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CN-121821410-B - Mechanical arm track tracking sliding mode control method and system

CN121821410BCN 121821410 BCN121821410 BCN 121821410BCN-121821410-B

Abstract

The invention discloses a sliding mode control method and a sliding mode control system for tracking a mechanical arm track, which aim at external interference and model uncertainty in a mechanical arm system, provide an improved nonsingular rapid terminal sliding mode surface, combine an adaptive disturbance upper bound estimation strategy, design a robust controller with limited time convergence characteristics, and provide an adaptive boundary layer thickness adjustment method based on a sliding mode surface norm so as to inhibit buffeting while ensuring tracking precision. The method comprises the steps of establishing a six-degree-of-freedom mechanical arm dynamics model, designing a sliding mode surface fusing exponential terms and fractional power terms, constructing an equivalent control law, designing an adaptive law to estimate an upper bound of an uncertain lumped parameter term, adopting an adaptive boundary layer saturation function to replace a traditional symbol function, and proving the limited time stability of a closed-loop system through Lyapunov theory. The invention can obviously weaken control input buffeting and reduce energy consumption, and is suitable for high-precision motion control scenes such as industrial manufacture, medical operation, aerospace and the like.

Inventors

  • WANG ZHAO
  • HU QINGWEN

Assignees

  • 中国石油大学(华东)

Dates

Publication Date
20260505
Application Date
20260312

Claims (8)

  1. 1. The mechanical arm track tracking sliding mode control method is characterized by comprising the following steps of: s1, establishing a dynamic model of a six-degree-of-freedom mechanical arm, and converting the dynamic model into a state space form containing a lumped parameter uncertain item; S2, defining a track tracking error of the mechanical arm, constructing a nonsingular rapid terminal sliding mode surface, and fusing an exponential term and a fractional power term by the sliding mode surface to realize finite time convergence and avoid singularity; s3, designing an adaptive law for estimating an unknown upper bound parameter of the lumped parameter uncertainty item on line; S4, designing a switching control law based on the sliding mode surface and the estimation result of the self-adaptive law; S5, designing a self-adaptive boundary layer saturation function to replace a symbol function in the switching control law, wherein the boundary layer thickness of the self-adaptive boundary layer saturation function is dynamically adjusted according to the norm of a sliding mode surface, namely, when the sliding mode surface norm is larger than a set threshold value, smaller boundary layer thickness is adopted to ensure the approaching speed, and when the sliding mode surface norm is smaller than or equal to the set threshold value, the boundary layer thickness is increased along with the reduction of the sliding mode surface norm so as to inhibit buffeting; And S6, combining an equivalent control law and a switching control law processed by the self-adaptive boundary layer saturation function to obtain a total control law, and acting on the mechanical arm to realize track tracking control.
  2. 2. The method of claim 1, wherein the nonsingular fast terminal sliding surface expression is: , Wherein, the , , As the actual joint angle of the mechanical arm, For the actual joint angular velocity of the mechanical arm, For a desired joint angle of the robotic arm, The joint angular velocity is expected for the robotic arm; 、 are all a matrix of sliding gains and, , ; Is a linear convergence term coefficient; And As a fraction of the power coefficient, , ; Is a standard sign function.
  3. 3. The method of claim 1, wherein the adaptive law is designed to: Wherein, the 、 、 Respectively unknown parameters 、 、 Is a function of the estimated value of (2); 、 、 Is a positive adaptive gain coefficient; Norms of the slip plane vectors; Is the norm of the joint angle vector; is the norm of the joint velocity vector.
  4. 4. The method of claim 1, wherein the adaptive boundary layer saturation function boundary layer thickness The following dynamic adjustment is carried out: , wherein, And Respectively minimum and maximum values of boundary layer thickness, satisfies ; Is a set threshold.
  5. 5. The method of claim 4, wherein the adaptive boundary layer saturation function is defined as: , The absolute value of the slip plane component for each joint.
  6. 6. The method of claim 1, wherein the equivalent control law Switching control law Form the overall control law Wherein 、 、 Is the nominal value of the mechanical arm dynamics system, Is a robust coefficient.
  7. 7. The method of any one of claims 1 to 6, wherein the robotic arm is a six degree of freedom serial robotic arm.
  8. 8. The utility model provides a arm orbit tracking slipform control system which characterized in that includes: At least one memory for storing computer-executable instructions; at least one processor configured to execute the computer-executable instructions to implement the method of any one of claims 1 to 7.

Description

Mechanical arm track tracking sliding mode control method and system Technical Field The invention relates to the field of mechanical arm track tracking control, in particular to a mechanical arm track tracking sliding mode control method and system, which are suitable for a high-precision mechanical arm control system with model uncertainty, external interference and strong nonlinear coupling. Background The mechanical arm is used as a core executing mechanism of a modern automatic system and is widely applied to the fields of industrial assembly, precise surgery, space operation and the like. The dynamics model has the characteristics of multiple variables, strong coupling and high nonlinearity, and is often influenced by parameter perturbation, unmodeled dynamics and external interference, so that the traditional control method is difficult to realize accurate track tracking. Sliding mode control is widely focused in mechanical arm control because of its good robustness to system uncertainty and external disturbances. However, the conventional sliding mode control has the following problems that firstly, the system state is only asymptotically converged on a sliding mode surface, and limited time stability cannot be ensured, secondly, high-frequency buffeting can be caused by discontinuity of a symbol function in a control law, so that control precision can be influenced, mechanical resonance can be more likely to be caused, and the service life of an actuator is reduced, thirdly, the control gain needs to be larger than a disturbance upper limit, and if the upper limit is unknown or the estimation is conservative, control performance is reduced or buffeting is aggravated. To increase the convergence speed, terminal sliding mode control is proposed which achieves finite time convergence by introducing nonlinear terms in the sliding mode plane. However, the conventional terminal sliding mode has a problem of singularity in that the control law of the system state in the vicinity of the balance point tends to infinity. Although the nonsingular terminal sliding mode and the rapid terminal sliding mode respectively solve the problems of singularity and convergence speed, the advantages of the nonsingular terminal sliding mode and the rapid terminal sliding mode are not considered, and the prior knowledge of the disturbance upper bound is still relied on. In terms of buffeting suppression, a saturation function is often used in engineering to replace a sign function, wherein the thickness of a boundary layer is a fixed value. However, the fixed boundary layer has the defects that if the thickness of the boundary layer is too small, the buffeting inhibition effect is limited, and if the thickness of the boundary layer is too large, buffeting can be effectively inhibited, but the steady-state tracking precision of the system is reduced, and even steady-state errors are caused. Therefore, how to dynamically adjust the thickness of the boundary layer on the premise of ensuring the tracking precision becomes a problem to be solved. Aiming at the problems, the research adopts an improved self-adaptive nonsingular rapid terminal sliding mode control method, and realizes the finite-time high-precision tracking of the mechanical arm on the premise of self-adaptively estimating disturbance and effectively inhibiting buffeting. And further provides a self-adaptive boundary layer thickness adjustment strategy based on the sliding mode surface norm, so that buffeting is further restrained and tracking precision is kept. Disclosure of Invention The invention aims to solve the problems of low convergence speed, obvious buffeting and dependence on disturbance upper bound priori knowledge in the prior art, and provides a method and a system for controlling a mechanical arm track tracking sliding mode. In order to achieve the above purpose, the invention provides a method for controlling a sliding mode of tracking a track of a mechanical arm, which comprises the following steps: s1, establishing a dynamic model of the six-degree-of-freedom mechanical arm, and converting the dynamic model into a state space form containing a lumped parameter uncertain term: Establishing a dynamics model of the six-degree-of-freedom mechanical arm: Wherein, the Respectively representing the joint position angle, the joint angular velocity and the joint angular acceleration vector of the mechanical arm,Is a symmetrical positive definite inertia matrix,Is a centrifugal coriolis force matrix of the mechanical arm,Representing a matrix of gravitational terms for the robotic arm,Representing an external disturbance such as a wind or a wind,An input vector representing a moment of the robotic arm; taking into account the uncertainty of the kinetic parameters of the mechanical arm, i.e ,,Wherein、、Representing the nominal value of the mechanical arm dynamics system,、、Representing the uncertainty of the parameters of the dynamic system, thus re-writing