Modeling and design of direct nonlinear velocity feedback for modal self-excitation in a class of multi degrees-of-freedom mechanical systems

Abstract

The paper presents a new nonlinear control design methodology for inducing modal, self-excited oscillation in a class of multi degrees-of-freedom mechanical systems. The system is assumed to be fully actuated and the controller operates in a centralized fashion based on the direct nonlinear velocity feedback. The linear part of the controller is designed to assign negative modal damping in the mode to be excited and positive modal damping in other modes. The nonlinear modal interaction is investigated using averaging analysis and different excitation regimes are delineated in the control parameter space. The nonlinear part of the controller is optimized to minimize the control cost. Numerical simulations of the control system are performed to substantiate the analytical results and validate the accuracy of the design. The control method is also shown to have some degree of robustness against parametric variations over the nominal values.

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.…”