Retrospective cost adaptive control of a planar multilink arm with nonminimum-phase zeros

We address the problem of adaptive command following and disturbance rejection for a nonlinear planar multilink mechanism interconnected by torsional springs and dashpots. We consider a nonlinear multilink mechanism where a control torque is applied to the hub of the multilink mechanism, and the objective is to control the angular position of the tip, which is separated from the hub by N links. In this paper, we derive the nonlinear equations of motion for the N link mechanism. We linearize these equations of motion and demonstrate that such systems have nonminimum-phase zeros when the control torque and angular position sensor are not colocated. To control this mechanism, we use a retrospective cost adaptive controller, which is effective for nonminimum-phase systems provided that you have an estimate of the nonminimum-phase zeros. We consider both command following and disturbance rejection problems, where the spectrum of the commands and disturbance are unknown.