A higher order sliding mode controller for a class of MIMO nonlinear systems: application to PM synchronous motor control

A new robust higher order sliding mode controller is proposed for a class of MIMO nonlinear systems. The controller synthesis takes three steps: a) the higher order sliding mode problem is formulated in input-output term; b) the problem is viewed in uncertain linear context by considering uncertain nonlinear functions as bounded non-structured parametric uncertainties; c) following the optimal sliding-mode design for linear systems, a time varying manifold is designed through the minimization of a quadratic cost function over a finite time interval with a fixed final state. The control law which engenders the sliding on the time varying surface, yields the establishment of an r/sup th/ order sliding mode. In order to show that the designed controller is well-adapted for practical implementation and that all the features of linear quadratic control can be used to synthesize the controller´s gain, a controller for a permanent magnet synchronous motor is designed and implemented on an experimental set-up.