A Super-Twisting Logarithmic Sliding Mode Control Method with Finite-Time Preset Performance Constraints

Abstract

The present invention discloses a super-twisting logarithmic sliding mode control method with a finite-time preset performance constraint, which relates to the technical field of preset performance control. The present invention proposes a piecewise preset performance function constructed based on the hyperbolic cotangent function. This performance function can converge within a finite time, weakens the dependence on the initial state of the system, and improves the applicability of the control method. At the same time, for a nonlinear second-order system, a logarithmic sliding mode surface with a large local gain near the equilibrium point is constructed. The logarithmic sliding mode observer is used to estimate the unknown mismatched nonlinear disturbance of the nonlinear second-order system, and a logarithmic super-twisting sliding mode controller based on the logarithmic sliding mode surface is applied to make the system state quickly converge to a small neighborhood near the equilibrium point in the form of the preset performance within a finite time. This control strategy can effectively suppress the chattering phenomenon in the sliding mode control and improve the convergence accuracy within a finite convergence time.

Description

Technical Field

[0001] The present invention relates to the technical field of preset performance control, and particularly relates to a super-twisting logarithmic sliding mode control method with finite-time preset performance constraints. Background Art

[0002] At present, preset performance control is a common method to improve the transient response quality of a control system. It can artificially set a performance envelope for the system state, so that the transient performance can be characterized by the convergence of the performance envelope function. However, the current preset performance control method has problems that the performance envelope curve cannot converge within a finite time and the initial envelope limit depends on prior knowledge.

[0003] Sliding mode control is an effective method to reduce the steady-state error of a control system. Due to its strong robustness to matched disturbances and the scalability of combining observer technology to suppress unmatched disturbances, it is commonly used in various control systems. However, sliding mode control has problems of chattering and inability to converge within a finite time in practical applications, and the control accuracy is poor. Summary of the Invention

[0004] Based on this, it is necessary to provide a super-twisting logarithmic sliding mode control method with finite-time preset performance constraints for the above technical problems.

[0005] The present invention adopts the following technical solutions:

[0006] The present invention provides a super-twisting logarithmic sliding mode control method with finite-time preset performance constraints. First, the present invention models a nonlinear second-order system to be controlled, where the nonlinear second-order system includes unknown unmatched nonlinear disturbances. Then, a preset performance function that converges in finite time and has no initial value dependence is constructed. Next, the state of the nonlinear second-order system is transformed through a state transformation function, converting the performance constraint problem corresponding to the performance function into an unconstrained problem and obtaining an equivalent system state. Then, based on the equivalent system state and its derivative function, a logarithmic sliding mode surface is constructed based on the logarithmic function, and a sliding mode disturbance observer is constructed based on the logarithmic sliding mode surface to estimate the unmatched nonlinear disturbances. The logarithmic sliding mode surface is transformed according to the sliding mode disturbance observer. Finally, the derivative of the transformed logarithmic sliding mode surface is obtained by differentiating the transformed logarithmic sliding mode surface, and a lumped uncertainty observer is constructed to observe the lumped uncertainty in the derivative of the transformed logarithmic sliding mode surface. A super-twisting logarithmic sliding mode controller is constructed according to the derivative of the transformed logarithmic sliding mode surface and the lumped uncertainty observer, and the state of the nonlinear second-order system to be controlled is controlled based on the super-twisting logarithmic sliding mode controller.

[0007] The present invention provides a super-twisting logarithmic sliding mode control system with finite-time preset performance constraints, including:

[0008] A modeling module for modeling a nonlinear second-order system to be controlled, where the nonlinear second-order system includes unknown mismatched nonlinear disturbances;

[0009] A performance function construction module for constructing a first analytical expression corresponding to when the time variable is less than the convergence time according to the sum of the difference between a preset constant parameter and a hyperbolic cotangent function based on the time variable and the converged performance boundary; constructing a second analytical expression corresponding to when the time variable is greater than or equal to the convergence time according to the converged performance boundary; and obtaining a performance function for preset performance control according to the first analytical expression and the second analytical expression;

[0010] A conversion module for converting the state of the nonlinear second-order system through a state conversion function, converting the performance constraint problem corresponding to the performance function into an unconstrained problem, and obtaining an equivalent system state;

[0011] A sliding mode surface construction module for constructing a logarithmic sliding mode surface based on the equivalent system state and its derivative function based on a logarithmic function; constructing a sliding mode disturbance observer to estimate the mismatched nonlinear disturbance based on the logarithmic sliding mode surface, and converting the logarithmic sliding mode surface according to the sliding mode disturbance observer;

[0012] A control module for taking the derivative of the converted logarithmic sliding mode surface to obtain the derivative function of the converted logarithmic sliding mode surface, constructing a lumped uncertainty observer to observe the lumped uncertainty in the derivative function of the converted logarithmic sliding mode surface, constructing a super-twisting logarithmic sliding mode controller according to the derivative function of the converted logarithmic sliding mode surface and the lumped uncertainty observer, and controlling the state of the nonlinear second-order system to be controlled based on the super-twisting logarithmic sliding mode controller.

[0013] 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 super-twisting logarithmic sliding mode control method with finite-time preset performance constraints is implemented.

[0014] 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 super-twisting logarithmic sliding mode control method with finite-time preset performance constraints is implemented.

[0015] At least one of the above technical solutions adopted by the present invention can achieve the following beneficial effects:

[0016] The present invention proposes a piecewise preset performance function constructed based on the hyperbolic cotangent function. This performance function can converge within a finite time, weaken the dependence on the initial state of the system, and improve the applicability of the control method. At the same time, for a nonlinear second-order system, a logarithmic sliding mode surface with a large local gain near the equilibrium point is constructed. The logarithmic sliding mode observer is used to estimate the unknown mismatched nonlinear disturbance of the nonlinear second-order system, and the logarithmic super-twisting sliding mode control strategy based on the logarithmic sliding mode surface is applied to make the system state quickly converge to a small neighborhood near the equilibrium point in the form of the preset performance within a finite time. This control strategy can effectively suppress the chattering phenomenon in the sliding mode control and improve the convergence accuracy within a finite convergence time. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] 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 to the present invention. In the drawings:

[0018] Figure 1 is a schematic flow chart of a hyper-twisting logarithmic sliding mode control method with finite-time preset performance constraints provided by the present invention;

[0019] Figure 2 is a schematic diagram of a finite-time convergence preset performance function provided by the present invention;

[0020] Figure 3 is a schematic diagram of the rotational speed tracking error of a hyper-twisting integral sliding mode control strategy based on a traditional preset performance function provided by the present invention;

[0021] Figure 4 is a schematic diagram of the rotational speed tracking error of a hyper-twisting logarithmic sliding mode control strategy based on the preset performance function of the present invention;

[0022] Figure 5 is a schematic diagram of the rotational speed tracking curve of different control strategies provided by the present invention;

[0023] Figure 6 is a schematic diagram of a hyper-twisting logarithmic sliding mode control system with finite-time preset performance constraints provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0024] 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 the 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 of 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 shall fall within the protection scope of the present invention.

[0025] At present, sliding mode control is an effective method to reduce the steady-state error of a control system. Due to its strong robustness to matched disturbances and the scalability of combining observer technology to suppress unmatched disturbances, it is commonly used in various control systems. However, sliding mode control faces the problems of chattering and finite-time convergence in practical applications. Current research shows that non-singular terminal sliding mode and high-order sliding mode represented by the super-twisting algorithm can effectively reduce chattering. However, it is still a challenge to combine the super-twisting algorithm with the non-singular terminal sliding mode surface to achieve finite-time convergence of the control system.

[0026] The present invention designs a finite-time pre-set performance pre-set super-twisting logarithmic sliding mode control method. A new pre-set performance function is proposed based on the hyperbolic cotangent function. This performance function weakens the dependence of the initial envelope boundary on prior knowledge and the envelope curve can converge in finite time. The logarithmic sliding mode manifold is used to reduce the order of the system, and a logarithmic sliding mode observer and a super-twisting logarithmic sliding mode controller are designed to achieve finite-time convergence of the state of the controlled system and effective suppression of the chattering phenomenon.

[0027] The following combines the accompanying drawings to detail the technical solutions provided by each embodiment of the present invention.

[0028] Figure 1 It is a schematic flow chart of a super-twisting logarithmic sliding mode control method with finite-time pre-set performance constraints in the present invention, specifically including the following steps:

[0029] S101: Model the non-linear second-order system to be controlled, and the non-linear second-order system includes unknown unmatched non-linear disturbances.

[0030] S102: Construct the first analytical formula corresponding to the time variable less than the convergence time according to the difference between the pre-set constant parameter and the hyperbolic cotangent function based on the time variable and the sum of the performance boundaries after convergence; construct the second analytical formula corresponding to the time variable greater than or equal to the convergence time according to the performance boundaries after convergence; obtain the performance function of the pre-set performance control according to the first analytical formula and the second analytical formula.

[0031] S103: Convert the state of the non-linear second-order system through the state conversion function, convert the performance constraint problem corresponding to the performance function into an unconstrained problem, and obtain the equivalent system state.

[0032] S104: Based on the equivalent system state and its derivative function, construct a logarithmic sliding mode surface based on the logarithmic function; construct a sliding mode disturbance observer based on the logarithmic sliding mode surface to estimate the unmatched non-linear disturbance, and convert the logarithmic sliding mode surface according to the sliding mode disturbance observer.

[0033] S105: Derive the derivative function of the transformed logarithmic sliding surface, construct a lumped uncertainty observer to observe the lumped uncertainty in the derivative function of the transformed logarithmic sliding surface, construct a super-twisting logarithmic sliding mode controller based on the derivative function of the transformed logarithmic sliding surface and the lumped uncertainty observer, and control the state of the nonlinear second-order system to be controlled based on the super-twisting logarithmic sliding mode controller.

[0034] For the convenience of description, only the server is used as the execution subject for description below. The server mentioned in the present invention may 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.

[0035] Generally, when designing the control of a nonlinear second-order system based on preset performance control, the server can first establish a nonlinear second-order system containing matching disturbances and non-matching disturbances through the following formula: .

[0036] Wherein, and represent different state variables of the nonlinear second-order system, and and and their respective first-order derivatives and second-order derivatives are measurable, and are known nonlinear functions, and are unknown non-matching nonlinear disturbances and matching nonlinear disturbances respectively, satisfying the constraint conditions and , the derivative with respect to time is approximately ignored, is an unknown finite upper bound, is the sliding mode variable designed later; is the control signal of the nonlinear second-order system; is the output of the nonlinear second-order system, is the time variable.

[0037] In order to constrain the state variables of the nonlinear second-order system, the first analytical formula corresponding to the time variable less than the convergence time can be constructed according to the difference between the preset constant parameter and the hyperbolic cotangent function based on the time variable and the sum of the converged performance boundaries; the second analytical formula corresponding to the time variable greater than or equal to the convergence time can be constructed according to the converged performance boundary; according to the first analytical formula and the second analytical formula, the performance function that does not depend on the initial value information and converges in finite time of the preset performance control can be constructed through the following formula: .

[0038] Wherein, is the performance function, and is a constant parameter set according to the control performance requirements, is a sufficient small constant that satisfies the condition , is the convergence time set according to the control performance requirements.

[0039] To transform the performance constraint problem corresponding to the performance function into an unconstrained problem, a transformation function of the state variables of the nonlinear second-order system is defined: .

[0040] Among them, is the transformation function, is the state function of the state variables of the nonlinear second-order system, is the upper bound of the error transformation function, is the lower bound of the error transformation function, is the natural constant, is the equivalent system state, which can be explicitly written as: .

[0041] The derivative of the equivalent system state with respect to time is , where is always bounded.

[0042] Based on the equivalent system state and its derivative function, a logarithmic sliding mode surface is constructed based on the logarithmic function by the following formula: .

[0043] Among them, and are constant parameters set according to the control performance requirements, and , , represents the sign function, is the logarithmic sliding mode surface, is the derivative function of the equivalent system state.

[0044] Since has mismatched nonlinear perturbations in it, even if holds, the state of the system will not converge to the vicinity of the equilibrium point. Therefore, based on the logarithmic sliding mode surface, a fast sliding mode disturbance observer is designed by the following formula to estimate the mismatched nonlinear perturbation : .

[0045] Among them, is the adaptive function updated according to the adaptive law , and is a constant parameter set according to the performance requirements of the sliding mode disturbance observer, and 、 ; is to take the absolute value,[[]]END]] is the state variable of the non - linear second - order system 's state function.[[]]END]]

[0046] Define the observation error of the sliding mode disturbance observer. From the above formula, it can be deduced that , so that the fast sliding mode disturbance observer can asymptotically converge.[[]]END]]

[0047] Furthermore, the logarithmic sliding mode surface can be transformed according to the sliding mode disturbance observer through the following formula. Specifically, the derivative of the above - mentioned equivalent system state can be changed to:[[]]END]] .

[0048] In the formula,[[]]END]] is the derivative function of the transformed equivalent system state,[[]]END]] is the derivative function of the performance function.[[]]END]]

[0049] Thus, the above - mentioned logarithmic sliding mode surface is changed to:[[]]END]] . In the formula,[[]]END]] is the transformed logarithmic sliding mode surface.[[]]END]]

[0050] For the convenience of the subsequent design of the control strategy, the derivative of the transformed logarithmic sliding mode surface is obtained through the following formula to get the derivative function of the transformed logarithmic sliding mode surface and the sliding mode reduced - order system:[[]]END]] .

[0051] Among them,[[]]END]] ,[[]]END]]

[0052] ,[[]]END]]

[0053] .

[0054] In the formula,[[]]END]] is the derivative function of the transformed logarithmic sliding mode surface,[[]]END]] is the derivative function of the sliding mode disturbance observer,[[]]END]] is the second - derivative function of the performance function,[[]]END]] is 's derivative function,[[]]END]] and are respectively the derivative functions of the state functions of the non - linear second - order system state variables and ,[[]]END]] is the unknown non - linear matching disturbance.[[]]END]]

[0055] According to the design idea of the logarithmic sliding mode surface, a lumped uncertainty observer is constructed by the following formula to observe the lumped uncertainty in the derivative function of the transformed logarithmic sliding mode surface as follows: .

[0056] wherein, is the lumped uncertainty observer, and are parameters set according to the performance requirements of the lumped uncertainty observer, and , , is the adaptive function updated according to the adaptive law .

[0057] Based on the above sliding mode reduced-order system and lumped uncertainty observer, the super-twisting logarithmic sliding mode controller can be designed according to the logarithmic sliding mode surface by the following formula as: .

[0058] wherein, and are the parameters of the super-twisting logarithmic sliding mode controller set according to the control performance requirements.

[0059] Furthermore, the update strategy of the adaptive function can also be , which means that there is no algebraic loop in the designed lumped uncertainty observer.

[0060] Based on Figure 1 the super-twisting logarithmic sliding mode control method with finite-time preset performance constraints shown, the present invention proposes a piecewise preset performance function constructed based on the hyperbolic tangent function. This performance function can converge within a finite time, weakens the dependence on the initial state of the system, and improves the applicability of the control method. At the same time, for a nonlinear second-order system, a logarithmic sliding mode surface with a large local gain near the equilibrium point is constructed. The unknown mismatched nonlinear disturbance of the nonlinear second-order system is estimated by a logarithmic sliding mode observer, and a logarithmic super-twisting sliding mode control strategy based on the logarithmic sliding mode surface is applied, so that the system state can quickly converge to a small neighborhood near the equilibrium point in the form of preset performance within a finite time. This control strategy can effectively suppress the chattering phenomenon in the sliding mode control and improve the convergence accuracy within a finite convergence time.

[0061] Taking the preset performance control based on integral sliding mode without considering mismatched disturbances as a comparison, its controller is written as: .

[0062] wherein, , , , , , is the integral sliding mode, , are the control gains to be adjusted.

[0063] The performance function used in the above control strategy is: .

[0064] Among them, , , are parameters set by the designer according to the control performance requirements, and the subscript in the lower right corner " r " represents the identifier of the comparison item.

[0065] For a non - linear second - order controlled system, the present invention proposes a new performance function and a super - twisting logarithmic sliding - mode control strategy based on a logarithmic sliding - mode surface, which can make the state of the system quickly converge to a small neighborhood near the equilibrium point in the form of a preset performance within a finite time, and this control strategy can effectively suppress the chattering phenomenon in sliding - mode control.

[0066] The new preset performance function proposed by the present invention weakens the dependence on prior knowledge of the initial envelope bound, and another feature is its finite - time convergence, as Figure 2 shown, while the preset performance function used as the comparison item above can only weaken the dependence on prior knowledge of the initial envelope bound and cannot determine the time for the system state to converge.

[0067] The super - twisting logarithmic sliding - mode control strategy based on a logarithmic sliding - mode surface in the present invention constructs a large local sliding - mode gain near the equilibrium point, so it has a higher convergence accuracy than the super - twisting sliding - mode control strategy based on an integral sliding - mode surface used as the comparison item above within a finite time.

[0068] When applying the super - twisting logarithmic sliding - mode control method with finite - time preset performance constraints 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.

[0069] In addition, the present invention also provides a comparative example of applying the present invention. This example considers a permanent - magnet synchronous motor driven by a field - oriented control method, and its model is as follows:

[0070] .

[0071] Among them, represents the angular velocity, and respectively represent the direct - axis and quadrature - axis stator currents, and respectively represent the direct - axis and quadrature - axis stator voltages, and represent the direct-axis and quadrature-axis stator inductances respectively, , J is the moment of inertia, is the number of pole pairs, is the rotor flux, is the armature resistance, is the viscous friction coefficient, is the unmatched uncertainty, which can include both the friction torque described by undetermined quantities and the unmodeled disturbances caused by the electromagnetic structure.

[0072] Define the nominal value of the angular acceleration and the state variable , then the above mathematical model can be transformed into: .

[0073] where, , . Define the desired speed of the speed tracking problem of the permanent magnet synchronous motor as , the speed tracking error can be expressed as and , then the mathematical model of the speed tracking problem can be written as: .

[0074] where, is the second derivative of the desired speed.

[0075] Obviously, being consistent with the form of the nonlinear second-order system described in the present invention, the above control method can be used for the speed tracking control of the permanent magnet synchronous motor.

[0076] Perform speed tracking control on an actual 4-pole permanent magnet synchronous motor, the desired speed , and the remaining actual relevant physical parameters are as follows: , , .

[0077] In order to converge the tracking error faster, the preset performance envelope parameters in the preset performance control scheme based on integral sliding mode are set to , , , ; the gain of the sliding mode surface and the corresponding controller parameters are respectively set to , , , . The speed tracking error curve based on the above controller parameters is shown in Fig. 3. Because at Since the initial value of the preset performance function is large enough, the dependence on the prior knowledge of the initial envelope boundary is weakened. Due to the rapid convergence of the preset performance boundary, the speed tracking error has reached a small neighborhood near the equilibrium point within 5 ms. However, this scheme cannot determine the convergence time of the system state.

[0078] To ensure the fairness of the comparative simulation, for the new performance function proposed in the present invention, let and then the parameter can be calculated through ; the parameters in the logarithmic sliding mode surface and the corresponding controller are set as and and and and . Under the action of the super-twisting logarithmic sliding mode control method designed in the present invention, the speed tracking error curve of the system is as Figure 4 shown. The results show that the control scheme proposed in the present invention can make the system tracking error converge in the form of preset performance within a finite time, and at the same time, the dependence on the prior knowledge of the initial envelope boundary is significantly relaxed. As Figure 5 shown, comparing the speed tracking error of the preset performance control scheme based on integral sliding mode, the control scheme of the present invention obtains higher convergence accuracy within a finite time.

[0079] The above is the super-twisting logarithmic sliding mode control method with finite-time preset performance constraints provided by one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding super-twisting logarithmic sliding mode control system with finite-time preset performance constraints, as Figure 6 shown.

[0080] Figure 6 FIG. is a schematic diagram of a super-twisting logarithmic sliding mode control system with finite-time preset performance constraints provided by the present invention, including:

[0081] A modeling module 201 for modeling the nonlinear second-order system to be controlled, where the nonlinear second-order system includes unknown mismatched nonlinear disturbances;

[0082] A performance function construction module 202 for constructing a first analytical formula corresponding to a time variable less than the convergence time according to the sum of the difference between a preset constant parameter and a hyperbolic cotangent function based on the time variable and the converged performance boundary; constructing a second analytical formula corresponding to a time variable greater than or equal to the convergence time according to the converged performance boundary; and obtaining a performance function for preset performance control according to the first analytical formula and the second analytical formula;

[0083] A conversion module 203, configured to convert the state of a non-linear second-order system through a state conversion function, convert a performance constraint problem corresponding to a performance function into an unconstrained problem, and obtain an equivalent system state;

[0084] A sliding mode surface construction module 204, configured to construct a logarithmic sliding mode surface based on the logarithmic function according to the equivalent system state and its derivative function; construct a sliding mode disturbance observer based on the logarithmic sliding mode surface to estimate the mismatched non-linear disturbance, and convert the logarithmic sliding mode surface according to the sliding mode disturbance observer;

[0085] A control module 205, configured to take the derivative of the converted logarithmic sliding mode surface to obtain the derivative function of the converted logarithmic sliding mode surface, construct a lumped uncertainty observer to observe the lumped uncertainty in the derivative function of the converted logarithmic sliding mode surface, construct a super-twisting logarithmic sliding mode controller according to the derivative function of the converted logarithmic sliding mode surface and the lumped uncertainty observer, and control the state of the non-linear second-order system to be controlled based on the super-twisting logarithmic sliding mode controller.

[0086] For the specific limitations of the super-twisting logarithmic sliding mode control system with finite-time preset performance constraints, reference can be made to the limitations of the super-twisting logarithmic sliding mode control method with finite-time preset performance constraints in the above text, which will not be elaborated here. Each module in the above super-twisting logarithmic sliding mode control system with finite-time preset performance constraints can be implemented in whole or in part by software, hardware, and their combination. The above-mentioned 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 that the processor can call and execute the operations corresponding to the above-mentioned modules.

[0087] The present invention also provides a computer-readable storage medium, which stores a computer program that can be used to execute the above Figure 1 provided super-twisting logarithmic sliding mode control method with finite-time preset performance constraints.

[0088] 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 provided super-twisting logarithmic sliding mode control method with finite-time preset performance constraints.

[0089] 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. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical memory, etc. 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.

[0090] 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 as the scope recorded in the present invention.

Claims

1. A hypertorsion logarithmic sliding mode control method with finite time preset performance constraints, characterized in that: include: Modeling a nonlinear second-order system to be controlled, the nonlinear second-order system including an unknown unmatched nonlinear disturbance; According to the sum of the difference between the preset constant parameter and the hyperbolic cotangent function based on the time variable and the performance boundary after convergence, a first analytical expression corresponding to when the time variable is less than the convergence time is constructed; according to the performance boundary after convergence, a second analytical expression corresponding to when the time variable is greater than or equal to the convergence time is constructed; and a performance function of the preset performance control is obtained according to the first analytical expression and the second analytical expression; The state of the nonlinear second-order system is converted through the state transition function, the performance constraint problem corresponding to the performance function is converted into an unconstrained problem, and the equivalent system state is obtained; According to the equivalent system state and its derivative function, a logarithmic sliding surface is constructed based on the logarithmic function; a sliding mode disturbance observer is constructed based on the logarithmic sliding surface to estimate the mismatched nonlinear disturbance, and the logarithmic sliding surface is transformed according to the sliding mode disturbance observer; The derivative function of the transformed logarithmic sliding surface is obtained by taking the derivative of the transformed logarithmic sliding surface, and the lumped uncertainty observer is constructed by the following formula to observe the lumped uncertainty in the derivative function of the transformed logarithmic sliding surface: ; According to the derivative function of the transformed logarithmic sliding mode surface and the lumped uncertainty observer, the hypertorsion logarithmic sliding mode controller is constructed by the following formula: , ， ， ； And the state of the nonlinear second-order system to be controlled is controlled based on the hypertorsion logarithmic sliding mode controller; in, is the lumped uncertainty observer, and is a constant parameter set according to the performance requirements of the lumped uncertainty observer, and is the constant parameter of the supertorque logarithmic sliding mode controller set according to the control performance requirements. According to the adaptive law Updated adaptive function, is the transformed logarithmic sliding surface, To take the absolute value, is the symbolic function, is a known nonlinear function, is the upper bound of the error transfer function, is the lower bound of the error transfer function, is the performance function, is the state variable of the nonlinear second-order system The state function of and It is a constant parameter set according to the control performance requirements. is the derivative function of the equivalent system state after transformation, is the equivalent system state, is a known nonlinear function, is the derivative function of the sliding mode disturbance observer.

2. The hypertorsion logarithmic sliding mode control method with finite time preset performance constraints as claimed in 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 are the state variables of the nonlinear second-order system. and The corresponding derivative functions are, and is a known nonlinear function, is the unknown mismatched nonlinear perturbation, is the unknown matching nonlinear perturbation, is the control signal of the nonlinear second-order system, is the output of the nonlinear second-order system.

3. The hypertorsion logarithmic sliding mode control method with finite time preset performance constraints as claimed in claim 1, characterized in that: The method comprises constructing a first analytical expression corresponding to when the time variable is less than the convergence time based on the sum of the difference between the preset constant parameter and the hyperbolic cotangent function based on the time variable and the performance boundary after convergence; and constructing a second analytical expression corresponding to when the time variable is greater than or equal to the convergence time based on the performance boundary after convergence; The performance function of the preset performance control is obtained according to the first analytical expression and the second analytical expression, specifically including: According to the sum of the difference between the preset constant parameter and the hyperbolic cotangent function based on the time variable and the performance boundary after convergence, the first analytical expression corresponding to the time variable being less than the convergence time is constructed; according to the performance boundary after convergence, the second analytical expression corresponding to the time variable being greater than or equal to the convergence time is constructed; according to the first analytical expression and the second analytical expression, the performance function of the preset performance control is constructed by the following formula: ， ， ； in, is the performance function, is the performance boundary after convergence, and It is a constant parameter set according to the control performance requirements. is the preset constant, is the time variable, is the convergence time.

4. The hypertorsion logarithmic sliding mode control method with finite time preset performance constraints as claimed in claim 1, characterized in that: The state of the nonlinear second-order system is converted by the state transition function, the performance constraint problem corresponding to the performance function is converted into an unconstrained problem, and an equivalent system state is obtained, which specifically includes: According to the state transition function The state of the nonlinear second-order system is transformed, the performance constraint problem corresponding to the performance function is converted into an unconstrained problem, and the equivalent system state is obtained: ； in, is the conversion function, is the state variable of the nonlinear second-order system The state function of is the performance function, is the upper bound of the error transfer function, is the lower bound of the error transfer function, is a natural constant, is the equivalent system state.

5. The hypertorsion logarithmic sliding mode control method with finite time preset performance constraints as claimed in claim 1, characterized in that: The method comprises: constructing a logarithmic sliding surface based on a logarithmic function according to an equivalent system state and its derivative function; constructing a sliding mode disturbance observer based on the logarithmic sliding surface to estimate the mismatched nonlinear disturbance; and converting the logarithmic sliding surface according to the sliding mode disturbance observer, specifically comprising: According to the equivalent system state and its derivative function, the logarithmic sliding surface is constructed based on the logarithmic function by the following formula: ； Based on the logarithmic sliding surface, the sliding mode disturbance observer is constructed by the following formula to estimate the mismatched nonlinear disturbance: ； According to the sliding mode disturbance observer, the logarithmic sliding surface is transformed by the following formula: ， ， ； in, is the logarithmic sliding surface, is the transformed logarithmic sliding surface, is the equivalent system state, is the derivative of the equivalent system state, is the derivative function of the equivalent system state after transformation, is the sliding mode disturbance observer, According to the adaptive law Updated adaptive function, is the conversion function, is the performance function, is the derivative of the performance function, and is a constant parameter set according to the observer performance requirements, and It is a constant parameter set according to the control performance requirements. and are the state variables of the nonlinear second-order system and The state function of is the upper bound of the error transfer function, is the lower bound of the error transfer function, To take the absolute value, is a symbolic function.

6. The hypertorsion logarithmic sliding mode control method with finite time preset performance constraints as claimed in claim 5, characterized in that: The step of deriving the converted logarithmic sliding mode surface to obtain a derivative function of the converted logarithmic sliding mode surface specifically includes: The derivative function of the transformed logarithmic sliding mode surface is obtained by taking the derivative of the transformed logarithmic sliding mode surface through the following formula: ， ， ， ； in, is the derivative function of the transformed logarithmic sliding surface, is the derivative function of the sliding mode disturbance observer, is the second-order derivative of the performance function, for The derivative function of and are the state variables of the nonlinear second-order system and The derivative of the state function of is a known nonlinear function, is the unknown nonlinear matching disturbance, u is the control signal of the nonlinear second-order system, is a known nonlinear function.

7. A hypertorsion logarithmic sliding mode control system with finite time preset performance constraints, characterized in that: include: A modeling module, for modeling a nonlinear second-order system to be controlled, wherein the nonlinear second-order system includes an unknown unmatched nonlinear disturbance; A performance function construction module is used to construct a first analytical expression corresponding to when the time variable is less than the convergence time according to the sum of the difference between a preset constant parameter and a hyperbolic cotangent function based on the time variable and the performance boundary after convergence; construct a second analytical expression corresponding to when the time variable is greater than or equal to the convergence time according to the performance boundary after convergence; and obtain a performance function of the preset performance control according to the first analytical expression and the second analytical expression; A conversion module is used to convert the state of the nonlinear second-order system through a state conversion function, convert the performance constraint problem corresponding to the performance function into an unconstrained problem, and obtain an equivalent system state; A sliding surface construction module is used to construct a logarithmic sliding surface based on a logarithmic function according to an equivalent system state and its derivative function; a sliding mode disturbance observer is constructed based on the logarithmic sliding surface to estimate the mismatched nonlinear disturbance, and the logarithmic sliding surface is converted according to the sliding mode disturbance observer; The control module is used to obtain the derivative function of the transformed logarithmic sliding surface by deriving the transformed logarithmic sliding surface, and to observe the lumped uncertainty in the derivative function of the transformed logarithmic sliding surface by constructing a lumped uncertainty observer through the following formula: ; According to the derivative function of the transformed logarithmic sliding mode surface and the lumped uncertainty observer, the hypertorsion logarithmic sliding mode controller is constructed by the following formula: , , , ; and control the state of the nonlinear second-order system to be controlled based on the hypertorsion logarithmic sliding mode controller; in, is the lumped uncertainty observer, and is a constant parameter set according to the performance requirements of the lumped uncertainty observer, and is the constant parameter of the supertorque logarithmic sliding mode controller set according to the control performance requirements. According to the adaptive law Updated adaptive function, is the transformed logarithmic sliding surface, To take the absolute value, is the symbolic function, is a known nonlinear function, is the upper bound of the error transfer function, is the lower bound of the error transfer function, is the performance function, is the state variable of the nonlinear second-order system The state function of and It is a constant parameter set according to the control performance requirements. is the derivative function of the equivalent system state after transformation, is the equivalent system state, is a known nonlinear function, is the derivative function of the sliding mode disturbance observer.

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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