Second-order low-pass filtering system voltage control method based on backstepping control method

Abstract

The invention discloses a second-order low-pass filtering system voltage control method based on a backstepping control method. The method comprises the following steps: setting an expected voltage curve of an inductance-capacitance second-order low-pass filtering system; modeling the relationship between the input and output signals of the inductance-capacitance second-order low-pass filtering system to obtain a strict feedback form of the signals of the inductance-capacitance second-order low-pass filtering system; measuring the output of the inductance-capacitance second-order low-pass filtering system to obtain the error of the system, and selecting a Lyapunov function; designing a virtual controller, defining a virtual error, and selecting a composite Lyapunov function; and designing an actual controller according to the derivative of the compound Lyapunov function and the virtual controller. According to the invention, the output voltage of the second-order low-pass filtering system can be stably and accurately controlled.

Description

Technical Field

[0001] The invention belongs to the field of low-pass filter system output voltage control, and in particular relates to a second-order low-pass filter system voltage control method based on a backstepping control method. Background Art

[0002] LC (inductor-capacitor) low-pass filter is a widely used frequency selection unit in electronic circuits. It is mainly used to filter out high-frequency signals and retain useful low-frequency signals below a certain frequency. LC low-pass filters are very popular in power management, analog and digital signal processing, communication systems and other fields. Among them, the LC second-order low-pass filter system is a commonly used electronic filter. It has two degrees of freedom and is usually composed of an inductor and a capacitor. For the problem of output voltage control of the LC second-order low-pass filter system, most of the current methods focus on changing internal parameters to achieve filter voltage control. There are also very few methods that achieve output voltage control by changing the voltage of the voltage source. However, these methods have problems with insufficient stability and accuracy. Summary of the invention

[0003] The purpose of the present invention is to provide a voltage control method for a second-order low-pass filter system based on a backstepping control method, a computer device, a computer-readable storage medium and a computer program product, which can stably and accurately control the output voltage of the second-order low-pass filter system.

[0004] In order to achieve the above object, one aspect of the present invention provides a voltage control method of a second-order low-pass filter system based on a backstepping control method, comprising:

[0005] Step S1: Set the desired voltage curve z of the inductor-capacitor second-order low-pass filter system d (t);

[0006] Step S2: Model the relationship between the input and output signals of the inductor-capacitor second-order low-pass filter system:

[0007]

[0008] Where u(t) is the input signal, x(t) is the output signal, L, R and C are the inductance, resistance and capacitance of the inductor-capacitor second-order low-pass filter system respectively;

[0009] The strict feedback form of the signal of the inductor-capacitor second-order low-pass filter system is obtained;

[0010]

[0011] in,

[0012] Step S3: Measure the output of the inductor-capacitor second-order low-pass filter system to obtain the system error e1(t)=z1(t)-z D (t), choose the Lyapunov function

[0013] Step S4: Design virtual controller Where c1>0, define the virtual error e2(t)=z2(t)-a1(t), and select the composite Lyapunov function

[0014] Step S5: Design the actual controller based on the derivative of the composite Lyapunov function and the virtual controller Where c2>0.

[0015] Preferably, in step S1, the initial control input, the initial state value is z1(0)=0.01, z2(0)=0.

[0016] Preferably, the composite Lyapunov function V2(t) is derived: Thus the system error converges.

[0017] Another aspect of the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above method.

[0018] Another aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the above method when executed by a processor.

[0019] Another aspect of the present invention provides a computer program product, comprising a computer program, which implements the steps of the above method when executed by a processor.

[0020] According to the above aspects of the present invention, the second-order low-pass filter system voltage control method based on the backstepping control method, the computer device, the computer-readable storage medium and the computer program product can stably and accurately control the output voltage of the second-order low-pass filter system. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings used in the description of the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work:

[0022] Figure 1is a circuit topology diagram of an inductor-capacitor second-order low-pass filter system according to an embodiment of the present invention;

[0023] Figure 2 It is a flow chart of a voltage control method of a second-order low-pass filter system based on a backstepping control method according to an embodiment of the present invention;

[0024] Figure 3 is a schematic diagram of an output voltage following a desired voltage curve according to an embodiment of the present invention;

[0025] Figure 4 is a schematic diagram of the absolute error between the output voltage and the expected voltage of an embodiment of the present invention;

[0026] Figure 5 It is a structural diagram of a computer device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. 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.

[0028] An embodiment of the present invention provides a voltage control method for a second-order low-pass filter system based on a backstepping control method. The backstepping control method is a system recursive algorithm used for designing a nonlinear system controller. The main idea is to achieve the stability of the target system by gradually controlling the stability of the subsystem. The method is particularly suitable for systems with strict feedback. The final control law is gradually determined by designing intermediate control laws and virtual control inputs.

[0029] Figure 1 FIG. 1 is a block diagram of an inductor-capacitor second-order low-pass filter system according to an embodiment of the present invention. Where y(t) is the output of the system, or the voltage of the capacitor; u p (t) is the input to the system, or the voltage of the power supply; u L (t) is the voltage of the inductor; i1(t), i2(t) and i3(t) are defined as the current flowing through the inductor, resistor and capacitor respectively. The inductor, resistor and capacitor are L, R and C respectively. The charge of capacitor C is q c (t). According to Kirchhoff’s current law, we can conclude that:

[0030] i1(t)=i2(t)+i3(t)

[0031] The voltage control method of the second-order low-pass filter system based on the backstepping control method of the embodiment of the present invention includes steps S1 to S5. Figure 2 shown.

[0032] Step S1: Set the desired voltage curve z of the system d (t), initial control input, initial state value z1(0)=0.01, z2(0)=0, where z is the output signal, z1(0) is the output signal at time zero, and z2(0) is the first-order derivative of the output signal at time zero.

[0033] Step S2: Modeling the relationship between the input and output signals of the LC second-order low-pass filter system;

[0034]

[0035] Among them, u(t) is the input signal and x(t) is the output signal.

[0036] Then, the strict feedback form of the LC second-order low-pass filter system signal is obtained:

[0037]

[0038] in,

[0039] Step S3: Measure the output of the system and obtain the system error e1(t)=z1(t)-z d (t); Select the Lyapunov function Where V1(t) is the energy function of the error e1(t), which is a common consideration for control system errors.

[0040] Step S4: Design a virtual controller based on step S3 Where c1 is an uncertain positive number, c1>0, which only affects the convergence speed but not the convergence characteristics. It is an empirical parameter; define the virtual error e2(t)=z2(t)-a1(t); select the composite Lyapunov function

[0041] The composite Lyapunov function Taking the derivative of the composite Lyapunov function V2(t) yields: Therefore, the system error converges.

[0042] Step S5: Design the actual controller based on step S4:

[0043] In a specific example, the output voltage is 0.01V at the initial moment, so z1(0)=0.01, z2(0)=0, and the expected voltage output curve is

[0044] Take c1=0.05,c2=8, then the actual controller is

[0045]

[0046] Then the actual output voltage z1(t) of the system follows the expected voltage z d (t) Figure 3 As shown, the actual output voltage z1(t) is different from the expected voltage z d The absolute error of (t) is Figure 4 shown.

[0047] According to the voltage control method of the second-order low-pass filter system based on the backstepping control method of the above embodiment of the present invention, the relationship between the input and output signals of the LC second-order low-pass filter system is firstly modeled; then, the strict feedback form of the LC second-order low-pass filter system signal is obtained; based on the strict feedback form of the LC second-order low-pass filter system, the backstepping control method is used to design the virtual controller and the actual controller. By conducting simulation experiments under different conditions, the simulation results verify the feasibility and effectiveness of the designed controller.

[0048] The voltage control method of the second-order low-pass filter system based on the backstepping control method in the above embodiment of the present invention has the following beneficial effects:

[0049] (1) The modeling of this method conforms to the system characteristics of the inductor-capacitor low-pass filter and has good application effect;

[0050] (2) The implementation of this method does not require accurate knowledge of the specific internal parameters of the inductor-capacitor low-pass filter, so the design requirements are low and it is easy to promote in practical engineering applications;

[0051] (3) This method is applicable to all systems that can be modeled as second-order strict feedback systems. It is independent of the specific parameters of the system and has a wide range of applications.

[0052] An embodiment of the present invention further provides a computer device, which may be a server, and its internal structure diagram may be as shown in FIG. Figure 5 As shown. The computer device includes a processor, a memory and a network interface connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store operating parameter data of each framework. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, the steps of the method of the embodiment of the present invention are implemented.

[0053] Those skilled in the art will understand that Figure 5The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0054] An embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the method of the embodiment of the present invention are implemented.

[0055] An embodiment of the present invention further provides a computer program product, including a computer program, which implements the steps of the method of the embodiment of the present invention when executed by a processor.

[0056] The above description is only by way of illustration of certain exemplary embodiments of the present invention. It is undoubted that those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the above drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A voltage control method for a second-order low-pass filter system based on a backstepping control method, characterized in that: include: Step S1: Set the desired voltage curve z of the inductor-capacitor second-order low-pass filter system d (t); Step S2: Model the relationship between the input and output signals of the inductor-capacitor second-order low-pass filter system: Where u(t) is the input signal, x(t) is the output signal, L, R and C are the inductance, resistance and capacitance of the inductor-capacitor second-order low-pass filter system respectively; The strict feedback form of the signal of the inductor-capacitor second-order low-pass filter system is obtained; in, Step S3: Measure the output of the inductor-capacitor second-order low-pass filter system to obtain the system error e1(t)=z1(t)-z d (t), choose the Lyapunov function Step S4: Design virtual controller Where c1>0, define the virtual error e2(t)=z2(t)-a1(t), and select the composite Lyapunov function Step S5: Design the actual controller based on the derivative of the composite Lyapunov function and the virtual controller Where c2>

0.

2. The method according to claim 1, characterized in that In step S1, initial control input, the initial state value is z1(0)=0.01, z2(0)=0.

3. The method according to claim 1 or 2, characterized in that Derivative of the composite Lyapunov function V2(t): Thus the system error converges.

4. A computer device comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

6. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

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