Digital backstepping control of induction motors

The problem of controlling induction motors is generally dealt with in the continuous-time context (using different nonlinear control approaches). The obtained continuous-time nonlinear regulators can not be exactly implemented using today´s digital equipments. Therefore, approximate versions, obtained through discretization and ZOH, are resorted to. However, the performances of these digital regulators may rapidly deteriorate if the sampling period is not sufficiently small. In this paper, a quite different alternative is considered to get digital regulators. First, the model of the controlled system is discretized using the delta operator formalism. Second, the (continuous-time) backstepping design technique is adapted to get a discrete-time regulator. Then, an upper bound on the sampling period is formally established so that the (discrete-time) closed-loop control system remains globally asymptotically stable and achieves the tracking performances it is designed for. On the other hand, the ZOH digital regulator thus obtained turns out to be less sensitive to the value of sampling period than digital the regulator designed by the continuous-time backstepping technique.