Differentiator construction method, device and equipment and electronic medium
By performing Laplace transformation and coupling of combined differentials, the problem of insufficient high-frequency gain of existing differentials is solved, the performance of approximately ideal differentials is achieved, and the performance of PID controller is improved.
Patent Information
- Application Number
- CN202510203600.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-24
- Publication Date
- 2025-05-13
AI Technical Summary
The high-frequency gain of existing differentials is poor, resulting in lower performance of PID controllers.
By performing the first and second Laplace transformations on the time constants of the combined differentializer, the Laplace transfer function of the combined differentializer and the phase compensator is obtained, and coupled it to obtain the target differentializer.
The gain of the differentiator is significantly improved, bringing it close to the performance of the ideal differentiator and improving the overall performance of the PID controller.
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Figure CN119987188A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of PID control technology, and in particular to a differentiator construction method, device, equipment and electronic medium. Background Art
[0002] In the field of industrial process control with pure hysteresis response, proportional-integral-derivative (PID) control is widely used. For example, in the energy storage and release process of compressed air energy storage units, the compressed air temperature is adjusted by adjusting the heat exchange between the heat storage medium and the compressed air. The temperature response has a pure hysteresis feature, and the compressed air temperature control accuracy is closely related to the heat recovery efficiency and utilization rate.
[0003] The differentiator in the PID controller is a practical differentiator, which is an engineering reconstruction of the ideal differentiator. However, the high-frequency gain of the current differentiator is poor, resulting in low performance of the PID controller. Summary of the invention
[0004] In view of this, the present invention provides a differentiator construction method, device, equipment and electronic medium, which solves the technical problem that the high-frequency gain of the current differentiator is poor, resulting in low performance of the PID controller.
[0005] A first aspect of the present invention provides a method for constructing a differentiator, comprising:
[0006] Performing a first Laplace transform on the time constant of the combined differentiator to obtain a Laplace transfer function of the combined differentiator;
[0007] Performing a second Laplace transform on the time constant of the combined differentiator to obtain a Laplace transfer function of the phase compensator;
[0008] According to the Laplace transfer function of the combined differentiator and the Laplace transfer function of the phase compensator, the combined differentiator and the phase compensator are coupled to obtain a target differentiator.
[0009] Optionally, the Laplace transfer function of the combined differentiator is:
[0010]
[0011] In the formula, f CD (s) is the Laplace transfer function of the combined differentiator, s is the Laplace operator, T CD is the time constant of the combined differentiator, and i is the differentiator index.
[0012] Optionally, the Laplace transfer function of the phase compensator is:
[0013]
[0014] In the formula, is the Laplace transfer function of the phase compensator.
[0015] Optionally, the method further comprises:
[0016] A proportional-differential controller is determined according to the target differentiator, and the Laplace transfer function of the proportional-differential controller is:
[0017]
[0018] In the formula, is the Laplace transfer function of the proportional-derivative controller, is the gain of the target differentiator, is the Laplace transfer function of the target differentiator.
[0019] Optionally, the method further comprises:
[0020] The proportional-differential controller is updated into the PID controller to obtain an updated PID controller.
[0021] In a second aspect, an embodiment of the present application provides a differentiator construction device, comprising:
[0022] A differentiator transformation module, used for performing a first Laplace transformation on a time constant of the combined differentiator to obtain a Laplace transfer function of the combined differentiator;
[0023] A compensator transformation module, used for performing a second Laplace transformation on the time constant of the combined differentiator to obtain a Laplace transfer function of the phase compensator;
[0024] The differentiator construction module is used to couple the combined differentiator and the phase compensator according to the Laplace transfer function of the combined differentiator and the Laplace transfer function of the phase compensator to obtain a target differentiator.
[0025] Preferably, the device further comprises:
[0026] A control combination module is used to determine a proportional-differential controller according to the target differentiator, and the Laplace transfer function of the proportional-differential controller is:
[0027]
[0028] In the formula, is the Laplace transfer function of the proportional-derivative controller, is the gain of the target differentiator, is the Laplace transfer function of the target differentiator.
[0029] In a third aspect, an embodiment of the present application provides an electronic device, comprising a memory and a processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the processor executes the steps of the differentiator construction method described in the first aspect.
[0030] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed, implements the steps of the differentiator construction method as described in the first aspect.
[0031] In a fifth aspect, an embodiment of the present application provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium, and the computer program includes program instructions, wherein when the program instructions are executed by a computer, the computer executes the steps of the differentiator construction method as described in the first aspect.
[0032] It can be seen from the above technical solutions that the present invention performs a first Laplace transform on the time constant of the combined differentiator to obtain the Laplace transfer function of the combined differentiator, and performs a second Laplace transform on the time constant of the combined differentiator to obtain the Laplace transfer function of the phase compensator. According to the Laplace transfer function of the combined differentiator and the Laplace transfer function of the phase compensator, the combined differentiator and the phase compensator are coupled to obtain a target differentiator, so that the gain of the differentiator is greatly increased, and relative to the existing actual differentiator, the performance of an approximate ideal differentiator is achieved. BRIEF DESCRIPTION OF THE DRAWINGS
[0033] Figure 1 A schematic diagram of compressed air temperature control for a compressed air energy storage system provided in an embodiment of the present invention;
[0034] Figure 2 A flowchart of a method for constructing a differentiator provided by an embodiment of the present invention;
[0035] Figure 3 A schematic diagram of a control loop of a conventional PID controller provided in an embodiment of the present invention;
[0036] Figure 4 A schematic diagram of a control loop of an updated PID controller provided in an embodiment of the present invention;
[0037] Figure 5a A phase-frequency-phase comparison diagram of a near-target differentiator and an ideal differentiator provided in an embodiment of the present invention;
[0038] Figure 5bA comparison diagram of the amplitude-frequency gain of a near-target differentiator and an ideal differentiator provided in an embodiment of the present invention;
[0039] Figure 6 A comparison chart of simulation results of the step response of the PID controller provided by the embodiment of the present invention and the conventional PID control;
[0040] Figure 7 A schematic diagram of the structure of a differentiator construction device provided by an embodiment of the present invention;
[0041] Figure 8 A schematic diagram of the structure of a differentiator construction device provided in an embodiment of the present invention. DETAILED DESCRIPTION
[0042] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0043] Compressed air energy storage is a form of electric energy storage that can achieve large-capacity and long-term electric energy storage. It can use off-peak electricity from the power grid and new energy electricity such as wind power and photovoltaics to compress air, store the compressed high-pressure air in gas storage facilities, and release the compressed air when needed to drive the turbine and drive the generator to generate electricity. Compressed air energy storage technology has the advantages of large energy storage capacity, long energy storage cycle, high system efficiency, and long operating life. It is considered to be one of the most promising large-scale energy storage technologies. In recent years, the integration and demonstration projects of compressed air energy storage systems in my country have increased significantly, and its promotion, application and industrialization have further developed.
[0044] When the compressed air energy storage unit is in the energy storage and release conditions, the compressed air temperature control is closely related to the unit efficiency and storage capacity. The compressed air temperature is adjusted by adjusting the heat exchange between the heat storage medium and the compressed air. The compressed air temperature control process of the compressed air energy storage system is as follows: Figure 1 As shown, there is a hysteresis process in the temperature response. In order to improve the quality of compressed air temperature control, the embodiment of the present application provides a differentiator construction method, which can be applied to Figure 1 The PID controller in the compressed air temperature control process of the compressed air energy storage system shown.
[0045] like Figure 2 As shown, the embodiment of the present application provides a method for constructing a differentiator, including steps S1 to S3. Among them:
[0046] Step S1, performing a first Laplace transform on the time constant of the combined differentiator to obtain a Laplace transfer function of the combined differentiator.
[0047] Among them, the Laplace transfer function of the combined differentiator is:
[0048]
[0049] In the formula, f CD (s) is the Laplace transfer function of the combined differentiator, s is the Laplace operator, T CD is the time constant of the combined differentiator, and i is the differentiator index.
[0050] Step S2: Perform a second Laplace transform on the time constant of the combined differentiator to obtain a Laplace transfer function of the phase compensator.
[0051] Among them, the Laplace transfer function of the phase compensator is:
[0052]
[0053] In the formula, is the Laplace transfer function of the phase compensator.
[0054] Step S3: according to the Laplace transfer function of the combined differentiator and the Laplace transfer function of the phase compensator, the combined differentiator and the phase compensator are coupled to obtain a target differentiator.
[0055] Among them, the combined differentiator and the phase compensator are coupled in series, and the target differentiator is obtained as follows:
[0056]
[0057] In the formula, is the Laplace transfer function of the target differentiator.
[0058] The control loop of a conventional PID controller is as follows Figure 3 The proportional-integral controller is
[0059]
[0060] In the formula, is the Laplace transfer function of the proportional-integral controller; K P is the proportional gain, unit is dimensionless; T I is the integration time, in s.
[0061] The first-order pure lag process control loop based on the target differentiator is as follows Figure 4As shown, the proportional-differential controller is determined according to the target differentiator, and the Laplace transfer function of the proportional-differential controller is:
[0062]
[0063] In the formula, is the Laplace transfer function of the proportional-derivative controller, is the gain of the target differentiator, is the Laplace transfer function of the target differentiator.
[0064] In one embodiment, the proportional-derivative controller is updated to the PID controller to obtain an updated PID controller, such as Figure 4 shown.
[0065] In practical applications, in the compressed air energy storage system compressor interstage temperature control system, the time constant T of the combined differentiator is set. CD = 100s and compared with the target differentiator;
[0066] When the time constant of the target differentiator is TD=100s, the comparison result between the differentiator proposed in the embodiment of the present application and the ideal differentiator is obtained, as shown in FIG. Figure 5a~5b shown.
[0067] Figure 5a In, P ID(ω) is the frequency phase of the ideal differentiator, in degrees (°); P AID(ω) is the phase frequency phase of the differentiator proposed in the embodiment of the present application, in degrees (°); G ID(ω) is the amplitude-frequency gain of the ideal differentiator, in dB; G AID(ω) This is the amplitude-frequency gain of the differentiator proposed in the embodiment of the present application, in dB.
[0068] For the differentiator proposed in the embodiment of the present application relative to the ideal differentiator, when the frequency ω is less than 0.01 rad / s, the differentiator proposed in the embodiment of the present application is approximately an ideal differentiator, the phase is +90°, and the maximum phase error is +0.1° / -0.02°.
[0069] The high-frequency gain of an ideal differentiator tends to infinity, and the high-frequency gain of the differentiator proposed in the embodiment of the present application tends to 18.4 dB.
[0070] The transfer function of the compressor interstage temperature response process is approximately a first-order pure lag process:
[0071]
[0072] Setting K AID=1 / 8.32, ensuring that the high-frequency gain of the proportional-differential controller proposed in this application is the same as that of the conventional proportional-differential controller, ensuring fair comparison, and the high-frequency gain is 2; for controlling a first-order pure lag process, the high-frequency gain should not be too high.
[0073] When the open-loop system gain is 0.5 and the open-loop system phase is -135°, the optimal parameters of the new PID controller are searched as follows: K P =0.4935, T I =88s, T CD =199.5s; Similarly, the optimal parameters of the conventional PID controller are: K P =0.4578, T I =100.5s, T D =27s;
[0074] The process is given as a unit step, the external disturbance is a ramp signal, the ramp signal rate is 0.001 / s, and the ramp signal length is 2000s. The simulation results are as follows Figure 6 shown.
[0075] The PID controller proposed in the embodiment of the present application is described by NPID, VNPID(t) is the process output of the new PID control, PVPID(t) is the process output of the PID control, and the control performance indicators are shown in Table 1.
[0076] Table 1
[0077]
[0078] The external disturbance suppression performance index is shown in Table 2.
[0079] Table 2
[0080]
[0081] It can be seen that the differentiator proposed in the embodiment of the present application is approximately an ideal differentiator, with a phase of +90° and a maximum phase error of +0.1° / -0.02°. The high-frequency gain of an ideal differentiator tends to infinity, and the high-frequency gain of the differentiator proposed in the embodiment of the present application tends to 18.4dB.
[0082] It should be noted that, in the embodiment of the present application, a Laplace transfer function of the combined differentiator is obtained by performing a first Laplace transform on the time constant of the combined differentiator, and a Laplace transfer function of the phase compensator is obtained by performing a second Laplace transform on the time constant of the combined differentiator. According to the Laplace transfer function of the combined differentiator and the Laplace transfer function of the phase compensator, the combined differentiator and the phase compensator are coupled to obtain a target differentiator, so that the gain of the differentiator is greatly increased, and relative to the existing actual differentiator, the performance of an approximate ideal differentiator is achieved.
[0083] Based on the same inventive concept, an embodiment of the present application further provides a differentiator construction device for implementing the above-mentioned differentiator construction method.
[0084] The implementation solution provided by the device to solve the problem is similar to the implementation solution recorded in the above method, so the specific limitations in one or more differentiator construction device embodiments provided below can refer to the limitations on the differentiator construction method above, and will not be repeated here.
[0085] like Figure 7 As shown, the embodiment of the present application provides a differentiator construction device, comprising:
[0086] A differentiator transformation module 100 is used to perform a first Laplace transform on a time constant of a combined differentiator to obtain a Laplace transfer function of the combined differentiator;
[0087] A compensator transformation module 200, configured to perform a second Laplace transformation on the time constant of the combined differentiator to obtain a Laplace transfer function of the phase compensator;
[0088] The differentiator construction module 300 is used to couple the combined differentiator and the phase compensator according to the Laplace transfer function of the combined differentiator and the Laplace transfer function of the phase compensator to obtain a target differentiator.
[0089] In some embodiments, the Laplace transfer function of the combined differentiator is:
[0090]
[0091] In the formula, f CD (s) is the Laplace transfer function of the combined differentiator, s is the Laplace operator, T CD is the time constant of the combined differentiator, and i is the differentiator index.
[0092] In some embodiments, the Laplace transfer function of the phase compensator is:
[0093]
[0094] In the formula, is the Laplace transfer function of the phase compensator.
[0095] In one embodiment, the device further comprises:
[0096] The control combination module is used to determine the proportional-derivative controller according to the target differentiator. The Laplace transfer function of the proportional-derivative controller is:
[0097]
[0098] In the formula, is the Laplace transfer function of the proportional-derivative controller, is the gain of the target differentiator, is the Laplace transfer function of the target differentiator.
[0099] In some embodiments, the device further comprises:
[0100] The updating module is used to update the proportional-differential controller into the PID controller to obtain an updated PID controller.
[0101] like Figure 8 As shown, an embodiment of the present application further provides an electronic device, the electronic device 10 includes a memory 20 and a processor 30, the memory 20 stores a computer program, and when the computer program is executed by the processor 30, the processor 30 executes the steps of the differentiator construction method in any of the above embodiments.
[0102] An embodiment of the present application further provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed, the steps of the differentiator construction method in any of the above embodiments are implemented.
[0103] An embodiment of the present application also provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium, and the computer program includes program instructions, wherein when the program instructions are executed by a computer, the computer executes the steps of the differentiator construction method in any of the above embodiments.
[0104] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described systems, electronic devices, computer storage media, and computer program products can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.
[0105] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.
[0106] In several embodiments provided by the present invention, it is understood that each box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and a part of a module, a program segment or a code includes one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from that marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved.
[0107] In the several embodiments provided by the present invention, it should be understood that the disclosed systems, electronic devices, computer storage media, computer program products and methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of units is only a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.
[0108] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
[0109] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.
[0110] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for executing all or part of the steps of the various embodiments of the method of the present invention through a computer device (which can be a personal computer, a server, or a network device, etc.). The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (full name in English: Read-Only Memory, English abbreviation: ROM), random access memory (full name in English: Random Access Memory, English abbreviation: RAM), disk or optical disk, etc. Various media that can store program codes.
[0111] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for constructing a differentiator, characterized in that: include: Performing a first Laplace transform on the time constant of the combined differentiator to obtain a Laplace transfer function of the combined differentiator; Performing a second Laplace transform on the time constant of the combined differentiator to obtain a Laplace transfer function of the phase compensator; According to the Laplace transfer function of the combined differentiator and the Laplace transfer function of the phase compensator, the combined differentiator and the phase compensator are coupled to obtain a target differentiator.
2. The method for constructing a differentiator according to claim 1, characterized in that: The Laplace transfer function of the combined differentiator is: In the formula, f CD (s) is the Laplace transfer function of the combined differentiator, s is the Laplace operator, T CD is the time constant of the combined differentiator, and i is the differentiator index.
3. The method for constructing a differentiator according to claim 2, characterized in that: The Laplace transfer function of the phase compensator is: In the formula, is the Laplace transfer function of the phase compensator.
4. The method for constructing a differentiator according to any one of claims 1 to 3, characterized in that: Also includes: A proportional-differential controller is determined according to the target differentiator, and the Laplace transfer function of the proportional-differential controller is: In the formula, is the Laplace transfer function of the proportional-derivative controller, is the gain of the target differentiator, is the Laplace transfer function of the target differentiator.
5. The method for constructing a differentiator according to claim 4, characterized in that: Also includes: The proportional-differential controller is updated into the PID controller to obtain an updated PID controller.
6. A differentiator construction device, characterized in that: include: A differentiator transformation module, used for performing a first Laplace transformation on a time constant of the combined differentiator to obtain a Laplace transfer function of the combined differentiator; A compensator transformation module, used for performing a second Laplace transformation on the time constant of the combined differentiator to obtain a Laplace transfer function of the phase compensator; The differentiator construction module is used to couple the combined differentiator and the phase compensator according to the Laplace transfer function of the combined differentiator and the Laplace transfer function of the phase compensator to obtain a target differentiator.
7. The differentiator construction device according to claim 6, characterized in that: Also includes: A control combination module is used to determine a proportional-differential controller according to the target differentiator, and the Laplace transfer function of the proportional-differential controller is: In the formula, is the Laplace transfer function of the proportional-derivative controller, is the gain of the target differentiator, is the Laplace transfer function of the target differentiator.
8. An electronic device, characterized in that: The electronic device includes a memory and a processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the processor executes the steps of the differentiator construction method according to any one of claims 1 to 6.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed, the steps of the differentiator construction method according to any one of claims 1 to 6 are implemented.
10. A computer program product, characterized in that The computer program product comprises a computer program stored on a non-transitory computer-readable storage medium, wherein the computer program comprises program instructions, wherein when the program instructions are executed by a computer, the computer is caused to perform the steps of the differentiator construction method according to any one of claims 1 to 6.