A numerical study on controlling a nonlinear multilink arm using a retrospective cost model reference adaptive controller

We address the model reference adaptive control problem for a nonlinear multilink planar arm mechanism, where links are interconnected by torsional springs and dashpots, a control torque is applied to the hub of the mechanism, and the objective is to control the angular position of the last link. It is known that the linearized transfer function for the multilink planar arm has nonminimum-phase zeros when the control torque and angular position sensor are not colocated. We use a retrospective cost model reference adaptive control (RC-MRAC) algorithm, which is effective for nonminimum-phase systems provided that the nonminimum-phase zeros are known.We demonstrate that RC-MRAC effectively controls the multilink arm for a range of reference model command signal amplitudes and frequencies.