Linear Control of a Nonlinear Equipment Mounting Link

Abstract

The linear control of a nonlinear response is investigated in this paper, and a nonlinear model of the system is developed and validated. The design of the control system has been constrained based on a suggested application, wherein mass and expense are parameters to be kept to a minimum. Through these restrictions, the array of potential applications for the control system is widened. The structure is envisioned as a robot manipulator link, and the control system utilises piezoelectric elements as both sensors and actuators. A nonlinear response is induced in the structure, and the control system is employed to attenuate these vibrations which would be considered a nuisance in practical applications. The nonlinear model is developed based on Euler–Bernoulli beam theory, where unknown parameters are obtained through optimisation based on a comparison with experimentally obtained data. This updated nonlinear model is then compared with the experimental results as a method of empirical validation. This research offers both a solution to unwanted nonlinear vibrations in a system, where weight and cost are driving design factors, and a method to model the response of a flexible link under conditions which yield a nonlinear response.

Basic Study on Mechanical Vibration Suppression System Using 2-Degree-of-Freedom Vibration Analysis

“…Previously, a 2-DOF system was actively studied for the design of a dynamic vibration absorber. Nishihara et al obtained an exact solution to optimize a dynamic vibration absorber in a 2-DOF system model that does not have a damping factor in the main system [22][23][24]. However, in the most general case, many machines are mounted using viscoelastic materials, such as rubber vibration insulators, and there is no realistic situation in which the main system does not have damping.…”