An Observation-Based Adaptive Logarithmic Terminal Sliding Mode Control Method and Device

Abstract

The present invention discloses an observation-based adaptive logarithmic terminal sliding mode control method and device, which relates to the technical field of sliding mode control. By nesting the terminal attractor into the natural logarithmic 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, and constructs an adaptive logarithmic terminal sliding mode controller based on the super-twisting sliding mode control and the adaptive gain. The adaptive gain is updated according to the adaptive law, and the adaptive law is constructed based on a preset non-linear barrier function, realizing the intelligent adaptation of the super-twisting sliding mode control gain, so that the sliding mode variable is constrained within the preset boundary, and the interference estimation error converges rapidly based on the estimation of the interference by the observer. Under the constraint of the sliding mode variable, the global fast convergence of the state tracking error is realized, with high steady-state accuracy, the chattering phenomenon is weakened, and the convergence efficiency and control accuracy 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. However, the discontinuous high-frequency switching term will cause chattering phenomenon. The 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 is still 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 when 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-convergence stage of the observer.

[0005] In summary, the existing sliding mode control methods for non-linear systems are difficult to achieve both 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:

[0008] The present invention provides an observation-based adaptive logarithmic terminal sliding mode control method. First, the present invention models the states of a non-linear second-order system to be controlled, which includes unmatched disturbances and matched disturbances. Then, according to the control objective of the non-linear second-order system, the tracking error representation of the non-linear 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 disturbances, and a second observer is constructed to estimate the matched disturbances. 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 the adaptive gain, and the non-linear second-order system is controlled based on the logarithmic terminal sliding mode controller.

[0009] The present invention provides an observation-based adaptive logarithmic terminal sliding mode control device, including:

[0010] A modeling module, configured to model a non-linear second-order system to be controlled, where the non-linear second-order system includes unmatched disturbances and matched disturbances;

[0011] A sliding mode surface construction module, configured to determine the tracking error representation of the non-linear second-order system according to the control objective of the non-linear 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;

[0012] An observer construction module, configured to construct a first observer to estimate the unmatched disturbances and construct a second observer to estimate the matched disturbances;

[0013] A control module, configured to construct an adaptive logarithmic terminal sliding mode controller based on the super-twisting sliding mode control and the adaptive gain according to the logarithmic terminal sliding mode surface, the first observer and the second observer, and control the non-linear 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 non-linear barrier function.

[0014] The present invention provides a computer-readable storage medium storing 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.

[0015] The present invention provides a computer device, including 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.

[0016] The above-mentioned at least one technical solution adopted by the present invention can achieve the following beneficial effects:

[0017] In the present invention, by nesting the terminal attractor into the natural logarithm function, the terminal sliding mode control and the logarithmic sliding mode control are effectively combined, enabling fast convergence both near and far from the equilibrium point, improving 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 adaption 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 interference estimation error to converge rapidly based on the estimation of the interference 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, and the chattering phenomenon is weakened, improving the convergence efficiency and the control accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The drawings described herein are used to provide a further understanding of the present invention and form 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 to the present invention. In the drawings:

[0019] Figure 1 is a schematic flow chart of an observation-based adaptive logarithmic terminal sliding mode control method provided by the present invention;

[0020] Figure 2 is a schematic phase plane diagram of different sliding surfaces provided by the present invention;

[0021] Figure 3 is a schematic diagram of interference and observer output provided by the present invention;

[0022] Figure 4 is a schematic diagram of the tracking responses of different controllers under disturbance provided by the present invention;

[0023] Figure 5 is a schematic diagram of the simulation corresponding interference and observer output provided by the present invention;

[0024] Figure 6 is a schematic diagram of the output signals of the simulation corresponding different controllers provided by the present invention;

[0025] Figure 7 is a schematic diagram of the tracking responses of different controllers under disturbance in the simulation provided by the present invention;

[0026] 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

[0027] 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.

[0028] 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.

[0029] The following will, in conjunction with the drawings, detail the technical solutions provided by each embodiment of the present invention.

[0030] Figure 1 It is a schematic flowchart of an observation-based adaptive logarithmic terminal sliding mode control method in the present invention, specifically including the following steps:

[0031] S101: Model the nonlinear second-order system to be controlled, where the nonlinear second-order system includes unmatched disturbances and matched disturbances.

[0032] S102: Determine the representation of the tracking error of the nonlinear second-order system according to the control objective of the nonlinear second-order system; according to the representation of the tracking error, nest the terminal attractor into the natural logarithmic function to construct a logarithmic terminal sliding mode surface.

[0033] S103: Construct a first observer to estimate the unmatched disturbance and a second observer to estimate the matched disturbance.

[0034] 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.

[0035] For the sake of convenience of description, only the server will be used as the execution subject for illustration below. The server mentioned in the present invention can be a server set up on the service platform or a device such as a desktop computer or a laptop computer that can execute the solution of the present invention.

[0036] Generally, when designing the control of a non - linear second - order system based on preset performance control, the server can first model the state of the non - linear second - order system to be controlled through the following formula: .

[0037] In the formula, and are different state variables of the non - linear second - order system, and are the state variables of the non - linear second - order system and corresponding derivative functions respectively, is the system control input signal, is a known non - linear function, is a slow - varying continuous non - matching disturbance, are slow - varying continuous matching disturbances respectively, is a known non - linear function.

[0038] The control objective is to make the system state track the desired command . According to the control objective of the non - linear second - order system, the tracking error representation of the non - linear second - order system can be determined through the following formula: , , .

[0039] In the formula, is the expected value corresponding to the state variable of the non - linear second - order system in the control objective, is the expected value corresponding to the state variable of the non - linear second - order system in the control objective, 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, subsequent explanations will all use and for corresponding representation. Similarly, for the relevant representation 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 non - linear second - order system in the control objective.

[0040] 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, the logarithm terminal sliding mode surface can be constructed based on the natural logarithm through the following formula: .

[0041] 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 .

[0042] In order to accurately compensate the unmatched disturbance in the non - linear second - order system , a first observer can be set for the unmatched disturbance through the following formula, and the unmatched disturbance can be estimated by the first observer: , , .

[0043] Among them, is the adaptive function updated according to the adaptive law , and it satisfies the above - mentioned adaptive law. , , and are all positive constants, and are both odd numbers and .

[0044] Let the estimated error of the unmatched disturbance be , then its derivative can be calculated as: .

[0045] Due to the existence of the inequality: .

[0046] Therefore, there exists a constant such that , so there is: . Therefore, the estimated error of the observer can quickly converge to the origin.

[0047] Similarly, an observer can be designed to estimate the matched disturbance. Specifically, a second observer can be set for the matched disturbance through the following formula, and the matched disturbance can be estimated by the second observer: , , .

[0048] wherein, is the observation estimate of the matching interference, is 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.

[0049] Similarly, there exists a positive constant such that the matching perturbation estimation error converges rapidly to the origin, that is: .

[0050] 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:

[0051] ,

[0052] .

[0053] wherein, is the logarithm terminal sliding mode controller, is the derivative function of the observation estimate of the unmatched interference, is the state variable of the nonlinear second-order system in the control target corresponding to the second derivative function of the expected value, is the adaptive function updated according to the adaptive law , is the adaptive function updated according to the adaptive law .

[0054] and follow the following adaptive law: .

[0055] wherein, 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 .

[0056] For the obtained 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 a neighborhood near the equilibrium point within a finite time under the action of the adaptive law. Then, the tracking error will quickly slide along the logarithmic sliding mode manifold based on the observer to a tiny neighborhood of the equilibrium point through the global high-gain mechanism. The specific proof process is as follows:

[0057] (1) Assume the mismatched disturbance and the matched disturbance satisfy and . Therefore, according to the formulas and , there exist two preset times and such that when , the observer output tends to 0. Thus, there exists an appropriate constant such that .

[0058] where , are positive constants, is the sliding mode surface.

[0059] Therefore, the sliding mode reduced-order system can be written as: . In the formula, .

[0060] (2) Select the Lyapunov candidate function as: .

[0061] where , the subscript "T" represents the transpose, is the auxiliary vector, is a positive real number such that , is a positive definite matrix, defined as: . is the operator to take the maximum eigenvalue of the matrix.

[0062] where , are constants. Then the derivative of the Lyapunov function is: .

[0063] where . Decompose the auxiliary vector into , , , then the positive definite function is rewritten as: Taking the derivative of the above formula, we can obtain:

[0064] .

[0065] In the formula, , .

[0066] Considering the formula , the above formula can be rewritten as:

[0067] .

[0068] It can be further compactly expressed as: .

[0069] Where , , .

[0070] To simplify the calculation, let Make The off - diagonal elements are 0. It can be calculated that when the control gain Satisfies the condition: .

[0071] Is a positive - definite matrix, and there exists a minimum positive eigenvalue of , then the compact expression can be further simplified to: .

[0072] Therefore, .

[0073] Since for the real - valued function There exists an inequality: .

[0074] The equality holds if and only if , so there is: .

[0075] In addition, for the bounded real - valued function There exists an inequality: .

[0076] Therefore, .

[0077] Substituting the above formula into the case where the equality holds when , then there is: .

[0078] Where .

[0079] (3) Considering the adaptive control gain And The Lyapunov candidate function is as follows: .

[0080] Where , , are positive constants. Taking the derivative of along the system trajectory gives:

[0081] .

[0082] According to the above, .

[0083] There exist positive constants and such that and . According to and substituting the adaptation law, the above formula can be rewritten as: .

[0084] Where , .

[0085] For , , , there exists an inequality , so the above formula can be further written as: .

[0086] Where . Thus, it is proved that the adaptive logarithmic terminal sliding mode controller proposed in the present invention can make the tracking error converge within the neighborhood of the equilibrium point in finite time.

[0087] 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.

[0088] Figure 2 It is a phase plane schematic diagram of different sliding surfaces in the present invention. The abscissa represents the state variable tracking error, and the ordinate represents the state variable change rate of the tracking error. As can be seen from Figure 2 , under the same parameters, compared with linear sliding mode ( ), terminal sliding mode ( ), logarithmic sliding mode ( ), practical terminal sliding mode function ( ), the logarithmic terminal sliding mode ( ) manifold proposed by the present invention has a global large slope on the phase plane, significantly improving the convergence speed of the nonlinear second-order system.

[0089] The corresponding controllers of the classical linear sliding mode (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) based on STA and the adaptive logarithmic terminal sliding mode (Adaptive Super Twisting Logarithmic TerminalSliding Mode, AST-LnTSM) proposed by the present invention are uniformly expressed as: .

[0090] Among them, is a subscript representing different sliding surfaces, such as , ; , ; , ; The sliding 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 non-singular terminal sliding mode (NTSM) is difficult to be improved by STA, it is mainly compared with the classical NTSM controller: .

[0091] As shown in Figure 3 ,Figure 3 It is a schematic diagram of the interference and the observer output in the present invention. Figure 3 In it, the solid line corresponds to the interference, and the dashed line corresponds to the observer output. As can be seen from Figure 3 , after setting the interference, the adaptive logarithmic terminal sliding mode control proposed by the present invention has the advantages of fast convergence speed, small overshoot, high control precision, etc. compared with other sliding mode controls. At the same time, the observer can quickly track the interference signal. Even if the instantaneous high-frequency signal causes the observation error to become larger, it can quickly converge after the error, and the overall effect is satisfactory.

[0092] Figure 4 It is a schematic diagram of the tracking response of different controllers under disturbance in the present invention. As can be seen from Figure 4 , due to the compensation effect of the observer, even under the condition of disturbance, compared with other sliding mode controls that all have larger 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" in it) still maintains high performance such as fast finite-time convergence and small overshoot.

[0093] 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 according to needs, and the present invention does not limit this.

[0094] 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: .

[0095] Wherein, is the total mass of the moving part of the linear motor, , , are respectively the position, speed and acceleration of the moving part of the linear motor, is the control input, is the force constant, representing the proportional coefficient for converting the control input into the motor output force, is the mass compensation coefficient, which is used to compensate 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.

[0096] Define the system state as , and the desired state as , the control objective is to make the linear motor position track the desired position, and let the tracking error be , then according to the mathematical model, we can get: .

[0097] Among them , , and represent the lumped disturbances caused by factors such as environmental temperature and power supply fluctuations.

[0098] The simulation sets the above parameters to be , , , , , , , and the desired signal is: .

[0099] 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 .

[0100] The simulation results are as shown in Figures 5 - 7 , Figure 5 is a schematic diagram of the corresponding interference and observer output in a simulation of the present invention, where the solid line corresponds to the interference and the dashed line corresponds to the observer output, Figure 5 showing that the observer proposed in the present invention can effectively estimate the interference signal. Figure 6 is a schematic diagram of the output signals of different controllers corresponding to a simulation in the present invention, Figure 6 showing the output signals of different controllers . It can be seen that although the non-singular 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 non-singular 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 is a schematic diagram of the tracking responses of different controllers corresponding to a simulation in the present invention under the condition of having disturbances. Figure 7shows the curves of different controllers tracking the desired position signal. The results show that in the presence of disturbances, the other sliding mode controls have relatively large tracking errors, while the adaptive logarithmic terminal sliding mode controller combining an observer and based on STA proposed by the present invention (corresponding to Figure 7 "the position signal of the adaptive super-twisting logarithmic terminal sliding mode controller with an observer" in

[0101] 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.

[0102] Figure 8 is a schematic diagram of an observation-based adaptive logarithmic terminal sliding mode control device provided by the present invention, including:

[0103] 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;

[0104] 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;

[0105] An observer construction module 203 for constructing a first observer to estimate the unmatched disturbance and a second observer to estimate the matched disturbance;

[0106] A control module 204 for constructing 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 controlling the nonlinear second-order system based on the adaptive logarithmic terminal sliding mode controller; wherein, the adaptive gain is updated according to an adaptation law to constrain the sliding mode variable within a preset boundary; and the adaptation law is constructed based on a preset nonlinear barrier function.

[0107] 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 or independent of the processor in the computer device in the form of hardware, or stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0108] The present invention also provides a computer-readable storage medium storing a computer program, which can be used to execute the above-mentioned Figure 1 observation-based adaptive logarithmic terminal sliding mode control method provided.

[0109] 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-mentioned Figure 1 observation-based adaptive logarithmic terminal sliding mode control method provided.

[0110] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods 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 above-mentioned method embodiments. Among them, any reference to a memory, storage, database, or other medium used in the various embodiments provided by the present invention can include at least one of non-volatile and volatile memories. The non-volatile memory can include a read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical memory, etc. The volatile memory can include a random access memory (RAM) or an 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.

[0111] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise 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 to be within 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 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: ， ， ， ， And the nonlinear second-order system is controlled based on the adaptive logarithmic terminal sliding mode controller; The adaptive gain is updated according to the adaptive law so that the sliding mode variable is constrained within a preset boundary; the adaptive law is constructed based on a preset nonlinear barrier function; 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.

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 slowly 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. 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; The control module is used to construct an adaptive logarithmic terminal sliding mode controller based on the logarithmic terminal sliding mode surface, the first observer and the second observer through the following formula based on the super spiral sliding mode control and the adaptive gain: ， , , , and control the nonlinear second-order system based on an adaptive logarithmic terminal sliding mode controller; The adaptive gain is updated according to the adaptive law so that the sliding mode variable is constrained within a preset boundary; the adaptive law is constructed based on a preset nonlinear barrier function; 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. 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 5 is implemented.

8. 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 5 is implemented.

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