Generalized fractional order system filter design method and device

Abstract

The invention discloses a generalized fractional order system filter design method and device. The method comprises the steps that a generalized fractional order system and performance parameters are given; constructing a reduced-order fractional order filter based on different values of the order of the fractional order and the generalized fractional order system; and tracking a to-be-estimated signal in the generalized fractional order system based on the reduced-order fractional order filter, so that a generalized fractional order error system constructed by the generalized fractional order system and the reduced-order fractional order filter is allowed and meets performance indexes. According to the embodiment of the invention, the problem of large filtering error of a generalized fractional order system is solved.

Description

Technical Field

[0001] The present application relates to a generalized fractional-order system filter design method and device, belonging to the field of filter design. Background Art

[0002] As an important topic in control theory research, system filtering has been widely studied in traditional system models. The core of system filtering is to design a filter to use the signal that can be measured in real time in the system to estimate the signal that the system cannot estimate or cannot measure in real time. The famous Kalman filter is a classic filtering technology that has been widely used in various fields of control and signal processing. However, when the system has uncertain disturbances, the standard Kalman filter algorithm cannot guarantee the filtering performance. Therefore, H ∞ Filtering methods are proposed to solve the problem of robust H ∞ Filtering problem. For H ∞ As for system filtering, most of the research results are mainly focused on integer-order systems, but there are also research results on fractional-order systems. ∞ As far as we know, there is a lack of effective conclusions on the filtering problem in both the full frequency domain and the limited frequency domain, so it is impossible to provide an accurate filtering solution. Summary of the invention

[0003] In view of this, the present application provides a generalized fractional-order system filter design method and device. The embodiments of the present application at least solve the problem of large filtering error of the generalized fractional-order system.

[0004] In a first aspect, an embodiment of the present application discloses a generalized fractional-order system filter design method, the method comprising: given a generalized fractional-order system and performance parameters; Fractional-based order Different values ​​and the generalized fractional-order system are used to construct a reduced-order fractional-order filter; Based on the reduced-order fractional-order filter, the signal to be estimated in the generalized fractional-order system is tracked, so that the generalized fractional-order error system constructed by the generalized fractional-order system and the reduced-order fractional-order filter is admissible and satisfies H ∞ Performance indicators; The generalized fractional-order system comprises: in, ∈(0,2) is the order of the fractional order, represents the Caputo fractional differential operator, is the system state variable, It is noise interference. is the system output, is the signal to be estimated that cannot be directly measured, Ao 、B o 、C o 、D o 、L and They all represent parameter matrices, A o 、B o 、C o 、D o 、L and , n, m, l, p represent the dimensions of the state vector, which are non-negative integers; The reduced-order fractional-order filter comprises: in, represents the state vector of the reduced-order fractional-order filter, represents the output signal of the reduced-order fractional-order filter, are the system parameters to be solved for the reduced-order fractional filter; , As follows: ; , As follows: ; in, represents a real matrix and I represents the identity matrix.

[0005] Furthermore, a generalized fractional-order error system is constructed, including: Build with is the state variable, to filter the error signal is the generalized fractional-order error system of the output variable: .

[0006] Furthermore, the generalized fractional-order error system is derived from the noise input To the filtered error signal output The transfer function is: ; is a given H ∞ Performance index, S represents the independent variable of the transfer function.

[0007] Furthermore, the input-output transfer function of the generalized fractional-order error system satisfies A sufficient condition is that there exists a complex matrix , real matrix , satisfying the equality constraints and LMI constraints.

[0008] Furthermore, the generalized fractional-order system is in the form of a circuit.

[0009] The second aspect of an embodiment of the present application discloses a generalized fractional-order system filter design device, the device comprising: a given module, used to give a generalized fractional-order system and performance parameters; a construction module, used to construct a reduced-order fractional-order filter based on different values ​​of the fractional order and the generalized fractional-order system; a tracking module, used to track the signal to be estimated in the generalized fractional-order system based on the reduced-order fractional-order filter, so that the generalized fractional-order system and the generalized fractional-order error system constructed by the reduced-order fractional-order filter are allowable and meet the performance indicators.

[0010] A third aspect of an embodiment of the present application discloses a computer-readable storage medium, which includes a stored program, wherein when the program is run, the generalized fractional-order system filter design method of the above embodiment is executed in a processor of a device where the program is located.

[0011] The fourth aspect of an embodiment of the present application discloses an electronic device, which includes: one or more processors; a storage device for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors execute the generalized fractional-order system filter design method of the above embodiment. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0013] Figure 1 A flowchart of a generalized fractional-order system filter design method provided in an embodiment of the present application.

[0014] Figure 2 A schematic diagram of a circuit system provided in an embodiment of the present application.

[0015] Figure 3 A schematic diagram of an error curve of an output signal and a measured signal varying with time provided in an embodiment of the present application.

[0016] Figure 4 A schematic diagram of an error curve of an output signal and a measured signal varying with time provided in an embodiment of the present application.

[0017] Figure 5 A schematic diagram of the structure of a generalized fractional-order system filter design device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0018] 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 should fall within the scope of protection of the present invention.

[0019] 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.

[0020] Embodiment 1: Figure 1 A flow chart of a generalized fractional-order system filter design method provided in an embodiment of the present application is shown in FIG. Figure 1 As shown, the method may include the following steps: 101Given the generalized fractional-order system and performance parameters.

[0021] In this step, the generalized fractional-order system includes: in, ∈(0,2) is the order of the fractional order, represents the Caputo fractional differential operator, is the system state variable, It is noise interference. is the system output, is the signal to be estimated that cannot be directly measured, A o 、B o、C o 、D o 、L and They all represent parameter matrices, A o 、B o 、C o 、D o 、L and , n, m, l, p represent the dimensions of the state vector and are non-negative integers.

[0022] It should be noted that the parameter matrix A o ，B o ，C o ，D o ， and L Represents a predetermined performance parameter. Exemplarily, they may be singular matrices.

[0023] 102 Fractional-based orders Different values ​​and the generalized fractional-order system are used to construct a reduced-order fractional-order filter.

[0024] In this step, the reduced-order fractional-order filter includes: in, represents the state vector of the reduced-order fractional-order filter, represents the output signal of the reduced-order fractional-order filter, are the system parameters to be solved for the reduced-order fractional filter; , (The first conclusion) is as follows: , , (Second conclusion) is as follows: ,in, represents a real matrix and I represents the identity matrix.

[0025] It should be noted that the constraints are equality constraints and LMI constraints.

[0026] when hour, The equality constraints can be: LMI constraints can be:

[0027] when When , the equality constraint can be: LMI constraints can be: is a feasible solution obtained according to the constraints.

[0028] 103. Track the signal to be estimated in the generalized fractional-order system based on the reduced-order fractional-order filter, so that the generalized fractional-order error system constructed by the generalized fractional-order system and the reduced-order fractional-order filter is admissible and satisfies H ∞ Performance indicators.

[0029] Furthermore, a generalized fractional-order error system is constructed, including: Build with is the state variable to filter the error signal is the generalized fractional-order error system of the output variable: .

[0030] Furthermore, the generalized fractional-order error system is derived from the noise input To the filtered error signal output The transfer function is: , is a given H ∞ Performance index, S represents the independent variable of the transfer function.

[0031] Furthermore, the input-output transfer function of the generalized fractional-order error system satisfies A sufficient condition is that there exists a complex matrix , real matrix , satisfying the equality constraints and LMI constraints.

[0032] Furthermore, the generalized fractional-order system is in the form of a circuit.

[0033] Specifically, this embodiment designs a generalized fractional-order RL circuit system. Figure 2 As shown, represents a voltage source, represents resistance, represents inductance, Represents current, inductance L Voltage on is its magnetic flux The derivative can be expressed as , Figure 2 The circuit system can be described as follows:

[0034] in: Consider system output and the signal to be estimated Then a generalized fractional-order system model (system model in step 101) can be obtained.

[0035] For the above generalized fractional-order circuit model, consider an admissible 5th-order generalized fractional-order system with the following parameters: Fixed the matrix that needs to be preset , and give performance indicators ,Based on the first conclusion, a stable reduced-order fractional-order filter is designed.

[0036] By using the YALMIP toolbox in MATLAB to solve the constraint set in the first conclusion of the theorem, the unknown variables in the conclusion can be solved as follows:

[0037] This shows that the constraint set given by the first conclusion has a feasible solution, that is, there is a suitable 2nd-order fractional filter, and then the parameters of the reduced-order filter are obtained:

[0038] Figure 3 The trend of the error curve changing with time is shown in Figure 1. It can be seen that the output error gradually stabilizes at 0 over time, which means that the obtained second-order fractional-order filter can gradually approach the signal to be measured.

[0039] Further, for the above generalized fractional-order circuit model, consider an admissible 5th-order generalized fractional-order system with the following parameters:

[0040] Similarly, referring to the second conclusion, the parameters of the reduced-order filter can be obtained:

[0041] Figure 4 The trend of the error curve changing with time is shown in Figure 1. It can be seen that the output error gradually stabilizes at 0 over time, which means that the obtained second-order fractional-order filter can gradually approach the signal to be measured.

[0042] Embodiment 2: Figure 5 A schematic diagram of the structure of a generalized fractional-order system filter design device provided in an embodiment of the present application is shown in FIG. Figure 5 As shown, the device may include the following modules: A given module 501 is used to give a generalized fractional-order system and performance parameters; Building block 502 for fractional order based Different values ​​and the generalized fractional-order system are used to construct a reduced-order fractional-order filter; A tracking module 503 is used to track the signal to be estimated in the generalized fractional-order system based on the reduced-order fractional-order filter, so that the generalized fractional-order error system constructed by the generalized fractional-order system and the reduced-order fractional-order filter is admissible and satisfies H ∞ Performance indicators.

[0043] Embodiment 3: The embodiments of the present application further provide an electronic device, comprising: a memory storing an executable program; and a processor for running the program, wherein the methods of the various embodiments of the present invention are executed when the program is running.

[0044] The above-mentioned memory may refer to a device inside a computer for storing data and programs, and may include memory, hard disk, etc., wherein the memory may be used to temporarily store running programs and data, the hard disk may be used to store programs and data for a long time, and the memory may be used to enable the computer to read and write data, and execute programs; the above-mentioned processor may be responsible for executing instructions in computer programs and performing data processing, and may be responsible for controlling and executing various operations, including arithmetic operations, logical operations, data transmission, etc.

[0045] Embodiment 4: The embodiments of the present application further provide a computer-readable storage medium, the computer-readable storage medium including a stored executable program, wherein when the executable program is running, the device where the computer-readable storage medium is located is controlled to execute the methods in various embodiments of the present invention.

[0046] The above-mentioned computer storage medium may refer to a medium in a computer memory used to store certain discontinuous physical quantities. Computer storage media mainly include semiconductors, magnetic cores, magnetic drums, magnetic tapes, laser disks, etc.; the stored program included in the computer-readable storage medium may be a set of instructions that can be recognized and executed by a computer, running on an electronic computer, and is an information tool that meets certain needs of people.

[0047] Embodiment 5: The embodiments of the present application further provide a computer program product, including a computer program, which implements the methods in various embodiments of the present invention when executed by a processor.

[0048] The above-mentioned computer program product may refer to a software program that has been written, tested and released and can be run on a computer or other device. The computer program product may include an application, an operating system, tool software, etc., which is used to implement specific functions or solve specific problems.

[0049] Embodiment 6: The embodiments of the present application further provide a computer program product, including a non-volatile computer-readable storage medium, the non-volatile computer-readable storage medium is used to store a computer program, and when the computer program is executed by a processor, the method in each embodiment of the present invention is implemented.

[0050] The above-mentioned non-volatile computer-readable storage medium may refer to a medium for storing data. The non-volatile computer-readable storage medium can keep the data from being lost when the power is off, and can be used to store long-term data, such as operating systems, applications, and user files. The non-volatile storage medium may include hard disk drives, solid-state drives, optical disks, and flash memory storage devices, etc.

[0051] Embodiment 7: The embodiments of the present application further provide a computer program, which implements the methods in the above-mentioned embodiments of the present invention when executed by a processor.

[0052] The above-mentioned computer program may refer to a collection of instructions used to tell a computer to perform a specific task or operation. A computer program may be written by a programmer using a specific programming language and may include algorithms, data structures, logic, and control flows. A computer program may be used for a variety of purposes, including application software, operating systems, and the like.

[0053] In the above embodiments of the present invention, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0054] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are only schematic. For example, the division of the units can be 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 units or modules, which can be electrical or other forms.

[0055] 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 units. Some or all of the units may be selected according to actual needs to achieve the purpose of the present embodiment.

[0056] 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.

[0057] 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. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, server or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, disk or optical disk, etc. Various media that can store program codes.

[0058] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A generalized fractional-order system filter design method, characterized in that: include: Given a generalized fractional-order system and performance parameters; Fractional-based order Different values ​​and the generalized fractional-order system are used to construct a reduced-order fractional-order filter; Based on the reduced-order fractional-order filter, the signal to be estimated in the generalized fractional-order system is tracked, so that the generalized fractional-order error system constructed by the generalized fractional-order system and the reduced-order fractional-order filter is admissible and satisfies H ∞ Performance indicators; The generalized fractional-order system comprises: in, ∈(0,2) is the order of the fractional order, represents the Caputo fractional differential operator, is the system state variable, It is noise interference. is the system output, is the signal to be estimated that cannot be directly measured, A o 、B o 、C o 、D o 、L and They all represent parameter matrices, A o 、B o 、C o 、D o 、L and , n, m, l, p represent the dimensions of the state vector, which are non-negative integers; The reduced-order fractional-order filter comprises: in, represents the state vector of the reduced-order fractional-order filter, represents the output signal of the reduced-order fractional-order filter, are the system parameters to be solved for the reduced-order fractional filter; , As follows: ; , As follows: ； in, represents a real matrix and I represents the identity matrix.

2. The generalized fractional-order system filter design method according to claim 1, characterized in that: Construct a generalized fractional-order error system, including: Build with is the state variable, to filter the error signal is the generalized fractional-order error system of the output variable: 。 3. The generalized fractional-order system filter design method according to claim 2, characterized in that: Generalized fractional-order error system from noise input To the filtered error signal output The transfer function is: ； is a given H ∞ Performance index, S represents the independent variable of the transfer function.

4. The generalized fractional-order system filter design method according to claim 3, characterized in that: The input-output transfer function of the generalized fractional-order error system satisfies A sufficient condition is that there exists a complex matrix , real matrix , satisfying the equality constraints and LMI constraints.

5. The generalized fractional-order system filter design method according to claim 1, characterized in that: The generalized fractional-order system is in the form of a circuit.

6. A generalized fractional-order system filter design device, characterized in that: include: Given modules, used for given generalized fractional-order systems and performance parameters; Building blocks for fractional-based orders Different values ​​and the generalized fractional-order system are used to construct a reduced-order fractional-order filter; A tracking module is used to track the signal to be estimated in the generalized fractional-order system based on the reduced-order fractional-order filter, so that the generalized fractional-order error system constructed by the generalized fractional-order system and the reduced-order fractional-order filter is admissible and satisfies H ∞ Performance indicators.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored program, wherein when the program is executed, the generalized fractional-order system filter design method according to any one of claims 1 to 5 is executed in a processor of a device where the program is controlled.

8. An electronic device, characterized in that: include: one or more processors; A storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors execute the generalized fractional-order system filter design method as described in any one of claims 1 to 5.

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