| Vibro-impact system is widely applied in the aviation,mechanical equipment,rail transportation and other field of the production practice.The existence of clearance makes the parts of the system contact frequently under the action of external excitation force,which leads to the system velocity jump before and after impact.Under certain parameter conditions,the system exhibits rich and complex dynamic behaviors(bifurcation and chaos).It has important theoretical significance and engineering application value to eliminate the negative effect of chaotic motion on the system performance.In this theme,ICPSO-OGY(Improved Chaotic Particle Swarm Optimization-OGY)is proposed to solve the chaos control problem of single-degree-of-freedom vibro-impact system.The main work of this theme is as follows:Firstly,the nonlinear dynamic model and mathematical model of the single-degree-of-freedom vibro-impact system are established.the analytical expression of the periodic solution of the system’s periodic motion is derived.The stability of the periodic motion of the system is analyzed by using the Poincare mapping theory,and the phase diagram,time history diagram and Poincare cross section diagram of the process from periodization bifurcation to chaos are numerically simulated.Secondly,to solve the problem that OGY method(parameter perturbation control method)has too long waiting time in the process of chaos control,ICPSO-OGY chaos control method is proposed.Based on the CPSO algorithm,an improved chaotic particle swarm optimization algorithm was proposed to search the feedback gain online,and the chaotic trajectory guidance problem was transformed into a high-dimensional numerical optimization problem,so that the trajectory of the system could enter the fixed point neighborhood of the target within the preset number of steps.In the simulation experiment,several kinds of classical test functions are used to analyze the optimization ability of ICPSO algorithm,and one-dimensional Logistic mapping and two-dimensional Henon mapping are used to verify the feasibility and effectiveness of ICPSO-OGY chaos control method.Meanwhile,the influence of system parameters on the control effect is also analyzed.Finally,the proposed ICPSO-OGY chaos control method is used to control the chaotic motion of the vibro-impact system.The Jacobi matrix and sensitivity vector required for periodic control of chaotic motion were deduced and calculated.The discrete mapping equation of vibro-impact system based on feedback and the fitness function for chaotic trajectory guidance were established.The success rate and average effective guidance rate were introduced to quantitatively evaluate the guidance effect of chaotic trajectory.The feasibility and effectiveness of the proposed control method are verified by simulation experiments.The results show that the ICPSO-OGY chaotic control method can realize periodic control of the chaotic motion of vibro-impact system with less waiting time.The size of the fixed point neighborhood has a great influence on the guidance effect of chaotic orbit,while the state disturbance and the preset number of guiding steps in the guidance process have a relatively small influence on the guidance effect of chaotic orbit... |
