Presettable convergence time control method, device, equipment and medium for second-order system

Abstract

The present application discloses a method, apparatus, device, and medium for controlling a second-order system with a preset convergence time, and relates to the field of automatic control technology. The method comprises: obtaining a first error state equation of the second-order system; obtaining a pre-constructed convergence function and substituting the convergence function into the first error state equation to obtain a second error state equation; the convergence function is used to make the state error of the second-order system converge from an initial state to zero along a preset convergence path and within a specified convergence time; constructing an extended state observer for the second error state equation based on a nonlinear function; constructing a control law based on the extended state observer; and controlling the second-order system using the control law. The convergence function of the present application can make the state error of the second-order system converge from an initial state to zero along a preset convergence path and within a specified convergence time, thereby realizing a control method for the second-order system with a preset convergence process and a preset convergence time, thereby improving the self-disturbance rejection performance of the second-order system.

Description

Technical Field

[0001] The present application relates to the field of automatic control technology, and in particular to a method, device, equipment and medium for controlling a preset convergence time of a second-order system. Background Art

[0002] Many systems in practice can be simplified into a second-order system, but existing technologies often have some errors when modeling second-order systems. These errors are mainly caused by the uncertain parts of the second-order system and external disturbances. The existence of errors will affect the performance of the second-order system, reduce the control effect of the second-order system, and in severe cases, cause the second-order system to diverge. Summary of the Invention

[0003] The main purpose of the embodiments of the present application is to propose a method, device, equipment and medium for controlling the preset convergence time of a second-order system, so as to realize the control of the preset convergence time of the second-order system and reduce the impact of errors.

[0004] To achieve the above objectives, an embodiment of the present application provides a method for controlling a preset convergence time of a second-order system, the method comprising:

[0005] Obtain the first error state equation of the second-order system;

[0006] Obtaining a pre-constructed convergence function and substituting the convergence function into the first error state equation to obtain a second error state equation; wherein the convergence function is used to make the state error of the second-order system converge from an initial state to zero along a preset convergence path and at a specified convergence time;

[0007] constructing an extended state observer for the second error state equation according to a nonlinear function;

[0008] constructing a control law based on the extended state observer;

[0009] The second-order system is controlled using the control law.

[0010] In some embodiments, obtaining a first error state equation of the second-order system includes:

[0011] Obtaining a general state equation of the second-order system;

[0012] The general state equation is:

[0013]

[0014] Wherein, x1 and x2 are both state variables in the second-order system, u is the control variable, b is the modeled part in the second-order system, and f is the unmodeled part in the second-order system and the external disturbance;

[0015] Substitute the signal to be tracked and the state error into the general state equation to obtain the first error state equation;

[0016] The first error state equation is:

[0017]

[0018] where, x 1d is the signal to be tracked, e1 and e2 are both the state errors, e1 = x1 - x 1d ,

[0019] In some embodiments, the obtaining the pre - constructed convergence function includes:

[0020] Obtain the pre - constructed convergence function as follows:

[0021]

[0022] where, ρ is the convergence function; ρ0 is the initial value of the convergence function; e is the natural base; p is the power coefficient, 0 < p < 1; t is time, and T f is the specified convergence time.

[0023] In some embodiments, the substituting the convergence function into the first error state equation to obtain the second error state equation includes:

[0024] Determine a new state error according to the convergence function;

[0025] Substitute the new state error into the first error state equation to obtain the second error state equation;

[0026] The second error state equation is:

[0027]

[0028] where, η1 and η2 are both the new state errors, η1 = e​1 - ρ, e1 and e2 are both the initial state errors; u is the control quantity, b is the modeled part in the second - order system, f is the unmodeled part and external disturbance in the second - order system; x 1d is the signal to be tracked.

[0029] In some embodiments, the constructing an extended state observer for the second error state equation according to a non - linear function includes:

[0030] Obtain the non - linear function as follows:

[0031]

[0032] Wherein, Yaln(e,a,δ) is the nonlinear function, δ, a, e are the parameters of the nonlinear function, 0 <a<1;

[0033] The extended state observer is constructed based on the second error state equation according to the nonlinear function as follows:

[0034]

[0035] Among them, β1=3ω0, ω0 is the bandwidth frequency of the extended state observer; a1 and a2 are the control parameters of the extended state observer, and their value range is (0,1]; u is the control quantity, b is the modeled part of the second-order system; η1 = e1-ρ, η1 and η2 are both new state errors, e1 is the initial state error, ρ is the convergence function, z1 is the estimated value of η1, z2 is the estimated value of η2, and z3 is The estimated value of , f is the unmodeled part of the second-order system and the external disturbance, x 1d The signal to be tracked.

[0036] In some embodiments, constructing a control law according to the extended state observer includes:

[0037] The control law is constructed according to the extended state observer as follows:

[0038]

[0039] M=b -1 (u0-z3);

[0040] Among them, ω c is the bandwidth frequency of the control law, a3 and a4 are the control parameters of the control law, and their value range is (0,1]; η2 is the new state error, e2 is the initial state error, u0 is the preset control quantity, and M is the control torque.

[0041] In some embodiments, controlling the second-order system using the control law includes:

[0042] The control law is used to control a robotic arm, a motor control system or a vehicle suspension system.

[0043] To achieve the above-mentioned purpose, another aspect of the present application provides a device for controlling a preset convergence time of a second-order system, the device comprising:

[0044] A first equation obtaining unit, used for obtaining a first error state equation of the second-order system;

[0045] a second equation acquisition unit, configured to acquire a pre-constructed convergence function and substitute the convergence function into the first error state equation to obtain a second error state equation; wherein the convergence function is configured to cause the state error of the second-order system to converge from an initial state to zero along a preset convergence path and within a specified convergence time;

[0046] An observer construction unit, configured to construct an extended state observer for the second error state equation according to a nonlinear function;

[0047] a control law construction unit, configured to construct a control law according to the extended state observer;

[0048] A system control unit is used to control the second-order system using the control law.

[0049] To achieve the above-mentioned purpose, another aspect of an embodiment of the present application provides an electronic device, which includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the above-mentioned method when executing the computer program.

[0050] To achieve the above-mentioned purpose, another aspect of an embodiment of the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program implements the above-mentioned method when executed by a processor.

[0051] The embodiments of the present application include at least the following beneficial effects:

[0052] The present application can obtain a first error state equation of a second-order system; obtain a pre-constructed convergence function and substitute the convergence function into the first error state equation to obtain a second error state equation; wherein the convergence function is used to make the state error of the second-order system converge from an initial state to zero along a preset convergence path and at a specified convergence time; construct an extended state observer for the second error state equation based on the nonlinear function; construct a control law based on the extended state observer; and use the control law to control the second-order system. The convergence function according to the present application can make the state error of the second-order system converge from an initial state to zero along a preset convergence path and at a specified convergence time, thereby realizing a control method for the second-order system with a preset convergence process and a preset convergence time, thereby improving the self-disturbance rejection performance of the second-order system. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. 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 these drawings without any creative work.

[0054] Figure 1 A flow chart of a method for controlling a preset convergence time of a second-order system provided in an embodiment of the present application;

[0055] Figure 2 A control block diagram of a second-order system with a preset convergence process and convergence time provided in an embodiment of the present application;

[0056] Figure 3 This is a comparison diagram of the errors of two nonlinear functions provided in the embodiment of the present application;

[0057] Figure 4 A gain comparison diagram of two nonlinear functions provided in an embodiment of the present application;

[0058] Figure 5 A schematic diagram of the structure of a preset convergence time control device for a second-order system provided in an embodiment of the present application;

[0059] Figure 6 A schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the embodiments of the present application. They are merely examples of devices and methods consistent with some aspects of the embodiments of the present application as detailed in the appended claims.

[0061] It will be understood that the terms "first", "second", etc. used in this application may be used herein to describe various concepts, but unless otherwise specified, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another. For example, without departing from the scope of the embodiments of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the words "if" and "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0062] The terms "at least one", "plurality", "each", "any", etc. used in this application include "at least one", "two" or more, "plurality" or "each", "any" or "any one", "each" or "any one" as used herein.

[0063] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this application pertains. The terms used herein are for the purpose of describing the embodiments of this application only and are not intended to limit this application.

[0064] Before describing the embodiments of the present application in detail, some related technologies that may be involved in the embodiments of the present application are first described as follows:

[0065] In the early 1990s, researchers proposed active disturbance rejection control (ADRC). This control technique, which includes a disturbance observer, can estimate system disturbances in real time during the control process. Simultaneously, the controller can compensate for these disturbances, thereby eliminating their effects. This allows for effective control even in uncertain environments. Compared to traditional control methods, ADRC requires less precise mathematical models of the controlled object. This makes it more flexible and applicable in practical applications, enabling it to handle the uncertainties and variations found in various real-world systems. Furthermore, it exhibits minimal overshoot and high accuracy, and has been successfully applied in numerous fields, demonstrating its high practical value. The ADRC controller consists of a TD tracking differentiator, an extended state observer, and a control law. With the development of ADRC, researchers have begun to adapt and refine its various components to suit diverse applications and control requirements.

[0066] The embodiments of the present application provide a method, device, equipment and medium for controlling a second-order system with a preset convergence time. The technical solution of the present application includes: obtaining a first error state equation of the second-order system; obtaining a pre-constructed convergence function and substituting the convergence function into the first error state equation to obtain a second error state equation; wherein the convergence function is used to make the state error of the second-order system converge from an initial state to zero from a preset convergence path and at a specified convergence time; constructing an extended state observer for the second error state equation according to a nonlinear function; constructing a control law according to the extended state observer; and controlling the second-order system using the control law. According to the convergence function of the present application, the state error of the second-order system can be made to converge from an initial state to zero from a preset convergence path and at a specified convergence time, thereby realizing a control method with a preset convergence process and a preset convergence time for the second-order system, thereby improving the self-disturbance rejection performance of the second-order system.

[0067] The embodiment of the present application provides a method for controlling the preset convergence time of a second-order system, which relates to the field of automatic control technology. The control method provided in the embodiment of the present application can be applied to a terminal, can be applied to a server, or can be software running in a terminal or a server. In some embodiments, the terminal can be a smart phone, a tablet computer, a laptop computer, a desktop computer, a smart speaker, a smart watch, and a car terminal, etc., but is not limited to this; the server side can be configured as an independent physical server, or as a server cluster or distributed system composed of multiple physical servers, or as a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network; the software can be an application that implements the control method, etc., but is not limited to the above forms.

[0068] The present application can be used in many general or special computer system environments or configurations. For example: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, and the like. The present application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, and the like that perform specific tasks or implement specific abstract data types. The present application can also be practiced in distributed computing environments in which tasks are performed by remote processing devices connected via a communication network. In a distributed computing environment, program modules can be located in local and remote computer storage media, including storage devices.

[0069] Reference Figure 1 The embodiment of the present application provides a method for controlling the preset convergence time of a second-order system. The method may include but is not limited to S100 to S140, as follows:

[0070] S100: Obtain the first error state equation of the second-order system.

[0071] As a further implementation, S100 may include:

[0072] Obtaining a general state equation of the second-order system;

[0073] The general state equation is:

[0074]

[0075] where x1 and x2 are both state variables in the second-order system, u is the control variable, b is the modeled part in the second-order system, and f is the unmodeled part and external disturbance in the second-order system;

[0076] Substitute the signal to be tracked and the state error into the general state equation to obtain the first error state equation;

[0077] The first error state equation is:

[0078]

[0079] where x 1d is the signal to be tracked, e1 and e2 are both state errors, e1 = x1 - x 1d ,

[0080] It should be noted that in the embodiments of this application, some variables have superscripts. Among them, variables with a single dot superscript are the first derivatives of the corresponding variables without superscripts, and variables with a double dot superscript are the second derivatives of the corresponding variables without superscripts. For example, is the first derivative of x 1d , is the second derivative of x 1d . The parameter definitions of the remaining variables can be referred to the above description.

[0081] S110: Obtain a pre-constructed convergence function and substitute the convergence function into the first error state equation to obtain a second error state equation; wherein, the convergence function is used to make the state error of the second-order system converge from a preset convergence path to zero at a specified convergence time from the initial state.

[0082] As a further implementation, the step of obtaining a pre-constructed convergence function in S110 may include:

[0083] Obtain a pre-constructed convergence function as follows:

[0084] <00002​​​​​​​​​​​​

[0088] Substituting the new state error into the first error state equation to obtain the second error state equation;

[0089] The second error state equation is:

[0090]

[0091] Wherein, η1 and η2 are both the new state errors, η1 = e1 - ρ, e1 and e2 are both initial state errors; u is the control variable, b is the modeled part of the second-order system, and f is the unmodeled part of the second-order system and the external disturbance; x 1d The signal to be tracked.

[0092] S120: Constructing an extended state observer for the second error state equation according to a nonlinear function.

[0093] As a further implementation, S120 may include:

[0094] The nonlinear function is obtained as follows:

[0095]

[0096] Wherein, Yaln(e,a,δ) is the nonlinear function, δ, a, e are the parameters of the nonlinear function, 0 <a<1;

[0097] The extended state observer is constructed based on the second error state equation according to the nonlinear function as follows:

[0098]

[0099] Among them, β1=3ω0, ω0 is the bandwidth frequency of the extended state observer; a1 and a2 are the control parameters of the extended state observer, with a value range of (0,1]; u is the control quantity, b is the modeled part of the second-order system; η1=e1-ρ, η1 and η2 are the new state errors, e1 is the initial state error, ρ is the convergence function, z 1 is η 1 The estimated value of z 2 is η 2 The estimated value of z 3 for The estimated value of , f is the unmodeled part of the second-order system and the external disturbance, x1 d The signal to be tracked.

[0100] S130: Constructing a control law according to the extended state observer.

[0101] As a further implementation, S130 may include:

[0102] The control law is constructed according to the extended state observer as follows:

[0103]

[0104] M=b -1 (u0-z3);

[0105] Among them, ω c is the bandwidth frequency of the control law, a3 and a4 are the control parameters of the control law, and their value range is (0,1]; η2 is the new state error, e2 is the initial state error, u0 is the preset control quantity, and M is the control torque.

[0106] S140: Control the second-order system using the control law.

[0107] It is understandable that this embodiment can use this control law to control various types of second-order systems. Furthermore, the second-order system can be a robotic arm, a motor control system, or a car suspension system, etc. Therefore, S140 can further include:

[0108] The control law is used to control a robotic arm, a motor control system or a vehicle suspension system.

[0109] Next, the solution of the embodiment of the present application will be described in detail and explained with reference to specific application examples:

[0110] Reference Figure 2 , this embodiment provides a control block diagram of a second-order system with a preset convergence process and convergence time.

[0111] For the sake of simplicity, the second-order system in this embodiment is referred to as the system. This embodiment may include the following steps:

[0112] Step 1:

[0113] Obtain the general state equation of the second-order system as follows:

[0114]

[0115] Among them, x1 and x2 are both state variables in the system, u is the control variable, b is the modeled part of the system, and f can be regarded as the unmodeled part and external disturbance.

[0116] For the general state equation (1) of the second-order system, assuming that the signal to be tracked is x 1d , define the initial state error as e1=x1-x 1d and The initial error state equation of the system (i.e., the first error state equation) is as follows:

[0117]

[0118] In order to make the state error e1 converge to zero at a specified time point from the initial state e1(0) along a preset convergence path, a convergence function with a specified convergence time can be constructed in this embodiment.

[0119] Step 2: Construct a convergence function whose convergence process and convergence time can be preset.

[0120] For Equation (2), construct the following convergence function:

[0121]

[0122] In the formula, ρ is the convergence function; ρ0 is the initial value of the convergence function; e is the natural logarithm base; p is the power coefficient, 0 < p < 1; t is the time, and T f is the specified convergence time, and the convergence function will reach the zero state at time T f . Therefore, ρ(0) = ρ0 = e1(0) and ρ(T f ) = 0.

[0123] Next, an explanation is given that the convergence function can preset the convergence process and convergence time:

[0124] First, when t < T f , the transformation of Equation (3) gives:

[0125]

[0126] Let and further simplification gives:

[0127] <着

[0128] Converting the above formula gives:

[0129]

[0130] Further simplification gives:

[0131]

[0132] From the above formula, y(ρ0) is a constant value (regardless of any value), and y(ρ) will gradually decrease under the action of (1 - t / T f ). When t = T 1 / (1-p) , y(ρ) will be equal to zero, and further it can be known that ρ(T f f ) = 0.​

[0133] By taking the derivative of equation (7), we can obtain:

[0134]

[0135] Thus:

[0136]

[0137] in When t = T f hour, According to equation (9), when t=T f , So far, it can be concluded that the convergence function can preset the convergence process and convergence time.

[0138] At this time, if we define new error variables η1 = e1-ρ and Then equation (2) becomes:

[0139]

[0140] If the controller is constructed so that η1 converges to zero, the system state error e1 will move to zero according to the convergence curve of ρ, thus achieving the goal of presetting the convergence process and convergence time.

[0141] Step 3: Construct an extended state observer based on nonlinear functions.

[0142] There are usually some unmodeled parts and external disturbances in equation (10), such as The extended state observer can generally be used for estimation and compensation. An example of a nonlinear function fal(e, a, δ) used in the active disturbance rejection controller is as follows:

[0143]

[0144] Where a∈(0,1) and δ is a small constant.

[0145] However, the fal(e, a, δ) function itself lacks continuity and smoothness, and is prone to high-frequency chattering in the vicinity of the origin. Furthermore, there are many parameters to be adjusted, and poor control effects may occur due to excessive gain. Therefore, this embodiment provides another nonlinear function, which is expressed as follows:

[0146]

[0147] where δ, 0 < a < 1, and e are function parameters. The nonlinear function of Equation (12) does not have an error switching control term, so it will not cause the problem of discontinuous control. At the same time, it is symmetric about the origin, differentiable everywhere, and has good convergence, continuity, and smoothness, and there are few parameters to be tuned. It follows the principle of "small error, large gain; large error, small gain", has good performance, and can solve the high-frequency chattering phenomenon of the traditional fal function. When the values of the two nonlinear functions are both a = 0.6 and δ = 0.01 and e ∈ [-2, 2], the error comparison results are as Figure 3 , and the gain comparison results are as Figure 4 shown.

[0148] From Figure 3 , it can be seen that the Yaln function has a smaller gain than the fal function when the error is large, and a larger gain when the error is small. At the same time, from Figure 4 , it can be seen that when the input error value tends to 0, the output gain of the fal function is large, which is likely to cause system oscillation. At the same time, when the input error is small, the gain of the Yaln function is higher than that of the fal function; when the input error is large, the gain of the Yaln function is lower than that of the fal function. Therefore, this nonlinear function has better performance.

[0149] Based on the nonlinear function of Equation (12), the following extended state observer can be constructed:

[0150]

[0151] where β1 = 3ω0, ω0 is the bandwidth frequency of the observer. a1 and a2 are control parameters, and their value ranges are (0, 1]. Through this extended observer, accurate estimation of z1 for η1, accurate estimation of z2 for η2, and accurate estimation of z3 for the total external disturbance can be achieved.

[0152] Step 4: Construct a control law based on the nonlinear function.

[0153] Based on the extended state observer and the new error state, the following nonlinear state error feedback control law can be constructed:

[0154]

[0155] M = b -1 (u0 - z3) (14)

[0156] where ω c is the bandwidth frequency of this control law, and a3 and a4 are control parameters, and their value ranges are (0, 1].

[0157] Step 5: Use the control law obtained in step 4 to control the second-order system, which can be a robotic arm, a motor control system, or a car suspension system.

[0158] This embodiment first obtains the general state equation of a second-order system, then constructs a convergence function with a preset convergence process and convergence time (eliminating the traditional TD tracking differentiator), and constructs an extended state observer based on a nonlinear function. Finally, a nonlinear control law applicable to a variety of second-order systems is constructed, and the second-order system is controlled based on this control law. The active disturbance rejection control law of this embodiment can be used to control common second-order systems. This active disturbance rejection control law has high precision, strong robustness, and fast response performance with a specified convergence time, which can reduce the error impact of the second-order system.

[0159] Reference Figure 5 The present application also provides a device for controlling the preset convergence time of a second-order system, which can implement the above-mentioned control method. The device includes:

[0160] A first equation obtaining unit, used for obtaining a first error state equation of the second-order system;

[0161] a second equation acquisition unit, configured to acquire a pre-constructed convergence function and substitute the convergence function into the first error state equation to obtain a second error state equation; wherein the convergence function is configured to cause the state error of the second-order system to converge from an initial state to zero along a preset convergence path and within a specified convergence time;

[0162] An observer construction unit, configured to construct an extended state observer for the second error state equation according to a nonlinear function;

[0163] a control law construction unit, configured to construct a control law according to the extended state observer;

[0164] A system control unit is used to control the second-order system using the control law.

[0165] It can be understood that the contents of the above method embodiments are all applicable to the present device embodiments, the functions specifically implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0166] The present application also provides an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the control method when executing the computer program. The electronic device can be any smart terminal including a tablet computer, an in-vehicle computer, or the like.

[0167] It can be understood that the contents of the above method embodiments are applicable to the present device embodiments, the functions specifically implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0168] See also Figure 6 , Figure 6 The hardware structure of an electronic device according to another embodiment is shown. The electronic device includes:

[0169] The processor 601 may be implemented as a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of the present application.

[0170] The memory 602 can be implemented in the form of a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). The memory 602 can store an operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 602 and is called by the processor 601 to execute the control method of the embodiments of this application;

[0171] Input / output interface 603, used to implement information input and output;

[0172] Communication interface 604, used to implement communication interaction between this device and other devices, which can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WiFi, Bluetooth, etc.);

[0173] Bus 605 , which transmits information between various components of the device (e.g., processor 601 , memory 602 , input / output interface 603 , and communication interface 604 );

[0174] The processor 601 , the memory 602 , the input / output interface 603 and the communication interface 604 are connected to each other in communication within the device via a bus 605 .

[0175] An embodiment of the present application further provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the above-mentioned control method is implemented.

[0176] It can be understood that the contents of the above method embodiments are all applicable to the present storage medium embodiment, the functions specifically implemented by the present storage medium embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0177] The memory, as a non-transient computer-readable storage medium, can be used to store non-transient software programs and non-transient computer executable programs. In addition, the memory may include a high-speed random access memory and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory may optionally include a memory remotely arranged relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0178] The embodiments described in the embodiments of this application are intended to more clearly illustrate the technical solutions of the embodiments of this application and do not constitute a limitation on the technical solutions provided by the embodiments of this application. Those skilled in the art will appreciate that with the evolution of technology and the emergence of new application scenarios, the technical solutions provided in the embodiments of this application are also applicable to similar technical problems.

[0179] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of the present application, and may include more or fewer steps than shown in the figures, or a combination of certain steps, or different steps.

[0180] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, i.e., they may be located in one place or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of this embodiment.

[0181] Those skilled in the art will appreciate that all or some of the steps in the methods, systems, and functional modules / units in the devices disclosed above may be implemented as software, firmware, hardware, or appropriate combinations thereof.

[0182] The terms "first", "second", "third", "fourth", etc. (if any) in the specification of the present application and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequential order. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present application 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 clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0183] It should be understood that in this application, "at least one (item)" means one or more, and "plurality" means two or more. "And / or" is used to describe the association relationship of associated objects, indicating that three relationships may exist. For example, "A and / or B" can mean: only A exists, only B exists, and A and B exist at the same time, where A and B can be singular or plural. The character " / " generally indicates that the previous and next associated objects are in an "or" relationship. "At least one of the following items" or similar expressions refers to any combination of these items, including any combination of single items or plural items. For example, at least one of a, b or c can mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, c can be single or multiple.

[0184] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the above-mentioned units is only a logical function division. In actual implementation, there may be other division methods, such as 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.

[0185] The units described above as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0186] In addition, the functional units in the various embodiments of the present application may be integrated into a single processing unit, or each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0187] 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 application, 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, which is stored in a storage medium and includes multiple instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of various embodiments of the present application. The aforementioned storage medium includes: various media that can store programs, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0188] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and essence of the present invention should be within the scope of the present invention.

Claims

1. A method for controlling the preset convergence time of a second-order system, characterized in that: The method comprises: Obtain the first error state equation of the second-order system; Obtaining a pre-constructed convergence function and substituting the convergence function into the first error state equation to obtain a second error state equation; wherein the convergence function is used to make the state error of the second-order system converge from an initial state to zero along a preset convergence path and at a specified convergence time; The obtaining of a pre-built convergence function comprises: Get the pre-built convergence function as follows: ； in, is the convergence function; is the initial value of the convergence function; is the natural base; p is the power coefficient, ; For time, The convergence time specified for the above; constructing an extended state observer for the second error state equation according to a nonlinear function; The nonlinear function is obtained as follows: ； in, is the nonlinear function, 、 、 are the parameters of the nonlinear function, ; constructing a control law based on the extended state observer; The second-order system is controlled using the control law.

2. The method for controlling the preset convergence time of a second-order system according to claim 1, wherein: The obtaining of the first error state equation of the second-order system includes: Obtaining a general state equation of the second-order system; The general state equation is: ； in, and are all state quantities in the second-order system, To control the amount, is the modeled part of the second-order system, is the unmodeled part of the second-order system and the external disturbance; Substituting the signal to be tracked and the state error into the general state equation to obtain the first error state equation; The first error state equation is: ； in, is the signal to be tracked, e 1. e 2 are the state errors, , .

3. The method for controlling the preset convergence time of a second-order system according to claim 1, wherein: Substituting the convergence function into the first error state equation to obtain a second error state equation includes: determining a new state error according to the convergence function; Substituting the new state error into the first error state equation to obtain the second error state equation; The second error state equation is: ； in, 、 are the new state errors, , , e 1. e 2 are the initial state errors; To control the amount, is the modeled part of the second-order system, is the unmodeled part of the second-order system and the external disturbance; The signal to be tracked.

4. The method for controlling the preset convergence time of a second-order system according to claim 1, wherein: The step of constructing an extended state observer for the second error state equation according to a nonlinear function includes: The extended state observer is constructed based on the second error state equation according to the nonlinear function as follows: ； in, , is the bandwidth frequency of the extended state observer; and are the control parameters of the extended state observer, and their value range is (0,1]; To control the amount, is the modeled part of the second-order system; , 、 are all new state errors, e 1 is the initial state error, is the convergence function, for The estimated value of for The estimated value of for The estimated value of is the unmodeled part of the second-order system and the external disturbance, The signal to be tracked.

5. The method for controlling the preset convergence time of a second-order system according to claim 4, characterized in that: The constructing of a control law according to the extended state observer comprises: The control law is constructed according to the extended state observer as follows: ； in, is the bandwidth frequency of the control law, and are the control parameters of the control law, and their values ​​are in the range of (0, 1]; , is the new state error, e 2 is the initial state error, is the preset control quantity, To control the torque.

6. A method for controlling a preset convergence time of a second-order system according to any one of claims 1 to 5, characterized in that: The controlling the second-order system by using the control law comprises: The control law is used to control a robotic arm, a motor control system or a vehicle suspension system.

7. A device for controlling the preset convergence time of a second-order system, characterized in that: The device comprises: A first equation obtaining unit, used for obtaining a first error state equation of the second-order system; a second equation acquisition unit, configured to acquire a pre-constructed convergence function and substitute the convergence function into the first error state equation to obtain a second error state equation; wherein the convergence function is configured to cause the state error of the second-order system to converge from an initial state to zero along a preset convergence path and within a specified convergence time; The obtaining of a pre-built convergence function comprises: Get the pre-built convergence function as follows: ； in, is the convergence function; is the initial value of the convergence function; is the natural base; p is the power coefficient, ; For time, The convergence time specified for the above; An observer construction unit, configured to construct an extended state observer for the second error state equation according to a nonlinear function; The nonlinear function is obtained as follows: ； in, is the nonlinear function, 、 、 are the parameters of the nonlinear function, ; a control law construction unit, configured to construct a control law according to the extended state observer; A system control unit is used to control the second-order system using the control law.

8. An electronic device, characterized in that: The electronic device includes a memory and a processor, the memory stores a computer program, and the processor implements the method according to any one of claims 1 to 6 when executing the computer program.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

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