On the Analysis and Control of a Flexible link robot

In this article, a mathematical model for controlling the end tip position of a single flexible link robot arm is presented. The model is derived using a finite modal approximation for the solution of the Euler-Bernoulli beam equation, with the clamped-free boundary conditions. The link is bounded to move on the horizontal plane, so that the gravity effects on the link are neglected. An appropriate output function is chosen for properly controlling the system, called, the negative mode reflected output. Passivity concepts are applied for properly stabilizing the system allowing the application of a simple control approach for controlling the tip position. Simulations of the controlled system show the obtained results.