Time-delay feedback control of a suspended cable driven by subharmonic and superharmonic resonance

The longitudinal time-delay feedback control strategy is implemented to suppress the subharmonic and superharmonic responses of the suspended cable. Formulated based on the Hamilton variational principle and the longitudinal time-delay feedback strategy, the in-plane nonlinear differential equations for a suspended cable are formulated, and Galerkin method is utilized to transform the equations into delayed differential equations. By using the method of multiple scales, approximate solutions for the 1/2-subharmonic and second-order superharmonic resonance responses of the controlled suspended cable were derived. The effects of the time delay and control gain are obtained through numerical examples. The research results demonstrate that through the adjustment of control gain and time delay, resonance regions can be avoided, effectively suppressing large-amplitude vibrations in the suspended cable, thereby achieving favorable control performance.