Distributed piezoelectric vibration control for a flexible-link manipulator based on an observer in the form of partial differential equations

This paper mainly focuses on designing a distributed observer-based controller for a flexible-link manipulator bonded with piezoelectric actuators. The dynamic model of the link can be taken as an Euler-Bernoulli beam and takes on the form of partial differential equations (PDEs). The proposed observer, which is proven exponentially stable, has the ability to estimate infinite dimensional states, and only the boundary practical measurement values are needed. A novel distributed observer-based controller is subsequently developed to make the joint position track a desired trajectory and rapidly regulate vibrations on the whole beam, which is the main contribution of the paper. The closed-loop system is guaranteed exponentially stable by theoretical analysis and its favorable performance is demonstrated by numerical simulations.