Application of discrete‐time model reference adaptive control to a flexible single‐link robot

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Abstract
This article addresses the feasibility of applying discrete‐time model reference adaptive control techniques to the flexible link of robot mechanisms. The method of separation of variables is used to represent the deflection of the link. A 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. The control algorithm is implemented for a collocated sensor and actuator system, and for a noncollocated end‐point sensor and actuator system. Results of computer simulation show the feasibility of this approach and the advantage of using an end‐point sensing system.

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