The Bifurcation And Chaos Control Of Non-smooth Mechanical Dynamics System

Non-smooth dynamic systems have many different dynamic phenomena compared to the usual smooth dynamic systems,such as bifurcation and chaos.The former refers to change the original nonlinear system's dynamic characteristics by applying a corresponding controller to the original system,thus obtain the desired dynamic behavior;while the latter uses the corresponding controller for the original system to transform the chaotic motion into periodic motion.Based on some theoretical knowledge in non-smooth mechanical dynamics,this paper mainly studies the bifurcation and chaos behaviors.The main research contents are as follows:1.Through the mechanical model of the vibrating screen,the non-smooth bifurcation in the collision between the material and the screen surface was explored,and the anti-control theory was applied to the vibrating screen's analysis.Through numerical calculation,Hopf-Hopf bifurcation solution is obtained by adjusting the original system's control parameters by the linear feedback controller,completed the anti-control of vibrating screen's Hopf-Hopf bifurcation.For some vibratory systems such as sand falling machine,vibrating rod,mixers,etc,the nearly periodic motion of the toroid produced by the Hopf-Hopf bifurcation can improve the working efficiency of such systems.For example,it can make the mixers mix more evenly and make the screening machine screening faster.2.Taking the symmetric elastic contact system as the research object,its dynamic behavior is analyzed,an appropriate phasing plane is selected,and an intermittent linear feedback control law is applied there.By analyzing the motion stability of the controlled system,explicit conditions for chaos control of the system are obtained.Using numerical simulation,gives the control parameter bifurcation diagram of the periodic motion of the system,and the appropriate control parameters can be directly selected to control the original system within the range of periodic motion.The model can also be applied to mechanical equipment including clearance pairs,vehicle wheel-rail systems,and gear transmission systems through extended changes.This method can be used to improve the operating stability,work efficiency,and service life of these equipment.Has a certain practical engineering significance.3.The explicit critical criterion of bifurcation control is used to control the chaotic motion of the mechanical system.Different from the classical methods such as the OGY method,delayed feedback control method,and extra driving force method,here according to the Schur-Cohn stability criterion,the conditions for the periodic motion of the system are obtained,and these conditions are expanded to obtain some inequalities containing the system parameters through Matlab.In the areas where the conditions are met select the system's parameters,under the system's parameters the chaotic motion of the original system can be controlled to the periodic motion.This method of controlling chaos is simpler and easier to apply.