A quarter cosine window generating device and a fast tracking filter

Abstract

The application discloses a quarter inverse raised cosine window generating device and a steepest tracking filter, and the generating device comprises an input end, a subtracter, a first adder, a second adder, a first integrator, a second integrator, a fixed proportional controller and a time delay device; the subtracter, the first integrator and the second integrator are sequentially connected, the second integrator is connected with the subtracter, a closed loop feedback is formed; the first integrator is connected with the first adder, the first adder is connected with the fixed proportional controller, the fixed proportional controller is connected with the time delay device, and the second integrator and the time delay device are respectively connected to the second adder. The quarter inverse raised cosine window function is generated by using multiple integrators, subtracters, time delay devices and multiple adders, which is different from the existing window function; the steepest tracking filter is constructed by using the quarter inverse raised cosine window, the steepest filtering tracking mechanism is realized, the exponential tracking mechanism of the first-order inertial filter is broken through, and the filtering performance is effectively improved.

Description

Technical Field

[0001] This invention relates to the technical fields of signal processing and industrial process control, and in particular to a device for generating a quarter-inverted raised cosine window and a fastest tracking filter. Background Technology

[0002] In the field of industrial process control technology, the proportional-integral-derivative (PID) controller is the preferred basic control technology. Its widespread application in industrial process control has cemented its fundamental control status.

[0003] However, from the perspective of industrial control technology development, with the increasing demands for deep peak shaving and rapid frequency regulation in thermal power units, basic PID control technology can no longer meet the needs of the control process. Today, the PID structure is based on a first-order inertial filter (FOIF), which represents a typical exponential tracking filtering mechanism. The main problem with FOIF is its poor output-to-input tracking performance, making efficient filtering impossible. The essence of replacing PID is to break through the exponential tracking filtering mechanism of FOIF from the perspective of tracking filtering mechanisms.

[0004] In signal processing technology, 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, and their passband ripple and stopband attenuation are equal, which can negatively impact filter performance. Window function methods are generally a fundamental and widely used filter design approach, used to design digital low-pass filters to achieve frequency domain filtering effects. However, existing window functions cannot construct the fastest tracking filter. Summary of the Invention

[0005] This invention proposes a device for generating a quarter-inverted raised cosine window and a quarter-inverted raised cosine type fastest tracking filter. The device uses multiple integrators, subtractors, delayers and multiple adders to generate a quarter-inverted raised cosine window function. Unlike existing window functions, the fastest tracking filter is constructed through a quarter-inverted raised cosine window, realizing the fastest filtering tracking mechanism. This breaks through the exponential tracking mechanism of the first-order inertial filter FOIF and effectively improves the filtering performance.

[0006] A first aspect of the present invention provides a device for generating a quarter-inverted raised cosine window. The device includes: an input terminal, a subtractor, a first adder, a second adder, a first integrator, a second integrator, a fixed proportional controller, and a delay. The subtractor, the first integrator, and the second integrator are connected sequentially, and the second integrator is connected to the subtractor to form a closed-loop feedback. The first integrator is connected to the first adder, the first adder is connected to the fixed proportional controller, the fixed proportional controller is connected to the delay, and the second integrator and the delay are respectively connected to the second adder.

[0007] The input signal passes through a subtractor to obtain a subtractor output signal. The subtractor output signal is input to a first integrator to obtain a first integral output signal. The first integral output signal is input to a second integrator to obtain a second integral output signal. The second integral output signal is input to a subtractor, forming a closed-loop feedback.

[0008] The input signal and the first integral output signal are respectively input to the first adder for addition processing to obtain the first adder output signal. The first adder output signal is input to the fixed proportional controller to obtain the fixed proportional control signal. The fixed proportional control signal is input to the delay unit to obtain the delay unit signal. The second integral output signal and the delay unit signal are respectively input to the second adder for addition processing to obtain the second adder output signal. The second adder output signal represents the output of the quarter-inverted raised cosine window.

[0009] In one possible implementation of the first aspect, the expression for the first integrator is:

[0010]

[0011] Among them, f FI (s) is the Laplace transfer function of the first integrator; T W This represents the window duration.

[0012] In one possible implementation of the first aspect, the expression for the second integrator is:

[0013]

[0014] Among them, f SI (s) is the Laplace transfer function of the second integrator; T W This represents the window duration.

[0015] In one possible implementation of the first aspect, the expression for the fixed-proportion controller is:

[0016] f K (s)=K

[0017] K = -1

[0018] Among them, f K (s) is the Laplace transfer function of the fixed proportional controller; K is the gain of the fixed proportional controller.

[0019] In one possible implementation of the first aspect, the expression for the delay is:

[0020]

[0021] Among them, f L (s) is the Laplace transfer function of the delay; T L is the delay time constant of the delay unit.

[0022] In one possible implementation of the first aspect, the expression for the quarter-inverted raised cosine window is:

[0023]

[0024] K = -1

[0025] Among them, f QICW (s) is the Laplace transfer function of a quarter-inverted raised cosine window; T W T is the window duration; L is the delay time constant of the delay unit; K is the gain of the fixed proportional controller.

[0026] In one possible implementation of the first aspect, the delay time constant of the delay is obtained from the window time length:

[0027]

[0028] Among them, T W T is the window duration; L is the delay time constant of the delay unit.

[0029] A second aspect of the present invention provides a quarter-inverted raised cosine type fastest tracking filter, which includes: a quarter-inverted raised cosine window generation device and a third integrator;

[0030] The generator for the quarter-inverted cosine window is connected to the third integrator;

[0031] The output signal of the quarter-inverted raised cosine window generated by the quarter-inverted raised cosine window generator is input to the third integrator for integration to obtain the third integrated signal, which represents the output signal of the quarter-inverted raised cosine type fastest tracking filter.

[0032] In one possible implementation of the second aspect, the expression for the third integrator is:

[0033]

[0034] Among them, f I (s) is the Laplace transfer function of the third integrator; T I is the integration time constant of the third integrator.

[0035] In one possible implementation of the second aspect, the integration time constant of the third integrator is obtained from the delay time constant of the delay unit in the generation device of the quarter-inverted raised cosine window, specifically:

[0036]

[0037] Among them, T I T is the integration time constant of the third integrator; L is the delay time constant of the delay unit.

[0038] In one possible implementation of the second aspect, the expression for the quarter-inverted raised cosine type fastest tracking filter is:

[0039]

[0040] Among them, f FTF (s) is the Laplace transfer function of the quarter-inverse raised cosine type fastest tracking filter; f QICW (s) is the Laplace transfer function of a quarter-inverted raised cosine window; T I The integration time constant of the third integrator. Compared with the prior art, the quarter-inverted raised cosine window generation device and the quarter-inverted raised cosine type fastest tracking filter provided by the embodiments of the present invention have the following advantages: The present invention uses multiple integrators, subtractors, delayers and multiple adders to generate a quarter-inverted raised cosine window function. Unlike the existing window functions, the fastest tracking filter is constructed through a quarter-inverted raised cosine window, realizing the fastest filtering tracking mechanism, breaking through the exponential tracking mechanism of the first-order inertial filter, and effectively improving the filtering performance. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the structure of a quarter-inverted raised cosine window generation device provided by the present invention;

[0042] Figure 2 This is a schematic diagram of the waveform of the first addition signal in an embodiment of the generation device for a quarter-inverted raised cosine window provided by the present invention.

[0043] Figure 3 This is a waveform diagram of the delay signal of an embodiment of the generation device for a quarter-inverted raised cosine window provided by the present invention.

[0044] Figure 4 This is a schematic diagram of the waveform output of a quarter-inverted raised cosine window according to an embodiment of the quarter-inverted raised cosine window generation device provided by the present invention.

[0045] Figure 5 This is a schematic diagram of the structure of a quarter-inverted raised cosine type fastest tracking filter provided by the present invention;

[0046] Figure 6 This is a schematic diagram of the waveform of the filtered signal according to an embodiment of the quarter-inverted raised cosine type fastest tracking filter provided by the present invention;

[0047] Figure 7 This is a comparison diagram of the output waveforms of a quarter-inverted raised cosine type fastest tracking filter and a first-order inertial filter, according to an embodiment of the present invention.

[0048] Figure 8 This is a waveform comparison diagram of the boiler main steam pressure process signal obtained by quarter-inverted raised cosine type fastest tracking filter and first-order inertial filter according to an embodiment of the present invention. Detailed Implementation

[0049] 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.

[0050] To address the aforementioned issues, the following detailed description and explanation of a quarter-inverted raised cosine window generation apparatus provided in this application will be provided through specific embodiments.

[0051] Reference Figure 1 The diagram shows a schematic representation of a device for generating a quarter-inverted cosine window according to an embodiment of the present invention.

[0052] The device for generating a quarter-inverted raised cosine window, as an example, may include: an input terminal, a subtractor, a first adder, a second adder, a first integrator, a second integrator, a fixed proportional controller, and a delay unit.

[0053] The subtractor, the first integrator, and the second integrator are connected in sequence, and the second integrator is connected to the subtractor to form a closed-loop feedback. The first integrator is connected to the first adder, the first adder is connected to the fixed proportional controller, the fixed proportional controller is connected to the delay, and the second integrator and the delay are respectively connected to the second adder.

[0054] The input signal passes through a subtractor to obtain a subtractor output signal. The subtractor output signal is input to a first integrator to obtain a first integral output signal. The first integral output signal is input to a second integrator to obtain a second integral output signal. The second integral output signal is input to the subtractor, forming a closed-loop feedback.

[0055] The input signal and the first integral output signal are respectively input to the first adder for addition processing to obtain the first adder output signal. The first adder output signal is input to the fixed proportional controller to obtain the fixed proportional control signal. The fixed proportional control signal is input to the delay unit to obtain the delay unit signal. The second integral output signal and the delay unit signal are respectively input to the second adder for addition processing to obtain the second adder output signal. The second adder output signal represents the output of the quarter-inverted raised cosine window, that is, it represents the output of the quarter-inverted raised cosine window signal.

[0056] In one embodiment, the input signal can be input to the minuend of the subtractor, and the subtractor output signal can be obtained at the output of the subtractor.

[0057] The subtractor 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.

[0058] In one embodiment, the expression for the first integrator is:

[0059]

[0060] 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).

[0061] In one 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.

[0062] In one embodiment, the expression for the second integrator is:

[0063]

[0064] 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).

[0065] Optionally, the second integral output signal can be input to the subtraction terminal of the first subtractor to form a closed-loop feedback second integral output signal.

[0066] In one embodiment, the input signal and the first integral output signal from the output of the first integrator are respectively input to the input of the first adder. That is, the input signal is input to the first input of the first adder, and the first integral output signal is input to the second input of the first adder. The first adder performs an addition operation on the input signal and the first integral output signal, thereby obtaining the first adder output signal at the output of the first adder. As an example of one embodiment, in T... W =201s, the process of obtaining the first addition signal output PV with a unit step input signal = 201s. AA (t), a schematic diagram of the waveform of the first addition signal, as shown below. Figure 2 As shown. The output signal of the first adder is input to the fixed-proportion controller to obtain a fixed-proportion control signal.

[0067] In one embodiment, the expression for the fixed proportional controller is:

[0068] f K (s)=K

[0069] Among them, f K (s) is the Laplace transfer function of the fixed proportional controller; K is the gain of the fixed proportional controller, in dimensionless form. Preferably, K = -1.

[0070] The fixed-proportion control signal at the output of the fixed-proportion controller is input to the delay unit to obtain the delay unit signal.

[0071] In one embodiment, the expression for the delay is:

[0072]

[0073] Among them, f L (s) is the Laplace transfer function of the delay; T L is the delay time constant of the delay unit.

[0074] Preferably, T L =T W / 2.01. Where, T W T represents the window duration in seconds. L T is the delay time constant of the delay unit. L By T W We obtain, i.e., T L =T W / 2.01. As an example of an embodiment, in T W =201s, TL =100s, K=-1, the input signal is a unit step, the process of obtaining the delay signal output PV L (t), a waveform diagram of the delay signal, as shown below. Figure 3 As shown. The second integral output signal from the second integrator and the delay output signal from the delay unit are respectively input to the second adder for addition to obtain the second adder output signal. The second adder output signal represents the output signal of the quarter-inverted raised cosine window. The second integral output signal is input to the first input terminal of the second adder, and the delay signal is input to the second input terminal of the second adder. The second adder performs an addition operation on the second integral output signal and the delay signal to obtain the second adder output signal, which is the output signal of the quarter-inverted raised cosine window.

[0075] In one embodiment, the expression for the quarter-inverted raised cosine window is:

[0076]

[0077] K = -1

[0078] T L =T W / 2.01

[0079] Among them, f QICW (s) is the Laplace transfer function of the quarter-inverted cosine window (QICW); T W T represents the window duration in seconds. L is the delay time constant of the delay unit; K is the gain of the fixed proportional controller, in dimensionless units.

[0080] As one example of an implementation, in T W =201s, T L =100s, K=-1, the input signal is a unit step, and the process of obtaining the output PV of the new window function, namely the quarter-inverse raised cosine window function, is as follows: QICW (t), a schematic diagram of the waveform output of a quarter-inverted raised cosine window, as shown below. Figure 4 As shown.

[0081] This invention provides a device for generating a quarter-inverted raised cosine window. Its advantages are: this invention can simultaneously utilize multiple integrators, subtractors, delayers, and adders to generate a novel window function, distinct from existing window functions, and can be used to construct the fastest tracking filter. This invention also provides a quarter-inverted raised cosine type fastest tracking filter, see [link to relevant documentation]. Figure 5The diagram shows a schematic of the structure of a quarter-inverted raised cosine type fastest tracking filter provided by the present invention.

[0082] As an example, the quarter-inverted raised cosine type fastest tracking filter may include: a quarter-inverted raised cosine window generation device and a third integrator as described in the above embodiments;

[0083] The generator for the quarter-inverted cosine window and the third integrator are connected in sequence;

[0084] The input signal is input to the generator of the quarter-inverted raised cosine window. The output signal of the quarter-inverted raised cosine window is obtained at the output of the generator. The output signal of the quarter-inverted raised cosine window is input to the third integrator for integration to obtain the third integrated output signal. The third integrated signal is the filter signal, which represents the output signal of the quarter-inverted raised cosine type fastest tracking filter.

[0085] In one embodiment, the filter constructed by sequentially connecting the generation device of the quarter-inverted raised cosine window and the third integrator can serve as a quarter-inverted raised cosine type fastest tracker.

[0086] In one embodiment, the expression for the third integrator is:

[0087]

[0088] Among them, f I (s) is the Laplace transfer function of the third integrator; T I is the integration time constant of the third integrator, in seconds.

[0089] In one embodiment, the expression for the quarter-inverted raised cosine type fastest tracking filter is:

[0090]

[0091]

[0092] Among them, f FTF (s) is the Laplace transfer function of the quarter-inverse raised cosine type fastest tracking filter; f QICW (s) is the Laplace transfer function of a quarter-inverted raised cosine window; T I T is the integration time constant of the third integrator. I By T L Result: T I =T L / 2.7, in seconds (s), in tons (T) L The delay time constant of the delay unit in the generation device of a quarter-inverted raised cosine window.

[0093] In one embodiment, in T W =201s, T L =100s, K=-1, T I =36.9s, the input signal is a unit step, resulting in the fastest tracking filter, i.e., the process output PV of the quarter-inverse raised cosine type fastest tracking filter. FTF (t), a schematic diagram of the waveform of the filtered signal, as shown below. Figure 6 As shown.

[0094] To further illustrate the filtering effect of the present invention, in one embodiment, the filtering characteristics of the fastest tracking filter of the present invention are compared with those of a first-order inertial filter in the prior art.

[0095] The expression for the first-order inertial filter is:

[0096]

[0097] 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.

[0098] In T W =201s, T FOIF =T L =100s, K=-1, T I =37s, the input signal is a unit step, and the process output PV of the fastest tracking filter of this invention is obtained. FTF The process output PV of (t) and the first-order inertial filter. FOIF (t), a comparison of the output waveforms of a quarter-inverted raised cosine type fastest tracking filter and a first-order inertial filter, as shown in the figure. Figure 7 As shown.

[0099] Depend on Figure 7 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 63% of the input from the output. Similarly, to track 63% of the input from the output, the fastest tracking filter needs 77s, while the first-order inertial filter needs 100s. It is evident that the fastest tracking filter is significantly more efficient at tracking the input than the first-order inertial filter.

[0100] In one embodiment, the fastest tracking filter is used to filter the main steam pressure process signal of a boiler in a 1000MW thermal power unit, and its filtering characteristics are compared with those of a first-order inertial filter.

[0101] Set T W =100.5s, T FOIF =T L=50s, K=-1, T I =18.5s, the comparison results of the quarter-inverted raised cosine type fastest tracking filter and the first-order inertial filter are obtained. The waveform comparison diagram of the results of the quarter-inverted raised cosine type fastest tracking filter and the first-order inertial filter for the boiler main steam pressure process signal is as follows. Figure 8 As shown, the output of the quarter-inverted raised cosine type fastest tracking filter significantly outpaces the output of the first-order inertial filter, and the filtering performance of the quarter-inverted raised cosine type fastest tracking filter is superior to that of the first-order inertial filter.

[0102] This invention can simultaneously utilize multiple integrators, subtractors, delayers, and adders to generate a novel window function, namely a quarter-inverted raised cosine window function. Unlike existing window functions, this invention constructs the fastest tracking filter using the novel quarter-inverted raised cosine window function, achieving the fastest filtering tracking and breaking through the exponential tracking mechanism, thereby improving the filtering effect and filtering performance.

[0103] Those skilled in the art will understand that, for ease of description and brevity, the specific working process of the device described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0104] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A device for generating a quarter-inverted cosine window, characterized in that, The generating device includes: an input terminal, a subtractor, a first adder, a second adder, a first integrator, a second integrator, a fixed-proportion controller, and a delay unit; the subtractor, the first integrator, and the second integrator are connected in sequence, and the second integrator is connected to the subtractor to form a closed-loop feedback; the first integrator is connected to the first adder, the first adder is connected to the fixed-proportion controller, the fixed-proportion controller is connected to the delay unit, and the second integrator and the delay unit are respectively connected to the second adder; The input signal passes through the subtractor to obtain the subtractor output signal. The subtractor output signal is input to the first integrator to obtain the first integral output signal. The first integral output signal is input to the second integrator to obtain the second integral output signal. The second integral output signal is input to the subtractor to form a closed-loop feedback. The input signal and the first integral output signal are respectively input to the first adder for addition processing to obtain the first adder output signal. The first adder output signal is input to the fixed ratio controller to obtain the fixed ratio control signal. The fixed ratio control signal is input to the delay unit to obtain the delay unit signal. The second integral output signal and the delay unit signal are respectively input to the second adder for addition processing to obtain the second adder output signal. The second adder output signal represents the output of a quarter-inverted raised cosine window.

2. The apparatus for generating a quarter-inverted cosine window according to claim 1, characterized in that, The expression for the first integrator is: in, f FI ( s Let ) be the Laplace transfer function of the first integrator; T W This represents the window duration.

3. The apparatus for generating a quarter-inverted cosine window according to claim 1, characterized in that, The expression for the second integrator is: in, f SI ( s ) is the Laplace transfer function of the second integrator; T W This represents the window duration.

4. The apparatus for generating a quarter-inverted cosine window according to claim 1, characterized in that, The expression for the fixed-proportion controller is: in, f K ( s ) is the Laplace transfer function of the fixed proportional controller; K The gain of the fixed-ratio controller.

5. The apparatus for generating a quarter-inverted cosine window according to claim 3, characterized in that, The expression for the delay is: in, f L ( s ) is the Laplace transfer function of the delay; T L is the delay time constant of the delay device.

6. The apparatus for generating a quarter-inverted cosine window according to claim 5, characterized in that, The delay time constant of the delay unit is obtained from the window time length, specifically as follows: in, T W The window time length; T L is the delay time constant of the delay device.

7. The apparatus for generating a quarter-inverted cosine window according to claim 1, characterized in that, The expression for the quarter-inverted raised cosine window is: in, f QICW ( s ) is the Laplace transfer function of the quarter-inverted raised cosine window; T W This refers to the window duration. T L The delay time constant of the delay device; K The gain of the fixed-ratio controller.

8. A quarter-inverted raised cosine type fastest tracking filter, characterized in that, include: The apparatus for generating a quarter-inverted raised cosine window and the third integrator as described in any one of claims 1-7; The device for generating the quarter-inverted cosine window is connected to the third integrator; The output signal of the quarter-inverted raised cosine window from the output of the generating device is input to the third integrator for integration to obtain the third integrated signal, which represents the output signal of the quarter-inverted raised cosine type fastest tracking filter.

9. The quarter-inverted raised cosine type fastest tracking filter according to claim 8, characterized in that, The expression for the third integrator is: in, The Laplace transfer function of the third integrator; T I The integration time constant of the third integrator.

10. The quarter-inverted raised cosine type fastest tracking filter according to claim 9, characterized in that, The integration time constant of the third integrator is obtained from the delay time constant of the delay unit in the generation device of the quarter-inverted raised cosine window, specifically: in, T I The integration time constant of the third integrator; T L is the delay time constant of the delay device.

11. The quarter-inverted raised cosine type fastest tracking filter according to claim 10, characterized in that, The expression for the quarter-inverted raised cosine type fastest tracking filter is: in, f FTF ( s ) is the Laplace transfer function of the quarter-inverse raised cosine type fastest tracking filter; f QICW ( s ) is the Laplace transfer function of the quarter-inverted raised cosine window; T I The integration time constant of the third integrator.

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