The analysis of gain selection in adaptive backstepping motion control

Traditionally controller and estimator gains are chosen ad hoc in adaptive control designs as long as the control objectives are achieved. This paper considers motor position and velocity control problems and provides some analysis and guidelines for gain selection. Specifically, the authors focus on an adaptive nonlinear backstepping motion control algorithm for motor position and velocity command tracking. They 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, they also make the connection between the gain selection and the overall motion control system convergence rate both qualitatively and quantitatively