Search

CN-120652811-B - Nonlinear robot system fixed time sliding mode control method based on double-layer nested self-adaptive law

CN120652811BCN 120652811 BCN120652811 BCN 120652811BCN-120652811-B

Abstract

The invention discloses a fixed time sliding mode control method of a nonlinear robot system based on a double-layer nested self-adaptive law, which comprises the steps of establishing a mathematical model of the nonlinear robot system with n degrees of freedom, establishing a track tracking error control equation of the nonlinear robot system with lumped unknown bounded disturbance according to the mathematical model of the nonlinear robot system with n degrees of freedom, designing a sliding variable based on a modified power-variable function according to the track tracking error equation of the nonlinear robot system, designing a fixed time approach control law based on the double-layer nested self-adaptive law according to the sliding variable, and designing a non-singular fixed time sliding mode controller of the nonlinear robot system according to the sliding variable and the fixed time approach control law based on the double-layer nested self-adaptive law. The invention can realize the rapid track tracking control of the nonlinear robot at different initial positions, and ensure the safety and reliability of the robot system in complex and changeable working environments.

Inventors

  • NA JING
  • WANG MIN
  • HUANG YINGBO
  • HE HAORAN
  • YANG CHUNXI

Assignees

  • 昆明理工大学

Dates

Publication Date
20260512
Application Date
20250630

Claims (6)

  1. 1. A nonlinear robot system fixed time sliding mode control method based on a double-layer nested self-adaptive law is characterized by comprising the following steps: The method comprises the steps of 1, establishing a mathematical model of an n-degree-of-freedom nonlinear robot system, and establishing a track tracking error control equation of the nonlinear robot system containing lumped unknown bounded disturbance according to the mathematical model of the n-degree-of-freedom nonlinear robot system; Step 2, designing a sliding variable based on a modified exponentiation function according to an established track tracking error equation of the nonlinear robot system, designing a fixed time approach control law based on a double-layer nested self-adaptive law according to the sliding variable, and designing a nonsingular fixed time sliding mode controller of the nonlinear robot system according to the sliding variable and the fixed time approach control law based on the double-layer nested self-adaptive law; The sliding variable based on the modified exponentiation finger function is designed according to the established track tracking error equation of the nonlinear robot system The method specifically comprises the following steps: Wherein, the 、 And Represents the control gain in the sliding variable and satisfies , , ; And Represents a positive constant and satisfies ; Represents a constant greater than 1; The sign function is represented by a sign function, Is the tracking error of the joints of the robot, Is the first derivative of (2) 。
  2. 2. The method for controlling the fixed time sliding mode of the nonlinear robot system based on the double-layer nested self-adaptive law according to claim 1, wherein the method is characterized in that the fixed time approach control law based on the double-layer nested self-adaptive law is designed according to a sliding variable, and specifically comprises the following steps: Wherein, the Indicating that the control law is approaching, A first time-varying parameter is indicated and, Representing a small positive constant of the current in the current, And Represents control gain in the approach control law and satisfies , ; 、 、 Represents a positive constant and satisfies , Represents a constant greater than 1; representing a double-layer nested adaptive law item; The sign function is represented by a sign function, Is a sliding variable which is a sliding variable, Representing natural constants.
  3. 3. The nonlinear robot system fixed time sliding mode control method based on the double-layer nested self-adaptive law according to claim 2, wherein the design of the double-layer nested self-adaptive law item is specifically as follows: Approach control law using low pass filtering operation Approximation is carried out to obtain Approximation of (2) The expression is: Wherein, the Representing a filter time constant; Representation of Is a approximation of (a); Representation of Is the first derivative of (a); obtained by low-pass filtering operation Approximation of (2) Thereby constructing a first time-varying parameter Ensuring the safety margin of the first time-varying parameter The method meets the following conditions: Wherein, the Represents a positive constant and satisfies ; Representing a positive constant; according to the constructed first time-varying parameter Defining the error variable of the adaptive law as the safety boundary of The expression is as follows: by defined error variables Obtaining a first time-varying parameter Is the first derivative of (2) The expression is: Wherein, the Represents a positive constant and satisfies ; A safety boundary representing the rate of change of the adaptive law, expressed as: second time-varying parameter Is the first derivative of (2) Can be expressed as: Wherein, the Represents a positive constant and satisfies ; Representing a sign function; the error change rate of the self-adaptive law is expressed as follows: Wherein, the Represents a positive constant and satisfies ; Representing the upper bound of the lumped unknown bounded perturbation first derivative.
  4. 4. The method for controlling a fixed time sliding mode of a nonlinear robot system based on a double-layer nested self-adaptive law according to claim 1, wherein the non-singular fixed time sliding mode controller of the robot system is characterized in that Wherein, the method comprises the steps of, A feedback term representing a compensating nonlinear dynamics; is an approach controller for handling nonlinear robotic systems that aggregates unknown bounded perturbations.
  5. 5. A nonlinear robot system fixed time sliding mode control system based on a double-layer nested self-adaptive law is characterized by comprising: The first module is used for establishing a mathematical model of the nonlinear robot system with n degrees of freedom, and establishing a track tracking error control equation of the nonlinear robot system containing lumped unknown bounded disturbance according to the mathematical model of the nonlinear robot system with n degrees of freedom; The second module is used for designing a sliding variable based on a modified exponentiation function according to the established track tracking error equation of the nonlinear robot system, designing a fixed time approach control law based on a double-layer nested self-adaptive law according to the sliding variable, and designing a nonsingular fixed time sliding mode controller of the nonlinear robot system according to the sliding variable and the fixed time approach control law based on the double-layer nested self-adaptive law; The sliding variable based on the modified exponentiation finger function is designed according to the established track tracking error equation of the nonlinear robot system The method specifically comprises the following steps: Wherein, the 、 And Represents the control gain in the sliding variable and satisfies , , ; And Represents a positive constant and satisfies ; Represents a constant greater than 1; The sign function is represented by a sign function, Is the tracking error of the joints of the robot, Is the first derivative of (2) 。
  6. 6. A processor, wherein the processor is configured to run a program, and wherein the program when run performs the method for controlling a fixed time sliding mode of a nonlinear robot system based on a double-layer nested adaptive law according to any one of claims 1 to 4.

Description

Nonlinear robot system fixed time sliding mode control method based on double-layer nested self-adaptive law Technical Field The invention relates to a fixed-time sliding mode control method of a nonlinear robot system based on a double-layer nested self-adaptive law, and belongs to the field of stability and control of nonlinear robot systems. Background In the development of modern technology, robots have shown tremendous potential and activity in various aspects of industrial manufacturing, medical treatment, military, entertainment, etc. Whether academic research or industrial application, designing a robust and effective control strategy is critical to ensuring the safety and reliability of a robotic system in a complex and diverse working environment. To achieve this goal, researchers have developed a number of advanced control methods such as active-disturbance-rejection control, adaptive control, intelligent control, model predictive control, and sliding-mode control. The sliding mode control method has the characteristics of simple structure, flexibility and variability, and provides huge playing space for sliding mode control method researchers, so that a mode of combining sliding mode control with a limited time stability theory and a fixed time stability theory to carry out controller design is widely focused in the control field. In the field of nonlinear system control, the fusion research of the finite time stabilization theory and the sliding mode control method has been significantly advanced. The literature "Shuanghe Yu,Xinghuo Yu,Bijan Shirinzadeh,et al.Continuous finite-time control for robotic manipulators with terminal sliding mode[J].Automatica,2005,Vol.41(11):1957-1964." proposes a limited-time terminal sliding mode control scheme, and lays a theoretical foundation for improving the dynamic response speed and the robust performance of a nonlinear system. Literature "Chuanbin Sun,Shubo Wang,Haisheng Yu.Finite-time sliding mode control based on unknown system dynamics estimator for nonlinear robotic systems,IEEE Transactions on Circuits and Systems II:Express Briefs,Vol.70(7):2535-2539,2023" designs a finite-time sliding mode controller based on an unknown system dynamic estimator, so that the robustness of a nonlinear system to unknown bounded disturbance is effectively enhanced. The finite time sliding mode control method ensures that the system state converges to the balance point within a time upper bound, but the convergence time upper bound changes along with the change of the initial state of the system, which reduces the application value of the finite time sliding mode control in engineering practice. In order to break through the limitation, a fixed time stabilization theory that the upper bound of convergence time is independent of the initial state of the system is proposed, and the fixed time stabilization theory is combined with a sliding mode control method, so that the method is widely applied to nonlinear systems. Literature "Zuo,Zongyu.Non-singular fixed-time terminal sliding mode control ofnon-linear systems.[J].IET Control Theory&Applications,2015,Vol.9(4):545-552." proposes a non-singular fixed time terminal sliding mode control scheme aiming at a nonlinear system, and the robustness of the nonlinear system is remarkably improved. But this scheme has the problem of conservative convergence time estimation. Literature "Moulay,Emmanuel,Lechappe,et al.Robust fixed-time stability:application to sliding-mode control.[J].IEEE Transactions onAutomatic Control,2022,Vol.67(2):1061-1066." innovatively adopts a power exponent function to construct a sliding variable, and although the problem of the singularity of a controller is solved, the convergence characteristic of the sliding variable still has the defect of being locally dependent on the initial state of a system. An adaptive fixed time sliding mode control strategy is proposed in literature "Yunsong Hu,Huaicheng Yan,Hao Zhang,et al.Robust adaptive fixed-time sliding-mode control for uncertain robotic systems with input saturation[J].IEEE Transactions on Cybernetics,2023,Vol.53(4):2636-2646." to address controller singularity problems through a switching function mechanism. But this approach may cause the controller to switch back and forth at the singular point near the switching point, affecting system stability. Robotic systems are typically nonlinear systems. The motion of the robot is affected by factors such as multi-joint coupling, time-varying inertial matrices, coriolis and centrifugal forces, gravity, and nonlinear friction, resulting in complex nonlinear relationships between input (torque) and output (motion). On the one hand, the rapid track tracking control of the nonlinear robot system at different initial positions is improved, the operation efficiency of the robot system can be improved, the energy loss is reduced, and the requirements of high efficiency and high precision are met. On the other hand, t