惯性式冲击振动落砂机周期倍化分岔的反控制

在不改变惯性式冲击振动落砂机系统平衡解结构的前提下,考虑碰撞振动系统的Poincaré映射的隐式特点以及经典的映射周期倍化分岔临界准则给反控制带来的困难,基于不直接依赖于特征值计算的周期倍化分岔显式临界准则,研究了落砂机系统周期倍化分岔的反控制.论文首先对落砂机系统施加线性反馈控制,得到受控闭环系统的Poincaré映射,并应用不直接依赖于特征值计算的周期倍化分岔显式临界准则,获得了系统发生周期倍化分岔的控制参数区域.然后应用中心流形-正则形方法分析了周期倍化分岔的稳定性.最终采用数值仿真验证了在任意指定的系统参数点通过控制能产生稳定的周期倍化分岔解.

Anti-controlling Period-doubling Bifurcation of an Inertial Impact Shaker System

In the premise of no change of periodic solutions of the original system and with consideration of the difficulties that given by the implicit Poincaré map of the impact shaker system and the classical critical criterion of mapping period-doubling bifurcation described by the properties of eigenvalues, the method of anti-control of period-doubling bifurcation of an inertial impact shaker system is proposed on basis of an explicit critical criterion without using eigenvalues calculation. Firstly, the linear feedback control is used to deduce the Poincaré map of close-loop system, and the period-doubling bifurcation explicit critical criterion without using eigenvalues calculation is applied to obtain the controlling parameters area. Then, the stability of the period-doubling bifurcation is further analyzed by utilizing the center manifold and normal formal theory. The ultimate numerical experiments verify that the stable period-doubling bifurcation solutions can be generated at an arbitrary specified parameters point by controlling.