Primary resonance control of flexible manipulator based on modal coupling and time-delay feedback

The flexible manipulator in primary resonance condition vibrates with a considerable magnitude that causes mechanism motion instability and structure destruction. To address this issue, this paper proposed a new primary resonance control method characterized by modal coupling and time-delay feedback. Unlike the original saturation control method based on the PD algorithm, which relies solely on internal resonance, our approach constructs a controllable quadratic modal coupling term to strengthen the 1:2 internal resonance relationship and designs an adjustable time-delay feedback to further strengthen saturation control performance. To elucidate the mechanisms underlying the further suppression of primary resonance by modal coupling and time-delay feedback, the approximate steady-state analytic solutions of the flexible manipulator and proposed absorber are derived, and their stability conditions are determined. Simulation analyses with various coupling coefficients and time-delay parameters demonstrate that the proposed method achieves superior performance in reducing saturation amplitude and accelerating the attainment of saturation compared to the original saturation control method. Optimal values for coupling coefficient and time-delay parameters are identified through simulations. Experimental results further confirm the superiority and effectiveness of the proposed primary resonance control method.