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Flexible mechanical arm sliding-mode control designing method based on singular perturbation theory

A singular perturbation theory and flexible manipulator technology, applied in the direction of adaptive control, general control system, control/regulation system, etc., can solve problems such as control problems

Active Publication Date: 2014-09-10
GUODIAN SCI & TECH RES INST
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Problems solved by technology

However, most of the research is based on the ODE model, and the resulting control problems also exist

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  • Flexible mechanical arm sliding-mode control designing method based on singular perturbation theory
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  • Flexible mechanical arm sliding-mode control designing method based on singular perturbation theory

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Embodiment Construction

[0091] The present invention will be further described in detail below in conjunction with the accompanying drawings and technical solutions.

[0092] See figure 1 , the present invention is based on a singular perturbation theory of flexible manipulator sliding mode control design method, the specific steps of the method are as follows:

[0093] Step 1: Dynamic modeling of the flexible manipulator

[0094] The model of the flexible mechanical arm that the present invention aims at is as figure 2 As shown, using Hamilton's principle, through the analysis of the system, the PDE model can be obtained.

[0095] The state variables θ(t) and y(x,t) used in modeling represent the joint angle of the manipulator at time t and the elastic deformation at point x, respectively. For convenience, θ(t) and y(x,t) are abbreviated as θ and y(x) respectively in the following analysis.

[0096] The natural boundary conditions of the flexible manipulator are

[0097] y(0)=y x (0) = 0 (1) ...

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Abstract

The invention relates to a flexible mechanical arm sliding-mode control designing method based on a singular perturbation theory. The method includes four steps that (1) dynamics modeling of a flexible mechanical arm is performed; (2) partial differential equation (PDE) model decomposition is performed; (3) a control law is designed; (4) designing is finished. According to the flexible mechanical arm sliding-mode control designing method based on the singular perturbation theory, firstly, a Hamilton principle is utilized, and a PDE model of a whole system is determined; the original PDE model is decomposed into a concentrating slow subsystem which represents whole rigidity movement and a quick subsystem which describes system vibration by means of the singular perturbation theory; then a sliding-mode control law is designed by respectively aiming at the quick and slow subsystems, the designed control law is subjected to convergence analysis by the aid of a lyapunov function, and reasonability and stability of the control law are verified. Finally, a compound control law is obtained according to the singular perturbation theory.

Description

technical field [0001] The present invention relates to a flexible manipulator sliding mode control design method based on singular perturbation theory. A sliding mode control design method belongs to the technical field of mechanical arm control. Background technique [0002] Due to the advantages of light weight, high speed, and low energy consumption, flexible robotic arms are increasingly used in aerospace and industrial fields. In the past, the research on the control method of flexible manipulators was mostly based on the ordinary differential equation (Ordinary Differential Equation, ODE) dynamic model (hereinafter referred to as the ODE model). ODE model is simple in form and provides convenience for control law design. However, since the ODE model is obtained by ignoring high-order oscillation modes, it is difficult to accurately describe the distributed parameter characteristics of flexible systems and may cause overflow instability. Therefore, it is of great pr...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G05B13/04
Inventor 陈宝林刘志杰刘金琨
Owner GUODIAN SCI & TECH RES INST
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