Novel systematic approach of gain selection for adaptive backstepping motion control

Traditionally, the controller gains and estimator parameters are chosen ad hoc in adaptive motion control systems to achieve the control objectives. This paper considers motor position and velocity control problems and provides novel systematic approach and analytic solution for gain and parameter selection. Specifically we focus on an adaptive nonlinear backstepping motion control algorithm for motor position and velocity command tracking. We reformulate the nonlinear motion control system as a linear time-invariant system plus a nonlinear element in the feedback loop. By this novel reformulation some of the gains appear in the linear system. Stability and convergence rate requirements for the linear system naturally lead to the selection of these gains. By this analysis we also make the connection between the gain selection and the overall motion control system convergence rate both qualitatively and quantitatively.