Parametric Resonance Control of Flexible Manipulator Based on Saturation and Quadratic Nonlinearity Enhancement

Parametric resonance is a complicated phenomenon that manifests itself in many areas. When subjected to parametric resonance, the amplitude of the flexible manipulator will increase abruptly, resulting in the rapid deterioration of working performance. Most conventional control methods are ineffective when approaching resonance. Because of this, a new method for suppressing the parametric resonance of the flexible manipulator is proposed. A novel parametric resonance absorber, characterized by controllable vibration parameters and adjustable nonlinear coupling parameters, is designed to strengthen quadratic modal coupling with the flexible manipulator and to construct a transfer tunnel for exchanging and dissipating parametric resonance energy. Dynamics equations of the controlled flexible arm mode and the parametric resonance absorber mode are derived, and the corresponding steady-state solutions of parametric resonance are solved. The saturation principle is revealed and implemented based on the stability analysis of the steady-state response of parametric resonance. With the help of the saturation principle, the parametric resonance response of the flexible manipulator can be effectively suppressed to a small amplitude by the proposed parametric resonance absorber. A series of numerical simulations and experiments have verified the proposed method’s effectiveness in suppressing the flexible manipulator’s parametric resonance.