CN105337588A - Combined integral filtering system - Google Patents

Abstract

The invention relates to a combined integral filtering system. The combined integral filtering system is characterized in that a first combined integral link and a time delay link are included, and signals from the first combined integral link and the time delay link are superposed to a second combined integral link; the overall transfer function of the combined integral filtering system is shown in the specification, the time delay constants tau1, tau2, tau3 and the constant K are adjusted according to requirements, and low-pass, high-pass and band-pass filtering is achieved. The filtered-out signals are stable, the signals with only one frequency are contained, noise is low, and the signals are smooth.

Description

A kind of combined integral filtering system

Technical field

The present invention relates to industrial control field, particularly relate to a kind of combined integral filtering system.

Background technology

Environment residing for Industry Control object is comparatively severe, and interference source is a lot, as strong electromagnetic, ambient temperature frequent variations, especially signal input channel, sampled value will be used for data processing and system fading margin, and the accuracy of sampled value is significant for the raising of robot control system(RCS) performance.Therefore in order to reduce the impact of interference on sampled value, the performance of guarantee system, first will carry out signal filtering to sampled value before data processing of being everlasting, to improve authenticity, the accuracy of signal, eliminate or reduce various interference and noise, improving the reliability of computer system further.

Filtering technique is often divided into two classes: analog filtering and digital filtering technique.Digital filtering technique overcomes the shortcoming of a lot of analog filtering, and mainly realize with programmed algorithm, reliability is high, good stability, can take different filtering methods according to signal type difference, very convenient.The goal in research of digital filtering algorithm can use up the interference removing other possible greatly after the signal digital process that can make to collect after digital filtering algorithm process, reverts to its actual value.

Enter into digital times now, people extremely pay close attention to Digital Signal Processing.Along with computer and microelectric technique develop, signal processing theory and algorithm obtain primary study, and be widely used in the field such as voice image processing, digital communication, analysis of spectrum, pattern recognition, automatically control, filter acts on significantly in digital signal processing.Digital filter be input as a Serial No., after mathematical operation rule, export as another Serial No..Change the relative scale of frequency content contained by input signal by operation relation or eliminate the signal of some frequency, by useful signal constituents extraction out, realizing the object weakening interference component.

Digital filter obtains general application, digital filter characteristic difference, hinders its application in other respects.As iir digital filter still has the excellent characteristic of analog filter, this sacrifices linear phase for cost.Namely utilize the methods such as Butterworth, Chebyshev and ellipse to complete digital filter design, make its width product characteristic close to ideal filter, the filter characteristic of acquisition is nonlinear often.Finite Impulse Response filter can use window function, frequency sampling, weighted least squares at any amplitude of design and frequency characteristic filter.

Classical digital filter is not enough:

(1) given technical indicator, select a kind of in multi-design methods of comforming, classical technology implies a lot of filter design method;

(2) iir filter transfer function limit is at unit circle Arbitrary distribution, and available lower-order number obtains multiple choices, and memory cell is few, high efficiency.Transfer function limit may be in outside unit circle, causes system unstable.Iir digital filter phase place is nonlinear, the non-linear decision selectivity quality of phase place;

(3) the transfer function limit of FIR filter is in initial point always, and selectivity is more, has come with high exponent number, and under design of filter index same case, the exponent number required by FIR filter than iir filter height 5-10 doubly, spends high, postpones a lot.

Summary of the invention

Technical problem to be solved by this invention is to provide a kind of combined integral filtering system, can improve filter effect.

The technical solution adopted for the present invention to solve the technical problems is: provide a kind of combined integral filtering system, comprise the first combined integral link and time delay process, described first combined integral link and time delay process Signal averaging to the second combined integral link out; The overall transfer function of described combined integral filtering system is wherein, for pure lag system, τ _itime delay constant; Regulate time delay constant τ according to demand ₁, τ ₂, τ ₃and constant K realizes low pass, high pass and bandpass filtering.

Described first combined integral link is low pass filter, and its transfer function is

The high pass filter that described first combined integral link and time delay process are formed, its transfer function is $g_h\left(s\right)=e^{-{\mathrm{\τ}}_{2}s}-\frac{1}{{\mathrm{\τ}}_{1}s}(1-e^{-{\mathrm{\τ}}_{1}s}).$

The transfer function of described second combined integral link is

Beneficial effect

Owing to have employed above-mentioned technical scheme, the present invention compared with prior art, has following advantage and good effect:

The present invention adopts combined integral and superposes with Time Delay, determines Selecting parameter principle, designs low pass, high pass, band pass filter respectively, realizes industrial collection signal filtering.Based on above reason, the special system performance analysis method for combined integral process of research and applying at other field of combined integral link have important theory and realistic meaning.

The present invention adopts the signal gone out based on the advanced filtering algorithm filtering of combined integral system very stable, and the signal only containing a kind of frequency, noise is few, signal smoothing.The Butterworth filter of contrast iir digital filter design, in filtered signal, noise is more, adopts combined integral system filter effect better.

Accompanying drawing explanation

Fig. 1 is the advanced filtering algorithm block diagram of combined integral system of the present invention.

Fig. 2 is the concrete block diagram of combined integral filtering system of the present invention.

Embodiment

Below in conjunction with specific embodiment, set forth the present invention further.Should be understood that these embodiments are only not used in for illustration of the present invention to limit the scope of the invention.In addition should be understood that those skilled in the art can make various changes or modifications the present invention, and these equivalent form of values fall within the application's appended claims limited range equally after the content of having read the present invention's instruction.

Embodiments of the present invention relate to a kind of combined integral filtering system, adopt combined integral and superpose with Time Delay, determine Selecting parameter principle, design low pass, high pass, band pass filter respectively, realize industrial collection signal filtering.

Principle of the present invention is:

(1) a kind of new filtering algorithm put forward on the basis of digital filtering algorithm, by constructing system model, regulates time delay constant τ according to demand ₁, τ ₂, τ ₃and constant K realizes filtering, is easily understood, easy to operate.

(2) define: combined integral is to liking a class open loop stabilization, and its transfer function is made up of two or more integration Object with Time Delay and can expresses with following form:

$\underset{i=1}{\overset{n}{\Σ}}\frac{k_i}{{\mathrm{sG}}_i\left(s\right)}(1-e^{-{\mathrm{\τ}}_{1i}s})e^{-{\mathrm{\τ}}_{2i}s}---\left(1\right)$

G _is () is a Stable Polynomials not comprising integral element; formula is included in the systems stabilisation in combined integral system; In order to ensure the continuity of this process, time delay constant τ _1i, τ _2i, must equation be met: τ _2i=τ _{2 (i-1)}+ τ _{1 (i-1)}, 1 < i < n, n is positive integer.Combined integral process comprises non-Left half-plane pole and zero simultaneously.There is anomalous integral minimum phase characteristic simultaneously.Integral process is classified: divide without time-lag process and time-lag process by time lag type; Single combined integral process and many combined integrals process is divided into by system complexity; Low order process and Advanced Process is divided into by systematic education.

Analysis on Mechanism modeling is adopted to obtain the transfer function model of the combined integral process in industrial process:

$G_p\left(s\right)=\frac{k}{\mathrm{\&tau;}s}(1-e^{-\mathrm{\&tau;}s})---\left(2\right)$

$G_p\left(s\right)=\frac{k}{{\mathrm{\&tau;}}_{1}s}(1-e^{-{\mathrm{\&tau;}}_{1}s})e^{-{\mathrm{\&tau;}}_{2}s}---\left(3\right)$

$G_p\left(s\right)=\frac{k}{\mathrm{\&tau;}s(Ts+1)}(1-e^{-\mathrm{\&tau;}s})---\left(4\right)$

$G_p\left(s\right)=\frac{k}{{\mathrm{\&tau;}}_{1}s(Ts+1)}(1-e^{-{\mathrm{\&tau;}}_{1}s})e^{-{\mathrm{\&tau;}}_{2}s}---\left(5\right)$

$G_p\left(s\right)=\frac{k}{{\mathrm{\&tau;}}_{1}s(TS+1)}(1-e^{-{\mathrm{\&tau;}}_{1}s})e^{-{\mathrm{\&tau;}}_{2}s}+\frac{k}{{\mathrm{\&tau;}}_{3}s(Ts+1)}(1-e^{-{\mathrm{\&tau;}}_{3}s})e^{-{\mathrm{\&tau;}}_{4}s}---\left(6\right)$

Suppose Bounded Index signal f (t), its Laplace is transformed to F (s), is multiplied by combined integral link g (s):

$g\left(s\right)=\frac{1}{\mathrm{\&tau;}s}(1-e^{-\mathrm{\&tau;}s})---\left(7\right)$

Obtain transfer function:

$G\left(s\right)=F\left(s\right)\frac{1}{\mathrm{\&tau;}s}(1-e^{-\mathrm{\&tau;}s})=\frac{1}{\mathrm{\&tau;}}(\frac{F\left(s\right)}{s}-\frac{F\left(s\right)e^{-\mathrm{\&tau;}s}}{s})---\left(8\right)$

Laplace inverse transformation is asked to obtain to formula (8):

$G\left(t\right)=L^{-1}\left(G\right(s))=\frac{1}{\mathrm{\&tau;}}\&lsqb;{\&Integral;}_0^{t}f\left(u\right)du-{\&Integral;}_0^{t-\mathrm{\&tau;}}f\left(u\right)du\&rsqb;=\frac{{\&Integral;}_{t-\mathrm{\&tau;}}^{t}f\left(u\right)du}{\mathrm{\&tau;}}---\left(9\right)$

It is that the τ time period (t-τ, t) carries out integration that formula (9) to may be interpreted as signal in length, carries out τ average to gained integration divided by time span, and being equivalent to signal in length is the Mean Filtering Algorithm that the τ time period carries out.Therefore the combined integral link that formula (7) defines is equal to a mean filter, has phase same-action with mean filter.Mean filter is the special case of low pass filter, and releasing this combined integral link is thus a low pass filter.There is the ability of certain restraint speckle, because its essence is equivalent to mean filter, some can be suppressed thus completely with the cyclical signal of specific period.

As shown in Figure 1, this combined integral filtering system, comprises the first combined integral link and time delay process, described first combined integral link and time delay process Signal averaging to the second combined integral link out; The overall transfer function of described combined integral filtering system is:

$G\left(s\right)=K(e^{-{\mathrm{\&tau;}}_{1}s}-\frac{1-e^{-{\mathrm{\&tau;}}_{2}s}}{{\mathrm{\&tau;}}_{1}s})\&CenterDot;\frac{1-e^{-{\mathrm{\&tau;}}_{3}s}}{{\mathrm{\&tau;}}_{3}s}---\left(10\right)$

Wherein, for pure lag system, τ _itime delay constant; Regulate time delay constant τ according to demand ₁, τ ₂, τ ₃and constant K realizes low pass, high pass and bandpass filtering.

Described first combined integral link is low pass filter, and its transfer function is

Derived by formula (8) and formula (9) and know, the mean filter in time range that this link completes [t-τ, t].This link realizes the effect of low pass signal filtering, time delay constant τ ₁controlled, determine the item number participating in mean filter.τ ₁larger, low-pass filter effect is better, and the high fdrequency component of elimination is more, and filtered signal is more level and smooth.

The high pass filter that described first combined integral link and time delay process are formed, its transfer function is $g_h\left(s\right)=e^{-{\mathrm{\&tau;}}_{2}s}-\frac{1}{{\mathrm{\&tau;}}_{1}s}(1-e^{-{\mathrm{\&tau;}}_{1}s}).$

As seen from Figure 2, former composite signal by after a time delay process with low-pass filtering after Signal averaging, because time delay can not change the characteristic of signal, just signal phase is had an impact.Known by low-pass filtering link, system by and signal passes through after link, only remaining low frequency signal in signal, then superpose with this link, namely deduct low frequency signal with original signal, so realize effect and be equal to High frequency filter effect, so link achieves the effect of high-pass filtering.

The transfer function of described second combined integral link is

G'(s) the equivalent g of effect is equal to ₁the effect of (s) link, different unlike the item number participating in low-pass filtering, i.e. parameter τ ₁, τ ₂vary in size, and also different for the signal superposed.G ₁s remaining in composite signal after () link is mixed signal medium and low frequency signal, with g _hs () link superposes, remaining is high-frequency signal in signal, again superposes a low frequency filtering link, as long as Selecting parameter is reasonable, can realize the effect of bandpass filtering.

Added a Proportional coefficient K herein, because original signal is by having decay after two filtering links, amplitude is less, after increasing this link, by the amplification K of filtered signal doubly, can reduce the error of signal and filtering signal, with the contrast of original signal, can check than being easier to.

Adopt the signal gone out based on the advanced filtering algorithm filtering of combined integral system very stable, the signal only containing a kind of frequency, noise is few, signal smoothing.The Butterworth filter of contrast iir digital filter design, in filtered signal, noise is more, adopts combined integral system filter effect better.

Claims (4)

1. a combined integral filtering system, is characterized in that, comprises the first combined integral link and time delay process, described first combined integral link and time delay process Signal averaging to the second combined integral link out; The overall transfer function of described combined integral filtering system is $G\left(s\right)=K(e^{-{\mathrm{\&tau;}}_{1}s}-\frac{1-e^{-{\mathrm{\&tau;}}_{2}s}}{{\mathrm{\&tau;}}_{1}s})\&CenterDot;\frac{1-e^{-{\mathrm{\&tau;}}_{3}s}}{{\mathrm{\&tau;}}_{3}s},$ Wherein, for pure lag system, τ _itime delay constant; Regulate time delay constant τ according to demand ₁, τ ₂, τ ₃and constant K realizes low pass, high pass and bandpass filtering.

2. combined integral filtering system according to claim 1, is characterized in that, described first combined integral link is low pass filter, and its transfer function is $g_1\left(s\right)=\frac{1}{{\mathrm{\&tau;}}_{1}s}(1-e^{-{\mathrm{\&tau;}}_{1}s}).$

3. combined integral filtering system according to claim 1, is characterized in that, the high pass filter that described first combined integral link and time delay process are formed, and its transfer function is

4. combined integral filtering system according to claim 1, is characterized in that, the transfer function of described second combined integral link is $g^{\&prime;}\left(s\right)=\frac{K}{{\mathrm{\&tau;}}_{3}s}(1-e^{-{\mathrm{\&tau;}}_{3}s}).$