Adaptive logarithmic terminal sliding mode control method and device based on observation

Abstract

The invention discloses a self-adaptive logarithmic terminal sliding mode control method and device based on observation, and relates to the technical field of sliding mode control. According to the method, the terminal attractors are nested into the natural logarithmic function, terminal sliding mode control and logarithmic sliding mode control are effectively combined, rapid convergence can be achieved near and far away from the balance point, the global dynamics of the sliding mode surface is improved, and the sliding mode control efficiency is improved. Meanwhile, a self-adaptive logarithmic terminal sliding mode controller is constructed on the basis of super-spiral sliding mode control and self-adaptive gain, the self-adaptive gain is updated according to a self-adaptive law, the self-adaptive law is constructed on the basis of a preset nonlinear obstacle function, intelligent self-adaption of the super-spiral sliding mode control gain is achieved, and therefore sliding mode variables are restrained within a preset boundary; and the interference estimation error is quickly converged based on the estimation of the observer on the interference, the global quick convergence of the state tracking error is realized under the constraint of the sliding mode variable, the steady-state precision is high, the chattering phenomenon is weakened, and the convergence efficiency and the control precision are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of sliding mode control, and particularly to an observation-based adaptive logarithmic terminal sliding mode control method and device. Background Art

[0002] Currently, sliding mode control is widely used to solve high-precision control problems due to its simplicity and high robustness.

[0003] Compared with the fact that the asymptotic convergence of classical linear sliding mode control cannot guarantee finite-time stability, terminal sliding mode control makes the system state converge to the equilibrium point within a finite time by introducing a non-linear function (such as a power term) in the design of the sliding surface, but the discontinuous high-frequency switching term will cause chattering. Second-order sliding mode control based on the Super Twisting Algorithm (STA) reduces the chattering phenomenon by introducing an integral term and a homogeneous function to smooth the control signal. However, how to integrate the terminal sliding mode control into the second-order sliding mode control system to achieve finite-time stability of the controlled system and reduce chattering simultaneously remains a challenge.

[0004] By constructing a local high gain at the equilibrium point, practical terminal sliding mode control and logarithmic sliding mode control have initially solved the above problems. However, the dynamic characteristics of their sliding surfaces are gentle far from the equilibrium point, and the convergence speed decreases significantly, making it impossible to achieve global fast convergence. At the same time, for unknown dynamic disturbances, they can be compensated by an observer, fuzzy approximation, or neural network approximation. However, the estimated disturbance may cause stability risks due to overshoot during the non-convergent stage of the observer.

[0005] In summary, the existing sliding mode control methods for non-linear systems are difficult to balance chattering suppression and global fast convergence, and have poor convergence efficiency and control accuracy. Summary of the Invention

[0006] Based on this, it is necessary to provide an observation-based adaptive logarithmic terminal sliding mode control method and device for the above technical problems.

[0007] The present invention adopts the following technical solutions: The present invention provides an observation-based adaptive logarithmic terminal sliding mode control method. First, the present invention models the state of a nonlinear second-order system to be controlled, which includes unmatched disturbances and matched disturbances. Then, according to the control objective of the nonlinear second-order system, the tracking error representation of the nonlinear second-order system is determined. Thus, according to the tracking error representation, the terminal attractor is nested into the natural logarithmic function to construct a logarithmic terminal sliding mode surface. Then, a first observer is constructed to estimate the unmatched disturbance, and a second observer is constructed to estimate the matched disturbance. Finally, according to the logarithmic terminal sliding mode surface, the first observer and the second observer, an adaptive logarithmic terminal sliding mode controller is constructed based on the super-twisting sliding mode control and an adaptive gain, and the nonlinear second-order system is controlled based on the logarithmic terminal sliding mode controller.

[0008] The present invention provides an observation-based adaptive logarithmic terminal sliding mode control device, comprising: a modeling module, configured to model a nonlinear second-order system to be controlled, where the nonlinear second-order system includes unmatched disturbances and matched disturbances; a sliding mode surface construction module, configured to determine the tracking error representation of the nonlinear second-order system according to the control objective of the nonlinear second-order system; and construct a logarithmic terminal sliding mode surface by nesting the terminal attractor into the natural logarithmic function according to the tracking error representation; an observer construction module, configured to construct a first observer to estimate the unmatched disturbance and construct a second observer to estimate the matched disturbance; a control module, configured to construct an adaptive logarithmic terminal sliding mode controller based on the super-twisting sliding mode control and an adaptive gain according to the logarithmic terminal sliding mode surface, the first observer and the second observer, and control the nonlinear second-order system based on the adaptive logarithmic terminal sliding mode controller; wherein, the adaptive gain is updated according to an adaptive law to constrain the sliding mode variable within a preset boundary; and the adaptive law is constructed based on a preset nonlinear barrier function.

[0009] The present invention provides a computer-readable storage medium, where the storage medium stores a computer program, and when the computer program is executed by a processor, the above-mentioned observation-based adaptive logarithmic terminal sliding mode control method is implemented.

[0010] The present invention provides a computer device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, and when the processor executes the program, the above-mentioned observation-based adaptive logarithmic terminal sliding mode control method is implemented.

[0011] The above at least one technical solution adopted by the present invention can achieve the following beneficial effects: By nesting the terminal attractor into the natural logarithm function, the present invention effectively combines the terminal sliding mode control and the logarithmic sliding mode control, realizes fast convergence both near and far from the equilibrium point, improves the global dynamics of the sliding surface. Meanwhile, an adaptive logarithmic terminal sliding mode controller is constructed based on the super-twisting sliding mode control and the adaptive gain, and the adaptive gain is updated according to the adaptive law based on the preset non-linear barrier function, realizing the intelligent adaptation of the super-twisting sliding mode control gain, thereby constraining the sliding mode variable within the preset boundary, improving the robustness of the control system, and enabling the disturbance estimation error to converge rapidly based on the estimation of the disturbance by the observer. Under the constraint of the sliding mode variable, the global fast convergence of the state tracking error is achieved, with high steady-state accuracy, the chattering phenomenon is weakened, and the convergence efficiency and control accuracy are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 is a schematic flow chart of an observation-based adaptive logarithmic terminal sliding mode control method provided by the present invention; Figure 2 is a schematic phase plane diagram of different sliding surfaces provided by the present invention; Figure 3 is a schematic diagram of the disturbance and the observer output provided by the present invention; Figure 4 is a schematic diagram of the tracking responses of different controllers under the condition of disturbance provided by the present invention; Figure 5 is a schematic diagram of the simulation corresponding disturbance and the observer output provided by the present invention; Figure 6 is a schematic diagram of the output signals of different controllers corresponding to the simulation provided by the present invention; Figure 7 is a schematic diagram of the tracking responses of different controllers corresponding to the simulation under the condition of disturbance provided by the present invention; Figure 8 is a schematic diagram of an observation-based adaptive logarithmic terminal sliding mode control device provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0013] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0014] The present invention proposes an adaptive logarithmic terminal sliding mode controller and observer: nesting the terminal attractor into the natural logarithmic function, analytically giving the sliding time of the system state on this manifold, and realizing the finite-time stability of the sliding dynamics. For systems with matched and unmatched uncertainties, corresponding controllers and observers are designed in combination with STA, and a new barrier function is used to adaptively adjust the STA control gain, enabling both the disturbance estimation error and the state tracking error to achieve global fast convergence.

[0015] The technical solutions provided by the embodiments of the present invention will be described in detail below in conjunction with the drawings.

[0016] Figure 1 It is a schematic flow diagram of an observation-based adaptive logarithmic terminal sliding mode control method in the present invention, specifically including the following steps: S101: Model the nonlinear second-order system to be controlled, where the nonlinear second-order system includes unmatched disturbances and matched disturbances.

[0017] S102: Determine the tracking error representation of the nonlinear second-order system according to the control objective of the nonlinear second-order system; according to the tracking error representation, nest the terminal attractor into the natural logarithmic function to construct a logarithmic terminal sliding mode surface.

[0018] S103: Construct a first observer to estimate the unmatched disturbance and a second observer to estimate the matched disturbance.

[0019] S104: Based on the logarithmic terminal sliding mode surface, the first observer, and the second observer, construct an adaptive logarithmic terminal sliding mode controller based on super-twisting sliding mode control and adaptive gain, and control the nonlinear second-order system based on the adaptive logarithmic terminal sliding mode controller; wherein, the adaptive gain is updated according to the adaptive law to constrain the sliding mode variable within a preset boundary; the adaptive law is constructed based on a preset nonlinear barrier function.

[0020] For the sake of convenience of description, only the server will be used as the execution entity for description below. The server mentioned in the present invention can be a server set up on a service platform or a device such as a desktop computer or a laptop computer that can execute the solution of the present invention.

[0021] Generally, when designing the control of a nonlinear second-order system based on preset performance control, the server can first model the state of the nonlinear second-order system to be controlled through the following formula: .

[0022] In the formula, and are different state variables of the nonlinear second-order system, and are the state variables of the nonlinear second-order system and corresponding to the derivative functions respectively, is the system control input signal, is a known nonlinear function, is a slow-varying continuous non-matching disturbance, are slow-varying continuous matching disturbances respectively, is a known nonlinear function.

[0023] The control objective is to make the system state track the desired command . According to the control objective of the nonlinear second-order system, the tracking error representation of the nonlinear second-order system can be determined through the following formula: , , .

[0024] In the formula, is the state variable of the nonlinear second-order system in the control objective corresponding to the expected value, is the state variable of the nonlinear second-order system in the control objective corresponding to the expected value, is the tracking error of the state variable , is the tracking error of the state variable , and represent that and are both functions of time t . For the sake of convenience of explanation, hereinafter, and will be correspondingly represented. Similarly, for the relevant representations of the observed values of and , represents approximately equal to, is the observed value of the derivative function of the tracking error , is the observed estimate of the non-matching disturbance, is the derivative function of the expected value corresponding to the state variable of the nonlinear second-order system in the control objective.

[0025] Based on the established non - linear second - order system model above, a logarithm terminal sliding mode surface with global fast convergence based on observation is further proposed. Specifically, according to the fractional - exponential power represented by the tracking error and the observed value of the derivative represented by the tracking error, a logarithm terminal sliding mode surface is constructed based on the natural logarithm through the following formula: .

[0026] In the formula, is the logarithm terminal sliding mode surface containing the disturbance estimator, , , and are all positive constants, and are both odd numbers and .

[0027] In order to accurately compensate the unmatched disturbance in the non - linear second - order system , a first observer is set for the unmatched disturbance through the following formula, and the unmatched disturbance is estimated by the first observer: , , .

[0028] Among them, is the adaptive function updated according to the adaptive law and satisfies the above - mentioned adaptive law. , , and are all positive constants, and are both odd numbers and .

[0029] Let the unmatched disturbance estimation error be , then its derivative can be calculated as: .

[0030] Since there is an inequality: .

[0031] Therefore, there exists a constant such that , so there is: . Therefore, the observer estimation error can quickly converge to the origin.

[0032] Similarly, an observer can be designed to estimate the matched disturbance. Specifically, a second observer is set for the matched disturbance through the following formula, and the matched disturbance is estimated by the second observer: , , .

[0033] Among them, For the observation estimation of matching interference, For the adaptive function updated according to the adaptive law , , , , , are all positive constants, and are odd numbers and , , is the sign function, is the coefficient of the corresponding power term.

[0034] Similarly, there exists a positive constant such that the matching disturbance estimation error quickly converges to the origin, that is: .

[0035] According to the logarithm terminal sliding mode surface, the first observer and the second observer designed above, an adaptive logarithm terminal sliding mode controller can be set based on the super-twisting sliding mode control by the following formula: , .

[0036] Among them, is the logarithm terminal sliding mode controller, is the derivative function of the observation estimation of unmatched interference, is the state variable of the nonlinear second-order system in the control target The second derivative function of the corresponding expected value, is the adaptive function updated according to the adaptive law , is the adaptive function updated according to the adaptive law .

[0037] and Follow the following adaptive law: .

[0038] Among them, a 1 , a 2 are positive constants, , are appropriate boundary constants, is the barrier function, so that the sliding mode variable is constrained within the boundary .

[0039] ​For the above-mentioned adaptive logarithmic terminal sliding mode controller, the Lyapunov stability theorem can be used to prove that the proposed adaptive logarithmic terminal sliding mode controller of the present invention can drive the tracking error to converge to the neighborhood near the equilibrium point in finite time under the action of the adaptive law, and then the tracking error will quickly slide to the tiny neighborhood of the equilibrium point along the logarithmic sliding mode manifold based on the observer through the global high-gain mechanism. The specific proof process is as follows: (1) Assume unmatched disturbance and matched disturbance satisfy and , so according to the formulas and , there exist two preset times and , when , the observer output tends to 0. Therefore, there exists an appropriate constant such that .

[0040] where , are positive constants, is the sliding mode surface.

[0041] Therefore, the sliding mode reduced-order system can be written as: . In the formula, .

[0042] (2) Select the Lyapunov candidate function as: .

[0043] where , the subscript "T" represents transpose, is the auxiliary vector, is a positive real number such that , is a positive definite matrix, defined as: . is the operator for taking the maximum eigenvalue of the matrix.

[0044] where , are constants. Then the derivative of the Lyapunov function is: .

[0045] where . Decompose the auxiliary vector into , , , then the positive definite function is rewritten as: . Take the derivative of the above formula, and we can get: 。

[0046] In the formula, , 。

[0047] Considering the formula , the above formula can be rewritten as: 。

[0048] It can be further compactly expressed as: 。

[0049] Where , , 。

[0050] To simplify the calculation, let Make The off-diagonal elements are 0, and it can be calculated that when the control gain Satisfies the condition: 。

[0051] Is a positive definite matrix, and there is a minimum positive eigenvalue of , then the compact expression can be further simplified to: 。

[0052] Therefore, 。

[0053] Since for the real function There is an inequality: 。

[0054] When and only when The equal sign holds, so there is: 。

[0055] In addition, for the bounded real function There is an inequality: 。

[0056] Therefore, 。

[0057] Substitute the above formula into When the equal sign holds, then there is: 。

[0058] Where 。

[0059] (3)Considering the Lyapunov candidate function containing the adaptive control gains And Is: 。

[0060] Where , , is a positive constant. For Differentiating along the system trajectory gives: .

[0061] According to the above, .

[0062] There exist positive constants and such that and . According to , and substituting into the adaptation law, the above formula can be rewritten as: .

[0063] where , .

[0064] For , , , there exists an inequality , so the above formula can be further written as: .

[0065] where . Thus, it is proved that the proposed adaptive logarithmic terminal sliding mode controller can make the tracking error converge to the neighborhood of the equilibrium point within a finite time.

[0066] Based on the observation-based adaptive logarithmic terminal sliding mode control method shown in Figure 1 , the present invention effectively combines terminal sliding mode control and logarithmic sliding mode control by nesting the terminal attractor into the natural logarithmic function, achieving fast convergence both near and far from the equilibrium point, improving the global dynamics of the sliding surface. At the same time, an adaptive logarithmic terminal sliding mode controller is constructed based on super-twisting sliding mode control and adaptive gain. The adaptive gain is updated according to the adaptation law, and the adaptation law is constructed based on a preset non-linear barrier function, realizing the intelligent adaptation of the super-twisting sliding mode control gain, thus constraining the sliding mode variable within the preset boundary, improving the robustness of the control system, and making the disturbance estimation error converge rapidly based on the estimation of the disturbance by the observer. Under the constraint of the sliding mode variable, global fast convergence of the state tracking error is achieved, with high steady-state accuracy, weakening the chattering phenomenon, and improving the convergence efficiency and control accuracy.

[0067] Figure 2 is a schematic diagram of the phase plane of a different sliding surface in the present invention. The abscissa represents the tracking error of the state variable , and the ordinate represents the change rate of the tracking error of the state variable . From Figure 2It can be seen that under the same parameters, compared with linear sliding mode ( ), terminal sliding mode ( ), logarithmic sliding mode ( ), and practical terminal sliding mode function ( ), the logarithmic terminal sliding mode ( ) manifold proposed by the present invention has a globally large slope in the phase plane, significantly improving the convergence rate of the nonlinear second-order system.

[0068] The corresponding controllers of the classical linear sliding mode based on STA (Super Twisting Linear Sliding Mode, ST-LSM), logarithmic sliding mode, practical terminal sliding mode (Super Twisting Practical Terminal Sliding Mode, ST-PTSM), logarithmic terminal sliding mode (Super Twisting Logarithmic Terminal Sliding Mode, ST-LnTSM), and the adaptive logarithmic terminal sliding mode (Adaptive Super Twisting Logarithmic TerminalSliding Mode, AST-LnTSM) proposed by the present invention are uniformly expressed as: .

[0069] Among them, is a subscript representing different sliding mode surfaces, such as , ; , ; , ; The sliding mode surface of LnTSM has been given above, ; The expression of the AST-LnTSM controller has been given above. In addition, corresponding to the terminal sliding mode ( Figure 2 ) in , since the nonsingular terminal sliding mode (NTSM) is difficult to be improved by STA, it is mainly compared with the classical NTSM controller: .

[0070] As shown in Figure 3 , Figure 3 is a schematic diagram of a disturbance and the output of an observer in the present invention, Figure 3 The solid line in corresponds to the disturbance, and the dashed line corresponds to the output of the observer. From Figure 3It can be seen that after setting the disturbance, the adaptive logarithmic terminal sliding mode control proposed by the present invention has the advantages of fast convergence speed, small overshoot, and high control accuracy compared with other sliding mode controls. At the same time, the observer can quickly track the disturbance signal. Even if the instantaneous high-frequency signal causes the observation error to increase, it can quickly converge after the error, and the overall effect is satisfactory.

[0071] Figure 4 It is a schematic diagram of the tracking response of different controllers under disturbances in the present invention. Figure 4 It can be seen that due to the compensation effect of the observer, even under disturbances, compared with other sliding mode controls that all show large tracking errors, the control strategy of AST-LnTSM combined with the observer proposed by the present invention (corresponding to Figure 4 "the position signal of the adaptive super-twisting logarithmic terminal sliding mode controller with an observer") still maintains high performance such as fast finite-time convergence and small overshoot.

[0072] When applying the observation-based adaptive logarithmic terminal sliding mode control method provided by the present invention, it is not necessary to execute according to the order of the steps shown in Figure 1 The specific execution order of each step can be determined as needed, and the present invention does not limit this.

[0073] In addition, the present invention also provides an embodiment of applying the observation-based adaptive logarithmic terminal sliding mode control method provided by the present invention. Considering a linear motor system, its mathematical model is expressed as: .

[0074] Among them, is the total mass of the moving part of the linear motor, , , are the position, velocity, and acceleration of the moving part of the linear motor respectively, is the control input, is the force constant, representing the proportional coefficient of converting the control input into the motor output force, is the mass compensation coefficient, used to compensate for the influence of the mass of the moving part of the motor on the system dynamics. is the friction force, including Coulomb friction and viscous friction , and are the friction coefficients.

[0075] Define the system state as , the desired state as , the control objective is to make the linear motor position track the desired position. Let the tracking error be , then according to the mathematical model, we can get: .

[0076] Among them , , and represent the lumped disturbances caused by factors such as ambient temperature and power supply fluctuations.

[0077] The simulation sets the above parameters to be , , , , , , , and the desired signal is: .

[0078] To ensure the fairness of comparison, the same parameter values of the controllers are equal: , , , , , , , , , . The initial value of the system state is set to 0, the fourth-order Runge-Kutta solver is selected, and the step size is .

[0079] The simulation results are as shown in Figures 5 - 7 , Figure 5 which is a schematic diagram of the simulation corresponding to the interference and the observer output in the present invention. The solid line corresponds to the interference, and the dashed line corresponds to the observer output. Figure 5 It shows that the observer proposed in the present invention can effectively estimate the interference signal. Figure 6 This is a schematic diagram of the simulation corresponding to the output signals of different controllers in the present invention. Figure 6 It shows the output signals of different controllers . It can be seen that although the nonsingular terminal controller has the advantage of finite-time convergence, the chattering phenomenon is obvious. However, for the adaptive logarithmic terminal controller proposed in the present invention, as the system state changes, and are adaptively adjusted, resulting in a nonsingular but sensitive mutation of the control signal, so that the system state is maintained near the sliding mode surface, and thus it has the advantage of small overshoot. Figure 7 This is a schematic diagram of the simulation corresponding to the tracking responses of different controllers under the condition of having disturbances in the present invention. Figure 7 It shows the curves of different controllers tracking the desired position signal. The results show that in the presence of disturbances, the other sliding mode controls all have relatively large tracking errors, while the adaptive logarithmic terminal sliding mode controller combining the observer and based on STA proposed in the present invention (corresponding to Figure 7The "position signal of the adaptive super-twisting logarithmic terminal sliding mode controller with an observer" can still converge quickly in finite time and has high control accuracy.

[0080] The above is the observation-based adaptive logarithmic terminal sliding mode control method provided by one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding observation-based adaptive logarithmic terminal sliding mode control device, as Figure 8 shown.

[0081] Figure 8 FIG. is a schematic diagram of an observation-based adaptive logarithmic terminal sliding mode control device provided by the present invention, including: A modeling module 201 for modeling the nonlinear second-order system to be controlled, where the nonlinear second-order system includes unmatched disturbances and matched disturbances; A sliding mode surface construction module 202 for determining the tracking error representation of the nonlinear second-order system according to the control objective of the nonlinear second-order system; and constructing a logarithmic terminal sliding mode surface by nesting the terminal attractor into the natural logarithmic function according to the tracking error representation; An observer construction module 203 for constructing a first observer to estimate the unmatched disturbance and a second observer to estimate the matched disturbance; A control module 204 for constructing an adaptive logarithmic terminal sliding mode controller based on the logarithmic terminal sliding mode surface, the first observer, and the second observer, based on super-twisting sliding mode control and an adaptive gain, and controlling the nonlinear second-order system based on the adaptive logarithmic terminal sliding mode controller; wherein, the adaptive gain is updated according to an adaptive law to constrain the sliding mode variable within a preset boundary; and the adaptive law is constructed based on a preset nonlinear barrier function.

[0082] For the specific limitations on the observation-based adaptive logarithmic terminal sliding mode control device, reference can be made to the limitations on the observation-based adaptive logarithmic terminal sliding mode control method in the above text, which will not be elaborated here. Each module in the above observation-based adaptive logarithmic terminal sliding mode control device can be implemented in whole or in part by software, hardware, and their combination. The above modules can be embedded in the processor of the computer device in hardware form or be independent of it, or be stored in the memory of the computer device in software form, so as to facilitate the processor to call and execute the operations corresponding to the above modules.

[0083] The present invention also provides a computer-readable storage medium storing a computer program, which can be used to execute the above Figure 1 provided observation-based adaptive logarithmic terminal sliding mode control method.

[0084] The present invention also provides a computer device. At the hardware level, the computer device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory. Of course, it may also include other hardware required for other services. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to implement the above Figure 1 observation-based adaptive logarithmic terminal sliding mode control method provided.

[0085] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided by the present invention can include at least one of non-volatile and volatile memories. The non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical memory, etc. The volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0086] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded by the present invention.

Claims

1. An observation-based adaptive logarithmic terminal sliding mode control method, characterized in that: include: Modeling a nonlinear second-order system to be controlled, wherein the nonlinear second-order system includes an unmatched disturbance and a matched disturbance; Determine the tracking error representation of the nonlinear second-order system according to the control objective of the nonlinear second-order system; According to the tracking error representation, the terminal attractor is embedded into the natural logarithmic function to construct the logarithmic terminal sliding surface; Constructing a first observer to estimate the non-matching interference, and constructing a second observer to estimate the matching interference; According to the logarithmic terminal sliding surface, the first observer and the second observer, an adaptive logarithmic terminal sliding mode controller is constructed based on superhelical sliding mode control and adaptive gain, and the nonlinear second-order system is controlled based on the adaptive logarithmic terminal sliding mode controller; wherein the adaptive gain is updated according to an adaptive law so that the sliding mode variable is constrained within a preset boundary; and the adaptive law is constructed based on a preset nonlinear barrier function.

2. The observation-based adaptive logarithmic terminal sliding mode control method according to claim 1, characterized in that: The modeling of the nonlinear second-order system to be controlled specifically includes: The nonlinear second-order system to be controlled is modeled as follows: ； in, and are different state variables of the nonlinear second-order system, and is the state variable of the nonlinear second-order system and The corresponding derivative functions are, is the system control input signal, and is a known nonlinear function, It is a slow-changing continuous non-matching interference. They are respectively slow-varying continuous matching interference.

3. The observation-based adaptive logarithmic terminal sliding mode control method according to claim 1, characterized in that: Determining a tracking error representation of the nonlinear second-order system according to a control target of the nonlinear second-order system; According to the tracking error representation, the terminal attractor is embedded into the natural logarithmic function to construct the logarithmic terminal sliding surface, which includes: According to the control objective of the nonlinear second-order system, the tracking error expression of the nonlinear second-order system is determined by the following formula: , , ; According to the tracking error representation, the terminal attractor is embedded into the natural logarithmic function, and the logarithmic terminal sliding surface is constructed by the following formula: ； in, and are different state variables of the nonlinear second-order system, is the state variable of the nonlinear second-order system in the control objective The corresponding expected value, is the state variable of the nonlinear second-order system in the control objective The corresponding expected value, is a state variable The tracking error, is a state variable The tracking error, t For time, It is approximately equal to, Tracking error The observed value of the derivative of is the observed estimate of the unmatched interference, is the state variable of the nonlinear second-order system in the control objective The corresponding expected value derivative is, is the logarithmic terminal sliding surface, , , and are all normal numbers, and are odd numbers and .

4. The observation-based adaptive logarithmic terminal sliding mode control method according to claim 1, characterized in that: The constructing a first observer to estimate the non-matching interference specifically includes: The first observer is constructed by the following formula to estimate the mismatched interference: ， ， ； in, is the observed estimate of the unmatched interference, According to the adaptive law Updated adaptive function, , , and are all normal numbers, and are odd numbers and , is a state variable The tracking error, is a state variable of tracking error.

5. The observation-based adaptive logarithmic terminal sliding mode control method according to claim 1, characterized in that: The constructing the second observer to estimate the matching interference specifically includes: The second observer is constructed by the following formula to estimate the matching interference: ， ， ； in, To match the observed estimate of the disturbance, According to the adaptive law Updated adaptive function, , , , , , are all normal numbers, and is an odd number and , is a state variable The tracking error, is a state variable The tracking error, Logarithmic terminal sliding surface, , is the symbolic function, is the corresponding power term coefficient, represents the integral, Indicates taking the absolute value, t For time.

6. The observation-based adaptive logarithmic terminal sliding mode control method according to claim 1, characterized in that: The method of constructing an adaptive logarithmic terminal sliding mode controller based on the logarithmic terminal sliding mode surface, the first observer and the second observer based on super spiral sliding mode control and adaptive gain specifically includes: According to the logarithmic terminal sliding mode surface, the first observer and the second observer, an adaptive logarithmic terminal sliding mode controller is constructed based on super spiral sliding mode control and adaptive gain by the following formula: ， ， ， ； in, is an adaptive logarithmic terminal sliding mode controller, is a known nonlinear function, , , and are all normal numbers, and are odd numbers and , and are different state variables of the nonlinear second-order system, is a state variable The tracking error, is a state variable The tracking error, is a known nonlinear function, is the observed estimate of the unmatched interference, To match the observed estimate of the disturbance, is the derivative of the observed estimate of the non-matching disturbance, is the state variable of the nonlinear second-order system in the control objective The corresponding second-order derivative of the expected value is, is the logarithmic terminal sliding surface, According to the adaptive law Updated adaptive function, According to the adaptive law Updated adaptive function, a 1. a 2. b and K 1 is a normal number, , is the symbolic function, is the corresponding power term coefficient, t For time.

7. An observation-based adaptive logarithmic terminal sliding mode control device, characterized in that: include: A modeling module, used for modeling a nonlinear second-order system to be controlled, wherein the nonlinear second-order system includes an unmatched disturbance and a matched disturbance; A sliding surface construction module for determining a tracking error representation of a nonlinear second-order system based on a control objective of the nonlinear second-order system; According to the tracking error representation, the terminal attractor is embedded into the natural logarithmic function to construct the logarithmic terminal sliding surface; An observer construction module, used to construct a first observer to estimate the non-matching interference, and to construct a second observer to estimate the matching interference; A control module is used to construct an adaptive logarithmic terminal sliding mode controller based on a logarithmic terminal sliding mode surface, a first observer and a second observer, based on superhelical sliding mode control and an adaptive gain, and to control a nonlinear second-order system based on the adaptive logarithmic terminal sliding mode controller; wherein the adaptive gain is updated according to an adaptive law so that the sliding mode variable is constrained within a preset boundary; and the adaptive law is constructed based on a preset nonlinear barrier function.

8. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

9. A computer device, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method according to any one of claims 1 to 6 is implemented.

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