Modeling and identification of an axially-moving cantilever beam

Abstract

An axially-moving cantilever beam is used to study identification o f time-varying systems. A circuitry for DC motor current control and sensor conditioning is built. The circuitry meets the design requirement of controlling the axial motion of the beam and amplifying the sensor signals. A linear time-varying model governing lateral vibration of the beam is developed. Computer simulation is conducted to study the dynamic properties of the system, such as transient responses, varying state transition matrices, “frozen” modal parameters, “pseudo” modal parameters, etc. A previously developed algorithm is applied to identify the system. Two identification tasks are carried out. The system identification determines the discrete-time state space model o f the system. The modal parameter identification determines the “pseudo” modal parameters of the system. In both cases, an ensemble of freely vibrating responses are used. The study addresses several critical issues encountered in the experiment such as excitation, data preprocessing, the beam motion control, etc. The study also investigates several important factors that affect the accuracy of identification, such as the number of necessary experiments, model order, the block row number, etc. An algorithm based on the moving-average method is developed to select the “pseudo” natural frequencies of vibratory modes. The study shows that the algorithm is capable of estimating the “pseudo” natural frequencies of the vibratory modes, present in responses, while it fails to give good estimates for the “pseudo” damping ratios.