Efficacy of a class of resonant nonlinear controllers of fractional-order for adaptive vibration control—Analysis, simulations and experiments

Abstract

The efficacy of different class of resonant controllers has been successfully established for active vibration control. This class of controllers utilize a second-order filter fed back with the structural response (displacement, velocity or acceleration) and the control signal is synthesized as the linear/nonlinear function of the filter response. However, the performance of the controller largely depends on the tuning of the filter frequency to the structural natural frequency. Thus, for structural systems where the natural frequency and the excitation frequency are uncertain, one requires to tune the filter frequency adaptively. The present paper introduces two computationally efficient, fractional-order nonlinear adaptive resonant controllers with acceleration feedback for vibration control. The control signal is synthesized as the linear/nonlinear function of the filter variable and its fractional order derivative. Two parameters, namely the filter frequency and the control gain, are adaptively varied to control the phase and amplitude of the control signal, respectively. The objective of frequency adaptation is to maintain the phase of the control signal in the quadrature of the system displacement/acceleration. Theoretical analysis of the system is performed by the method of multiple scales under the assumption of slowly varying parameters. The results are verified by both numerical simulations and experiments. The theoretical and experimental results demonstrate the robustness of the proposed adaptive control against uncertainties in excitation force and system parameters. It is comprehensively shown that the fractional-order control is superior to the integer-order control already studied in previous works. Moreover, the effect of feedback time-delay is also studied, and it is shown that the fraction-order control can offset the detrimental effects of time-delay on the frequency response of the system.