A method and device for constructing a parabolic window function and a filter

Abstract

This invention discloses a method, apparatus, and filter for constructing a parabolic window function. The construction method includes performing feedback integration on the input signal to obtain a first integral output signal; performing delay superposition on the first integral output signal to obtain a first adder output signal; and constructing a parabolic window function by adding the input signal after performing a first delay subtraction and the first adder output signal. This embodiment achieves efficient tracking filtering by designing a fastest tracking filter using a parabolic window function, overcoming the limitation of low tracking efficiency in the exponential tracking mechanism of first-order inertial filtering and enhancing the filtering effect.

Description

Technical Field

[0001] This invention relates to the fields of signal processing technology and industrial process control technology, and in particular to a method, apparatus and filter for constructing a parabolic window function. Background Technology

[0002] In signal processing technology, the window function method is a fundamental and widely used filter design approach. Digital low-pass filters are designed using window functions to achieve frequency domain filtering effects. Common window functions include rectangular windows, isosceles triangular windows, Hanning windows, Hamming windows, Blackman windows, and Chebyshev windows. However, these common window functions have fixed parameters such as stopband attenuation and sidelobe peak values, resulting in equal passband ripple and stopband attenuation, which can negatively impact filter performance.

[0003] In the field of industrial process control, high-frequency random noise interference is prevalent in process signals. Using low-pass filters (LPFs) to filter out this interference is a common technique, with the first-order inertial filter (FOIF) being a widely used and fundamental type. From the perspective of improving industrial process control performance, LPFs are required to reduce hysteresis while effectively filtering out high-frequency random noise interference.

[0004] In the field of industrial process control, the widely used proportional-integral-derivative (PID) controller represents a preferred fundamental control technology, and its fundamental control status remains unshakable. From the perspective of industrial control technology development, fundamental control technology cannot remain solely based on PID control; a new foundation control (NFC) technology is needed to replace existing PID control. The essence of achieving NFC as a replacement for PID control lies in breaking through the exponential tracking filtering mechanism of the field of effect (FOIF) from the perspective of the linear flow filter (LPF). The PID structure is based on FOIF, which represents a typical exponential tracking filtering mechanism. FOIF mainly suffers from poor output-to-input tracking performance and cannot achieve efficient filtering. Summary of the Invention

[0005] This invention provides a method, apparatus, and filter for constructing a parabolic window function, achieving efficient tracking filtering. It overcomes the limitation of low tracking efficiency of the exponential tracking mechanism of first-order inertial filtering in tracking input signals, thereby enhancing the filtering effect.

[0006] To address the aforementioned technical problems, embodiments of the present invention provide a method for constructing a parabolic window function, comprising:

[0007] The input signal is processed by feedback integration to obtain the first integral output signal;

[0008] The first integral output signal is delayed and superimposed to obtain the first adder output signal;

[0009] A parabolic window function is constructed by performing delayed numerical operations on the input signal and the output signal of the first adder.

[0010] In implementing this embodiment of the invention, the input signal is processed by feedback integration to obtain a first integral output signal; the first integral output signal is then delayed and superimposed to obtain a first adder output signal; by performing delayed numerical operations on the input signal and the first adder output signal, a parabolic window function is constructed. This parabolic window function, during filtering, causes the filtered output phase to lead, fundamentally overcoming the exponential tracking filtering mechanism of a first-order inertial filter and its limitation in tracking the input signal. This forms a typical and original exponential tracking filtering mechanism, improving the performance of the output tracking the input signal, achieving efficient tracking filtering, and enhancing the filtering effect.

[0011] As a preferred solution, the input signal is processed by feedback integration to obtain the first integral output signal, specifically:

[0012] The input signal is input to the minuend of the first subtractor, and the second integral output signal is input to the subtrahend of the first subtractor. The input signal and the second integral output signal are subtracted to obtain the feedback output signal; wherein, the second integral output signal is obtained by integrating the first integral output signal.

[0013] The feedback output signal is integrated to obtain the first integrated output signal.

[0014] As a preferred solution, the feedback output signal is integrated to obtain the first integrated output signal, specifically:

[0015] The feedback output signal is input to the input terminal of the first integrator, and the first integrated output signal is obtained at the output terminal of the first integrator; wherein, the first integrator is expressed as:

[0016]

[0017] Among them, f FI (s) is the Laplace transfer function of the first integrator, T W This represents the window duration.

[0018] As a preferred embodiment, the second integral output signal is obtained by integrating the first integral output signal, specifically as follows:

[0019] The first integral output signal is input to the input terminal of the second integrator, and the second integral output signal is obtained at the output terminal of the second integrator; wherein, the second integrator is expressed as:

[0020]

[0021] Among them, f SI (s) is the Laplace transfer function of the second integrator; T W This represents the window duration.

[0022] As a preferred embodiment, a parabolic window function is constructed by performing delayed numerical operations on the input signal and the output signal of the first adder, specifically as follows:

[0023] The input signal is delayed to obtain the first delayed output signal;

[0024] The first delayed output signal is input to the subtrahend terminal of the second subtractor, and the input signal is input to the minuend terminal of the second subtractor. The first delayed output signal is subtracted from the input signal in the second subtractor to obtain the output signal of the second subtractor.

[0025] The output signal of the second subtractor is input to the first input terminal of the second adder, and the output signal of the first adder is input to the second input terminal of the second adder. The output signal of the second subtractor is added to the output signal of the first adder in the second adder to obtain the output signal of the second adder.

[0026] Construct a parabolic window function based on the output signal of the second adder.

[0027] As a preferred embodiment, the first integral output signal is delayed and superimposed to obtain the first adder output signal, specifically as follows:

[0028] The first integral output signal is input to the input terminal of the second delay unit, and the second delayed output signal is obtained at the output terminal of the second delay unit; wherein, the second delay unit is expressed as:

[0029]

[0030] Among them, f L:B (s) is the Laplace transfer function of the second delay, T F:B The delay time constant of the second delay unit;

[0031] The first integral output signal is input to the first input terminal of the first adder, and the second delay output signal is input to the second input terminal of the first adder. The first integral output signal and the second delay output signal are added together in the first adder to obtain the first adder output signal.

[0032] As a preferred solution, the input signal is delayed to obtain a first delayed output signal, specifically as follows:

[0033] The input signal is input to the input terminal of the first delay unit, and the first delayed output signal is obtained at the output terminal of the first delay unit; wherein, the first delay unit is expressed as:

[0034]

[0035] Among them, f L:A (s) is the Laplace transfer function of the first delay, T F:A is the delay time constant of the first delay unit.

[0036] As a preferred approach, a parabolic window function is constructed based on the output signal of the second adder, specifically as follows:

[0037] The output signal of the second adder is used as the output of the parabolic window function. The parabolic window function is constructed as follows:

[0038]

[0039] T F:A =T F:B =T W

[0040] Among them, f PWF (s) is the Laplace transfer function of the parabolic window function, T W T is the window duration. F:A T is the delay time constant of the first delay unit. F:B is the delay time constant of the second delay unit.

[0041] To address the same technical problem, this invention also provides a device for constructing a parabolic window function, comprising: a feedback integration processing module, a delay superposition processing module, and a construction module;

[0042] The feedback integration processing module is used to perform feedback integration processing on the input signal to obtain the first integral output signal.

[0043] The delay superposition processing module is used to perform delay superposition processing on the first integral output signal to obtain the first adder output signal;

[0044] The construction module is used to construct a parabolic window function by performing delayed numerical operations on the input signal and the output signal of the first adder.

[0045] To address the same technical problem, embodiments of the present invention also provide a filter, including a parabolic window function construction device, a third integrator, and a proportional controller; wherein the parabolic window function construction device performs a parabolic window function construction method;

[0046] By connecting the parabolic window function construction device, the third integrator, and the proportional controller in series, a filter is obtained, as shown in the formula:

[0047]

[0048] T I =T W

[0049] Among them, f FTF (s) is the Laplace transfer function of the filter, f PWF (s) is the Laplace transfer function of the parabolic window function, T I K is the integration time of the third integrator. P For the gain of the proportional controller, T W This represents the window duration. Attached Figure Description

[0050] Figure 1 : A flowchart illustrating an embodiment of a method for constructing a parabolic window function provided by the present invention;

[0051] Figure 2 : A structural diagram of the constructed parabolic window function, which is an embodiment of the method for constructing a parabolic window function provided by the present invention;

[0052] Figure 3 : A flowchart illustrating the process of the first integral output signal in an embodiment of a method for constructing a parabolic window function provided by the present invention;

[0053] Figure 4 This is a flowchart illustrating the process of the second delayed output signal in one embodiment of a method for constructing a parabolic window function provided by the present invention.

[0054] Figure 5 This is a flowchart illustrating the output process of a parabolic window function, representing an embodiment of a method for constructing a parabolic window function provided by the present invention.

[0055] Figure 6 : A schematic diagram of an embodiment of a parabolic window function construction device provided by the present invention;

[0056] Figure 7 : A connection diagram of one embodiment of a filter provided by the present invention;

[0057] Figure 8 : A diagram illustrating the output process of a fastest tracking filter, one embodiment of a filter provided by the present invention;

[0058] Figure 9 : A tracking comparison result diagram of one embodiment of a filter provided by the present invention;

[0059] Figure 10 This is a comparison diagram of the filtering output results of one embodiment of the filter provided by the present invention. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] It should be noted that the specific abbreviations of the terms used in this invention are: Parabolic window function (PWF), First order inertial filter (FOIF), and Fastest tracking filter (FTF).

[0062] Example 1

[0063] Please refer to Figure 1 This is a flowchart illustrating a method for constructing a parabolic window function according to an embodiment of the present invention. The method for constructing the parabolic window function in this embodiment is applicable to tracking filtering. By constructing a parabolic window function, this embodiment overcomes the limitations of first-order inertial filtering in tracking input signals, achieving efficient tracking filtering. The method for constructing the parabolic window function includes steps 101 to 103, each step as follows:

[0064] Step 101: Perform feedback integration on the input signal to obtain the first integral output signal.

[0065] In this embodiment, the structure diagram of the parabolic window function is constructed as follows: Figure 2 As shown, when constructing the parabolic window function, the output of the second integral is fed back to the first subtractor. Through the form of closed-loop feedback s, the input signal is continuously tracked. During the tracking process, the first integral output signal is obtained. After processing the first integral output signal and the input signal, the output signal of the parabolic window function is obtained.

[0066] Optionally, step 101 specifically includes steps 1011 to 1013, each step being as follows:

[0067] Step 1011: Input the input signal to the minuend of the first subtractor, and input the second integral output signal to the subtrahend of the first subtractor. Perform subtraction on the input signal and the second integral output signal to obtain the feedback output signal.

[0068] In this embodiment, the input signal is input to the minuend of the first subtractor, and a feedback output signal is obtained at the output of the first subtractor. The second integral output signal is input to the subtrahend of the first subtractor to form a closed-loop feedback.

[0069] Step 1012: Integrate the feedback output signal to obtain the first integrated output signal.

[0070] Optionally, step 1012 specifically involves: inputting the feedback output signal to the input terminal of the first integrator, and obtaining the first integrated output signal at the output terminal of the first integrator; wherein, the first integrator is expressed as:

[0071]

[0072] Among them, f FI (s) is the Laplace transfer function of the first integrator, T W This represents the window duration, measured in seconds (s).

[0073] In this embodiment, the feedback output signal is input to the input terminal of the first integrator, and the first integrated output signal is obtained at the output terminal of the first integrator. The window time length T of the parabolic window function... W =100s, when the input signal of the parabolic window function is a unit step, the process of obtaining the first integral output signal PV FI (t), such as Figure 3 As shown.

[0074] Step 1013: Integrate the first integral output signal to obtain the second integral output signal.

[0075] Optionally, step 1013 specifically involves: inputting the first integral output signal to the input terminal of the second integrator, and obtaining the second integral output signal at the output terminal of the second integrator; wherein, the second integrator is expressed as:

[0076]

[0077] Among them, f SI (s) is the Laplace transfer function of the second integrator; T W This represents the window duration, measured in seconds (s).

[0078] In this embodiment, the first integral output signal is input to the input terminal of the second integrator, and the second integral output signal is obtained at the output terminal of the second integrator.

[0079] Step 102: Delay and superimpose the first integral output signal to obtain the first adder output signal.

[0080] Optionally, step 102 specifically includes steps 1021 to 1022, each of which is as follows:

[0081] Step 1021: Input the first integral output signal to the input terminal of the second delay unit, and obtain the second delayed output signal at the output terminal of the second delay unit; wherein, the second delay unit is expressed as:

[0082]

[0083] Among them, f L:B (s) is the Laplace transfer function of the second delay, T F:B T is the delay time constant of the second delay unit, in seconds. Preferably, T F:B =T W .

[0084] In this embodiment, the first integral output signal is input to the second delay unit, and the second delayed output signal is obtained at the output of the second delay unit. The window time length T of the parabolic window function... W =100s, T W =T F:B =100s, when the input signal of the parabolic window function is a unit step, the process PV of obtaining the second delayed output signal. L (t), that is, the process of the first integral delay output, such as Figure 4 As shown.

[0085] Step 1022: Input the first integral output signal to the first input terminal of the first adder, input the second delay output signal to the second input terminal of the first adder, and add the first integral output signal and the second delay output signal in the first adder to obtain the first adder output signal.

[0086] In this embodiment, the first integral output signal is input to the first input terminal of the first adder, the second delay output signal is input to the second input terminal of the first adder, and the first integral output signal and the second delay output signal are added together to obtain the first adder output signal.

[0087] Step 103: Construct a parabolic window function by performing delayed numerical operations on the input signal and the output signal of the first adder.

[0088] Optionally, step 103 specifically includes steps 1031 to 1034, each of which is as follows:

[0089] Step 1031: Delay the input signal to obtain the first delayed output signal.

[0090] Optionally, step 1031 specifically involves: inputting the input signal to the input terminal of the first delay unit, and obtaining the first delayed output signal at the output terminal of the first delay unit; wherein, the first delay unit is expressed as:

[0091]

[0092] Among them, f L:A (s) is the Laplace transfer function of the first delay, T F:A T is the delay time constant of the first delay unit, in seconds. Preferably, T F:A =T W .

[0093] In this embodiment, the input signal is input to the first delay unit to obtain the first delayed output signal.

[0094] Step 1032: Input the first delayed output signal to the subtrahend terminal of the second subtractor, input the input signal to the minuend terminal of the second subtractor, and subtract the first delayed output signal from the input signal in the second subtractor to obtain the output signal of the second subtractor.

[0095] In this embodiment, the first delayed output signal is input to the subtrahend terminal of the second subtractor, and the input signal is input to the minuend terminal of the second subtractor. The second subtractor subtracts the first delayed output signal from the input signal to obtain the output signal of the second subtractor.

[0096] Step 1033: Input the output signal of the second subtractor to the first input terminal of the second adder, input the output signal of the first adder to the second input terminal of the second adder, and add the output signal of the second subtractor and the output signal of the first adder in the second adder to obtain the output signal of the second adder.

[0097] In this embodiment, the output signal of the second subtractor is input to the first input terminal of the second adder, and the output signal of the first adder is input to the second input terminal of the second adder. The second adder adds the output signal of the second subtractor to the output signal of the first adder to obtain the output signal of the second adder. The output signal of the second adder represents the output of the parabolic window function.

[0098] Step 1034: Construct a parabolic window function based on the output signal of the second adder.

[0099] Optionally, step 1034 specifically involves: using the output signal of the second adder as the output of a parabolic window function, constructing the parabolic window function, with the following formula:

[0100]

[0101] T F:A =T F:B =T W

[0102] Among them, f PWF (s) is the Laplace transfer function of the parabolic window function, T W T represents the window duration in seconds. F:A T is the delay time constant of the first delay unit, in seconds. F:B is the delay time constant of the second delay unit, in seconds.

[0103] In this embodiment, the window time length T of the parabolic window function W =100s, T W =T F:A =T F:B =100s, when the input signal to the parabolic window function is a unit step, the process PV of the parabolic window function output is obtained. PWF (t), such as Figure 5 As shown.

[0104] In implementing this embodiment of the invention, the input signal is processed by feedback integration to obtain a first integral output signal; the first integral output signal is then delayed and superimposed to obtain a first adder output signal; by performing delayed numerical operations on the input signal and the first adder output signal, a parabolic window function is constructed. This parabolic window function, during filtering, causes the filtered output phase to lead, fundamentally overcoming the exponential tracking filtering mechanism of a first-order inertial filter and its limitation in tracking the input signal. This forms a typical and original exponential tracking filtering mechanism, improving the performance of the output tracking the input signal, achieving efficient tracking filtering, and enhancing the filtering effect.

[0105] Example 2

[0106] Accordingly, see Figure 6 , Figure 6 This is a schematic diagram of a second embodiment of the device for constructing a parabolic window function provided by the present invention. Figure 6 As shown, the device for constructing a parabolic window function includes a feedback integration processing module 601, a delay superposition processing module 602, and a construction module 603.

[0107] The feedback integration processing module 601 is used to perform feedback integration processing on the input signal to obtain the first integrated output signal.

[0108] Optionally, the input signal is input to the minuend of the first subtractor, and the second integral output signal is input to the subtrahend of the first subtractor. The input signal and the second integral output signal are subtracted to obtain a feedback output signal. The second integral output signal is obtained by integrating the first integral output signal. The feedback output signal is then integrated to obtain the first integral output signal.

[0109] Optionally, the feedback output signal is integrated to obtain the first integrated output signal, specifically:

[0110] The feedback output signal is input to the input terminal of the first integrator, and the first integrated output signal is obtained at the output terminal of the first integrator; wherein, the first integrator is expressed as:

[0111]

[0112] Among them, f FI (s) is the Laplace transfer function of the first integrator, T W This represents the window duration.

[0113] Optionally, the second integral output signal is obtained by integrating the first integral output signal, specifically as follows:

[0114] The first integral output signal is input to the input terminal of the second integrator, and the second integral output signal is obtained at the output terminal of the second integrator; wherein, the second integrator is expressed as:

[0115]

[0116] Among them, f SI (s) is the Laplace transfer function of the second integrator; T W This represents the window duration.

[0117] The delay superposition processing module 602 is used to perform delay superposition processing on the first integral output signal to obtain the first adder output signal.

[0118] Optionally, the first integral output signal is delayed and superimposed to obtain the first adder output signal, specifically as follows:

[0119] The first integral output signal is input to the input terminal of the second delay unit, and the second delayed output signal is obtained at the output terminal of the second delay unit; wherein, the second delay unit is expressed as:

[0120]

[0121] Among them, f L:B (s) is the Laplace transfer function of the second delay, T F:B The delay time constant of the second delay unit;

[0122] The first integral output signal is input to the first input terminal of the first adder, and the second delay output signal is input to the second input terminal of the first adder. The first integral output signal and the second delay output signal are added together in the first adder to obtain the first adder output signal.

[0123] The construction module 603 is used to construct a parabolic window function by performing delayed numerical operations on the input signal and the output signal of the first adder.

[0124] Optionally, a parabolic window function is constructed by performing delayed numerical operations on the input signal and the output signal of the first adder, specifically as follows:

[0125] The input signal is delayed to obtain a first delayed output signal; the first delayed output signal is input to the subtrahend terminal of a second subtractor, and the input signal is input to the minuend terminal of the second subtractor. The first delayed output signal is subtracted from the input signal in the second subtractor to obtain the second subtractor output signal; the second subtractor output signal is input to the first input terminal of a second adder, and the first adder output signal is input to the second input terminal of the second adder. The second subtractor output signal and the first adder output signal are added in the second adder to obtain the second adder output signal; a parabolic window function is constructed based on the second adder output signal.

[0126] Optionally, the input signal is delayed to obtain a first delayed output signal, specifically as follows:

[0127] The input signal is input to the input terminal of the first delay unit, and the first delayed output signal is obtained at the output terminal of the first delay unit; wherein, the first delay unit is expressed as:

[0128]

[0129] Among them, f L:A (s) is the Laplace transfer function of the first delay, T F:A is the delay time constant of the first delay unit.

[0130] Optionally, a parabolic window function is constructed based on the output signal of the second adder, specifically as follows:

[0131] The output signal of the second adder is used as the output of the parabolic window function. The parabolic window function is constructed as follows:

[0132]

[0133] T F:A =T F:B =T W

[0134] Among them, f PWF (s) is the Laplace transfer function of the parabolic window function, T W T is the window duration. F:A T is the delay time constant of the first delay unit. F:B is the delay time constant of the second delay unit.

[0135] In implementing this embodiment of the invention, the input signal is processed by feedback integration to obtain a first integral output signal; the first integral output signal is then delayed and superimposed to obtain a first adder output signal; by performing delayed numerical operations on the input signal and the first adder output signal, a parabolic window function is constructed. This parabolic window function, during filtering, causes the filtered output phase to lead, fundamentally overcoming the exponential tracking filtering mechanism of a first-order inertial filter and its limitation in tracking the input signal. This forms a typical and original exponential tracking filtering mechanism, improving the performance of the output tracking the input signal, achieving efficient tracking filtering, and enhancing the filtering effect.

[0136] Example 3

[0137] Accordingly, see Figure 7 , Figure 7 This is a connection diagram of a third embodiment of a filter provided by the present invention. Figure 7 As shown, the filter includes a parabolic window function construction device, a third integrator, and a proportional controller; wherein, the parabolic window function construction device performs the method of constructing the parabolic window function.

[0138] By connecting the parabolic window function construction device, the third integrator, and the proportional controller in series, a filter is obtained, as shown in the formula:

[0139]

[0140] T I =T W

[0141] Among them, f FTF (s) is the Laplace transfer function of the filter, f PWF (s) is the Laplace transfer function of the parabolic window function, T I K is the integration time of the third integrator. P For the gain of the proportional controller, T W This represents the window duration.

[0142] In this embodiment, a parabolic window function is used to construct the fastest tracking filter. The parabolic window function is connected in series with an integrator and a proportional controller to obtain the fastest tracking filter, which is expressed as:

[0143]

[0144] T I =T W

[0145] Among them, f FTF (s) is the Laplace transfer function of the filter that achieves the fastest tracking, f PWF (s) is the Laplace transfer function of the parabolic window function, according to T W Get T I T I K represents the integration time of the integrator, expressed in seconds. P The gain of the proportional controller is dimensionless, T. W This represents the window duration, measured in seconds (s).

[0146] In this embodiment, the window time length T of the parabolic window function W =100s, T W =T F:A =T F:B =T I =100s, K P =0.6, when the input signal of the parabolic window function is a unit step, the output process PV of the fastest tracking filter is obtained. FTF (t), such as Figure 8 As shown.

[0147] In this embodiment, the filtering characteristics of the fastest tracking filter and the first-order inertial filter are compared to illustrate the advantages of the tracking filtering performance of the present invention. The expression for the first-order inertial filter is:

[0148]

[0149] Among them, f FOIF (s) is the Laplace transfer function of the first-order inertial filter; T FOIF is the filtering time constant of the first-order inertial filter, in seconds.

[0150] Set K P =0.6, T FOIF =50s, T W =50s, T F:A =T F:B =T W =50s, T I =TW =50s, the input signal is a unit step, and the process output PV of the fastest tracking filter is obtained respectively. FTF The process output PV of (t) and the first-order inertial filter. FOIF (t), the tracking comparison results between the fastest tracking filter and the first-order inertial filter, such as Figure 9 As shown. By Figure 9 It can be seen that when t > 100s, the fastest tracking filter has already tracked the input from the output, while the first-order inertial filter has tracked 64% of the input from the output. Conversely, when the output tracks 64% of the input, the fastest tracking filter takes 60s, while the first-order inertial filter takes 100s. Therefore, it is evident that the fastest tracking filter is significantly more efficient at tracking the input than the first-order inertial filter.

[0151] As an example of this embodiment, the fastest tracking filter of the present invention is used to filter the primary wind temperature process signal of a 1000MW thermal power unit, and its filtering characteristics are compared with those of the first-order inertial filter commonly used in the prior art.

[0152] Set K P =0.6, T FOIF =50s, T W =50s, T F:A =T F:B =T W =50s, T I =T W =50s, and the comparison results of the filtering outputs of the fastest tracking filter and the first-order inertial filter are obtained, such as Figure 10 As shown, the output of the fastest tracking filter significantly outpaces the output of the first-order inertial filter. The parabolic fastest tracking filter designed with a parabolic window function outperforms the first-order inertial filter.

[0153] In implementing this embodiment of the invention, the first-order inertial filter belongs to an exponential filtering tracking mechanism, which has low tracking efficiency and requires a breakthrough tracking filtering mechanism. The window function also needs to be improved. The fastest tracking filter designed with a parabolic window function can fundamentally break through the exponential tracking filtering mechanism of the first-order inertial filter, realize the fastest tracking filtering mechanism, and improve filtering performance.

[0154] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention for those skilled in the art.

Claims

1. A method for constructing a parabolic window function, characterized in that, include: The input signal is processed by feedback integration to obtain a first integral output signal. Specifically, the input signal is input to the minuend of a first subtractor, and the second integral output signal is input to the subtrahend of the first subtractor. The input signal and the second integral output signal are subtracted to obtain a feedback output signal. The second integral output signal is obtained by integrating the first integral output signal. The feedback output signal is then integrated to obtain the first integral output signal. The first integral output signal is delayed and superimposed to obtain the first adder output signal. Specifically, the first integral output signal is input to the input terminal of the second delay unit, and a second delayed output signal is obtained at the output terminal of the second delay unit; the first integral output signal is input to the first input terminal of the first adder, and the second delayed output signal is input to the second input terminal of the first adder; the first integral output signal and the second delayed output signal are added in the first adder to obtain the first adder output signal. A parabolic window function is constructed by performing delayed numerical operations on the input signal and the output signal of the first adder. Specifically, the input signal is delayed to obtain a first delayed output signal; the first delayed output signal is input to the subtrahend terminal of a second subtractor, and the input signal is input to the minuend terminal of the second subtractor. The first delayed output signal is subtracted from the input signal in the second subtractor to obtain a second subtractor output signal; the second subtractor output signal is input to the first input terminal of a second adder, and the first adder output signal is input to the second input terminal of the second adder. The second subtractor output signal is added to the first adder output signal in the second adder to obtain a second adder output signal; the parabolic window function is constructed based on the second adder output signal.

2. The method for constructing the parabolic window function as described in claim 1, characterized in that, The step of integrating the feedback output signal to obtain the first integrated output signal is specifically as follows: The feedback output signal is input to the input terminal of the first integrator, and the first integrated output signal is obtained at the output terminal of the first integrator; wherein, the first integrator is expressed as: in, f FI ( s Let be the Laplace transfer function of the first integrator. T W This represents the window duration.

3. The method for constructing the parabolic window function as described in claim 2, characterized in that, The second integral output signal is obtained by integrating the first integral output signal, specifically: The first integral output signal is input to the input terminal of the second integrator, and the second integral output signal is obtained at the output terminal of the second integrator; wherein, the second integrator is expressed as follows: in, f SI ( s ) is the Laplace transfer function of the second integrator; T W The window duration is denoted as .

4. The method for constructing the parabolic window function as described in claim 1, characterized in that, The second delay is expressed as follows: in, f L:B ( s Let be the Laplace transfer function of the second delay. T F:B is the delay time constant of the second delay unit.

5. The method for constructing the parabolic window function as described in claim 1, characterized in that, The step of delaying the input signal to obtain a first delayed output signal specifically involves: The input signal is input to the input terminal of the first delay unit, and the first delayed output signal is obtained at the output terminal of the first delay unit; wherein, the first delay unit is expressed as follows: in, f L:A ( s Let be the Laplace transfer function of the first delay. T F:A is the delay time constant of the first delay unit.

6. The method for constructing the parabolic window function as described in any one of claims 1-5, characterized in that, The construction of the parabolic window function based on the output signal of the second adder is specifically as follows: The output signal of the second adder is used as the output of the parabolic window function to construct the parabolic window function, as shown in the formula: in, f PWF ( s ) is the Laplace transfer function of the parabolic window function. T W The window duration. T F:A Let be the delay time constant of the first delay unit. T F:B is the delay time constant of the second delay unit.

7. A device for constructing a parabolic window function, characterized in that, include: The module consists of a feedback integral operation processing module, a delay superposition processing module, and a construction module. The feedback integration processing module is used to perform feedback integration processing on the input signal to obtain a first integral output signal. Specifically, the input signal is input to the minuend of a first subtractor, and a second integral output signal is input to the subtrahend of the first subtractor. The input signal and the second integral output signal are subtracted to obtain a feedback output signal. The second integral output signal is obtained by integrating the first integral output signal. The feedback output signal is then integrated to obtain the first integral output signal. The delay superposition processing module is used to perform delay superposition processing on the first integral output signal to obtain the first adder output signal. Specifically, the first integral output signal is input to the input terminal of the second delay unit, and a second delayed output signal is obtained at the output terminal of the second delay unit; the first integral output signal is input to the first input terminal of the first adder, and the second delayed output signal is input to the second input terminal of the first adder; the first integral output signal and the second delayed output signal are added in the first adder to obtain the first adder output signal. The construction module is used to construct a parabolic window function by performing delayed numerical operations on the input signal and the output signal of the first adder. Specifically, it performs a delay on the input signal to obtain a first delayed output signal; inputs the first delayed output signal to the subtrahend terminal of a second subtractor, inputs the input signal to the minuend terminal of the second subtractor, subtracts the first delayed output signal from the input signal in the second subtractor to obtain a second subtractor output signal; inputs the second subtractor output signal to the first input terminal of a second adder, inputs the first adder output signal to the second input terminal of the second adder, adds the second subtractor output signal to the first adder output signal in the second adder to obtain a second adder output signal; and constructs the parabolic window function based on the second adder output signal.

8. A filter, characterized in that, The system includes a device for constructing a parabolic window function, a third integrator, and a proportional controller; wherein the device for constructing the parabolic window function performs the method for constructing a parabolic window function as described in any one of claims 1 to 6. The filter is obtained by connecting the parabolic window function construction device, the third integrator, and the proportional controller in series, as shown in the formula: in, f FTF ( s Let be the Laplace transfer function of the filter. f PWF ( s ) is the Laplace transfer function of the parabolic window function. T I K is the integration time of the third integrator. P The gain of the proportional controller. T W This represents the window duration.

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