Identification and modeling of a nonlinear vibrating beam for real-time control and estimation

Paper in proceeding, 2018

The real-time implementation of control and estimation algorithms on microcontrollers with limited memory and computational power requires a model that describes the dynamics of the vibrating system in sufficient detail, yet makes real-time deployment on sampled systems feasible. While extracting a model from finite element analysis is always possible, this approach yields models that are too complex to be evaluated in sample timing that is typical for vibration phenomena. In case of nonlinear vibrations, this is even more critical as state-of-the-art optimal control and estimation algorithms will have to evaluate a non-convex objective function. This paper introduces the modeling and system identification procedure of a nonlinear vibrating beam that results a real-time feasible mathematical model. Position and velocity measurements are made on a slender vibrating beam mounted equipped with a tip mass on a linear excitation stage using non-contact laser Doppler vibrometry. The measurement results are then fitted to two model candidates by using genetic algorithms to identify unknown parameters. Models are verified in simulation and their outputs are compared to experimental measurements.