Stability Analysis for One-Link Flexible Arm with Some Linear Feedback Control Schemes

Abstract

In order to realize accurate positioning or tracking of flexible one-link arm, the rigid-body motions and elastic behaviors have to be controlled simultaneously. Moreover, we must reach such a goal by using only one joint-actuator. In this case, the stability analysis of the controlled system is very important, since the properties of distributed parameters of the arm can lead to potential instability. In this paper, a model of one link flexible arm rotating in horizontal plane is derived by applying Hamilton's principle, and then, the stability of the system with some linear control laws is analyzed by Mikhailov's theorem.Some interesting results are as follows:1) Conventional local PD control schemes for rigid-link robots always make the flexible system stable.2) Under the additional feedback of elastic modes by using vibration-detecting sensors, the system becomes conditionally stable. It is profoundly related to the location of the sensor and gain tuning.