Robust control of nonlinear resonance in a clamped rectangular plate

This work is concerned with the control of nonlinear oscillations and resonance in a thin rectangular clamped plate representative of an aircraft panel with forcing frequency near to that of the first linear mode. The response of the plate to unsteady pressure force is modeled using the nonlinear von Kármán plate equation, the solution of which is obtained using modal expansion with the linear eigen modes. To suppress the vibrations, an input–output linearization (IOL) and uncertainty and disturbance estimator (UDE) based robust active vibration controller are proposed. The UDE is employed to estimate the composite uncertainty that comprises the effects of system nonlinearities and external disturbances and the estimate is used to augment the IOL controller to achieve robustness. The resulting controller, however, requires output derivatives for its implementation and to address the issue, an observer that employs the UDE estimated uncertainties for robustness is designed. Closed-loop stability for the overall system is established using Lyapunov’s direct method. The notable feature of the proposed design is that it neither requires an accurate plant model nor any detailed information about the external disturbances. Also, the design needs only the measurement of the center displacement of the plate for its implementation. Simulations are carried out for different disturbances and the results are presented to demonstrate the efficacy of the proposed controller. Lastly, performance comparison with some existing vibration control designs is carried out to showcase the effectiveness of the proposed formulation.