CN-121374562-B - Self-adaptive sliding mode control method and system for mechanical arm

CN121374562BCN 121374562 BCN121374562 BCN 121374562BCN-121374562-B

Abstract

The invention belongs to the technical field of mechanical arm control, and provides a mechanical arm self-adaptive sliding mode control method and a system, wherein the self-adaptive sliding mode approach law is constructed and comprises a system state variable, a distance function based on position error and speed error and a gain item self-adaptively adjusted along with the convergence state of the system, and when the difference value between the Euclidean distance between a balance point and the current position in a state space and a set value is larger than a set range, the distance function based on the position error and the speed error is dominant and changes exponentially, the approach speed to the sliding mode surface is larger than the set value, and when the difference value between the Euclidean distance between the balance point and the current position in the state space and the set value is in the set range, the system state variable is dominant and the approach speed to the sliding mode surface is in the preset range.

Inventors

WAN YI
SONG WEIYE
HUANG JIAQI
LIANG XICHANG
HOU JIARUI
LI YANAN
Tao Zhonghan
WU WEILI
WANG JILAI
JI SHUAI

Assignees

山东大学

Dates

Publication Date: 20260512
Application Date: 20251021

Claims (10)

1. The mechanical arm self-adaptive sliding mode control method is characterized by comprising the following steps of: An adaptive sliding mode approach law is constructed, wherein the adaptive sliding mode approach law comprises a system state variable, a distance function based on a position error and a speed error and a gain item adaptively adjusted along with a system convergence state, when the difference value between the Euclidean distance between a balance point and a current position in a state space and a set value is larger than a set range, the distance function based on the position error and the speed error is dominant and changes exponentially, the approach speed to a sliding mode surface is larger than the set value, when the difference value between the Euclidean distance between the balance point and the current position in the state space and the set value is in the set range, the system state variable is dominant, and the approach speed to the sliding mode surface is in a preset range.
2. The method for controlling an adaptive sliding mode of a mechanical arm according to claim 1, wherein the adaptive sliding mode approach law is: Wherein k 1 、k 2 、k 3 、k 4 are all coefficients and are all greater than zero, E represents the Euclidean distance between the balance point and the current position in the state space, d is a normal number, Is a saturation function.
3. The method for controlling an adaptive sliding mode of a mechanical arm according to claim 2, wherein the saturation function is: Where x is the input value of the sat () function.
4. The method of claim 2, wherein when the sliding state is far from the desired track, then The item becomes the dominant factor in the movement of the driving state trajectory towards the sliding surface.
5. The method for controlling the self-adaptive sliding mode of the mechanical arm according to claim 1, wherein the joint expression of the mechanical arm after the self-adaptive sliding mode approach law is introduced is as follows: Wherein, the , , Respectively inertia matrix, coriolis matrix and gravity vector of mechanical arm, , , The angle, the angular velocity and the angular acceleration of the mechanical arm joint are respectively, , , The estimated values of the joint torque and the friction torque and the estimated value of the external disturbance torque are respectively obtained.
6. The method of claim 5, wherein the estimated value of the friction torque is obtained by a friction model.
7. The method for controlling an adaptive slip form of a mechanical arm according to claim 1, wherein the estimated value of the external disturbance torque is obtained by a sensor.
8. The method of claim 1, wherein the coriolis matrix and the gravity vector of the mechanical arm are identified by mechanical arm parameters.
9. The mechanical arm self-adaptive sliding mode control system is characterized by being configured to construct a self-adaptive sliding mode approach law, wherein the self-adaptive sliding mode approach law comprises a system state variable, a distance function based on a position error and a speed error and a gain item which is self-adaptively adjusted along with a system convergence state, when the difference value between the Euclidean distance between a balance point and a current position in a state space and a set value is larger than a set range, the distance function based on the position error and the speed error is dominant, the distance function is exponentially changed, the approach speed to a sliding mode surface is larger than the set value, and when the difference value between the Euclidean distance between the balance point and the current position in the state space and the set value is within the set range, the system state variable is dominant, and the approach speed to the sliding mode surface is within a preset range.
10. A robotic arm comprising the robotic arm adaptive slip-mode control system of claim 9 or comprising a memory and a processor and computer instructions stored on the memory and running on the processor, which when executed by the processor, perform the steps in the method of any one of claims 1-8.

Description

Self-adaptive sliding mode control method and system for mechanical arm Technical Field The invention belongs to the technical field of mechanical arm control, and particularly relates to a mechanical arm self-adaptive sliding mode control method and system. Background The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art. Mechanical arms have found wide application in a variety of industries, including agriculture, industry, and service. In practical tasks, such as grabbing, carrying, stacking, etc., the mechanical arm often faces the influence of the change of the effective load. Even if the load is unchanged, the motion control precision is reduced due to factors such as strong nonlinearity, model uncertainty, unmodeled dynamics and the like. The introduction of the load can quickly change an inertia matrix and a gravity matrix, and the dynamic characteristics of the mechanical arm are obviously influenced, so that higher requirements are provided for high-precision track tracking control. The design of a sliding mode controller by adopting a sliding mode approach law is a typical method of sliding mode control. Because of the convenience in design and the advantages in calculation, the approach law has been widely studied in recent years, and the approach law has the effect of driving the system state track to reach the designed sliding mode surface in a limited time. However, the conventional slip-form approach law may suffer from slow arrival rates, both when the system is near and far from the slip-form face. In practical applications, this may lead to poor dynamic performance of the system and reduced anti-interference capability. The traditional sliding mode approach law method has inherent technical limitations, and the fundamental problem is that the approach law design adopting static fixed parameters cannot adapt to the contradiction of requirements of different stages of a system state track in the dynamic approach process. Specifically, when the system state is far away from the sliding mode surface, the approach speed is limited by the fixed gain of the conservative design to ensure the feasibility of the control signal and inhibit buffeting, so that the initial stage is slow in convergence and the dynamic response is delayed, and when the state is close to the sliding mode surface, the approach speed is forcedly reduced to avoid high-frequency buffeting caused by discontinuous control law and is limited by the fixed gain, so that the system approaches to the weak state in a critical area, and the convergence time is prolonged. The mismatch between the static design and the dynamic demand not only deteriorates the comprehensive dynamic performance of the system, but also seriously weakens the inherent strong robustness advantage of the sliding mode control due to the insufficient interference suppression capability in the approach stage, and becomes a key technical bottleneck for restricting the development of the sliding mode control in the high-performance control application. Disclosure of Invention In order to solve the problems, the invention provides a self-adaptive sliding mode control method and a self-adaptive sliding mode control system for a mechanical arm. According to some embodiments, the present invention employs the following technical solutions: A self-adaptive sliding mode control method for a mechanical arm comprises the following steps: An adaptive sliding mode approach law is constructed, wherein the adaptive sliding mode approach law comprises a system state variable, a distance function based on a position error and a speed error and a gain item adaptively adjusted along with a system convergence state, when the difference value between the Euclidean distance between a balance point and a current position in a state space and a set value is larger than a set range, the distance function based on the position error and the speed error is dominant and changes exponentially, the approach speed to a sliding mode surface is larger than the set value, when the difference value between the Euclidean distance between the balance point and the current position in the state space and the set value is in the set range, the system state variable is dominant, and the approach speed to the sliding mode surface is in a preset range. As an alternative embodiment, the adaptive sliding mode approach law is: Wherein k 1、k2、k3、k4 are all coefficients and are all greater than zero, E represents the Euclidean distance between the balance point and the current position in the state space, d is a normal number, Is a saturation function. As a further embodiment, the saturation function is: Where x is the input value of the sat () function. Alternatively, when the sliding state is away from the desired trajectory, thenThe item becomes the dominant factor in the movement of the driving state trajectory