The effect of unmodeled flexible dynamics in discrete-time model reference adaptive control of a flexible single-link robot

This paper addresses the feasibility of applying discrete-time model reference adaptive control (MRAC) techniques to the flexible link of robot mechanisms. The method of separation of variables is used to represent the deflection of the link. The nonlinear model is obtained using a Lagrangian equation, and the candidate frequencies and the associated mode functions are obtained using Bernoulli-Euler beam theory. By considering the effect of flexibility as an internal disturbance torque acting on the rigid body motion of the system, a discrete-time MRAC is determined for a single non-rigid link. Considering the effect of unmodeled flexible dynamics, this approach is investigated by computer simulation.