Super-torsion logarithmic sliding mode control method with finite time preset performance constraint

Abstract

The invention discloses an over-torsion logarithmic sliding mode control method with finite time preset performance constraint, and relates to the technical field of preset performance control. According to the invention, the segmented preset performance function constructed based on the hyperbolic cotangent function is provided, the performance function can converge in finite time, the dependence on the initial state of the system is weakened, and the applicability of the control method is improved. Meanwhile, for a non-linear second-order system, a logarithmic sliding mode surface with large local gain near a balance point is constructed, unknown mismatched non-linear disturbance of the non-linear second-order system is estimated by using a logarithmic sliding mode observer, and a logarithmic super-twist sliding mode controller based on the logarithmic sliding mode surface is applied, so that the non-linear disturbance of the non-linear second-order system is estimated. According to the control strategy, the system state is rapidly converged to the tiny neighborhood near the balance point in a preset performance mode within the finite time, the buffeting phenomenon in sliding mode control can be effectively restrained, and the convergence precision within the limited convergence time is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of preset performance control, and in particular to a hypertorsion 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 control systems. 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 the problem 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 the control system. It is often used in various control systems due to its strong robustness to matched disturbances and its scalability in suppressing mismatched disturbances in combination with observer technology. However, sliding mode control has problems such as jitter and failure to converge within a finite time in practical applications, and its control accuracy is poor. Summary of the invention

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

[0005] The present invention adopts the following technical solutions: The present invention provides a hypertorsion logarithmic sliding mode control method with finite-time preset performance constraints. The present invention first models a nonlinear second-order system to be controlled, wherein the nonlinear second-order system includes unknown unmatched nonlinear disturbances, and then constructs a preset performance function that converges in finite time and has no initial value dependence. Then, the state of the nonlinear second-order system is converted through a state transition function, and the performance constraint problem corresponding to the performance function is converted into an unconstrained problem, and an equivalent system state is obtained. Then, according to the equivalent system state and its derivative function, a logarithmic sliding mode surface is constructed based on the logarithmic function, and based on the logarithmic function, a logarithmic sliding mode surface is constructed. A sliding mode disturbance observer is constructed on the logarithmic sliding surface to estimate the mismatched nonlinear disturbance, the logarithmic sliding surface is transformed according to the sliding mode disturbance observer, and finally the transformed logarithmic sliding surface is differentiated to obtain the derivative function of the transformed logarithmic sliding surface, and a lumped uncertainty observer is constructed to observe the lumped uncertainty in the derivative function of the transformed logarithmic sliding surface, a hyper-torsion logarithmic sliding mode controller is constructed according to the derivative function of the transformed logarithmic sliding surface and the lumped uncertainty observer, and the state of the nonlinear second-order system to be controlled is controlled based on the hyper-torsion logarithmic sliding mode controller.

[0006] The present invention provides a hypertorsion logarithmic sliding mode control system with a finite time preset performance constraint, comprising: 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; A control module is used to derive the transformed logarithmic sliding surface to obtain the derivative function of the transformed logarithmic sliding surface, and construct a lumped uncertainty observer to observe the lumped uncertainty in the derivative function of the transformed logarithmic sliding surface, construct a hyper-torsion logarithmic sliding mode controller according to 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 hyper-torsion logarithmic sliding mode controller.

[0007] The present invention provides a computer-readable storage medium, wherein the storage medium stores a computer program, and when the computer program is executed by a processor, the hypertorsion logarithmic sliding mode control method with a finite time preset performance constraint is implemented.

[0008] The present invention provides a computer device, comprising 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 hypertorsion logarithmic sliding mode control method with finite time preset performance constraints is implemented.

[0009] At least one of the above technical solutions adopted by the present invention can achieve the following beneficial effects: The present invention proposes a piecewise preset performance function constructed based on a hyperbolic cotangent function, which can converge within a finite time and reduce the dependence on the initial state of the system, thereby improving 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, and the unknown mismatched nonlinear disturbance of the nonlinear second-order system is estimated using a logarithmic sliding mode observer. A logarithmic supertorsion sliding mode control strategy based on the logarithmic sliding mode surface is applied, so that the system state converges rapidly to a small neighborhood near the equilibrium point in a finite time in the form of a preset performance. This control strategy can effectively suppress the chattering phenomenon in the sliding mode control and improve the convergence accuracy within a limited convergence time. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary 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 A flow chart of a hypertorsion logarithmic sliding mode control method with a finite time preset performance constraint provided by the present invention; Figure 2 A schematic diagram of a finite time convergence preset performance function provided by the present invention; Figure 3 A schematic diagram of a speed tracking error of a super-torsion integral sliding mode control strategy based on a traditional preset performance function provided by the present invention; Figure 4 A schematic diagram of a speed tracking error of a supertorque logarithmic sliding mode control strategy based on a preset performance function of the present invention provided by the present invention; Figure 5 A schematic diagram of a speed tracking curve of a different control strategy provided by the present invention; Figure 6 A schematic diagram of a hypertorsion logarithmic sliding mode control system with finite-time preset performance constraints provided by the present invention. DETAILED DESCRIPTION

[0011] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution 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 part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0012] At present, sliding mode control is an effective method to reduce the steady-state error of the control system. It is often used in various control systems because of its strong robustness to matched disturbances and its scalability in suppressing mismatched disturbances combined with observer technology. However, sliding mode control faces the problems of chattering and finite-time convergence in practical applications. Current research shows that non-singular terminal sliding modes and high-order sliding modes represented by supertorsion algorithms can effectively reduce chattering. However, it is still a challenge to combine the supertorsion algorithm with the non-singular terminal sliding surface to achieve finite-time convergence of the control system.

[0013] The present invention designs a hypertorsion logarithmic sliding mode control method with finite time preset performance. A new preset performance function is proposed based on the hyperbolic cotangent function, which reduces the dependence of the initial envelope limit on prior knowledge and the envelope curve can converge in finite time. The order of the system is reduced by using the logarithmic sliding mode manifold, and a logarithmic sliding mode observer and a hypertorsion 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.

[0014] The technical solutions provided by various embodiments of the present invention are described in detail below in conjunction with the accompanying drawings.

[0015] Figure 1 The present invention is a flow chart of a hypertorsion logarithmic sliding mode control method with a finite time preset performance constraint, which specifically includes the following steps: S101: Modeling a nonlinear second-order system to be controlled, wherein the nonlinear second-order system includes an unknown unmatched nonlinear disturbance.

[0016] S102: 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, construct a first analytical expression corresponding to when the time variable is less than the convergence time; based on 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; and obtain the performance function of the preset performance control based on the first analytical expression and the second analytical expression.

[0017] S103: 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.

[0018] S104: constructing a logarithmic sliding surface based on the logarithmic function according to the 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.

[0019] S105: The transformed logarithmic sliding surface is differentiated to obtain the derivative function of the transformed logarithmic sliding surface, and a lumped uncertainty observer is constructed to observe the lumped uncertainty in the derivative function of the transformed logarithmic sliding surface, a hyper-torsion logarithmic sliding mode controller is constructed according to the derivative function of the transformed logarithmic sliding surface and the lumped uncertainty observer, and the state of the nonlinear second-order system to be controlled is controlled based on the hyper-torsion logarithmic sliding mode controller.

[0020] For the convenience of explanation, the following description is only based on the server as the execution subject. The server mentioned in the present invention can be a server set up on the business platform, or a device such as a desktop computer, a notebook computer, etc. that can execute the solution of the present invention.

[0021] Generally, when performing control design for a nonlinear second-order system based on preset performance control, the server can first establish a nonlinear second-order system containing matched disturbances and non-matched disturbances by the following formula: .

[0022] in, and denote the different state variables of the nonlinear second-order system, and and and their respective first-order and second-order derivatives can be measured. and is a known nonlinear function, and They are the unknown unmatched nonlinear perturbations and matched nonlinear perturbations, satisfying the constraints and , the time derivative is approximately ignored, is an unknown finite upper bound, is the sliding mode variable for subsequent design; is the control signal of the nonlinear second-order system; is the output of the nonlinear second-order system, is the time variable.

[0023] In order to constrain the state variables of a nonlinear second-order system , 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 can be 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 can be constructed; according to the first analytical expression and the second analytical expression, the performance function of the preset performance control that does not depend on the initial value information and converges in a finite time is constructed by the following formula: .

[0024] in, is the performance function, and It is a constant parameter set according to the control performance requirements. It satisfies the conditions A sufficiently small constant, It is the convergence time set according to the control performance requirements.

[0025] In order to transform the performance function corresponding to the performance constraint problem into an unconstrained problem, the conversion function of the state variables of the nonlinear second-order system is defined: .

[0026] in, is the conversion function, is the state variable of the nonlinear second-order system The state function of is the upper bound of the error transfer function, is the lower bound of the error transfer function, is a natural constant, The equivalent system state can be explicitly written as: .

[0027] The equivalent system state derivative with respect to time is ,in Always bounded.

[0028] Based on the equivalent system state and its derivative function, the logarithmic sliding surface is constructed based on the logarithmic function by the following formula: .

[0029] in, and is a constant parameter set according to the control performance requirements, and , , represents the symbolic function, is the logarithmic sliding surface, is the derivative of the equivalent system state.

[0030] because There is an unmatched nonlinear perturbation in ,even though If the system state is established, the system state will not converge to the equilibrium point. Therefore, based on the logarithmic sliding surface, a fast sliding mode disturbance observer is designed by the following formula For mismatched nonlinear perturbations estimate: .

[0031] in, According to the adaptive law Updated adaptive function, and is a constant parameter set according to the performance requirements of the sliding mode disturbance observer, and , ; To take the absolute value, is the state variable of the nonlinear second-order system The state function.

[0032] Define the observation error of the sliding mode disturbance observer , it can be deduced from the above formula , thus the fast sliding mode disturbance observer converges asymptotically.

[0033] The logarithmic sliding surface can be further transformed according to the sliding mode disturbance observer through the following formula. Specifically, the derivative of the above equivalent system state can be changed to: .

[0034] In the formula, is the derivative function of the equivalent system state after transformation, is the derivative of the performance function.

[0035] Thus, the above logarithmic sliding surface is changed to: In the formula, is the transformed logarithmic sliding surface.

[0036] In order to facilitate the design of subsequent control strategies, the derivative function of the transformed logarithmic sliding mode surface is obtained by the following formula to obtain the sliding mode reduced-order system: .

[0037] in, , , .

[0038] In the formula, 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 the unknown nonlinear matching disturbance.

[0039] According to the design idea of ​​the logarithmic sliding surface, the lumped uncertainty observer is constructed by the following formula to calculate the lumped uncertainty in the derivative function of the transformed logarithmic sliding surface: Make an observation: .

[0040] in, is the lumped uncertainty observer, and is a parameter set according to the performance requirements of the lumped uncertainty observer, and , , According to the adaptive law Updated adaptive function.

[0041] Based on the above sliding mode reduced-order system and lumped uncertainty observer, the hypertorsion logarithmic sliding mode controller can be designed according to the logarithmic sliding mode surface as follows: .

[0042] in, and It is the parameter of the super-torsion logarithmic sliding mode controller set according to the control performance requirements.

[0043] Furthermore, the adaptive function The update strategy can also be , which means that there is no algebraic loop in the designed lumped uncertainty observer.

[0044] based on Figure 1 The hypertorsion logarithmic sliding mode control method with finite time preset performance constraints shown in the figure proposes a piecewise preset performance function constructed based on a hyperbolic cotangent function, which can converge within a finite time and reduces the dependence on the initial state of the system, thereby improving 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, and the unknown mismatched nonlinear disturbance of the nonlinear second-order system is estimated using a logarithmic sliding mode observer. A logarithmic hypertorsion sliding mode control strategy based on the logarithmic sliding mode surface is applied, so that the system state converges rapidly 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 limited convergence time.

[0045] Taking the preset performance control based on integral sliding mode without considering the non-matching disturbance as a comparison, its controller is written as: .

[0046] in, , , , , , is the integral sliding mode, , is the control gain to be adjusted.

[0047] The performance function used in the above control strategy is: .

[0048] in, , , It is a parameter set by the designer according to the control performance requirements. r ” indicates the identification of the comparison item.

[0049] For nonlinear second-order controlled systems, the present invention proposes a new performance function and a hyper-torsion logarithmic sliding mode control strategy based on a logarithmic sliding surface, which can make the system state converge rapidly to a small neighborhood near the equilibrium point in the form of preset performance within a finite time, and this control strategy can effectively suppress the chattering phenomenon in the sliding mode control.

[0050] The new preset performance function proposed in the present invention reduces the dependence of the initial envelope limit on prior knowledge, and another feature is that it converges in a finite time, such as Figure 2 As shown, the preset performance function as a comparison item can only weaken the dependence of the initial envelope limit on prior knowledge, and cannot determine the time when the system state converges.

[0051] The hypertorsion logarithmic sliding mode control strategy based on the logarithmic sliding mode surface of the present invention constructs a large local sliding mode gain near the equilibrium point, and therefore has higher convergence accuracy within a limited time than the hypertorsion sliding mode control strategy based on the integral sliding mode surface as a comparison item.

[0052] When applying the hypertorsion logarithmic sliding mode control method with finite time preset performance constraints provided by the present invention, it is not necessary to Figure 1 The steps are executed in the order shown. The specific execution order of the steps can be determined according to needs, and the present invention does not limit this.

[0053] In addition, the present invention also provides a comparative embodiment of the present invention. This embodiment considers a permanent magnet synchronous motor driven by a field oriented control method, and its model is as follows: .

[0054] in, represents the angular velocity, and denote the direct-axis and quadrature-axis stator currents respectively, and denote the direct-axis and quadrature-axis stator voltages, respectively, and denote the direct-axis and quadrature-axis stator inductances respectively, , J is the moment of inertia, is the extreme logarithm, is the rotor flux, is the armature resistance, is the viscous friction coefficient, is the uncertainty of the mismatch, which may include both the friction torque that is not quantitatively described and the unmodeled disturbance caused by the electromagnetic structure.

[0055] Define the nominal value of angular acceleration And state variables , then the above mathematical model can be transformed into: .

[0056] in, , The desired speed of the permanent magnet synchronous motor speed tracking problem is defined as , the speed tracking error can be expressed as and , then the mathematical model of the speed tracking problem can be written as: .

[0057] in, is the second derivative of the desired speed.

[0058] Obviously, consistent with the form of the nonlinear second-order system described in the present invention, the above control method can be used to perform speed tracking control of the permanent magnet synchronous motor.

[0059] Perform speed tracking control on an actual 4-pole permanent magnet synchronous motor, and the expected speed , the other actual relevant physical parameters are as follows: , , .

[0060] 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 gains of the sliding surface and the corresponding controller parameters are set to , , , The speed tracking error curve based on the above controller parameters is shown in Figure 3. The initial value of the preset performance function is large enough, so the dependence on the prior knowledge of the initial envelope limit is reduced, and due to the rapid convergence of the preset performance boundary, the speed tracking error has reached a small neighborhood near the equilibrium point within 5ms. However, this scheme cannot determine the time when the system state converges.

[0061] In order to ensure the fairness of the comparative simulation, the new performance function proposed in this invention is specified as ,set up , , then you can Calculate the parameters , ; The parameters in the logarithmic sliding surface and the corresponding controller are set to , , , Under the action of the super-torque logarithmic sliding mode control method designed in the present invention, the speed tracking error curve of the system is as follows: Figure 4 As 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 limited time, while the dependence on the prior knowledge of the initial envelope limit is significantly relaxed. Figure 5 As shown, compared with the speed tracking error of the preset performance control scheme based on integral sliding mode, the control scheme of the present invention achieves higher convergence accuracy within a limited time.

[0062] The above is a hypertorsion logarithmic sliding mode control method with a finite time preset performance constraint provided by one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding hypertorsion logarithmic sliding mode control system with a finite time preset performance constraint, such as Figure 6 shown.

[0063] Figure 6 A schematic diagram of a hypertorsion logarithmic sliding mode control system with a finite time preset performance constraint provided by the present invention includes: A modeling module 201, for modeling a nonlinear second-order system to be controlled, wherein the nonlinear second-order system includes an unknown unmatched nonlinear disturbance; The performance function construction module 202 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 the preset constant parameter and the 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 203 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 204 is used to construct a logarithmic sliding surface based on a logarithmic function according to an equivalent system state and its derivative function; construct a sliding mode disturbance observer based on the logarithmic sliding surface to estimate the mismatched nonlinear disturbance, and convert the logarithmic sliding surface according to the sliding mode disturbance observer; The control module 205 is used to derive the transformed logarithmic sliding surface to obtain the derivative function of the transformed logarithmic sliding surface, and construct a lumped uncertainty observer to observe the lumped uncertainty in the derivative function of the transformed logarithmic sliding surface, construct a hyper-torsion logarithmic sliding mode controller according to 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 hyper-torsion logarithmic sliding mode controller.

[0064] For the specific definition of the hyper-torque logarithmic sliding mode control system with finite time preset performance constraints, please refer to the definition of the hyper-torque logarithmic sliding mode control method with finite time preset performance constraints in the above text, which will not be repeated here. Each module in the above-mentioned hyper-torque logarithmic sliding mode control system with finite time preset performance constraints can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be 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.

[0065] The present invention also provides a computer-readable storage medium, which stores a computer program, which can be used to execute the above Figure 1 A hypertorsion logarithmic sliding mode control method with finite-time preset performance constraints is proposed.

[0066] 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 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 achieve the above Figure 1 A hypertorsion logarithmic sliding mode control method with finite-time preset performance constraints is proposed.

[0067] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and 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-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention can include at least one of non-volatile and volatile memory. 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. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0068] The technical features of the above embodiments may be arbitrarily combined. To make the description concise, 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, they should be considered to be within the scope of 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 transformed logarithmic sliding surface is differentiated to obtain the derivative function of the transformed logarithmic sliding surface, and a lumped uncertainty observer is constructed to observe the lumped uncertainty in the derivative function of the transformed logarithmic sliding surface. A hyper-torsion logarithmic sliding mode controller is constructed according to the derivative function of the transformed logarithmic sliding surface and the lumped uncertainty observer, and the state of the nonlinear second-order system to be controlled is controlled based on the hyper-torsion logarithmic sliding mode controller.

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. The hypertorsion logarithmic sliding mode control method with finite time preset performance constraints as claimed in claim 6, characterized in that: The method of constructing a lumped uncertainty observer to observe the lumped uncertainty in the derivative function of the converted logarithmic sliding mode surface and constructing a hypertorsion logarithmic sliding mode controller according to the derivative function of the converted logarithmic sliding mode surface and the lumped uncertainty observer specifically includes: 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 hyper-twist logarithmic sliding mode controller is constructed by the following formula: , 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.

8. 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; A control module is used to derive the transformed logarithmic sliding surface to obtain the derivative function of the transformed logarithmic sliding surface, and construct a lumped uncertainty observer to observe the lumped uncertainty in the derivative function of the transformed logarithmic sliding surface, construct a hyper-torsion logarithmic sliding mode controller according to 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 hyper-torsion logarithmic sliding mode controller.

9. 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 7 is implemented.

10. 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 7 is implemented.

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