Saddle-node bifurcation control of a spring pendulum with single-frequency excitation
单频外激励弹簧摆的鞍结分岔控制

Spring pendulum under single-frequency excitation can be described by a group of very complicated nonlinear equations. The paper studies the amplitude of the spring pendulum, and feedback controllers are designed. Analytic method is used to obtain the control equation of amplitude, the relationship function between control parameter and amplitude is also abtained,which may act as an implementation of feedback control method for saddle-node bifurcation control, and also brings multi-scale method to numerical calculation of multiple-degree-of-freedom nonlinear systems.