A fast on-line algebraic estimation of a single-link flexible arm applied to GPI control

In this article, we propose an output feedback controller of the generalized proportional integral type (GPI), combined with an on-line closed loop identification method, for the control of an uncertain flexible robotic arm with unknown mass at the tip, motor inertia, viscous friction and electromechanical constant, and including a Coulomb friction term in the motor dynamics. A fast, non-asymptotic, algebraic identification method is used to identify the unknown system parameter and update the designed certainty equivalence GPI controller. The GPI controller is designed using a two-stage design procedure entitling an outer loop, designed under the singular perturbation assumption of no motor dynamics, and subsequently an inner loop which forces the motor response to track the control input position reference trajectory derived in the previous design stage. In both, the inner and the outer loop, the GPI controller design method leads to, easily implementable, classical compensation networks whose feedforward part requires the unknown system parameters which are updated from the on-line algebraic identifier