Stability Analysis And Vibration Control Of Nonlinear Manipulator With Time Delay

Firstly,Article introduces the structure and composition of the manipulator,the origin of the time delay in the manipulator,and the research progress of nonlinear time delay systems.The content of this issue is explained by combining the research progress of nonlinear time delay systems and the significance of researching the nonlinear manipulator with time delay:whether the time delay will lead to the instability of the manipulator,and how to control the nonlinear vibration of the manipulator caused by the time delay.Then,article considers Spong's manipulator connected by elastic joint system model according to references,and builds the dynamic of nonlinear manipulator with time delay according to theoretical mechanics.Finally,A method considering Nayfeh's improved multi-scale method is used to analyze the stability and bifurcation of the nonlinear manipulator with time delay,and mathematical software is used to study the vibration control of the manipulator.In the improved multi-scale method,the time delay parameters are taken as the only variable parameter to study the vibration of the manipulator.In the process of studying the vibration control of the manipulator,a controller is directly added to the dynamics model of the nonlinear manipulator with time delay after analyzing the example of the references.In order to illustrate the results of stability analysis and the control effect of the controller,the time history diagram of the manipulator is obtained by using mathematical software,and the time history diagram is compared with the calculation analysis results.There are two innovative places of the project.One is to connect directly the time delay with the nonlinear vibration of the manipulator and study the vibration control of the manipulator caused by the time delay.The second is to improve the multi-scale method when analyzing the nonlinear dynamics model of the manipulator with time delay.It is rare to take the time delay parameter as the only parameter to affect the vibration of the manipulator in related references.Therefore,the method of studying new problems also needs to be improved.According to the characteristics of the nonlinear dynamics model of the manipulator with time delay,this paper makes an improvement of multi-scale method.In this paper,the following conclusions are obtained through stability analysis and after designing the control method of nonlinear manipulator with time delay: 1.the manipulator will be unstable when the parameter of time delay increases to a critical value.2.The improved multi-scale method can be used to analyze the vibration of nonlinear manipulator with time delay.3.The controller designed in this paper can make the manipulator return to a stable state within a certain time-delay range.4.Different controllers will have different control effects.For example,controller 1 with the best effect can make the manipulator enter the stable state at the fastest speed,while controller 2 and controller 3 have slower control speeds.