finished surface smoothness, drop
The quality of low product.The high rotating speed of the main shaft of large-size steam turbine at work can produce vibration, can cause serious breaking axis.
The displacement transducer that domestic mechanical vibration displacement measuring system mainly uses at present has：Analog acceleration meter, it is non-
The current vortex sensor of contact, high-precision grating scale, piezoelectric ceramics etc..Analog signal accelerometer needs expensive
A/D conversion chips, and front end signal conditioning amplifying circuit, the cost of system are very high.The noise of current vortex sensor is larger, has
Effect precision only has more than ten microns.Although grating scale can reach the precision of micron, the requirement to environment and hardware is very high,
And installation and maintenance complexity, usage amount is very limited at present.The system constituting method used has：Virtual instrument software
LabVIEW combination data collecting cards, data collecting instrument combination computer etc..Although existing method can measure vibration displacement,
But because the condition of sensor itself limits so that the limited precision of measuring system, installation is complicated, is not easy to promote.
The content of the invention
In order to solve the above technical problems, the present invention provides a kind of motor oscillating measuring instrument based on MEMS sensor, use
Digital micro-acceleration gauge FXLS8471Q is measuring cell, and high-performance low-power-consumption single-chip microcomputer MSP430F5638 is as controller, knot
Kalman filter method and cumulative summation displacement method are closed, realizes the high-acruracy survey of mechanical vibration displacement.
To realize above-mentioned technical purpose, used technical scheme is：Motor oscillating measuring instrument based on MEMS sensor,
Including micro-acceleration gauge FXLS8471Q, being motor oscillating measurement sensor, detecting motor oscillating signal, and pass through iic bus
The vibration data that sensor gathers is transmitted to single-chip microcomputer；
Single-chip microcomputer MSP430F6638, by the vibration data of collection after filtering out the kalman filter method of noise jamming except making an uproar, then
Using it is cumulative summation displacement method vibration displacement is calculated, by liquid crystal display and serial ports deliver to host computer carry out display and
Processing.
Kalman filter method of the present invention, the vibration signal that measuring instrument gathers is represented with noisy difference equation
For：
xj=axj-1+buj+wj (1)
xjRepresent the value of the vibration acceleration of current measuring instrument measurement, xj-1Represent the measured value of the vibration acceleration of previous moment.
A, b are the characteristic parameters of system, ujIt is the control input of system, wjIt is that average is zero, covariance is Q system white noise.
In order to acceleration magnitude xjIt is filtered, and realizes noise wjMinimize, define the observation z of accelerationj：
zj=hxj+vj (2)
H is the characteristic parameter of system, because measuring instrument is directly sampled using A/D module, without controlling unit, so h=1.vjIt is
Average is zero, and covariance is R observation noise.The task of Kalman filtering is exactly to zjIt is filtered, to estimate xjValue, make
Noise w, v are minimum.
The main core content of Kalman filtering is：Estimate and correct.Corresponding error is designated as priori predictor error
With posteriority predictor error ej：
Corresponding covariance is：
Prior estimate acceleration measurementWith observational variable zjAnd its predictionThe linear combination of difference constitute posteriority state
Estimation
Size reflect the difference of prediction acceleration magnitude and actual measurement acceleration, referred to as estimation is remaining or pre-
Survey renewal.K is used for redefining estimate, makes the covariance P of Posterior estimator errorkMinimum, referred to as kalman gain, and card
The core of Kalman Filtering method.After formula (7) is brought into (4), then (6) are brought into equation to K first derivations, make the derivative be
Zero, the expression formula for obtaining K is：
The process of estimating of wave filter is that the prior estimate of current state is drawn using predicting equation, predict current state variable and
The value of covariance.Trimming process is to play feedback effect, is set up using discreet value and measured value after improving current state
Posterior estimator.This process is exactly the core process of Kalman filtering, is derived by above-mentioned formula (1)-(8) and predicting equation can be written
(9) and (10), correction equation (11)-(13)：
By above-mentioned derivation, equation (9) to (13) is exactly that kalman filter method writes foundation.It is exactly filtered acceleration
Angle value.The noise covariance Q and predictor error covariance P of program initialization, are determined by empirical value Binding experiment.
Cumulative summation displacement method of the present invention is calculated vibration displacement.
Because the acceleration magnitude between any two sampled point is consecutive variations, sampling of the accelerometer to vibration data
It is only effective in sample point, therefore the displacement calculated between two sampled points can only use approximation technique, using 2 acceleration
Average value as the acceleration magnitude in this period, can thus use constant acceleration moving displacement calculation formula to calculate position
Move：
Wherein, speed calculation formula is：
Formula (14) from s0It is added to snJust obtaining total displacement is：
The cumulative item of speed in formula (16)Added up and obtained item by item by formula (15)：
Because anIt is the acceleration near equilbrium position, its value is approximately zero, so saving all a in formulan.(17) formula band
Enter (16) formula and obtain total displacement calculation formula and be：
The inside and outside power supply of FXLS8471Q numerals micro-acceleration gauge of the present invention is grounded using 0.1 μ F ceramic disc capacitors.
Present invention has the advantages that：Use FXLS8471Q to devise one kind for measurement sensor and be based on digital micro-acceleration
The rotating machinery vibrating displacement measurement system of meter.Employ kalman filter method and the vibration signal to collection be filtered,
White noise is removed, remains the actual signal of vibration.Vibration displacement is calculated using to cumulative summation displacement method.This
The precision for the measuring system measurement that the measurement result of system and existing grinding machine use is closer to, and can reflect each shape of grinding machine
The error character of state.
Brief description of the drawings
Fig. 1 is the theory diagram of the present invention；
Fig. 2 is the cumulative summation displacement method schematic diagram of the present invention；
Fig. 3 is the FXLS8471 cut-away views of the present invention；
Fig. 4 is the FXLS8471Q circuit diagrams of the present invention；
Fig. 5 is the main program flow chart of the present invention；
Fig. 6 is the test system structure figure of the present invention；
Fig. 7 is the measuring probe structural representation of the present invention；
Fig. 8 is the original vibrational waveform figure of the present invention；
Fig. 9 is the frequency analysis figure of the present invention；
The test experiments figure of Figure 10 present invention；
Figure 11 is the measurement result comparison diagram of the present invention.
Embodiment
Motor oscillating measuring instrument based on MEMS sensor, utilize the high accuracy number micro-acceleration gauge based on MEMS technology
For measuring cell, the limitation of traditional measurement method is overcome.The element has compact, low in energy consumption, and integrated level is high, directly
The advantages that output digit signals, the acceleration especially suitable for various industrial vibration objects measure for a long time.Meanwhile using high-performance
The single-chip microcomputer of the big program's memory space of low-power consumption can not only realize sensor communication and data acquisition, also as control core
The real-time display of liquid crystal display can be realized, there is good human-computer interaction function.Control software is entered using filtering algorithm to data
Row noise reduction process, with reference to displacement measurement algorithm, realize mechanical vibration displacement, the high-acruracy survey in cycle.
1st, measuring instrument master-plan
Measuring instrument is using sensor of the FXLS8471Q numerals micro-acceleration gauge of Freescale company as measurement displacement, output
Data signal single-chip microcomputer is delivered to by IIC communication bus.Use the MSP430F6638 Low Power High Performance single-chip microcomputers of TI companies
As control core.The single-chip microcomputer uses 16 RISC reduced instruction set computer frameworks, has the RAM of 18K sizes, it is possible to achieve computing
The storage of data, meet that single-chip microcomputer carries out the needs of data buffer storage during mass data computing.Inside has the Flash of 256K sizes
Program's memory space, can accommodate the conversion of vibration acceleration signal, and the calculating and displacement of vibration period data calculate scheduling algorithm.
Utilize the MSP430F6638 16 bit timing device TA traffic rate interrupted come control single chip computer to sensor.In single-chip microcomputer
Portion is handled the data of collection by software, the displacement vibrated, acceleration maximum, the vibration period, the ginseng such as frequency
Number.Shown by liquid crystal display.The system integration has 232 serial ports of industrial general, in that context it may be convenient to and calculate connection and carry out data
Transmission and preservation.The fusion of measuring instrument and intelligent terminal is realized, system architecture diagram is as shown in Figure 1.
2nd, Design on Kalman Filter
Due to sensor internal amplifying circuit, the superposition of the noises of A/D change-over circuits in signal transduction process, displacement is caused to be examined
Method of determining and calculating produces error.Therefore before displacement is calculated, it is necessary to which noise is handled.Conventional filtering algorithm has：Go extreme value
Average filter method, digital averaging filtering, medium filtering, limit filtration algorithm etc., these algorithms are all with substantial amounts of data storage
It is poor for operating basis, flatness, it is impossible to fast-changing signal is produced and timely reacted, influences the accurate calculating of displacement.
Kalman filter is a kind of efficient autoregressive filter, according to the State Estimation of previous moment and can be worked as
The observation at preceding moment estimates new State Estimation by recursive algorithm.Therefore, measuring instrument need not store a large amount of history numbers
According to calculating speed is fast, and algorithm is simplified, and is adapted to real time signal processing.
Measuring instrument is with certain frequency collection vibration signal, therefore measurement data is discrete time-domain signal, with making an uproar
The difference equation of sound is expressed as：
xj=axj-1+buj+wj (1)
xjRepresent the value of the vibration acceleration of current measuring instrument measurement, xj-1Represent the measured value of the vibration acceleration of previous moment.
A, b are the characteristic parameters of system, ujIt is the control input of system, wjIt is that average is zero, covariance is Q system white noise.
In order to acceleration magnitude xjIt is filtered, and realizes noise wjMinimize, define the observation z of accelerationj：
zj=hxj+vj (2)
H is the characteristic parameter of system, because measuring instrument is directly sampled using A/D module, without controlling unit, so h=1.vjIt is
Average is zero, and covariance is R observation noise.The task of Kalman filtering is exactly to zjIt is filtered, to estimate xjValue, make
Noise w, v are minimum.
The main core content of Kalman filtering is：Estimate and correct.Corresponding error is designated as priori predictor error
With posteriority predictor error ej：
Corresponding covariance is：
Prior estimate acceleration measurementWith observational variable zjAnd its predictionThe linear combination of difference constitute posteriority state
Estimation
Size reflect the difference of prediction acceleration magnitude and actual measurement acceleration, referred to as estimation is remaining or pre-
Survey renewal.K is used for redefining estimate, makes the covariance P of Posterior estimator errorkMinimum, referred to as kalman gain, and card
The core of Kalman Filtering method.After formula (7) is brought into (4), then (6) are brought into equation to K first derivations, make the derivative be
Zero, the expression formula for obtaining K is：
The process of estimating of wave filter is that the prior estimate of current state is drawn using predicting equation, predict current state variable and
The value of covariance.Trimming process is to play feedback effect, is set up using discreet value and measured value after improving current state
Posterior estimator.This process is exactly the core process of Kalman filtering, and predicting equation (9) and (10) can be written by above-mentioned derivation,
Correction equation (11)-(13)：
By above-mentioned derivation, equation (9) to (13) is exactly that kalman filter method writes foundation.It is exactly filtered acceleration
Angle value.The noise covariance Q and predictor error covariance P of program initialization, are determined by empirical value Binding experiment.
3rd, add up summation displacement method
Most of motor due to driving manufacturing machine rotation is constant rotational speed, so the waveform of vibration is with cyclophysis
, it can be considered simple harmonic oscillation.The characteristics of from simple harmonic oscillation, the amplitude and acceleration of waveform are directly proportional.Then vibrate from displacement
The motion of maximum to equilbrium position can be considered that acceleration subtracts acceleration movement from maximum to one of zero, and this process can be by
Fig. 2 shows.Assuming that vibration is in t0Moment is the maximum a of acceleration0, move to tnMoment to equilbrium position, acceleration zero.
Because the acceleration magnitude between any two sampled point is consecutive variations, sampling of the accelerometer to vibration only exists
Sample point is effective, therefore the displacement calculated between two sampled points can only use approximation technique, using putting down for 2 acceleration
Average can thus use constant acceleration moving displacement calculation formula to calculate displacement as the acceleration magnitude in this period：
Wherein, speed calculation formula is：
Formula (14) from s0It is added to snJust obtaining total displacement is：
The cumulative item of speed in formula (16)Added up and obtained item by item by formula (15)：
Because anIt is the acceleration near equilbrium position, its value is approximately zero, so saving all a in formulan.(17) formula band
Enter (16) formula and obtain total displacement calculation formula and be：
It is obvious that t in actual operation0Moment is not necessarily just in the peak of vibration, anAlso not necessarily in equilbrium position,
Error is also brought along to calculate displacement using average acceleration simultaneously, but the sampling rate of high speed can ensure that sampled point is enough
Ideal point is approached, this error will not produce serious influence to calculating, and thus calculating the error brought can be right in use
Result of calculation is demarcated to find the error relationship between calculated value and actual value, is then write in a program directly to (18) formula
Result of calculation amendment.This method is commonly used in engineering, has good precision and operation efficiency.
4th, accelerometer hardware circuit design
FXLS8471Q chips are powered using 1.95V-3.6V Width funtions.It has been internally integrated for measuring three couple of 3-axis acceleration
Differential capacitor, there is that ± 2g, ± 4g range are optional, and for 14 bit resolution ADC in ± 2g ranges, resolution ratio can reach 0.244mg/
LSB, output data rate 1.563Hz-800Hz, have in 200Hz bandwidthLow noise tonal density, internal structure
Figure is shown in Fig. 3.
According to the requirement of the stability of probe power circuit design, FXLS8471Q inside and outside power supply uses 0.1
μ F ceramic disc capacitors are grounded, and are disturbed with filtering out the high-frequency ac carried by Switching Power Supply, SCL and SDA pins connect pull-up resistor to protect
The height for demonstrate,proving level is effective.SA0 and SA1 pins are grounded, and the address for making sensor is 0x1E for single-chip microcomputer identification.Circuit is as schemed
Shown in 4.
5th, system initialization is set
5.1 clocks initialize
Single-chip microcomputer uses internal clock source REFOCLK (the Referance out clock) conduct of crystal oscillator speed for 32.768kHz
Each clock source, between REFOCLK and system clock, adds FLL (Frequence lock loop) inside single-chip microcomputer
Unit, using DCO (Digitally controlled oscillator) function inside FLL come the frequency to system clock
It is adjusted, improves the arithmetic speed of displacement algorithm.DCO output clock frequencies DCOCLK calculation formula is as follows：
fDCO=(N+1) fFLLREFCLK (19)
Wherein fFLLREFCLKFor 32.768kHz, due to requiring that the operation frequency of main program is 25MHz, and register setting requirements are
Integer, so calculating N as 762.
5.2 timers initialize
The effect of timer is to be accurately controlled the sampling interval, is interrupting the IIC programmed acquisition data of intrinsic call sensor.It is fixed
When device timing length be to overflow to realize by the counting of counter, timer is produced using counting up when counting full
The method interrupted is overflowed, counter TA1CCR0 automatic clears after spilling, using SMCLK as count pulse source.
The frequency setting that sampling interval namely interrupts is 1250Hz, SMCLK 25MHz, and the calculating of counter upper limit is public
Formula is：
The value for drawing TA1CCR0 registers is 19999.
5.3 accelerometer function settings
FXLS8471Q uses iic bus and single chip communication, and single-chip microcomputer is write using iic bus to the register of accelerometer
Corresponding numerical value sets function.According to the design requirement to sensor function, the register mainly set has two, address point
It is not 0x2A and 0x2B, corresponds to control register 1 (CTRL_REG1), control register 2 (CTRL_REG2) respectively.
The parameter of 0x2A major controls has：Traffic rate under sleep pattern, data output rate, reduce noise, quickly
Read, work standby mode etc..According to design requirement, using non-sleep pattern, data output rate 400Hz, low noise mould
Formula, normal data are read, and the register value of setting is：0x11.
The parameter of 0x2B major controls has：Self test mode, enable and reset, over-sampling pattern during sleep, sleep mode automatically, just
Often over-sampling pattern during work etc..According to design requirement, using self-test function is forbidden, forbid resetting, forbid sleep mode automatically, it is high
Resolution model.The register value of setting is：0x02.
After 16 complement of two's two's complement data that sensor output is collected inside single-chip microcomputer, it is necessary to which data are carried out with weight
Build.What sensing data register DATAX0 was stored is the least-significant byte of data, and what DATAX1 was stored is the most-significant byte of data.It is wherein high
The 0-5 positions of 8 are data, and 6-7 positions are symbols, and the 0-1 positions of least-significant byte are rooms, and 2-7 positions are data.Then actual acceleration is corresponding
Binary code Temp calculated by formula (21)：
Temp=(DATA1 × 256+DATA0)/4 (21)
6 measuring instrument Software for Design
6.1 acceleration calculation programmings
By formula (21) obtain be sensor measurement overall acceleration, be containing the value that offsets.Accelerometer itself is static
When bear between+1g~-1g acceleration skew, when electric airborne measurements are vibrated, this value will necessarily disturb real acceleration
Angle value, therefore, this skew is handled.
First pass through bubbling algorithm and draw vibration acceleration maximum and minimum value in several vibration periods, obtain average
Value, this average value is exactly the equilbrium position in displacement accumulation algorithm.Then with four points where the acceleration maximum measured
One of acceleration information in the cycle subtract this equilbrium position acceleration magnitude, that removes+1g~-1g acceleration is inclined
Shifting amount, obtain the real vibration acceleration g values of each sampled point.
6.2 general design of software
Survey Software by：SCM system is initialized, display screen initialization, accelerometer initialization, and timer A is interrupted, and IIC leads to
Letter, the calculating of peak acceleration, a quarter vibration period selects, displacement it is cumulative etc..The main program flow chart of software is shown in
Fig. 5.
7 measurement experiments and data analysis
7.1 test systems are built
Vibration test system is adjusted by AC servo motor, special servo controller, gear drive, flywheel, eccentric vibrating
The part such as screw, sensor, SCM system, liquid crystal display, host computer Survey Software is saved to form.The system is by AC servo
Motor passes through gear mechanism flywheel driven constant velocity rotation.Servo controller is adjusted by host computer with accurate adjustment motor to turn
Speed.There is eccentric screw on flywheel, by the nut of activity on screw, the amplitude of vibration can be adjusted by the position of nut.Respectively
System is tested by frequency measurement and displacement measurement experiment.Structure chart is as shown in Figure 6.
In the test of reality, the hardware circuit board of micro-acceleration gauge is encapsulated in diameter 3cm cylindrical stainless steel metal
Shield in shell, using shielding shell outside electromagnetic interference can be avoided to have an impact the signal of sensor.Bottom epoxy
Resin is fixed and is tamping, and outer casing bottom is sealed by neodymium-iron-boron steel disc.It can be adsorbed during use by manual operation in whirler
The optional position of tool metal surface, as shown in Figure 7.
7.2 vibration frequency test experiments
Sensor is placed on fly-wheel motor fixed mount, the principle vibrated according to solid transmission, the eccentric vibrating of flywheel can wait frequency
Rate is delivered on sensor, the rotating speed for carrying out analysis can by gathering sensing data and drawing flywheel.Pass through sensor
The data of collection are delivered to host computer by serial ports and drawn.Exemplified by actual vibration when 2800r/min, waveform such as Fig. 8 institutes
Show.It is the approximate sine wave for having periodic property in it can be seen from the figure that vibrational waveform, there is shown during motor periodic vibration
Waveform, substantial amounts of noise has been mingled with it in synchronous signal.
Filtering is tracked to Wave data by kalman filter method, then pair also have noise data carry out it is bad
Point is rejected and fitting draws the data of a vibrational waveform afterwards, then is entered by fft algorithm and carried out spectrum analysis to time-domain signal,
Show that the spectrogram of vibration signal is as shown in Figure 9.
128 points of FFT computings are employed in software, and the point of each transverse axis represents a frequency values, in FFT result
The frequency of middle amplitude peak is correspondingly 47Hz, and the rotating speed that can calculate motor is 2820r/min, and existing error is due to
Caused by FFT operation result round numbers frequencies.It can be obtained by the no-load speed of motor, per poor 1Hz frequencies, speed error 48.833
Turn, test 20 turns of the error drawn within the scope of this.The vibrational waveform and actual machine for illustrating measuring instrument measurement shake
Dynamic waveform is accurate on the cycle.
7.3 vibration displacement test experiments
Different vibration amplitudes is set in vibration test system by the position of adjusting nut, so as to test and correct displacement
Algorithm.Because the system is directed to the motor oscillating measurement of precision grinder, technological requirement is to refine displacement no more than 10 μm, therefore
It is real to carry out multiplicating as vibration amplitude is referred to every 1 μm of amplitude for interval adjustment flywheel in the range of 1 μm to 10 μm
Test.Each experimental result is after Fitting Analysis, displacement error that amendment accumulation summation is drawn, then measures, draw compared with
It is as shown in Figure 10 for accurate experimental result.
By the displacement of measurement and the reference bit phase shift ratio of vibration, the worst error of measuring instrument is 0.25 μm, average to miss
Difference is 0.154 μm, and the worst error for being fitted the experiment curv slope drawn is 0.0117, and the error of intercept is 0.05264.Explanation
The measurement of displacement has the good linearity and measurement accuracy.
7.4 vibration displacements measure contrast experiment
The vibration data of the in-process measuring instrument produced on motorcycle engine crankshaft grinding machine with Italian Marposs S.P.A is carried out
Control experiment.Using the measured value of in-process measuring instrument as canonical reference, the grinding wheel drive mitor of crankshaft grinding machine is kept in whole work
At the uniform velocity rotate, rotating speed 1480r/min.Object is contrasted by measurement of the grinding process of multiple bent axles, from the standby shape of emery wheel idle running
State starts, and finishing emery wheel to grinding retracts original position to terminate, by multigroup measurement peak value under two measuring instrument different conditions
Carry out comparing analysis.As shown in figure 11, the line being linked to be by round dot is the measurement result of in-process measuring instrument, and triangle line is this
The result of measuring instrument.In order to distinguish, after the measuring instrument result to be added to 2 μm of offset, two groups of data are plotted in one
It is compared in figure.
Drawn after carrying out global analysis to the data of measurement, maximum measurement error occurs in withdrawing state, is
0.67μm.Minimum measurement error occurs when standby after push broach, is 0.3 μm.From data summarization as can be seen that new type measuring instrument exists
The vibration displacement peak value and the result of horse Persian measuring instrument measured during different conditions is identical.After illustrating corrected algorithm
Measuring instrument being capable of accurate measurement vibration displacement.
Claims (4)
1. the motor oscillating measuring instrument based on MEMS sensor, it is characterised in that：Including,
Micro-acceleration gauge FXLS8471Q, it is motor oscillating measurement sensor, detects motor oscillating signal, and pass through iic bus handle
The vibration data of sensor collection is transmitted to single-chip microcomputer；
Single-chip microcomputer MSP430F6638, by the vibration data of collection after filtering out the kalman filter method of noise jamming except making an uproar, then
Vibration displacement is calculated using cumulative summation displacement method, delivering to host computer by liquid crystal display and serial ports is shown and located
Reason.
2. the motor oscillating measuring instrument based on MEMS sensor as claimed in claim 1, it is characterised in that：Described Kalman
Filtering method is to be expressed as the vibration signal that measuring instrument gathers with noisy difference equation：
xj=axj-1+buj+wj (1)
xjRepresent the value of the vibration acceleration of current measuring instrument measurement, xj-1The measured value of the vibration acceleration of previous moment is represented,
A, b are the characteristic parameters of system, ujIt is the control input of system, wjIt is that average is zero, covariance is Q system white noise；
In order to acceleration magnitude xjIt is filtered, and realizes noise wjMinimize, define the observation z of accelerationj：
zj=hxj+vj (2)
H is the characteristic parameter of system, because measuring instrument is directly sampled using A/D module, without controlling unit, so h=1, vjIt is
Average is zero, and covariance is R observation noise；
Corresponding error is designated as priori predictor errorWith posteriority predictor error ej：
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<mo>=</mo>
<mi>a</mi>
<msubsup>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>-</mo>
</msubsup>
<mo>+</mo>
<msub>
<mi>bu</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msubsup>
<mi>P</mi>
<mi>j</mi>
<mo>-</mo>
</msubsup>
<mo>=</mo>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
<msub>
<mi>P</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<mi>Q</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>K</mi>
<mo>=</mo>
<msubsup>
<mi>P</mi>
<mi>j</mi>
<mo>-</mo>
</msubsup>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>P</mi>
<mi>j</mi>
<mo>-</mo>
</msubsup>
<mo>+</mo>
<mi>R</mi>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>P</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<msubsup>
<mi>P</mi>
<mi>j</mi>
<mo>-</mo>
</msubsup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>k</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
Equation (9) to (13) is exactly that kalman filter method writes foundation；For filtered acceleration magnitude, program initialization
Noise covariance Q and predictor error covariance P, determined by empirical value Binding experiment.
3. the motor oscillating measuring instrument based on MEMS sensor as claimed in claim 1, it is characterised in that：It is described cumulative to ask
It is with displacement method, vibration displacement is calculated, accelerometer is sampled to vibration data, and two are calculated using approximation technique
Displacement between sampled point, using the average value of 2 acceleration as the acceleration magnitude in this period, transported with constant acceleration
Dynamic displacement calculation formula calculates displacement：
<mrow>
<msub>
<mi>s</mi>
<mi>n</mi>
</msub>
<mo>=</mo>
<msub>
<mi>v</mi>
<mi>n</mi>
</msub>
<mi>t</mi>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>a</mi>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mi>n</mi>
</msub>
</mrow>
<mn>2</mn>
</mfrac>
<mo>)</mo>
</mrow>
<msup>
<mi>t</mi>
<mi>n</mi>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, speed calculation formula is：
<mrow>
<msub>
<mi>v</mi>
<mi>n</mi>
</msub>
<mo>=</mo>
<msub>
<mi>v</mi>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>a</mi>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mi>n</mi>
</msub>
</mrow>
<mn>2</mn>
</mfrac>
<mi>t</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
Formula (14) from s0It is added to snJust obtaining total displacement is：
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mi>n</mi>
</mrow>
</munderover>
<msub>
<mi>s</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mi>n</mi>
</mrow>
</munderover>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mi>t</mi>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<mn>2</mn>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</munderover>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>16</mn>
<mo>)</mo>
</mrow>
</mrow>
The cumulative item of speed in formula (16)Added up and obtained item by item by formula (15)：
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mi>n</mi>
</mrow>
</munderover>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mi>t</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msub>
<mi>na</mi>
<mn>0</mn>
</msub>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</munderover>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>-</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mi>n</mi>
</mrow>
</munderover>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>17</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, anIt is the acceleration near equilbrium position, its value is approximately zero, that is, saves all a in formulan, (17) formula brings into
(16) formula obtains total displacement calculation formula and is：
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mi>n</mi>
</mrow>
</munderover>
<msub>
<mi>s</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>n</mi>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mo>)</mo>
</mrow>
<msub>
<mi>a</mi>
<mn>0</mn>
</msub>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</munderover>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>-</mo>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>18</mn>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
4. the motor oscillating measuring instrument based on MEMS sensor as claimed in claim 1, it is characterised in that：Described micro- acceleration
Degree meter FXLS8471Q inside and outside power supply is grounded using 0.1 μ F ceramic disc capacitors.
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Cited By (3)
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| CN109388392A (en) * | 2018-10-31 | 2019-02-26 | 陈黎明 | A kind of command processing method |
| WO2019230520A1 (en) * | 2018-05-28 | 2019-12-05 | 光洋電子工業株式会社 | Abnormality diagnosis system and vibration sensor |
| CN115693368A (en) * | 2021-07-23 | 2023-02-03 | 北京科益虹源光电技术有限公司 | Vibration control method and device of double-cavity excimer laser |
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Cited By (4)
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| WO2019230520A1 (en) * | 2018-05-28 | 2019-12-05 | 光洋電子工業株式会社 | Abnormality diagnosis system and vibration sensor |
| JP2019207126A (en) * | 2018-05-28 | 2019-12-05 | 光洋電子工業株式会社 | Abnormality diagnosis system and oscillation sensor |
| CN109388392A (en) * | 2018-10-31 | 2019-02-26 | 陈黎明 | A kind of command processing method |
| CN115693368A (en) * | 2021-07-23 | 2023-02-03 | 北京科益虹源光电技术有限公司 | Vibration control method and device of double-cavity excimer laser |
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