Robust control of nonlinear resonance in a clamped rectangular plate

Abstract

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.

Disturbance rejection based consensus controller for swarm system

“…This approach was initially introduced by QC Zhong in [17]. Subsequently, Talole et al explored its application in various aerospace contexts in [18,19], and [20]. Notable contributions to UDE-based control strategies for both Multiple Input Multiple Output (MIMO) and Single Input Single Output (SISO) systems can be observed in works such as [21] and [22].…”

Active disturbance rejection vibration control for an all-clamped piezoelectric plate with delay

“…However, the conventional feed-forward-based vibration controllers are commonly infeasible in many practical structural vibration suppression applications, since the mechanism models or measurements of the disturbances are generally unavailable. To this end, several disturbance estimation methods, such as extended state observer (ESO), disturbance observer (DOB), perturbation observer (PO), equivalent input disturbance (EID), generalized proportional integral observer (GPIO), uncertainty and disturbance estimator (UDE) and unknown input observer (UIO), have been proposed as alternatives to design such composite vibration control methods [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] . Many researchers have presented a variety of practical and effective vibration control techniques based on these disturbance estimation methods.…”

“…It can suppress the structural vibrations caused by sinusoids, constants and parabolas disturbances, and can be easily combined with other advanced feedback control methods. Considering the model uncertainties, UDE-based vibration control method can estimate and compensate the internal and external disturbances by introducing an appropriate filter in frequency domain [43][44][45] . The disturbances can be mainly estimated by using the system state variables to improve the dynamic and static vibration suppression performance of the whole system in UIO-based vibration control methods [46,47] .…”

Wave Mode Control of Cantilever Slab Structure of T‐Beam Bridge with Large Aspect Ratio

“…e abovementioned will cause the vibration of the bridge structure. If effective vibration suppression measures are not taken, the vibration will decay very slowly, which will not only affect the position of the beam bridge structure, but also cause the vibration of the plate structure, cause fatigue damage, and have a serious impact on the safety and service life of the beam bridge [3].…”