Higher-order singular perturbations for control design with application to the control of induction motors

We present a new approach for the control design of a two-timescale dynamical system. When using standard singular perturbations, the controller is typically designed to drive the "fast" dynamics rapidly to a steady state that has been chosen in a way that makes the "slow" dynamics behave according to the control objective. However, such a controller requires the time scales to be sufficiently separated and such a separation is sometimes impossible to achieve, resulting in degraded performance. We therefore propose to redesign this controller based on a higher-order singular perturbation analysis to gain in precision and obtain performance that are closer to the expected ones. In particular, we show the benefits of this method on the control of induction motors.