Chaos Control Of Vibro-impact Systems With Clearance Based On SVM

Vibro-impact systems exist widely in daily life and engineering practice.It is unavoidable that there are clearances between mechanical internal components or mechanical components and motion constraints in vibro-impact systems due to factors such as structure,manufacture,assembly and wear.When the amplitude of moving parts exceeds the critical condition,impact vibration will occur between parts or between parts and constraints.The vibro-impact system has strong non-linearity and non-smoothness and presents complex dynamic behavior(such as chaos)because of the existence of impact vibration.In most engineering practice,chaotic vibration is a harmful form of motion,which will cause many hazards.Therefore,it is of great significance to explore a suitable control method for chaotic motion of vibro-impact with clearance,and to control unstable chaotic motion into a stable periodic motion so as to reduce the negative effects caused by the chaotic motion.Aiming at the control problem of chaotic motion for single-degree-of-freedom rigid vibro-impact system with clearance and single-degree-of-freedom elastic vibro-impact system with clearance,an intelligent optimization control strategy based on Support Vector Machine(SVM)is proposed in this dissertation.A three-layer network structure of SVM is adopted to design the parameter feedback chaotic controller.Meanwhile,in virtue of the advantages of Particle Swarm Optimization(PSO)algorithm,such as stronger global search ability,faster convergence speed and gradient information independent of fitness function,the parameters of chaos controller are optimized and selected.The simulation results verify the feasibility and effectiveness of this method.The main content of this dissertation is organized in the following manner:Firstly,the chaotic behavior of a single-degree-of-freedom rigid vibro-impact system with clearance and a single-degree-of-freedom elastic system with clearance is studied.Taking excitation frequency ? and damping coefficient ? as bifurcation parameters,the bifurcation phenomena of system state x(5)with bifurcation parameters changing are numerically simulated.Combing with the phase diagram of the system,the Poincaré section projection and the spectrum diagram,the chaotic motion of the system is qualitatively judged,and the parameters of the chaotic system is analyzed according to the dynamic response characteristics of the system obtained by simulation.Secondly,based on the three-layer network structure of SVM,the input/output variables of the controller and the mapping mode between input and output are determined to complete the design of the SVM parameter feedback chaos controller;the fitness function is constructed according to the distance between two adjacent points on the Poincaré section;and the fitness function is used to guide the PSO algorithm to optimize the parameters of the SVM parameter feedback chaos controller.Finally,the chaotic attractor of the system is simulated by using the intelligent optimization control strategy of SVM proposed in this dissertation,and the control effect diagram of the system is simulated.The simulation results verify the effectiveness of the method for chaotic motion control of the vibro-impact system with clearance.At the same time,the fitness function constructed in this dissertation is used to quantitatively evaluate the control effect of chaos controller based on SVM on the chaotic motion of the controlled system.Furthermore,the relationship between control start time and control effect is studied,and the influence of controller bias on control effect is analyzed.In addition,by comparing and analyzing the effect of controllers with different hidden layer nodes on chaotic motion control,the structure of the controller is optimized.