A second-order sliding mode control method, device and equipment based on a preset performance function

Abstract

The application discloses a second-order sliding mode control method and device based on a preset performance function, and equipment, and the method comprises the following steps: obtaining a preset dynamic equation and a preset expected value, and combining to obtain an error dynamic equation; obtaining a monotonically increasing scalar function; obtaining a preset performance function, and bringing the scalar function into a preset performance function lemma to obtain a specified time preset performance function; determining the product of the specified time preset performance function and a preset error initial value, subtracting the product from the error dynamic equation to obtain a specified time error dynamic equation; and determining a predetermined time sliding mode controller according to the specified time error dynamic equation, so that the specified time error dynamic equation converges before the predetermined time. The application can upgrade the predetermined time controller to the specified time controller, solves the high-precision and high-time-dependent control problem of a second-order system, and can be widely applied to the technical field of system control.

Description

Technical Field

[0001] This application relates to the field of system control technology, and in particular to a second-order sliding mode control method, apparatus and equipment based on a preset performance function. Background Technology

[0002] In the field of control, second-order dynamic models are frequently used in controller design and system analysis. By establishing a second-order dynamic model of the system, we can understand its dynamic characteristics, such as response speed, stability, and oscillations, and select appropriate control strategies to influence the system's behavior. Common control methods, such as proportional-integral-derivative control (PID control), model predictive control (MPC), and linear quadratic regulation (LQR), are typically designed and tuned based on the system's second-order dynamic model. Second-order dynamic models often exhibit complex nonlinearities and uncertainties, and contain multiple coupled motion modes. Traditional control methods struggle to handle this complexity, often requiring empirical parameter tuning and failing to meet the requirements of high performance and robustness. This necessitates addressing the inability of traditional control methods to handle unknown nonlinear functions in systems and the non-smoothing nature of existing saturation control.

[0003] Prior art 1 (Publication No. CN114035436A) proposes a backstepping control method, storage medium, and device based on saturated adaptive law. For the controlled object, a two-dimensional nonlinear system state-space model is established, and the controlled object is controlled using the saturated adaptive law. This method can directly estimate and process unknown nonlinear functions of the system; however, it is asymptotically convergent and cannot theoretically guarantee the speed of control. Predetermined-time control uses a single parameter to set the upper bound of the controller's convergence time, which can improve the convergence speed. Prior art 2 (Publication No. CN116166044A) proposes a predetermined-time control method for UAV formations with random link failures. A communication compensation controller is designed based on a model combined with a predetermined-time function to ensure that the system tracking error converges within a predetermined time. Although predetermined-time control can guarantee convergence within the predetermined time, the convergence speed is greatly affected by the initial value and is very prone to premature convergence, resulting in a highly conservative controller. Summary of the Invention

[0004] In view of this, this application provides a second-order sliding mode control method, apparatus and device based on a preset performance function to upgrade a predetermined time controller to a specified time controller, thereby solving the problem of high-precision and high-time-dependent control of second-order systems.

[0005] One aspect of this application provides a second-order sliding mode control method based on a preset performance function, comprising:

[0006] Obtain the preset dynamic equation and the preset expected value, and combine them to obtain the error dynamic equation;

[0007] Obtain a monotonically increasing scalar function;

[0008] Obtain a preset performance function, and substitute the scalar function into the preset performance function lemma to obtain a preset performance function for a specified time;

[0009] The product of the preset performance function at the specified time and the preset initial error value is determined, and the product is subtracted from the error dynamics equation to obtain the error dynamics equation at the specified time.

[0010] A predetermined time sliding mode controller is determined based on the specified time error dynamics equation so that the specified time error dynamics equation converges before a predetermined time.

[0011] Optionally, obtaining the preset dynamic equation and the preset expected value, and combining them to obtain the error dynamic equation, includes:

[0012] The preset dynamic equations are obtained as follows:

[0013]

[0014]

[0015] in, For system state variable x i The derivatives of f1(x1) and f2(x1, x2) are system functions, g1(x1) and g2(x1, x2) are control functions, and u is the control input;

[0016] By obtaining the expected value and its derivative, and combining the dynamic equation with the expected value, the error dynamic equation is obtained as follows:

[0017]

[0018] Where, x d , is the expected value. The derivative of the expected value, and Let X1 and X2 be the derivatives of the error variables, respectively. For the expected value x d The second derivative of .

[0019] Optionally, obtaining the monotonically increasing scalar function includes:

[0020] Obtain a monotonically increasing scalar function, wherein the scalar function includes a predefined scalar function or at least one of the following:

[0021] κ(x) = 1 - exp(-ax);

[0022]

[0023]

[0024]

[0025] Where κ(x) is a scalar function, and each scalar function satisfies κ(0) = 0, lim r→∞ (r) = 1; x is the state variable, and a and τ are the parameters of the scalar function.

[0026] Optionally, obtaining the preset performance function includes:

[0027] The preset performance function is obtained as follows:

[0028]

[0029] Where ρ(t) is the preset performance function, t is time, p is an adjustable parameter, and the value of p ranges from 0.5 to 1. a For the specified time parameter, ρ0 is the initial value of the preset performance function, ρ ∞ The preset performance function at t=T a The value at time; the preset performance function satisfies ρ(0)=ρ0, ρ(T) a )=ρ ∞ ,

[0030] Optionally, determining the product of the preset performance function at the specified time and the preset initial error value, and subtracting the product from the error dynamics equation to obtain the error dynamics equation at the specified time, includes:

[0031] The specified time preset performance function is used as the expected error value, and the initial value of the specified time preset performance function is used as the initial error value.

[0032] The error at a specified time and location is determined as follows:

[0033] e1 = X1 - ρ;

[0034] Where e1 is the specified time error, ρ is the preset performance function for the specified time, ρ0 is the initial value of the error, and ρ ∞ Set to 0;

[0035] Based on the error dynamics equation and the specified time position error, a specified time error dynamics equation is determined, and the specified time error dynamics equation is as follows:

[0036]

[0037]

[0038] Where e2 is the derivative of e1, It is the second derivative of the expected value.

[0039] Optionally, the method further includes:

[0040] The sliding surface is established as follows:

[0041] S = ke1 + e2;

[0042] Where S is the sliding surface; k is a control parameter, and k > 0;

[0043] The derivative of the sliding surface is determined as follows:

[0044]

[0045] The predetermined time control law is determined as follows:

[0046]

[0047] The predetermined time control law is substituted into the specified time error dynamic equation so that the specified time error converges at the predetermined time.

[0048] Optionally, determining a predetermined time sliding mode controller based on the specified time error dynamics equation to ensure that the specified time error dynamics equation converges before a predetermined time includes:

[0049] Obtain a positive definite Lyapunov function, and combine the Lyapunov function with the specified time error dynamic equation to obtain a predetermined time sliding mode controller;

[0050] The Lyapunov function Represents the set of real numbers. Representing n-dimensional space as follows:

[0051]

[0052] Where 0 < a1 < 1, 0 < p1 < 1, T p Here are the controller parameters, and e is a natural constant.

[0053] Another aspect of this application provides a second-order sliding mode control device based on a preset performance function, comprising:

[0054] The first unit is used to obtain the preset dynamic equation and the preset expected value, and combine them to obtain the error dynamic equation;

[0055] The second unit is used to obtain monotonically increasing scalar functions;

[0056] The third unit is used to obtain a preset performance function and substitute the scalar function into the preset performance function lemma to obtain a preset performance function for a specified time.

[0057] The fourth unit is used to determine the product of the preset performance function at the specified time and the preset initial error value, and to subtract the product from the error dynamics equation to obtain the error dynamics equation at the specified time.

[0058] The fifth unit is used to determine a predetermined time sliding mode controller based on the specified time error dynamics equation, so that the specified time error dynamics equation converges before the predetermined time.

[0059] Another aspect of this application provides an electronic device, including a processor and a memory;

[0060] The memory is used to store programs;

[0061] The processor executes the program to implement the method.

[0062] Another aspect of this application provides a computer-readable storage medium storing a program that is executed by a processor to implement the method.

[0063] This application also discloses a computer program product or computer program including computer instructions stored in a computer-readable storage medium. A processor of an electronic device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the electronic device to perform the method described above.

[0064] This application has the following beneficial effects:

[0065] The specified-time method allows for precise specification of the system's convergence time using a single parameter, preventing premature convergence and enabling the controller to adapt to different tasks through simple parameter adjustments. This application provides a general design scheme for a specified-time sliding mode controller, which combines a specified-time preset performance function with a predetermined-time convergence controller to achieve specified-time convergence control. Existing theorem-based specified-time convergence control methods switch the controller at the specified time, causing discontinuities and abrupt changes in the control law. This application maintains continuity at the specified time, avoiding the impact of abrupt changes in the control law on the control effect. Attached Figure Description

[0066] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0067] Figure 1 A flowchart illustrating a second-order sliding mode control method based on a preset performance function, provided for an embodiment of this application;

[0068] Figure 2 An example flowchart of a second-order sliding mode control method based on a preset performance function provided in this application embodiment;

[0069] Figure 3 and Figure 4 These are schematic diagrams of the preset performance function at a specified time under different parameters provided in the embodiments of this application;

[0070] Figure 5 This is a structural block diagram of a second-order sliding mode control device based on a preset performance function, provided in an embodiment of this application. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0072] It should be noted that although functional modules are divided in the device schematic diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart.

[0073] The terms "first," "second," etc., used in the specification, claims, and accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0074] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used herein is for descriptive purposes only and is not intended to be limiting of the application.

[0075] To facilitate understanding of the embodiments of this application, the keywords and related technologies that may be involved in the embodiments of this application are described below:

[0076] A second-order dynamic model is a mathematical model describing the behavior of a physical or control system, containing second-order differential equations. This model is commonly used to describe systems with inertia and damping, such as spring oscillators or vibrating systems in mechanical systems. To ensure the second-order dynamic model asymptotically converges to the desired value, different control methods can be employed. First, the proportional-integral-derivative (PID) controller is a classic control method that regulates the system's behavior through a combination of proportional, integral, and derivative equations. However, PID controllers can be affected by parameter inaccuracies and system nonlinearities.

[0077] To overcome these problems, finite-time control can be employed, aiming to stabilize the system state from its initial state to the desired state within a finite time. Finite-time control methods aim to achieve fast system response and convergence, typically combining nonlinear control and optimization techniques to achieve precise control within a finite time. Fixed-time control is a control method where the upper bound function of the convergence time depends only on the controller parameters and is independent of the initial error value. This makes the value of the upper bound function of the convergence time "fixed" by the controller parameters. However, the upper bound function of a fixed-time controller depends on multiple parameters, making it difficult to simultaneously consider the convergence process and convergence time. To address this issue, predefined time control has been proposed. Predefined time control allows the value of the upper bound function of the convergence time to be set through a single controller parameter, thus facilitating controller design and parameter tuning. This method is more flexible and can achieve a certain degree of precise control over the convergence time of the control system.

[0078] Although finite-time control, fixed-time control, and predetermined-time control all constrain the upper bound of the convergence time, the actual convergence time of the system still strongly depends on the initial values. While the upper bound of time can guarantee fast convergence, it cannot achieve precise control over the actual convergence time. To achieve precise control on the time scale, another related technique has proposed appointed-time control. Appointed-time control allows the actual convergence time of the system to be specified directly through a single parameter. This method provides a more direct and specific control mechanism, enabling the control system to achieve the desired actual convergence time.

[0079] The following section provides a detailed description of the second-order sliding mode control method based on a preset performance function provided in this application, referring to... Figure 1 The method may include steps S100 to S140, as follows:

[0080] S100: Obtain the preset dynamic equation and the preset expected value, and combine them to obtain the error dynamic equation.

[0081] Furthermore, S100 may include:

[0082] The preset dynamic equations are obtained as follows:

[0083]

[0084]

[0085] in, For system state variable x i The derivatives of f1(x1) and f2(x1, x2) are system functions, g1(x1) and g2(x1, x2) are control functions, and u is the control input;

[0086] By obtaining the expected value and its derivative, and combining the dynamic equation with the expected value, the error dynamic equation is obtained as follows:

[0087]

[0088] Where, x d’ For the expected value, The derivative of the expected value, and Let X1 and X2 be the derivatives of the error variables, respectively. For the expected value x d The second derivative of .

[0089] S110: Obtain a monotonically increasing scalar function.

[0090] Specifically, the scalar function in this embodiment can be a strictly monotonically increasing function.

[0091] Furthermore, S110 may include:

[0092] Obtain a monotonically increasing scalar function, wherein the scalar function includes a predefined scalar function or at least one of the following:

[0093] κ(x) = 1 - exp(-ax);

[0094]

[0095]

[0096]

[0097] Where κ(x) is a scalar function, and each scalar function satisfies κ(0) = 0, lim r→∞ (r) = 1; x is the state variable, and a and τ are the parameters of the scalar function.

[0098] It should be noted that the scalar function in this embodiment can be a scalar function predefined according to actual needs, or it can be a variable function shown above, or it can be other optional forms of scalar function, which will not be listed here.

[0099] S120: Obtain a preset performance function, and substitute the scalar function into the preset performance function lemma to obtain a preset performance function for a specified time.

[0100] Furthermore, S120 may include:

[0101] The preset performance function is obtained as follows:

[0102]

[0103] Where ρ(t) is the preset performance function, t is time, p is an adjustable parameter, and the value of p ranges from 0.5 to 1. a For the specified time parameter, ρ0 is the initial value of the preset performance function, ρ ∞ The preset performance function at t=T a The value at time; the preset performance function satisfies ρ(0)=ρ0, ρ(T) a )=ρ ∞ ,

[0104] S130: Determine the product of the preset performance function at the specified time and the preset initial error value, and subtract the product from the error dynamics equation to obtain the error dynamics equation at the specified time.

[0105] Furthermore, S130 may include:

[0106] The specified time preset performance function is used as the expected error value, and the initial value of the specified time preset performance function is used as the initial error value.

[0107] The error at a specified time and location is determined as follows:

[0108] e1 = X1 - ρ;

[0109] Where e1 is the specified time error, ρ is the preset performance function for the specified time, ρ0 is the initial value of the error, and ρ ∞ Set to 0;

[0110] Based on the error dynamics equation and the specified time position error, a specified time error dynamics equation is determined, and the specified time error dynamics equation is as follows:

[0111]

[0112]

[0113] Where e2 is the derivative of e1, It is the second derivative of the expected value.

[0114] Furthermore, this embodiment may also include:

[0115] The sliding surface is established as follows:

[0116] S = ke1 + e2;

[0117] Where S is the sliding surface; k is a control parameter, and k > 0;

[0118] The derivative of the sliding surface is determined as follows:

[0119]

[0120] The predetermined time control law is determined as follows:

[0121]

[0122] The predetermined time control law is substituted into the specified time error dynamic equation so that the specified time error converges at the predetermined time.

[0123] S140: Determine a predetermined time sliding mode controller based on the specified time error dynamics equation so that the specified time error dynamics equation converges before a predetermined time.

[0124] Furthermore, S140 may include:

[0125] Obtain a positive definite Lyapunov function, and combine the Lyapunov function with the specified time error dynamic equation to obtain a predetermined time sliding mode controller;

[0126] The Lyapunov function Represents the set of real numbers. Representing n-dimensional space as follows:

[0127]

[0128] Where 0 < a1 < 1, 0 < p1 < 1, T p Here are the controller parameters, and e is a natural constant.

[0129] To illustrate in more detail the second-order sliding mode control method based on a preset performance function provided in this application, a complete and specific example will be used for explanation.

[0130] Reference Figure 2 This embodiment provides an example flowchart of a second-order sliding mode control method based on a preset performance function.

[0131] Specifically, to solve the problem of specified time control for second-order systems (hereinafter referred to as systems), this embodiment provides a specified time control method based on a combination of a specified time preset performance function and a predetermined time theorem. The method includes the following steps:

[0132] S1: Combine the dynamic equation with the expected value to obtain the error dynamic equation.

[0133] For example, consider a second-order system:

[0134]

[0135]

[0136] in It is the system state variable x i The derivatives of f1(x1) and f2(x1, x2) represent the system functions. g1(x1) and g2(x1, x2) are the control functions. u is the control input.

[0137] Assume the expected value and its derivative are... The dynamic model of the system, i.e., equation (1), is combined with the expected value X1=x1-x d , The error dynamics equation can be obtained as follows:

[0138]

[0139] in and These are the derivatives of the error variables X1 and X2. For the expected value x d The second derivative of .

[0140] S2: Design or use a strictly monotonically increasing scalar function K(x).

[0141] Specifically, define a strictly monotonically increasing function κ(x) that satisfies κ(0) = 0, lim r→∞ (r) = 1.

[0142] The following are examples of scalar functions κ(x) that can be used in this embodiment:

[0143]

[0144]

[0145] Where x represents the state variable, and a and τ are the parameters of the function.

[0146] S3: Substitute the scalar function K(x) into the preset performance function lemma to obtain the preset performance function for the specified time.

[0147] The preset performance function is determined as follows:

[0148]

[0149] Where ρ(t) is the preset performance function, t is time, 0.5 < p < 1 represents an adjustable parameter, and T a The specified time parameter is ρ0, which is the initial value of the function. ∞ For the function at t=T a The value at time. For a function satisfying the above preset performance function definition, we can obtain ρ(0) = ρ0, ρ(T) = ρ(0). a )=ρ ∞ ,

[0150] To demonstrate the preset performance function curve and convergence characteristics, this embodiment can use κ(x) = cos(π / 2exp(-ax)) substituted into the definition of ρ(t) above, with the initial value of the function set to ρ0 = 1, and the function at t = T a The value of time is set to ρ ∞ =0. Figure 3 and Figure 4 The display shows preset performance function curves with parameters p and a set to different values. It can be seen that parameters p and a only change the convergence process, and the function convergence time is changed by T. a The only certainty is that the preset performance function ρ(t) converges at a specified time.

[0151] Next, we will explain why the preset performance function converges at a specified time.

[0152] Specifically, equation (4) is first simplified to the following form:

[0153]

[0154] This can be further simplified to:

[0155]

[0156] For κ(ρ-ρ) ∞ Differentiation yields:

[0157]

[0158] Further, there are:

[0159]

[0160] Further derivative of the preset performance function yields:

[0161]

[0162] According to equations (8)-(9), we can obtain and When t = T a ,κ(ρ-ρ ∞ If ) = 0, then ρ(T) a )=ρ ∞ .

[0163] S4: Subtract the product of the preset performance function and the initial error value from the error dynamics equation to obtain the error dynamics at the specified time.

[0164] Specifically, to ensure a lower limit for the error convergence time, this embodiment can use a preset performance function ρ at a specified time as the expected error value. Define the position error e1 at a specified time:

[0165] e1=X1-ρ (10)

[0166] Where ρ is a preset performance function for a specified time, ρ0 equals the initial error, and ρ ∞ It was set to 0.

[0167] Based on the error dynamics equation (2) and the definition of the position error at a specified time (10), the dynamics equation for the error at a specified time is obtained as follows:

[0168]

[0169]

[0170] Where e2 is the derivative of e1, It is the second derivative of the expected value.

[0171] S5: Design a sliding mode controller with a predetermined time so that the error dynamics converge before the predetermined time, thus ensuring that the actual error converges at the predetermined time.

[0172] Specifically, this embodiment proposes a general method that can combine any pre-defined performance function and a predetermined time theorem. For example, this embodiment can use a predetermined time convergence theorem as an example for illustration, as follows:

[0173] Example Theorem: Suppose there exists a positive definite Lyapunov function. ( Represents the set of real numbers. (representing n-dimensional space) is as follows:

[0174]

[0175] Where 0 < a1 < 1, 0 < p1 < 1, T p Let represent the controller parameters, and e represent the natural constant. The system is considered stable at a predetermined time when the derivative of the Lyapunov function satisfies the above inequality.

[0176] Equation (12) can be used to explain why V(t, x):

[0177] Define ξ(t) as a solution to the following equation:

[0178]

[0179] Integrating equation (13) gives:

[0180]

[0181] Where x0 is the initial value of equation (13). Simplifying equation (13) yields equation (14), as follows:

[0182]

[0183] Optionally, this implementation may define the intermediate function as follows:

[0184]

[0185] Therefore, equation (15) can be changed to:

[0186]

[0187] Therefore, we can obtain Make

[0188] Based on the specified time error variables e1 and e2 established by equation (11), the following sliding surface is established:

[0189] s = ke1 + e2 (18)

[0190] Where k > 0 is a control parameter. The derivative of the sliding surface is defined as follows:

[0191]

[0192] Finally, the predetermined time control law is designed as follows:

[0193]

[0194] Substituting the predetermined time control law, i.e., equation (20), into the specified time error dynamic equation, i.e., equation (11), will make the specified time error variable e1 converge at the predetermined time.

[0195] Define the Lyapunov function as:

[0196] V=||S|| (21)

[0197] The derivative of the Lyapunov function is:

[0198]

[0199] Substituting equation (20) into equation (22) yields:

[0200]

[0201] According to the example theorem, the specified time error variable e1 converges at a predetermined time.

[0202] The predetermined time control law u guarantees that X1 converges to the preset performance function ρ within a predetermined time. Furthermore, the preset performance function is set to converge at a specified time, when the predetermined time parameter T... p And the preset performance function parameter T at a specified time a If the same value T is set, the convergence time of the system error X1 can be preset using a single parameter T.

[0203] This embodiment uses a preset performance function at a specified time as the expected value of the error, and uses a predetermined time controller to make the error converge to the expected value of the error. This is achieved by adjusting the parameter T of the preset performance function at a specified time. a and the predetermined time controller parameter T p By setting the same value T, the convergence time of the system error can be pre-specified through a single parameter T.

[0204] Reference Figure 5This application provides a second-order sliding mode control device based on a preset performance function, comprising:

[0205] The first unit is used to obtain the preset dynamic equation and the preset expected value, and combine them to obtain the error dynamic equation;

[0206] The second unit is used to obtain monotonically increasing scalar functions;

[0207] The third unit is used to obtain a preset performance function and substitute the scalar function into the preset performance function lemma to obtain a preset performance function for a specified time.

[0208] The fourth unit is used to determine the product of the preset performance function at the specified time and the preset initial error value, and to subtract the product from the error dynamics equation to obtain the error dynamics equation at the specified time.

[0209] The fifth unit is used to determine a predetermined time sliding mode controller based on the specified time error dynamics equation, so that the specified time error dynamics equation converges before the predetermined time.

[0210] The specific implementation of this second-order sliding mode control device is basically the same as the specific implementation of the second-order sliding mode control method described above, and will not be repeated here.

[0211] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described second-order sliding mode control method. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc. Specifically, the electronic device can be a user terminal or a server.

[0212] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described second-order sliding mode control method.

[0213] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0214] This application also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. The processor of an electronic device can read the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, causing the electronic device to perform... Figure 1 The method shown.

[0215] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this application are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed and sub-operations described as part of a larger operation are executed independently.

[0216] Furthermore, although this application is described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the described functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding this application. Rather, given the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the module will be understood within the scope of conventional technology for an engineer. Therefore, those skilled in the art can implement the application set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and not intended to limit the scope of this application, which is determined by the full scope of the appended claims and their equivalents.

[0217] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0218] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0219] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0220] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0221] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0222] Although embodiments of this application have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of this application, the scope of which is defined by the claims and their equivalents.

[0223] The above is a detailed description of the preferred embodiments of this application, but this application is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of this application, and these equivalent modifications or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A second-order sliding mode control method based on a preset performance function, characterized in that, include: Obtain the preset dynamic equation and the preset expected value, and combine them to obtain the error dynamic equation; Obtain a monotonically increasing scalar function; Obtain a preset performance function, and substitute the scalar function into the preset performance function lemma to obtain a preset performance function for a specified time; The product of the preset performance function at the specified time and the preset initial error value is determined, and the product is subtracted from the error dynamics equation to obtain the error dynamics equation at the specified time. A predetermined time sliding mode controller is determined based on the specified time error dynamics equation so that the specified time error dynamics equation converges before the predetermined time. The process of obtaining a preset dynamic equation and a preset expected value, and combining them to obtain an error dynamic equation, includes: The preset dynamic equations are obtained as follows: ； ； in, System state variables The derivative of , , For system functions, , For control functions, For control input; By obtaining the expected value and its derivative, and combining the dynamic equation with the expected value, the error dynamic equation is obtained as follows: ； in, For the expected value, The derivative of the expected value, and Error variables and The derivative of Expected value The second derivative; The step of determining the product of the preset performance function at the specified time and the preset initial error value, and subtracting the product from the error dynamics equation to obtain the error dynamics equation at the specified time, includes: The specified time preset performance function is used as the expected error value, and the initial value of the specified time preset performance function is used as the initial error value. The error at a specified time and location is determined as follows: ； in, For the specified time error, Preset a performance function for a specified time. Let the initial value of the error be... Set to 0; Based on the error dynamics equation and the specified time position error, a specified time error dynamics equation is determined, and the specified time error dynamics equation is as follows: ； ； in, for The derivative of The second derivative of the expected value; The method further includes: The sliding surface is established as follows: ； in, S It is a sliding surface; For control parameters, and ; The derivative of the sliding surface is determined as follows: ； ； The predetermined time control law is determined as follows: ； in, For controller parameters, For the parameters of a scalar function; The predetermined time control law is substituted into the specified time error dynamic equation so that the specified time error converges at the predetermined time.

2. The second-order sliding mode control method based on a preset performance function according to claim 1, characterized in that, The process of obtaining a monotonically increasing scalar function includes: Obtain a monotonically increasing scalar function, wherein the scalar function includes a predefined scalar function or at least one of the following: ； ； ； ； in, Let be a scalar function, and each scalar function satisfies ; For state variables, and These are the parameters of a scalar function.

3. The second-order sliding mode control method based on a preset performance function according to claim 1, characterized in that, The process of obtaining the preset performance function includes: The preset performance function is obtained as follows: ； in, For the preset performance function, For time, It is an adjustable parameter. The range of values ​​is , To specify the time parameter, The initial value of the preset performance function, For the preset performance function in The value at time; the preset performance function satisfies , , , .

4. The second-order sliding mode control method based on a preset performance function according to claim 1, characterized in that, The step of determining a predetermined time sliding mode controller based on the specified time error dynamics equation, so that the specified time error dynamics equation converges before a predetermined time, includes: Obtain a positive definite Lyapunov function, and combine the Lyapunov function with the specified time error dynamic equation to obtain a predetermined time sliding mode controller; The Lyapunov function , Represents the set of real numbers. Representing n-dimensional space as follows: ； Where e is the natural constant.

5. A second-order sliding mode control device based on a preset performance function, characterized in that, The device is used to implement the second-order sliding mode control method based on a preset performance function as described in claim 1, and the device includes: The first unit is used to obtain the preset dynamic equation and the preset expected value, and combine them to obtain the error dynamic equation; The second unit is used to obtain monotonically increasing scalar functions; The third unit is used to obtain a preset performance function and substitute the scalar function into the preset performance function lemma to obtain a preset performance function for a specified time. The fourth unit is used to determine the product of the preset performance function at the specified time and the preset initial error value, and to subtract the product from the error dynamics equation to obtain the error dynamics equation at the specified time. The fifth unit is used to determine a predetermined time sliding mode controller based on the specified time error dynamics equation, so that the specified time error dynamics equation converges before the predetermined time.

6. An electronic device, characterized in that, Including the processor and memory; The memory is used to store programs; The processor executes the program to implement the method as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, The storage medium stores a program that is executed by a processor to implement the method as described in any one of claims 1 to 4.

Images