The invention discloses a flexible mechanical arm main
resonance control method based on nonlinear feedback and time
delay feedback, and the method mainly comprises the steps: carrying out the
discretization of the transverse deformation of a flexible mechanical arm through employing a
hypothesis modal method, and obtaining a vibration equation of the flexible mechanical arm; a linear
feedback control item, a nonlinear
feedback control item and a time-
delay feedback control item are introduced to form a
control signal model of the vibration absorber. Constructing a vibration absorber
control signal model; a Kane equation is used for establishing a flexible mechanical arm
system vibration control model including the vibration absorber; solving an approximate analytic solution of the
system vibration equation by applying a multi-scale method to obtain a single-mode solution and a dual-mode solution of the
system steady-state response; and finally, under the coexistence state of the
internal resonance condition and the main
resonance condition of the flexible mechanical arm system in which the vibration absorber is included, the main
resonance of the flexible mechanical arm is controlled, and the
modal amplitude of the first-order
modal of the main resonance of the flexible mechanical arm is well inhibited.