On The Chaotic Motion And Controlling Of Underactuated 2R Manipulator Mounted On A Flexible Element

It has attracted many wide attentions since chaos was proposed in the nonlinear science, and good deal of achievements has been obtained. Nowadays, a great progress of chaos study in mechanism science has been made.Deformation and vibration of the foundation aggravate the vibration of mechanism, and make the stability of the machinery decreased especially for precision terminal trajectory of a robotic arm. Therefore, it’s of great significance both in theory and practice to analyze the dynamics of a mechanism mounted on a flexible element.Bond graph is a method of modeling based on energy conservation law. It has great advantages in multi-energy domain and allows analyzing the power flow and energy dissipation, storage and conversion in the system. It provides a valid tool for dynamical analysis from the power point of view.The motion of an underactuated 2R manipulator mounted on a flexible element is analyzed in this thesis. The dynamical model of the system is established with bond graph theory. The edges of chaos for single and double parameters of driving excitation are determined. The method of controller design based on double-parameter edge of chaos is proposed for control and anti-control chaos.The main research work and conclusion in this thesis are as following.1. The bond graph modeling of 2R manipulator is established with bond graph theory, and the dynamical equations of the system are derived according to the relationship between flows and efforts. The effects of elastic and damping coefficients of flexible element as well as excitation parameters and structure parameters are analyzed. It is shown that all of them have influences on the motion of the system in different degrees.2. The thesis focuses on the effects of the excitation parameters on the motion of the system for the reason that it is hard to change structure parameters once the system has been set up. By setting the amplitude and frequency of driving force as variable parameters, the edge of chaos is determined for both single and double parameters. The evolution process of periodic motion, and variation of the power flow with respecting to the changing of motion states are studied. It is found that the periodicity of power flow is approximately 2 times of its periodic motion.3. Based on the edge of chaos for double-parameter of the system, a method to determine the coefficients of controller is proposed by taking the coefficients of controller as internal parameter of controlled system and depicting the edge of chaos. The simulation results demonstrate that the method is efficient.This thesis provides a new design method for the controller of controlling and anti-controlling chaos based on the edge of chaos. Some relationships between power flow and motion state are found through the using of bond graph. It makes a valuable reference to study of mechanism of chaos arising.