Stability analysis of a single-link flexible arm driven by a motor of speed reference type

Abstract

The stability analyses for motion and vibration control of a single-link flexible arm having a tip payload are investigated using a linear distributed parameter model. The controller design in this paper includes the joint angle proportional–integral–derivative (PID), the bending strain (S) and bending strain integration (SI) feedbacks, and their combinations. The paper presents a new method applying the properties of an irrational passive transfer function and root locus to study the effect of various feedbacks on the infinitely many open loop poles, necessary and sufficient conditions in terms of the dimensionless positive gain constants are reported such that the closed-loop is asymptotically stable. The exact solutions of the infinite-dimensional closed-loop system are obtained using the infinite product formulation. Since the controller design is based on the infinite-dimensional system and is independent of system parameters, the proposed system promises stability robustness to parameter uncertainties and is also free of spillover problems. The validity of the controllers is assessed and compared with the experimental results in the existing literature.