Logarithmic terminal sliding mode control method, device and equipment of nonlinear system

Abstract

The invention discloses a logarithmic terminal sliding mode control method, device and equipment of a nonlinear system, and relates to the technical field of sliding mode control. Aiming at the control problem of the non-linear second-order system, the logarithmic terminal sliding mode surface is provided by combining the terminal sliding mode surface and a natural logarithmic function, and the logarithmic terminal sliding mode surface accelerates the convergence rate of the state of the non-linear second-order system when the state is far away from an equilibrium point on the basis of the terminal sliding mode surface. Meanwhile, in consideration of unknown matching nonlinear disturbance which is often contained in a nonlinear second-order system and can influence the stability and the control precision of the system, the sliding mode disturbance observer is designed based on the proposed logarithmic terminal sliding mode surface, rapid convergence of disturbance estimation errors is achieved, and design of a follow-up controller is facilitated. And finally, a stable first-order logarithmic terminal sliding mode controller is designed based on the Lyapunov stability theory, the nonlinear second-order system state is globally and rapidly converged to a balance point, and the convergence rate and the control precision are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of sliding mode control, and in particular to a logarithmic terminal sliding mode control method, device and equipment for a nonlinear system. Background Art

[0002] At present, sliding mode control, as an advanced control method with strong robustness and simple structure, has been widely used in nonlinear drive systems, robotics and other fields.

[0003] The classic linear sliding surface can only converge to the equilibrium point asymptotically at an exponential rate. It has a satisfactory convergence rate when far away from the equilibrium point, but the convergence rate is very slow near the equilibrium point, and the system state cannot converge within a finite time. The terminal sliding surface and the non-singular terminal sliding surface achieve finite time convergence by introducing nonlinear terminal attractors to form infinite gain near the equilibrium point, but the convergence rate is still slow when the system state is far away from the equilibrium point; although the fast non-singular terminal sliding surface accelerates the convergence rate by introducing additional nonlinear terms, it still cannot achieve global fast convergence. At the same time, when using a sliding mode observer to estimate lumped uncertainty, it is also expected that the estimated error of the observer can converge quickly along the sliding surface. Both of them require the sliding surface to converge globally quickly. Summary of the invention

[0004] Based on this, it is necessary to provide a logarithmic terminal sliding mode control method, device and equipment for a nonlinear system to address the above technical problems.

[0005] The present invention adopts the following technical solutions: The present invention provides a logarithmic terminal sliding mode control method for a nonlinear system. The method comprises the following steps: firstly, a nonlinear second-order system to be controlled is modeled; then, according to a terminal sliding mode surface based on a state of the nonlinear second-order system, a terminal attractor is embedded into a natural logarithmic function to construct a logarithmic terminal sliding mode surface; then, based on the logarithmic terminal sliding mode surface, a disturbance observer is constructed so that an observation error satisfies a fast convergence condition, and the lumped uncertainty in the nonlinear second-order system is observed; finally, according to the logarithmic terminal sliding mode surface and the disturbance observer, a first-order logarithmic terminal sliding mode controller is constructed based on the Lyapunov stability theory, and the nonlinear second-order system is controlled by the first-order logarithmic terminal sliding mode controller.

[0006] The present invention provides a logarithmic terminal sliding mode control device for a nonlinear system, comprising: A modeling module for modeling the nonlinear second-order system to be controlled; A sliding surface construction module, used for embedding a terminal attractor into a natural logarithmic function to construct a logarithmic terminal sliding surface according to a terminal sliding surface based on a state of a nonlinear second-order system; The observer construction module is used to construct a disturbance observer based on the logarithmic terminal sliding surface so that the observation error meets the fast convergence condition and observe the lumped uncertainty in the nonlinear second-order system; The control module is used to construct a first-order logarithmic terminal sliding mode controller based on the logarithmic terminal sliding mode surface and the disturbance observer based on Lyapunov stability theory, and control the nonlinear second-order system through the first-order logarithmic terminal 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 logarithmic terminal sliding mode control method of the nonlinear system 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 the processor implements the logarithmic terminal sliding mode control method of the nonlinear system when executing the program.

[0009] At least one of the above technical solutions adopted by the present invention can achieve the following beneficial effects: The present invention aims at the control problem of nonlinear second-order systems, and proposes a logarithmic terminal sliding surface in combination with a terminal sliding surface and a natural logarithmic function. The logarithmic terminal sliding surface accelerates the convergence rate of the state of the nonlinear second-order system when it is far away from the equilibrium point on the basis of the terminal sliding surface. At the same time, considering that nonlinear second-order systems often contain unknown matching nonlinear disturbances, which will affect the stability and control accuracy of the system, a sliding mode disturbance observer is designed based on the proposed logarithmic terminal sliding surface, which realizes the rapid convergence of the disturbance estimation error and facilitates the design of subsequent controllers. Finally, a stable first-order logarithmic terminal sliding mode controller is designed based on the Lyapunov stability theory, which realizes the rapid global convergence of the state of the nonlinear second-order system to the equilibrium point, and improves the convergence rate and control accuracy. 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 logarithmic terminal sliding mode control method for a nonlinear system provided by the present invention; Figure 2 A schematic diagram of a phase plane diagram of a different sliding surface provided by the present invention; Figure 3 A schematic diagram of a motor speed curve under different control strategies provided by the present invention; Figure 4A schematic diagram of a controller output voltage curve under different control strategies provided by the present invention; Figure 5 A schematic diagram of a current response curve under different control strategies provided by the present invention; Figure 6 A schematic diagram of a logarithmic terminal sliding mode control device for a nonlinear system 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] The current sliding surface cannot achieve global rapid convergence of sliding mode control. At the same time, when using the sliding mode observer to estimate the lumped uncertainty, similar to the sliding mode control, it is also expected that the estimation error of the uncertainty converges quickly and smoothly to the equilibrium point.

[0013] The present invention embeds the terminal attractor into the natural logarithmic function, proposes a globally fast finite-time convergent logarithmic terminal sliding surface, and analytically solves the time required for the system state to slide to zero. Based on the improved logarithmic terminal sliding surface, the corresponding disturbance observer and controller are designed. The control method can make the system state converge to a small neighborhood near the equilibrium point in a finite time.

[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 logarithmic terminal sliding mode control method for a nonlinear system, which specifically includes the following steps: S101: Model the nonlinear second-order system to be controlled.

[0016] S102: According to the terminal sliding mode surface based on the state of the nonlinear second-order system, the terminal attractor is embedded into the natural logarithmic function to construct a logarithmic terminal sliding mode surface.

[0017] S103: Based on the logarithmic terminal sliding surface, a disturbance observer is constructed to make the observation error meet the fast convergence condition, and the lumped uncertainty in the nonlinear second-order system is observed.

[0018] S104: According to the logarithmic terminal sliding surface and the disturbance observer, a first-order logarithmic terminal sliding mode controller is constructed based on Lyapunov stability theory, and the nonlinear second-order system is controlled by the first-order logarithmic terminal sliding mode controller.

[0019] 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.

[0020] Generally, when the server controls a nonlinear second-order system, it can first establish a nonlinear second-order system model containing matching disturbances: .

[0021] in, and are different state variables of a nonlinear second-order system, and they and their respective first-order and second-order derivatives can be measured. and The state variables and The derivative function of and are all known nonlinear functions. is an unknown matching disturbance, which is smooth, continuous and changes slowly, and its derivative with respect to time can be approximately ignored. is the control signal of the nonlinear second-order system.

[0022] Based on the nonlinear second-order system model established above, a global fast logarithmic terminal sliding surface with analytical convergence time is designed. Specifically, the logarithmic terminal sliding surface can be constructed based on the terminal sliding surface and the natural logarithm by the following formula: , .

[0023] in, is the logarithmic terminal sliding surface, , , and It is a constant parameter set according to the control performance requirements, satisfying , , ,and , and are all odd constants.

[0024] To accurately compensate for matching disturbances in nonlinear second-order systems , the disturbance observer can be constructed by the following formula to observe the unknown matching disturbance in the nonlinear second-order system: , .

[0025] in, is the disturbance observer, According to the adaptive law Updated adaptive function, , , and It is a constant parameter set according to the control performance requirements, satisfying , ,and , and are all odd constants. The observation error is defined as , can be obtained ,in .

[0026] because and are greater than 0, so is positive definite, the observation error converges asymptotically, and can be used estimate .

[0027] Finally, according to the logarithmic terminal sliding mode surface and disturbance observer designed above, a first-order logarithmic terminal sliding mode controller can be constructed by the following formula based on Lyapunov stability theory: ; .

[0028] in, is the first-order logarithmic terminal sliding mode control output, is a known nonlinear function The reciprocal of represents the symbolic function, is the upper bound of the observation error of the disturbance observer.

[0029] Consider the Lyapunov function and , their derivatives can be expressed as and .

[0030] when hour, , so the system state can reach the sliding surface in a finite time.

[0031] when When the disturbance observer converges to after, , the system state converges asymptotically to a narrow boundary layer near the logarithmic terminal sliding surface , and then we can get , when the state of the nonlinear second-order system satisfies the condition When , the state of the nonlinear second-order system can converge to the logarithmic terminal sliding surface in a finite time.

[0032] When the logarithmic terminal sliding surface When established, the state variables of the nonlinear second-order system are in finite time It converges to the equilibrium point, where the analytical expression of the finite convergence time is: .

[0033] in, is the logarithmic terminal sliding surface The state of the nonlinear second-order system when it is established.

[0034] based on Figure 1 The logarithmic terminal sliding mode control method of the nonlinear system shown in the figure, the present invention aims at the control problem of nonlinear second-order system, combines the terminal sliding surface and the natural logarithmic function to propose a logarithmic terminal sliding surface, which, on the basis of the terminal sliding surface, accelerates the convergence rate of the state of the nonlinear second-order system when it is far away from the equilibrium point. At the same time, considering that the nonlinear second-order system often contains unknown matching nonlinear disturbances, which will affect the stability and control accuracy of the system, a sliding mode disturbance observer is designed based on the proposed logarithmic terminal sliding surface, which realizes the rapid convergence of the disturbance estimation error and facilitates the design of the subsequent controller. Finally, based on the Lyapunov stability theory, a stable first-order logarithmic terminal sliding mode controller is designed, which realizes the rapid global convergence of the state of the nonlinear second-order system to the equilibrium point, and improves the convergence rate and control accuracy.

[0035] In contrast, the traditional terminal sliding surface is expressed as: .

[0036] in The definition of is consistent with that in the logarithmic terminal sliding surface. The controller designed based on the traditional terminal sliding surface is consistent with the controller designed based on the logarithmic terminal sliding surface: .

[0037] in, .

[0038] When the terminal attractor index remains the same, the logarithmic terminal sliding surface proposed by the present invention has better dynamic performance in the global range than the traditional terminal sliding surface. When , the logarithmic terminal sliding surface degenerates into a fast terminal sliding surface. However, compared with the fast terminal sliding surface, it does not increase the slope near the equilibrium point while improving the convergence rate away from the equilibrium point, thus avoiding The noise contained in is amplified, such as Figure 2Shown is a schematic diagram of a phase plane diagram of a different sliding surface in the present invention.

[0039] The control strategy based on the logarithmic terminal sliding surface of the present invention produces a more satisfactory control effect than the control strategy based on the traditional terminal sliding surface, which is reflected in smaller overshoot, faster convergence speed, higher control accuracy and the like.

[0040] The control strategy proposed by the present invention is in the system state It is singular when it approaches 0. This problem can be solved in many ways, such as when When and Replace with This will not affect the effect of the present invention, the state of the system will still quickly enter the narrow boundary layer of the sliding surface and move at a high gain Converge to a tiny neighborhood around the equilibrium point.

[0041] When applying the logarithmic terminal sliding mode control method for nonlinear systems 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.

[0042] In addition, the present invention also provides an embodiment of the logarithmic terminal sliding mode control method of the nonlinear system of the present invention. Taking a permanent magnet synchronous motor system driven by a magnetic field oriented control method as an example, its mathematical model is expressed as follows: .

[0043] in, is the angular velocity of the motor, , , , , and They represent direct-axis current, quadrature-axis current, direct-axis voltage, quadrature-axis voltage, direct-axis inductance and quadrature-axis inductance respectively. is the stator winding, , is the extreme logarithm, is the rotor flux, is the viscous friction coefficient, It is the disturbance caused by temperature rise and magnetic leakage.

[0044] Considering the speed tracking problem of permanent magnet synchronous motor, define is the expected speed, and the speed tracking error can be expressed as and Then the above mathematical model can be rewritten as: .

[0045] in, Obviously, the control strategy mentioned above can be used to perform speed tracking control of the permanent magnet synchronous motor, which is the same as the nonlinear second-order system proposed in the present invention.

[0046] The speed tracking control of an actual 4-pole 24V permanent magnet synchronous motor is performed, and the actual relevant physical parameters are as follows: , , , , , , .

[0047] When the method of the present invention is applied, the parameters in the logarithmic terminal sliding surface are taken as: , , ; The parameters in the disturbance observer are taken as: , ; The parameters in the first-order logarithmic terminal sliding mode controller are: In practical applications, in order to make the designed controller output a smooth voltage signal, it can be used in the experiment Replace the symbol function In order to ensure the fairness of the comparison, the parameters in the traditional terminal sliding surface and controller are kept consistent with the above parameters.

[0048] The proposed logarithmic terminal sliding mode control strategy and the traditional terminal sliding mode control strategy are applied to the speed tracking problem of permanent magnet synchronous motor. The speed tracking curve is as follows: Figure 3 As shown, Figure 3 This is a schematic diagram of the motor speed curve under different control strategies in the present invention. It can be found that the first-order logarithmic terminal sliding mode controller proposed in the present invention will produce more satisfactory overshoot, drive the motor rotor to reach the desired speed faster, and have higher steady-state accuracy. When the large switching term can reduce overshoot and speed tracking error, the control quality is still not as good as the present invention. Figure 4 and Figure 5 The output voltage and resulting current responses of the two controllers are shown in Figure 2, where: Figure 4 is a schematic diagram of the controller output voltage curve under different control strategies in the present invention, Figure 4 The left side corresponds to the classic terminal sliding mode controller, Figure 4 The right side corresponds to the first-order logarithmic terminal sliding mode controller of the present invention, Figure 5 is a schematic diagram of a current response curve under different control strategies in the present invention, Figure 5 The left side corresponds to the classic terminal sliding mode controller, Figure 5The right side corresponds to the first-order logarithmic terminal sliding mode controller of the present invention. Obviously, the voltage signal output by the controller based on the logarithmic terminal sliding mode has a more sensitive response to the lumped disturbance.

[0049] The above is a logarithmic terminal sliding mode control method for a nonlinear system provided by one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding logarithmic terminal sliding mode control device for a nonlinear system, such as Figure 6 shown.

[0050] Figure 6 A schematic diagram of a logarithmic terminal sliding mode control device for a nonlinear system provided by the present invention includes: A modeling module 201, used for modeling a nonlinear second-order system to be controlled; A sliding surface construction module 202 is used to embed the terminal attractor into the natural logarithmic function to construct a logarithmic terminal sliding surface according to the terminal sliding surface based on the state of the nonlinear second-order system; An observer construction module 203 is used to construct a disturbance observer based on a logarithmic terminal sliding surface so that the observation error satisfies a fast convergence condition, and observe the lumped uncertainty in the nonlinear second-order system; The control module 204 is used to construct a first-order logarithmic terminal sliding mode controller based on the logarithmic terminal sliding mode surface and the disturbance observer and Lyapunov stability theory, and control the nonlinear second-order system through the first-order logarithmic terminal sliding mode controller.

[0051] The specific definition of the logarithmic terminal sliding mode control device for nonlinear systems can be found in the definition of the logarithmic terminal sliding mode control method for nonlinear systems mentioned above, which will not be repeated here. Each module in the logarithmic terminal sliding mode control device for the above nonlinear system can be implemented in whole or in part by software, hardware and a combination thereof. The above 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 in the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0052] 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 logarithmic terminal sliding mode control method for nonlinear systems is provided.

[0053] 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 logarithmic terminal sliding mode control method for nonlinear systems is provided.

[0054] 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).

[0055] 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 logarithmic terminal sliding mode control method for a nonlinear system, characterized in that: include: Modeling of the nonlinear second-order system to be controlled; According to the terminal sliding surface based on the state of the nonlinear second-order system, the terminal attractor is embedded into the natural logarithmic function to construct the logarithmic terminal sliding surface; Based on the logarithmic terminal sliding surface, a disturbance observer is constructed to make the observation error meet the fast convergence condition, and the lumped uncertainty in the nonlinear second-order system is observed. According to the logarithmic terminal sliding surface and the disturbance observer, a first-order logarithmic terminal sliding mode controller is constructed based on Lyapunov stability theory, and the nonlinear second-order system is controlled by the first-order logarithmic terminal sliding mode controller.

2. The logarithmic terminal sliding mode control method for a nonlinear system according to claim 1, characterized in that: The modeling of the nonlinear second-order system to be controlled specifically includes: The nonlinear second-order system to be controlled is modeled as follows: ； in, and are different state variables of the nonlinear second-order system, and The state variables and The derivative function of and is a known nonlinear function, is the unknown aggregate uncertainty, is the control signal of the nonlinear second-order system.

3. The logarithmic terminal sliding mode control method for a nonlinear system according to claim 1, characterized in that: The terminal sliding mode surface based on the state of the nonlinear second-order system is embedded in the terminal attractor into the natural logarithmic function to construct the logarithmic terminal sliding mode surface, which specifically includes: According to the terminal sliding surface based on the state of the nonlinear second-order system, the terminal attractor is embedded into the natural logarithmic function, and the logarithmic terminal sliding surface is constructed by the following formula: ， ， ； in, is the logarithmic terminal sliding surface, , , and is a constant parameter set according to the control performance requirements, and and is an odd constant, is the state variable of the nonlinear second-order system, is a state variable The derivative function of .

4. The logarithmic terminal sliding mode control method for a nonlinear system according to claim 1, characterized in that: The method of constructing a disturbance observer based on the logarithmic terminal sliding surface so that the observation error satisfies the fast convergence condition and observing the lumped uncertainty in the nonlinear second-order system specifically includes: Based on the logarithmic terminal sliding surface, the disturbance observer is constructed by the following formula to observe the lumped uncertainty in the nonlinear second-order system: ， ， ， ； in, is the disturbance observer, According to the adaptive law Updated adaptive function, , , and is a constant parameter set according to the control performance requirements, and and is an odd constant, and are different state variables of the nonlinear second-order system, and is a known nonlinear function, is the control signal of the nonlinear second-order system.

5. The logarithmic terminal sliding mode control method for a nonlinear system according to claim 1, characterized in that: The first-order logarithmic terminal sliding mode controller is constructed based on the logarithmic terminal sliding mode surface and the disturbance observer and Lyapunov stability theory, specifically including: According to the logarithmic terminal sliding mode surface and the disturbance observer, a first-order logarithmic terminal sliding mode controller is constructed based on the Lyapunov stability theory by the following formula: ， ， ， ； in, is a first-order logarithmic terminal sliding mode controller, is the disturbance observer, is the upper bound of the observation error of the disturbance observer, , , and is a constant parameter set according to performance requirements, and and is an odd constant, and are different state variables of the nonlinear second-order system, and is a known nonlinear function, is a symbolic function.

6. A logarithmic terminal sliding mode control device for a nonlinear system, characterized in that: include: A modeling module for modeling the nonlinear second-order system to be controlled; A sliding surface construction module, used for embedding a terminal attractor into a natural logarithmic function to construct a logarithmic terminal sliding surface according to a terminal sliding surface based on a state of a nonlinear second-order system; The observer construction module is used to construct a disturbance observer based on the logarithmic terminal sliding surface so that the observation error meets the fast convergence condition and observe the lumped uncertainty in the nonlinear second-order system; The control module is used to construct a first-order logarithmic terminal sliding mode controller based on the logarithmic terminal sliding mode surface and the disturbance observer based on the Lyapunov stability theory, and control the nonlinear second-order system through the first-order logarithmic terminal sliding mode controller.

7. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

8. A computer device, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method according to any one of claims 1 to 5 is implemented.

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