Design method and working method of linear tracking differentiator

Abstract

The invention relates to the technical field of filters, discloses a design method and a working method of a linear tracking differentiator, and provides a new asymptotic time delay compensation mode by introducing a concept of time delay compensation and compensating and correcting a function of the linear tracking differentiator in a form of a delay compensation function. The technical problem that in the prior art, time delay of a linear tracking differentiator is serious is effectively solved.

Description

Technical Field

[0001] The embodiments of the present invention relate to the technical field of filters, and in particular to a design method and a working method of a linear tracking differentiator. Background Art

[0002] Filtering digital signals and extracting differential signals are common problems in the field of digital signal processing. For this purpose, there are many relatively mature digital signal filtering technologies, such as the commonly used Kalman filter, αβγ filter, linear tracking differentiator, nonlinear tracking differentiator, etc. These digital signal processing methods can realize the extraction of differential signals of digital signals and filtering of original signals and differential signals. However, there is a common contradiction, that is, the contradiction between the real-time and filtering performance of the output signal. That is, the stronger the noise filtering performance of the signal processing tool, the greater the time lag of the output signal relative to the input signal. This is not conducive to applications that require both real-time and smoothness of the signal. Summary of the invention

[0003] In view of the above problems, the present invention provides a design method and a working method of a linear tracking differentiator, which are used to solve the technical problem of serious time lag of the linear tracking differentiator in the prior art.

[0004] According to one aspect of an embodiment of the present invention, a design method of a linear tracking differentiator includes:

[0005] Step S1, obtaining a linear tracking differential model;

[0006] Step S2, performing time lag analysis on the linear tracking differential model to determine a time lag compensation function;

[0007] Step S3, updating the linear tracking differential model according to the time lag compensation function to obtain a time lag compensation tracking differential model, wherein the time lag compensation tracking differential model is connected to an input signal, and the time lag compensation tracking differential model outputs a first output signal and a second output signal, wherein the first output signal of the time lag compensation tracking differential model tracks the input signal, and the second output signal of the time lag compensation tracking differential model tracks the differential of the input signal.

[0008] In an optional manner, the step S3 further includes:

[0009] Step S4, performing signal fluctuation correction on the time lag compensation tracking differential model to obtain an asymptotic time lag compensation tracking differential model, wherein the asymptotic time lag compensation tracking differential model is connected to the input signal, and the asymptotic time lag compensation tracking differential model outputs a first output signal and a second output signal, wherein the first output signal of the asymptotic time lag compensation tracking differential model tracks the input signal, and the second output signal of the asymptotic time lag compensation tracking differential model tracks the differential of the input signal.

[0010] In an optional manner, after the step of performing signal fluctuation correction on the time lag compensation tracking differential model to obtain the asymptotic time lag compensation tracking differential model, the method further includes:

[0011] Step S5, establishing a series asymptotic time lag compensation tracking differential model according to the asymptotic time lag compensation tracking differential model, wherein the series asymptotic time lag compensation tracking differential model is connected to the input signal, and the series asymptotic time lag compensation tracking differential model outputs a first output signal and a second output signal, wherein the first output signal of the series asymptotic time lag compensation tracking differential model tracks the input signal, and the second output signal of the series asymptotic time lag compensation tracking differential model tracks the differential of the input signal;

[0012] The series asymptotic time lag compensation tracking differential model is composed of two asymptotic time lag compensation tracking differential models, and the two asymptotic time lag compensation tracking differential models are respectively a first asymptotic time lag compensation tracking differential model and a second asymptotic time lag compensation tracking differential model connected in sequence;

[0013] The input signal of the second asymptotic time lag compensation tracking differential model is the second output signal output by the previous first asymptotic time lag compensation tracking differential model.

[0014] In an optional manner, the linear tracking differential model is:

[0015]

[0016] Where u(t) is the input signal, x 11 (t) is the first output signal of the linear tracking differential model; x 22 (t) is the second output signal of the linear tracking differential model, and r is the fast factor.

[0017] In an optional manner, the time lag compensation tracking differential model is:

[0018]

[0019] Among them, u(t) is the input signal, x3(t) is the first output signal of the time lag compensation tracking differential model; x4(t) is the second output signal of the time lag compensation tracking differential model, r is the fast factor, and τ(r) is the lag time of the linear tracking differential model.

[0020] In an optional manner, the asymptotic time lag compensation tracking differential model includes:

[0021]

[0022] Among them, u(t) is the input signal, x1(t) is the first output signal of the asymptotic time lag compensation tracking differential model, x2(t) is the second output signal of the asymptotic time lag compensation tracking differential model, α is the asymptotic compensation coefficient, ατ(r) is the asymptotic compensation transition time, r is the fast factor, and τ(r) is the lag time of the linear tracking differential model.

[0023] In an optional manner, the series asymptotic time lag compensation tracking differential model is:

[0024]

[0025] Wherein, u(t) is the input signal, x1(t) is the first output signal of the first asymptotic time lag compensation tracking differential model, and is also the first output signal of the serial asymptotic time lag compensation tracking differential model, x2(t) is the second output signal of the first asymptotic time lag compensation tracking differential model, y1(t) is the first output signal of the second asymptotic time lag compensation tracking differential model, and is also the second output signal of the serial asymptotic time lag compensation tracking differential model, y2(t) is the second output signal of the second asymptotic time lag compensation tracking differential model. Two output signals, α1 is the asymptotic compensation coefficient of the first asymptotic time lag compensation tracking differential model, α1τ(r1) is the asymptotic compensation transition time of the first asymptotic time lag compensation tracking differential model, r1 is the fast factor of the first asymptotic time lag compensation tracking differential model, α2 is the asymptotic compensation coefficient of the second asymptotic time lag compensation tracking differential model, α2τ(r2) is the asymptotic compensation transition time of the second asymptotic time lag compensation tracking differential model, and r2 is the fast factor of the second asymptotic time lag compensation tracking differential model. In a second aspect of the present application, a working method of a linear tracking differentiator is also proposed, the linear tracking differentiator is designed by the design method of the linear tracking differentiator as described above, and the working method of the linear tracking differentiator includes:

[0026] Step S11, obtaining an input signal;

[0027] Step S12: input the input signal into the time lag compensation tracking differential model to obtain a first output signal and a second output signal, and output the second output signal of the time lag compensation tracking differential model as a filtered differential signal.

[0028] In a third aspect of the present application, a working method of a linear tracking differentiator is further proposed. The linear tracking differentiator is designed by the design method of the linear tracking differentiator as described above. The working method of the linear tracking differentiator includes:

[0029] The working method of the linear tracking differentiator includes:

[0030] Step S13, obtaining an input signal;

[0031] Step S14, inputting the input signal into the asymptotic time lag compensation tracking differential model to obtain a first output signal and a second output signal, and outputting the second output signal of the asymptotic time lag compensation tracking differential model as a filtered differential signal.

[0032] On the fourth side of the present application, a series asymptotic time lag compensation tracking differential model is also proposed, wherein the linear tracking differentiator is designed by the design method of the linear tracking differentiator as described above, and the working method of the linear tracking differentiator includes:

[0033] Step S15, obtaining an input signal;

[0034] Step S16, inputting the input signal into the series asymptotic time lag compensation tracking differential model to obtain a first output signal and a second output signal, and outputting the second output signal of the series asymptotic time lag compensation tracking differential model as a filtered differential signal.

[0035] This application introduces the concept of time lag compensation and compensates the function of the linear tracking differentiator in the form of a lag compensation function, thereby proposing a new asymptotic time lag compensation method, which effectively solves the technical problem of serious time lag of the linear tracking differentiator.

[0036] The above description is only an overview of the technical solution of the embodiment of the present invention. In order to more clearly understand the technical means of the embodiment of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the embodiment of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The accompanying drawings are only used to illustrate the embodiments and are not to be considered as limiting the present invention. In addition, the same reference symbols are used to represent the same components throughout the accompanying drawings. In the accompanying drawings:

[0038] Figure 1 A schematic flow chart of a design method of a linear tracking differentiator provided by the present invention is shown;

[0039] Figure 2 A schematic flow chart of another embodiment of a design method for a linear tracking differentiator provided by the present invention is shown;

[0040] Figure 3 A schematic flow chart showing another embodiment of a design method for a linear tracking differentiator provided by the present invention;

[0041] Figure 4 A schematic diagram showing the time lag characteristics of a linear tracking differential model under different parameters r of the design method of a linear tracking differentiator provided by the present invention is shown;

[0042] Figure 5 A schematic diagram showing the effect of the first output signal tracking the input signal of the linear tracking differential model and the time lag compensation tracking differential model in the design method of the linear tracking differentiator provided by the present invention when processing a noise-contaminated low-frequency sinusoidal signal;

[0043] Figure 6 A schematic diagram showing the comparative effect of the second output signal tracking the differential signal of the input signal when processing a noise-contaminated low-frequency sinusoidal signal between the linear tracking differential model and the time lag compensation tracking differential model in the linear tracking differentiator with asymptotic time lag compensation function provided by the present invention;

[0044] Figure 7 The signal flow chart of the linear tracking differentiator with time lag compensation function provided by the present invention is shown;

[0045] Figure 8 The signal flow chart of the linear tracking differentiator with asymptotic time lag compensation function provided by the present invention is shown; Fig. 9 A comparison diagram of the first output signal of the time lag compensation tracking differentiator provided by the present invention and the linear tracking differentiator with asymptotic time lag compensation function when processing a noise-contaminated low-frequency sinusoidal signal is shown;

[0046] Fig.10 A comparison diagram of the second output signals of the time lag compensation tracking differentiator provided by the present invention and the linear tracking differentiator with asymptotic time lag compensation function when processing noise-contaminated low-frequency sinusoidal signals is shown;

[0047] Fig.11 The signal flow chart of the tracking differentiator with the series asymptotic time lag compensation function provided by the present invention is shown.

[0048] Fig.12It is a comparison diagram of the effect of the second output signal tracking the differential signal of the input signal when the asymptotic time lag compensation tracking differential model and the series asymptotic time lag compensation tracking differential model are processing noise-contaminated low-frequency sinusoidal signals;

[0049] Fig.13 A schematic diagram of the application flow of the design method of the linear tracking differentiator provided by the present invention is shown;

[0050] Fig.14 A schematic diagram of the application flow of the design method of the linear tracking differentiator provided by the present invention is shown;

[0051] Fig.15 A schematic diagram of the application flow of the design method of the linear tracking differentiator provided by the present invention is shown. DETAILED DESCRIPTION

[0052] Exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0053] In the exemplary technology, the linear tracking differentiator has been widely used in various fields of digital signal processing due to its simple calculation and easy implementation. Its form is as follows:

[0054]

[0055] The linear tracking differentiator has only one adjustable parameter r, which is defined as the fast factor. Its size determines how fast the differentiator converges. The larger r is, the faster the tracking differentiator converges, that is, the stronger the real-time performance of the output signal, but the worse the filtering performance of the noise. Therefore, when applying the linear tracking differentiator in practice, it is necessary to comprehensively consider the real-time and filtering requirements and provide a compromise parameter setting method, which will lose both part of the filtering capability and part of the real-time performance, and it is impossible to take both into account at the same time.

[0056] The present application proposes a design method for a linear tracking differentiator, which can design a linear tracking differentiator with a time lag compensation function, and is used to solve the technical problem of a relatively serious time lag of a linear tracking differentiator.

[0057] Step S1, obtaining a linear tracking differential model;

[0058] Linear tracking differential model reference formula (1): accomplish.

[0059] Among them, u(t) is the input signal, x1(t) is the first output signal of the linear tracking differential model, x2(t) is the second output signal of the linear tracking differential model, and r is the fast factor.

[0060] Step S2, performing time lag analysis on the linear tracking differential model to determine a time lag compensation function;

[0061] The time lag compensation function is obtained by analyzing the linear tracking differential model. The specific analysis process is as follows:

[0062] The traditional linear tracking differentiator is of the following form:

[0063]

[0064] Where u(t) is the input signal of the system, x 11 (t) and x 22 (t) are the two output signals of the system, where the signal x 11 (t) tracking signal u(t), signal x 22 (t) tracks the differential signal of the signal u(t). From input u(t) to output x 11 The transfer function of (t) is:

[0065]

[0066] The transfer function amplitude is:

[0067]

[0068] The transfer function phase is:

[0069]

[0070] The time lag when processing a time signal with frequency ω is:

[0071]

[0072] like Figure 4 As shown in the figure, the time lag τ is given when different parameter r values ​​are taken. delay (ω) changes with the frequency ω. It can be seen that when the parameter r is determined, when processing a lower frequency slow-varying time signal, the time lag τ of the linear tracking differentiator is delay (ω) is almost a constant, so the time lag characteristic of the linear tracking differentiator when processing low-frequency slow-varying signals can be analyzed by calculating the time lag when ω→0. According to L’Hôpital’s rule, we get:

[0073]

[0074] It can be seen that when the linear tracking differentiator tracks a low-frequency, slow-time-varying signal, the time lag of the output signal relative to the input signal is a function of the parameter r, denoted as τ(r), which is inversely proportional to r. According to formula (4), the linear tracking differentiator's ability to suppress high-frequency noise signals decreases as r increases. Therefore, when setting parameters for the linear tracking differentiator, there is a contradiction between "real-time" and "filtering", which is also a "common problem" of many filters. Therefore, when setting parameters, a "compromise" must be adopted to take into account both the ability to respond quickly to low-frequency signals and the ability to suppress high-frequency noise. Based on the above analysis, the time lag compensation function τ(r) can be introduced as the lag time of the linear tracking differential model.

[0075] Step S3, updating the linear tracking differential model according to the time lag compensation function to obtain a time lag compensation tracking differential model, the time lag compensation tracking differential model is connected to the input signal, and the time lag compensation tracking differential model outputs a first output signal and a second output signal, wherein the first output signal tracks the input signal, and the second output signal tracks the differential signal of the input signal.

[0076] This application introduces the concept of time lag compensation and compensates the function of the linear tracking differentiator in the form of a lag compensation function, that is, the output signal is time-shifted to compensate for the time lag problem of the low-frequency signal caused by the algorithm.

[0077] Optionally, the time lag compensation tracking differential model is:

[0078]

[0079] Among them, u(t) is the input signal, x3(t) is the first output signal of the time lag compensation tracking differential model; x4(t) is the second output signal of the time lag compensation tracking differential model, r is the fast factor, and τ(r) is the lag time of the linear tracking differential model.

[0080] In an alternative embodiment, referring to Figure 2 As shown, after step S3, the step further includes:

[0081] Step S4, performing signal fluctuation correction on the time lag compensation tracking differential model to obtain an asymptotic time lag compensation tracking differential model, wherein the asymptotic time lag compensation tracking differential model is connected to the input signal, and the asymptotic time lag compensation tracking differential model outputs a first output signal and a second output signal, wherein the first output signal of the asymptotic time lag compensation tracking differential model tracks the input signal, and the second output signal of the asymptotic time lag compensation tracking differential model tracks the differential of the input signal.

[0082] In the above scheme, the asymptotic time lag compensation tracking differential model is obtained by performing signal fluctuation correction on the time lag compensation tracking differential model. That is, the above scheme proposes a new asymptotic time lag compensation method, which effectively solves the problem of signal fluctuation in the transition process caused by time lag compensation.

[0083] Optionally, the asymptotic time lag compensation tracking differential model is:

[0084]

[0085] Among them, u(t) is the input signal, x1(t) is the first output signal of the asymptotic time lag compensation tracking differential model, x2(t) is the second output signal of the asymptotic time lag compensation tracking differential model, α is the asymptotic compensation coefficient, ατ(r) is the asymptotic compensation transition time, r is the fast factor, and τ(r) is the lag time of the linear tracking differential model.

[0086] The process obtained by the above formula is as follows:

[0087] Firstly, the concept of time shift is introduced into the linear tracking differential model. By analyzing the functional relationship τ(r) between the time lag and the fast factor r of the linear tracking differential model when processing low-frequency slow-varying signals, the first output signal x1(t) that is subtracted from the input signal u(t) in the linear tracking differential model is changed from the current moment to a signal x1(t-τ(r)) with time lag. In this way, the problem of time lag of x1(t) relative to u(t) can be solved, and a time lag compensated tracking differential model can be obtained.

[0088] Specifically, refer to Figure 5 as well as Figure 6 As shown, Figure 5 as well as Figure 6 A set of linear tracking differentiators using a linear tracking differential model and a linear tracking differentiator using a time lag compensation tracking differential model are compared in processing sinusoidal signals contaminated by noise. Figure 5 The schematic diagram shows the effect of the first output signal tracking the input signal when the linear tracking differential model and the time lag compensation tracking differential model in the design method of the linear tracking differentiator provided by the present invention process a noise-contaminated low-frequency sinusoidal signal. Figure 6 The schematic diagram shows the comparative effect of the second output signal tracking the differential signal of the input signal between the linear tracking differential model and the time lag compensation tracking differential model in the linear tracking differentiator with asymptotic time lag compensation function provided by the present invention when processing noise-contaminated low-frequency sinusoidal signals.

[0089] When the input signal is:

[0090] u(t)=sin(0.01t)+n(t) (10)

[0091] Where n(t) is white noise with an amplitude of ±0.1, h = 0.01, r = 0.5, τ(r) = 4. Figure 5 as well as Figure 6 It can be seen that the linear tracking differential model has a strong filtering effect on the original signal. The first output is almost smooth, but has an obvious 4s time lag. The time lag compensation tracking differential model has the same filtering effect on the noise as the linear tracking differentiator, and effectively compensates for the 4s time lag.

[0092] In addition, the cost of time lag compensation is that the transition process of the output signal is significantly deteriorated, and it takes a period of fluctuation to converge to the true value. Moreover, the greater the time lag of compensation, the longer the fluctuation time. This is also an undesirable phenomenon in the field of signal processing. To solve this problem, the present invention sets an asymptotic compensation coefficient α, and realizes asymptotic compensation for the time lag after a transition time ατ(r). This effectively avoids the signal fluctuation problem caused by time lag compensation, and achieves simultaneous protection of signal real-time and filtering performance, while ensuring the smoothness of the signal throughout the process.

[0093] Fig. 9 as well as Fig.10 A comparison diagram of the effect of processing the input signal (10) is given, where the parameters r = 0.5, α = 15. Here, only the comparison curves of the linear tracking differentiator with time lag compensation and the linear tracking differentiator with asymptotic time lag compensation are given. It can be seen that by using the asymptotic compensation method, the long-term fluctuation of the output signal is effectively avoided. After a transition time of ατ(r), the output signal of the differentiator with asymptotic time lag compensation smoothly tracks the original input signal without lag.

[0094] In an alternative embodiment, referring to Figure 2 As shown, after step S4, the step further includes:

[0095] Step S5: Establish a serial asymptotic time lag compensation tracking differential model according to the asymptotic time lag compensation tracking differential model, wherein the serial asymptotic time lag compensation tracking differential model is connected to the input signal, and the serial asymptotic time lag compensation tracking differential model outputs a first output signal and a second output signal, wherein the first output signal of the serial asymptotic time lag compensation tracking differential model tracks the input signal, and the second output signal of the serial asymptotic time lag compensation tracking differential model tracks the differential of the input signal. The input signal of the subsequent second asymptotic time lag compensation tracking differential model is the second output signal output by the previous first asymptotic time lag compensation tracking differential model.

[0096] refer to Fig.11 As shown, the series asymptotic time lag compensation tracking differential model is composed of two asymptotic time lag compensation tracking differential models, and the two asymptotic time lag compensation tracking differential models are respectively a first asymptotic time lag compensation tracking differential model and a second asymptotic time lag compensation tracking differential model connected in sequence, and the signal diagram of each asymptotic time lag compensation tracking differential model is referred to as Figure 8 The output differential signal comparison diagram of differentiators using different differential models is shown in Figure 2. Fig.12 shown.

[0097] In the attached figure of the specification, the linear tracking differentiator with asymptotic time lag compensation indicates that the differentiator used in the experiment at this time is equipped with a asymptotic time lag compensation tracking differential model, and the series linear tracking differentiator with asymptotic time lag compensation indicates that the differentiator used in the experiment at this time is equipped with a series asymptotic time lag compensation tracking differential model.

[0098] In the above scheme, the series asymptotic time lag compensation tracking differential model architecture further solves the problem of transition process signal fluctuation caused by time lag compensation.

[0099] Optionally, the series asymptotic time lag compensation tracking differential model is:

[0100]

[0101] Wherein, u(t) is the input signal, x1(t) is the first output signal of the first asymptotic time lag compensation tracking differential model, and is also the first output signal of the serial asymptotic time lag compensation tracking differential model, x2(t) is the second output signal of the first asymptotic time lag compensation tracking differential model, y1(t) is the first output signal of the second asymptotic time lag compensation tracking differential model, and is also the second output signal of the serial asymptotic time lag compensation tracking differential model, y2(t) is the second output signal of the second asymptotic time lag compensation tracking differential model. Two output signals, α1 is the asymptotic compensation coefficient of the first asymptotic time lag compensation tracking differential model, α1τ(r1) is the asymptotic compensation transition time of the first asymptotic time lag compensation tracking differential model, r1 is the fast factor of the first asymptotic time lag compensation tracking differential model, α2 is the asymptotic compensation coefficient of the second asymptotic time lag compensation tracking differential model, α2τ(r2) is the asymptotic compensation transition time of the second asymptotic time lag compensation tracking differential model, and r2 is the fast factor of the second asymptotic time lag compensation tracking differential model.

[0102] It should be noted that the parameters r1, r2, α1, and α2 in the series asymptotic time lag compensation tracking differential model can be designed separately, and the output x1(t) tracks the signal u(t), and the output y1(t) tracks the signal Note that the input of the second asymptotic time lag compensation tracking differential model is the output of the first asymptotic time lag compensation tracking differential model, which implements secondary filtering of the second output of the first asymptotic time lag compensation tracking differential model. It is suitable for the case where the differential signal filtering using primary processing is not ideal, and the output y2(t) can be used as the signal Estimates. Fig.12 A comparison chart of the differential signal directly output by the differential model with asymptotic time lag compensation tracking and the differential signal output by the series linear tracking differentiator is given, where r1=0.5, α1=15, r2=0.3, α2=30. It can be seen that the series type can achieve secondary filtering and smoothing of the differential signal. Since the present invention provides a method for asymptotically compensating the algorithm time lag, it is possible to design the above-mentioned series tracking differentiator to perform secondary filtering on the differential signal.

[0103] In the above process, for signals with serious noise pollution, if you want to achieve high-precision filtering of the original signal and the differential signal at the same time, you need to make the fast factor r very small. At this time, the transition time of the compensation time lag will be significantly prolonged. To solve this problem, the present invention provides a series asymptotic time lag compensation tracking differential model, that is, two linear tracking differentiators with asymptotic time lag compensation are connected in series, and the parameters of the two are independently designed, wherein the parameter setting of the first tracking differentiator ensures the filtering characteristics of the original signal, while the parameter setting of the second tracking differentiator ensures the filtering characteristics of the differential signal.

[0104] The above-mentioned series linear tracking differentiator with asymptotic time lag compensation can track the original signal and its differential signal without time lag after a certain transition process, and has strong filtering performance for both the original signal and the differential signal. Two tracking differentiators can be independently designed according to the signal-to-noise ratio of the signal. The signal processing method is all linear calculation, the algorithm is simple and easy to implement, and it can realize online real-time processing without high requirements on computing hardware, which is convenient for promotion and application.

[0105] The invention provides a linear tracking differentiator with asymptotic time lag compensation by analyzing the time lag of the linear tracking differentiator, which is used for filtering the digital signal polluted by strong noise and extracting the differential signal, reconciles the contradiction between the filtering performance and the real-time performance of the traditional differentiator, and effectively avoids the signal fluctuation in the transition process by asymptotic compensation for the time lag, and realizes the secondary filtering of the differential signal by the series design. The method can be widely used in the field of digital signal processing, and the algorithm has a small amount of calculation and can be implemented in real time online in a host computer or an embedded computer.

[0106] In an optional embodiment, a linear tracking differentiator designed according to the design method of a linear tracking differentiator can perform a corresponding working method, referring to Figure 3 As shown, including:

[0107] Step S11, obtaining an input signal;

[0108] Step S12: input the input signal into the time lag compensation tracking differential model to obtain a first output signal and a second output signal, and output the second output signal of the time lag compensation tracking differential model as a filtered differential signal.

[0109] At this time, the linear tracking differentiator with time lag compensation has the same filtering effect on noise as the linear tracking differentiator, and effectively performs time compensation, effectively solving the technical problem of serious time lag of the linear tracking differentiator in the prior art.

[0110] In an optional embodiment, a linear tracking differentiator designed according to the design method of a linear tracking differentiator can perform a corresponding working method, including:

[0111] Step S13, obtaining an input signal;

[0112] Step S14, inputting the input signal into the asymptotic time lag compensation tracking differential model to obtain a first output signal and a second output signal, and outputting the second output signal of the asymptotic time lag compensation tracking differential model as a filtered differential signal.

[0113] Among them, by using the asymptotic compensation method, the long-term fluctuation of the output signal is effectively avoided. The output signal of the differentiator with asymptotic time lag compensation tracks the original input signal smoothly and without lag after a transition time of ατ(r).

[0114] In an optional embodiment, a linear tracking differentiator designed according to the design method of a linear tracking differentiator can perform a corresponding working method, including:

[0115] Step S15, obtaining an input signal;

[0116] Step S16, inputting the input signal into the series asymptotic time lag compensation tracking differential model to obtain a first output signal and a second output signal, and outputting the second output signal of the series asymptotic time lag compensation tracking differential model as a filtered differential signal.

[0117] Among them, the strong noise-contaminated digital signal is filtered and the differential signal is extracted in the form of a series asymptotic time lag compensation tracking differential model, which reconciles the contradiction between the filtering and real-time performance of the traditional differentiator, and effectively avoids signal fluctuations in the transition process by asymptotic compensation for time lag. Through the series design, the secondary filtering of the differential signal is realized. This method can be widely used in the field of digital signal processing, and the algorithm has a small amount of calculation and can be implemented in real time online in a host computer or embedded computer.

[0118] In the description provided herein, a large number of specific details are described. However, it is understood that embodiments of the present invention can be practiced without these specific details. Similarly, in order to simplify the present invention and help understand one or more of the various inventive aspects, in the above description of exemplary embodiments of the present invention, the various features of the embodiments of the present invention are sometimes grouped together into a single embodiment, figure, or description thereof. Wherein, the claims that follow the specific embodiment are hereby expressly incorporated into the specific embodiment, wherein each claim itself is a separate embodiment of the present invention.

[0119] Those skilled in the art will appreciate that the modules in the devices in the embodiments may be adaptively changed and arranged in one or more devices different from the embodiments. The modules or units or components in the embodiments may be combined into one module or unit or component, and further may be divided into a plurality of submodules or subunits or subcomponents. Except that at least some of such features and / or processes or units are mutually exclusive.

[0120] It should be noted that the above embodiments illustrate the present invention rather than limit it, and that those skilled in the art may design alternative embodiments without departing from the scope of the appended claims. In the claims, any reference symbol between brackets shall not be construed as a limitation on the claims. The word "comprising" does not exclude the presence of elements or steps not listed in the claims. The word "one" or "an" preceding an element does not exclude the presence of a plurality of such elements. The present invention may be implemented by means of hardware comprising a number of different elements and by means of a suitably programmed computer. In a unit claim enumerating a number of devices, several of these devices may be embodied by the same hardware item. The use of the words first, second, and third, etc. does not indicate any order. These words may be interpreted as names. The steps in the above embodiments, unless otherwise specified, should not be understood as limitations on the order of execution.

Claims

1. A design method for a linear tracking differentiator, characterized in that: include: Step S1, obtaining a linear tracking differential model; Step S2, performing time lag analysis on the linear tracking differential model to determine a time lag compensation function; Step S3, updating the linear tracking differential model according to the time lag compensation function to obtain a time lag compensation tracking differential model, wherein the time lag compensation tracking differential model is connected to an input signal, and the time lag compensation tracking differential model outputs a first output signal and a second output signal, wherein the first output signal of the time lag compensation tracking differential model tracks the input signal, and the second output signal of the time lag compensation tracking differential model tracks the differential of the input signal.

2. The design method of a linear tracking differentiator according to claim 1, characterized in that: After step S3, the following steps are also included: Step S4, performing signal fluctuation correction on the time lag compensation tracking differential model to obtain an asymptotic time lag compensation tracking differential model, wherein the asymptotic time lag compensation tracking differential model is connected to the input signal, and the asymptotic time lag compensation tracking differential model outputs a first output signal and a second output signal, wherein the first output signal of the asymptotic time lag compensation tracking differential model tracks the input signal, and the second output signal of the asymptotic time lag compensation tracking differential model tracks the differential of the input signal.

3. The design method of a linear tracking differentiator as claimed in claim 2, characterized in that: After the step of performing signal fluctuation correction on the time lag compensation tracking differential model to obtain an asymptotic time lag compensation tracking differential model, the method further includes: Step S5, establishing a series asymptotic time lag compensation tracking differential model according to the asymptotic time lag compensation tracking differential model, wherein the series asymptotic time lag compensation tracking differential model is connected to the input signal, and the series asymptotic time lag compensation tracking differential model outputs a first output signal and a second output signal, wherein the first output signal of the series asymptotic time lag compensation tracking differential model tracks the input signal, and the second output signal of the series asymptotic time lag compensation tracking differential model tracks the differential of the input signal; The series asymptotic time lag compensation tracking differential model is composed of two asymptotic time lag compensation tracking differential models, and the two asymptotic time lag compensation tracking differential models are respectively a first asymptotic time lag compensation tracking differential model and a second asymptotic time lag compensation tracking differential model connected in sequence; The input signal of the second asymptotic time lag compensation tracking differential model is the second output signal output by the previous first asymptotic time lag compensation tracking differential model.

4. The design method of a linear tracking differentiator according to claim 1, characterized in that: The linear tracking differential model is: Where u(t) is the input signal, x 11 (t) is the first output signal of the linear tracking differential model; x 22 (t) is the second output signal of the linear tracking differential model, and r is the fast factor.

5. The design method of a linear tracking differentiator according to claim 1, characterized in that: The time lag compensation tracking differential model is: Among them, u(t) is the input signal, x3(t) is the first output signal of the time lag compensation tracking differential model; x4(t) is the second output signal of the time lag compensation tracking differential model, r is the fast factor, and τ(r) is the lag time of the linear tracking differential model.

6. The design method of a linear tracking differentiator as claimed in claim 2, characterized in that: The asymptotic time lag compensation tracking differential model includes: Among them, u(t) is the input signal, x1(t) is the first output signal of the asymptotic time lag compensation tracking differential model, x2(t) is the second output signal of the asymptotic time lag compensation tracking differential model, α is the asymptotic compensation coefficient, ατ(r) is the asymptotic compensation transition time, r is the fast factor, and τ(r) is the lag time of the linear tracking differential model.

7. The design method of a linear tracking differentiator as claimed in claim 3, characterized in that: The series asymptotic time lag compensation tracking differential model is: Wherein, u(t) is the input signal, x1(t) is the first output signal of the first asymptotic time lag compensation tracking differential model, x2(t) is the second output signal of the first asymptotic time lag compensation tracking differential model, y1(t) is the first output signal of the second asymptotic time lag compensation tracking differential model, y2(t) is the second output signal of the second asymptotic time lag compensation tracking differential model, α1 is the asymptotic compensation coefficient of the first asymptotic time lag compensation tracking differential model, α1τ(r1) is the asymptotic compensation transition time of the first asymptotic time lag compensation tracking differential model, r1 is the fast factor of the first asymptotic time lag compensation tracking differential model, α2 is the asymptotic compensation coefficient of the second asymptotic time lag compensation tracking differential model, α2τ(r2) is the asymptotic compensation transition time of the second asymptotic time lag compensation tracking differential model, and r2 is the fast factor of the second asymptotic time lag compensation tracking differential model.

8. A method for operating a linear tracking differentiator, characterized in that: The linear tracking differentiator is designed by the design method of the linear tracking differentiator according to any one of claims 1 to 7, and the working method of the linear tracking differentiator includes: Step S11, obtaining an input signal; Step S12: input the input signal into the time lag compensation tracking differential model to obtain a first output signal and a second output signal, and output the second output signal of the time lag compensation tracking differential model as a filtered differential signal.

9. A method for operating a linear tracking differentiator, characterized in that: The linear tracking differentiator is designed by the design method of the linear tracking differentiator according to claim 2 or 6, and the working method of the linear tracking differentiator includes: Step S13, obtaining an input signal; Step S14, inputting the input signal into the asymptotic time lag compensation tracking differential model to obtain a first output signal and a second output signal, and outputting the second output signal of the asymptotic time lag compensation tracking differential model as a filtered differential signal.

10. A method for operating a linear tracking differentiator, characterized in that: The linear tracking differentiator is designed by the design method of the linear tracking differentiator according to claim 3 or 7, and the working method of the linear tracking differentiator includes: Step S15, obtaining an input signal; Step S16, inputting the input signal into the series asymptotic time lag compensation tracking differential model to obtain a first output signal and a second output signal, and outputting the second output signal of the series asymptotic time lag compensation tracking differential model as a filtered differential signal.

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