Analysis Of Nonliner Dynamic Characteristics Of Flexible Manipulator Sliding Mode Control System

With the rapid development of robotic technologies,flexible manipulators began to attract the attention of researchers.Compared to the conventional rigid manipulators,flexible manipulators have many advantages such as lightweight structures,fast response,high load-weight ratio,low power consumption and so on.However,structural flexibility and its inherent nonlinear dynamics makes the flexible manipulators typical multiple input multiple output nonlinear systems.In this paper,the two-arm flexible manipulator is selected as the controlled object,aiming to study the nonlinear dynamic behaviors in the flexible manipulator arise from sliding mode control from the following four aspects,phase trajectory and transient analysis,joint motor drive characteristics,un-modeled dynamics and steady-state periodic motion characteristics.In this paper,the distribution rule and arrival time of the phase trajectory from the initial point to the sliding surface are studied.This paper takes the two-link flexible manipulator as an example to research on its point-to-point position control.The nonminimum phase control problem is solved by using output redefinition method,and the system is decomposed.On this basis,the nonsingular terminal sliding mode controller is designed for input-output subsystem so that it could converge to the equilibrium point in a finite time.The stability of the zero dynamic subsystem is guaranteed by pole configuration.For input-output subsystem with nonsingular terminal sliding mode control,the relationship between the initial states and phase trajectory patterns is studied and the concept of critical surface is given.Based on the distribution of phase trajectories,a reaching time estimation algorithm is explored.This paper considers the influence of the dynamic characteristics of the drive motor and parameter uncertainty on the flexible manipulator.Since the joint of flexible manipulator is driven by motor,this paper first establishes the mathematical model of the two-link flexible manipulator containing motor drive characteristics,and a linear sliding mode controller is designed so that the end-point of flexible manipulator converges to zero.In addition,the parameter uncertainty of the model is considered,introduce uncertainty into each subsystem by analyzing the uncertainties evolved from original system,and the error range of the end-point position is given.This paper considers the effect of un-modeled dynamics on the sliding mode control system of the flexible manipulator.Un-modeled dynamics may affect the nonlinear dynamic behavior of the system.It will induce high frequency chattering of the system and make the system oscillate.In this paper,the flexible manipulator model containing the dynamics of actuators is established.The existence of chattering is proved by theoretical analysis.Then the high-frequency chattering induced by un-modeled dynamics is quantified based on the description function method.The factors which may affect the frequency and amplitude of the chattering are also explored.This paper considers the effect of time-delay during sliding mode switching on the dynamic response of the manipulator sliding mode control system.This paper firstly establishes the flexible manipulator model with time-delayed sliding mode control,and uses the phase plane method to observe the phase trajectory of the flexible manipulator with nonsingular sliding mode control system.In addition,Poincaré map and Lyapunov exponent method are used to judge the motion state of the system,which proves the existence of the limit cycle.