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根据固相振荡燃烧模型的动力学方程,揭示了系统随自身参数λ变化的动力学行为及混沌现象,并用棒棒控制法和多变量注入反馈控制法对系统进行了控制。数值仿真结果显示,随着系统参数的逐渐减小,系统处于周期二运动轨道,当参数进一步减小时,系统发生倍化分岔,最终通过倍化分岔序列通向混沌,当参数继续减小时,系统从混沌态转化为周期运动。棒棒控制法和多变量注入反馈控制法都能将系统控制到稳定的单周期轨道,只是控制后单周期的相轨迹图不同。系统随多变量注入反馈控制法控制参数变化时,其动力学行为与系统随自身参数变化的动力学行为很相似。本文工作进一步揭示了固相振荡燃烧模型的动力学行为,给出了该模型混沌控制的参数依据,为该模型进一步工程应用奠定了理论基础。
According to the kinetic equation of the solid-phase oscillating combustion model, the dynamic behaviors and chaos phenomena of the system with its own parameter λ are revealed. The system is controlled by the method of the stick-rod control and multivariable injection feedback control. Numerical simulation results show that the system is in period two orbit as the system parameters decrease gradually. When the parameters are further reduced, the system takes on a bifurcated bifurcation and eventually leads to chaos through the bifurcation bifurcation sequence. When the parameters continue to decrease , The system changes from chaos to periodic motion. Both the stick control method and the multivariable injection feedback control method can control the system to a stable single-cycle orbit, but the single-phase phase trajectory after the control is different. When the system changes with the control parameters of multivariable injection feedback control method, its dynamic behavior is very similar to the dynamic behavior of the system with its own parameters. The work of this paper further reveals the dynamic behavior of the solid-phase oscillating combustion model, and gives the parameter basis of the chaos control of the model, which lays a theoretical foundation for the further engineering application of the model.