Modal self-excitation in a class of mechanical systems by nonlinear displacement feedback

Abstract

Many devices and processes utilize self-excited oscillation to enhance performance. Recently, much research work has been devoted to the induction of self-excited oscillation in mechanical systems by nonlinear feedback. The present paper investigates the efficacy of a displacement feedback technique in generating self-excited oscillation at the desired mode(s) in a multiple degrees-of-freedom mechanical system. The controller couples the system with a bank of second-order filters and generates the required control force as a nonlinear function of the filter output. The describing function method theoretically explores the dynamics of the system with the control law. The control cost of the controller is studied for the proper choice of the filter parameters. The analytical results are substantiated by the numerical simulation results. The present study reveals that the proposed control laws, if used in an appropriate way, can generate self-excited oscillation in the system at the desired mode(s).

Nonlinear Feedback Synthesis and Control of Periodic, Quasiperiodic, Chaotic and Hyper-Chaotic Oscillations in Mechanical Systems

“…In order to maintain the desired amplitude of the response, they have proposed an adaptive control law. They have also used displacement feedback resonant controller [18], where the control law was signum function of the output signal of a bank of second-order filters. The controller is efficient to produce self-excited oscillation of desired amplitude and modal frequency (single as well as mixed mode) for minimum control cost.…”

“…The controller can change the mode of oscillation by changing the frequency of the sine wave producing the self-excited oscillation. Malas and Chatterjee studied the efficacy of resonant controllers based on acceleration [17] and displacement [18] feedback for artificially generating self-excited oscillation of desired amplitude and frequency in a multi-DOF mechanical system, where the control is a nonlinear function of the output signal of a bank of second-order filters. Zhou et al [19] proposed linear and nonlinear feedback to produce a self-excited oscillation near higher modes of a cantilever, which is a practical model for the resonators used in nano-and micro-sensors.…”

Review of applications of self‐excited oscillations to highly sensitive vibrational sensors

“…For example, vibrating machines that perform ultrasonically assisted cutting use autoresonance because the resonance is maintained despite the varying cutting load 5. Many applications of autoresonance have been developed 38–40. Highly accurate vibrational sensing is another application in which the self‐excited resonator always resonates with the natural frequency.…”