CN105656449B - A kind of electric spark voltage across poles signal processing method based on kalman filter - Google Patents
A kind of electric spark voltage across poles signal processing method based on kalman filter Download PDFInfo
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H17/02—Frequency selective networks
- H03H17/0202—Two or more dimensional filters; Filters for complex signals
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H2017/0072—Theoretical filter design
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H17/02—Frequency selective networks
- H03H17/0202—Two or more dimensional filters; Filters for complex signals
- H03H2017/0205—Kalman filters
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Abstract
The present invention relates to a kind of electric spark voltage across poles signal processing method based on kalman filter, assuming that voltage across poles is to be produced by white noise by a linear filter, on the basis of this hypothesis, gain matrix method is newly ceased using Yule Walker to handle the voltage across poles signal of collection, it can draw a transmission function from white noise to voltage across poles, then as the state equation needed for the transmission function is converted into design kalman filter.The noise jamming in the voltage across poles signal of collection can be greatly decreased in the present invention, so as to avoid the servo motion in edm process is influenced due to noise reasons, reduce some unnecessary axis servomotors and move back and forth, lift the efficiency of electrical discharge machining.
Description
Technical Field
The invention relates to electric spark process control, belongs to the technical field of special machining, and particularly relates to a Kalman filter design method for detecting voltage between electric spark poles.
Background
Electrical discharge machining is a process of removing material from a workpiece by a series of spark discharges between the workpiece and an electrode. Electrical discharge machining is commonly used in the fields of molds, aerospace, medical instruments and the like. There are many different places where electrical discharge machining is compared to conventional milling. For example, the speed of the electric discharge machining is determined by the machining gap state, since whether the machining direction is forward or backward is determined according to the measured gap state, and the forward or backward speed is determined according to the difference between the currently measured gap voltage and the set servo voltage, unlike the given speed feed according to the milling. Since the interpolar voltage determines the direction and speed of movement of the servo axis, detection and estimation of the interpolar voltage is important. The most commonly used method for detecting the inter-pole voltage at present is an average voltage method and a moving average voltage method, in which the moving average voltage is calculated from the inter-pole voltage in the past several cycles to the current sampling cycle, and the calculation result is compared with a preset servo voltage, as shown in fig. 1.
The chinese patent application publication No. 101791728A, "electrostatic induction micro electric discharge machining non-contact interelectrode voltage detection method and circuit design" proposes a non-contact interelectrode voltage detection method for electrostatic induction micro electric discharge machining. The method used for this is for detecting the interelectrode voltage, but is generally implemented by a hardware method. Moreover, the method still cannot solve the problem of noise interference in the interelectrode voltage signal. In the invention, for detecting the subsequent steps, the inter-pole voltage is supposed to be generated by white noise through a linear filter, and on the basis of the hypothesis, a Kalman filtering model is established to carry out Kalman filtering processing on the inter-pole voltage signal so as to reduce noise interference in the signal, so the content of the model is completely different from that of the invention.
Due to strong electric field and magnetic field interference generated during electric spark machining, collected interelectrode voltage contains strong noise interference, and in such a case, the adoption of a Kalman filter is a good choice. Since the kalman filter is an optimal linear filter, the estimation error of the signal can be considered as white noise. The design of the kalman filter is based on the state equation of the system and the autocovariance matrix of the signal, and the design can be carried out only with the information. For electrical discharge machining, however, both the equation of state and the autocovariance matrix must be derived from the acquired interpolar voltages.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides the method for processing the voltage signal between the electric spark poles based on the Kalman filter, which can greatly reduce the noise interference in the acquired voltage signal between the electric sparks poles, avoid the influence on the servo motion in the electric spark machining process due to the noise, reduce the unnecessary back-and-forth motion of a servo shaft and improve the efficiency of the electric spark machining.
The technical solution of the invention is as follows:
a method for processing an electric spark interpolar voltage signal based on a Kalman filter comprises the following steps:
the method comprises the following steps: acquiring an interelectrode voltage signal in real time, and transmitting the interelectrode voltage signal to a numerical control system for calculating a subsequent transfer function, a state equation and a steady-state gain;
step two: assuming that the interelectrode voltage is generated by white noise through a linear filter, establishing a transfer function between the white noise and the interelectrode voltage, and converting the transfer function into a standard controllable equation of state;
step three: solving an autocovariance matrix between the measurement noise and the process noise and a cross covariance matrix between the measurement noise and the process noise by using a state equation and a white noise variance so as to obtain a steady gain between the interelectrode voltage and the estimated voltage;
step four: designing a Kalman filter according to a state equation and a covariance matrix;
step five: the Kalman filter model is utilized to process the interelectrode voltage signal, the filtered interelectrode voltage is used as a feedback signal of the servo controller, and noise in the interelectrode voltage signal can be greatly reduced, so that unnecessary servo axis movement is reduced, the machining efficiency is improved, and the machining service is realized. The unnecessary servo axis movement means that the voltage signal which can be normally processed originally is smaller than the minimum threshold value set by the current servo movement due to the interference of noise, so that the numerical control system considers that the current short circuit is generated, or the servo axis backspacing is generated, or the maximum threshold value is exceeded, so that the numerical control system considers that the current open circuit is generated, and the servo axis overshoot is caused.
The principle of the invention is as follows:
the invention assumes that the interelectrode voltage is generated by white noise through a linear filter, and on the basis of the assumption, a Yule-Walker auto-covariance method is used for processing the collected interelectrode voltage signal, so as to obtain a transfer function from the white noise to the interelectrode voltage. Converted to an equation of state by this transfer function. The transfer function between white noise and interelectrode voltage can be expressed as
Where q is-1Is a time-shift operator, e (k) is white noise, aiI is 1 … n, b is a coefficient on the denominator0Is a constant that makes the steady-state gain 1, and y (k) is the interelectrode voltage. In order to obtain equation (1), the coefficient is solved by using Yule-Walker auto-covariance method, which is as follows:
where r (k) is the autocovariance at time offset k, k ranging from 0 to M. Equation (2) can be expressed in a more compact matrix form
Rc＝r (3)
Where R is the autocovariance matrix, so that a coefficient vector c can be obtained
c＝R-1The relationship between r (4) coefficient vector c and coefficient vector a can be expressed as
c＝[c1,c2,…,cM]＝[-a1,-a2,…,-aM](5)
After having the transfer equation, it is desirable to test the assumption that the input signal is white noise. White to interelectrode voltage signal transfer function can be usedInverse function of noise to interpolar voltage transfer functionTo detect whether the input e (k) of the transfer function is white noise. e (k) can be prepared from
And (6) obtaining. White noise can be judged by the following conditions:
from the transfer function equation (1), the equation of state can be solved in a standard controllable form
y(k)＝[(b1-b0a1)(b2-b0a2)…(bn-b0an)]x(k)+Hw(k)+v(k)
Where w (k) is process noise and v (k) is measurement noise. Equation (8) can be expressed in a more compact matrix form:
x(k+1)＝Ax(k)+Gw(k)
y(k)＝Cx(k)+Hw(k)+v(k) (9)
wherein,
C＝[(b1-b0a1)(b2-b0a2)…(bn-b0an)],H＝b0。
the process noise w (k), the measurement noise v (k) and the white noise e (k) can be expressed as
w(k)＝e(k) (10)
v(k)＝e(k) (11)
In the design of the Kalman filter, two autocovariance matrixes and one cross-covariance matrix are needed, and for the convenience of derivation of the variance matrixes, the noise in the composite process is defined firstlyAnd composite measurement noise
With noise of composite processAnd composite measurement noiseThe equation of state can be written as
From equation of state (14), an autocovariance matrix of the complex process noise can be derived
The autocovariance matrix of the composite measurement noise can be obtained by:
composite process noiseAnd composite measurement noiseThe cross covariance matrix between can be expressed as:
wherein three variance matrices Q (k), R (k) and N (k) are used and are respectively defined as
Q(k)＝E(w(k)wT(k)) (18)
R(k)＝E(v(k)vT(k)) (19)
N(k)＝E(w(k)vT(k)) (20)
After the state equation and the information of the three variance matrixes are available, the Kalman filter can be designed. Posterior state vectorCan be expressed as a prior stateA correction of (1).
Where M (k) is the innovation gain matrix,is the prediction error. L (k) is the Kalman gain matrix.
The state estimation error matrix is needed in the calculation and can be expressed as:
after the transient state process has elapsed, P (k) enters steady state. To reduce the amount of real-time calculations, a steady state P may be applied during spark machining. The steady state P can be calculated by
P(1|0)＝pI (27)
Where P (1|0) is the initial value of P, I is the identity matrix, and P is a constant, it may be taken as 100.
During the electric spark machining process, the measured interelectrode voltage is filtered by a Kalman filter. To make the range of the processed filtering voltage value sumThe acquired raw voltage remains within the same reading range and the signals from the raw signal y (k) to the filtered one have to be foundThe steady state gain in between. Thus obtainingThe inverse of the steady state gain can then be multiplied to maintain the input and output voltages of the kalman filter in the same range.
From y (k) toSteady state gain of
The equation of state is expressed as follows:
by z-transforming equations (29) to (31), we can obtain
Thus, it is possible to provideThe transfer function between is:
wherein:therefore substituting z to 1The transfer function between can be obtained from y (k) toSteady state gain of
Compared with the prior art, the original interelectrode voltage signal diagram has strong noise interference, under the condition, the actual state of the current machining cannot be reflected, and the interference of the noise causes that the voltage signal of the original normal machining is smaller than the minimum threshold set by the current servo motion, so that the numerical control system considers the current machining short circuit and generates the servo shaft short circuit backspacing, or exceeds the maximum threshold to cause the numerical control system to consider the current machining open circuit, so that the servo shaft overshooting is caused, and the normal machining is influenced. The invention can greatly reduce the noise interference in the acquired interelectrode voltage signals, thereby avoiding the influence on the servo motion in the electric spark machining process due to the noise, reducing the unnecessary back-and-forth motion of the servo shaft and improving the efficiency of the electric spark machining.
Drawings
FIG. 1 is a servo control diagram of gap voltage detection of the present invention.
Fig. 2 is a schematic diagram of an implementation platform of the present invention.
Fig. 3 is a diagram of inter-pole voltage signal acquisition according to an embodiment of the present invention, wherein (a) is an unprocessed raw diagram and (b) is kalman filtered.
FIG. 4 is a graph of the processing rate of a 10mm deep hole processed in the same manner for different processing of the interpolar voltage signals, respectively, in one embodiment.
Detailed Description
The specific embodiment of the invention is implemented on an HE 70 electric spark forming machine manufactured by Shanghai Hanba electromechanical Co., Ltd, a schematic view of a platform is shown in FIG. 2, and the motion control of the whole machine tool is realized by a PMAC motion control card. The real-time sampling period set by the PC is 2ms, the servo period of the PMAC motion control card is 0.88ms, and the PC and the PMCA motion control card are realized through a DPRAM module on the PMAC motion control card. The interelectrode voltage signal is collected through an ACC-28A card connected with a PMAC control card and is transmitted to a PC machine in real time through a DPRAM module.
Example (b):
first, assuming that the interelectrode voltage is generated by white noise through a linear filter, a transfer function of the white noise and the interelectrode voltage is established, and the relevant parameters in equation (1) are obtained, as shown in table 1:
TABLE 1 dynamic model sampling period of gap Voltage 2ms
Then, a karman filter based on the above model was used to machine a small hole of 10mm in depth, and a comparative experiment was performed with a sliding average filter using a graphite rod electrode of Φ 10 as a workpiece, and the workpiece was a tool steel. The processing conditions are shown in table 2 below:
TABLE 2 pinhole processing experiment parameters
| Servo voltage | Peak current | Pulse width | Pulse interval | Time of lifting the cutter | Lifting period |
| 49V | 28A | 60μs | 40μs | 1s | 5s |
The moving average filter is defined to process the interpolar voltage signal acquired in the PMAC sampling period as follows:
where u (k) is the sampled signal for the current sampling period.
In the specific embodiment, the kalman filtering effect is shown in fig. 3, the original inter-electrode voltage signal diagram has strong noise interference, in this case, the actual state of the current machining cannot be reflected, and there is a possibility that the voltage signal is smaller than the minimum threshold set by the current servo motion due to the noise interference, so that unnecessary short-circuit backspacing is generated, or the voltage signal exceeds the maximum threshold, so that the numerical control system considers that the current open circuit is generated, thereby causing overshoot and affecting the normal machining.
The specific processing results are shown in table 3:
TABLE 3 comparison of the results of two filtering processes
Wherein the back-off time ratio is defined as follows:
wherein, TretractFor a back-off time, TtotalIncluding the total machining time of the lifting of the tool.
As can be seen from table 3, the results obtained using kalman filtering are better than the moving average filtering, regardless of the processing time or the back-off time ratio, and specifically the speed comparison from 1mm processing to 10mm is shown in fig. 4. In addition, in terms of processing effect, carbon deposition is generated by adopting the sliding average filtering for 3 times, and no carbon deposition is generated by adopting the Kalman filtering for 3 times, namely the processing stability of the Kalman filtering is better than that of the sliding average filtering.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It will be apparent to those skilled in the art that many modifications and variations can be made in the concept of the present invention without departing from its scope. Therefore, the technical solutions that can be obtained by a person skilled in the art by changing the materials or the characteristics based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (2)
1. A method for processing an interelectrode voltage signal based on a Kalman filter is characterized by comprising the following steps:
the method comprises the following steps: acquiring an interelectrode voltage signal in real time and transmitting the interelectrode voltage signal to a numerical control system;
step two: assuming that the interelectrode voltage is generated by white noise through a linear filter, establishing a transfer function between the white noise and the interelectrode voltage, and converting the transfer function into a standard controllable equation of state;
the transfer function between the white noise and the interelectrode voltage is expressed as:
<mrow> <mover> <mi>G</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <msup> <mi>q</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>e</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <msub> <mi>b</mi> <mn>0</mn> </msub> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msup> <mi>q</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mo>...</mo> <mo>+</mo> <msub> <mi>a</mi> <mi>n</mi> </msub> <msup> <mi>q</mi> <mrow> <mo>-</mo> <mi>n</mi> </mrow> </msup> </mrow> </mfrac> </mrow>
in the formula, q-1Is a time-shift operator, e (k) is white noise, aiI is 1 … n, b is a coefficient on the denominator0Is a constant that gives a steady state gain of 1, and y (k) is the filtered white noise;
the transfer function adopts Yule-Walker autocovariance to solve the coefficient, and the formula is as follows:
wherein r (k) is the autocovariance at time offset k, k ranging from 0 to M;
step three: solving an autocovariance matrix between the measurement noise and the process noise and a cross covariance matrix between the measurement noise and the process noise by using a state equation and a white noise variance so as to obtain a steady gain between the interelectrode voltage and the estimated voltage;
step four: designing a Kalman filter according to a state equation and a covariance matrix;
step five: and processing the interelectrode voltage signal by using a Kalman filter model, wherein the filtered interelectrode voltage is used as a feedback signal of the servo controller.
2. The method for processing the electric spark interpolar voltage signal based on the kalman filter of claim 1, wherein the step one collects the interpolar voltage by an ACC-28A card and transmits the collected interpolar voltage to a numerical control system in real time by a DPRAM module of a PMAC.
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| CN104729492A (en) * | 2013-12-18 | 2015-06-24 | 广西大学 | Optical fiber gyroscope signal processing method based on Kalman filtering |
| CN105092711A (en) * | 2015-08-04 | 2015-11-25 | 哈尔滨工业大学 | Steel rail crack acoustic emission signal detecting and denoising method based on Kalman filtering |
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| CN104729492A (en) * | 2013-12-18 | 2015-06-24 | 广西大学 | Optical fiber gyroscope signal processing method based on Kalman filtering |
| CN105092711A (en) * | 2015-08-04 | 2015-11-25 | 哈尔滨工业大学 | Steel rail crack acoustic emission signal detecting and denoising method based on Kalman filtering |
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| "Evaluation of linear Kalman filter processing geodetic kinematic measurements";Sonja Bogatin等;《Measurement》;20080630;第41卷(第5期);第561-578页 * |
| "电火花加工放电状态的自适应滤波";周明等;《哈尔滨工程大学学报》;20151130;第36卷(第11期);第1522-1525页 * |
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