Discrete implementation of sliding mode controllers satisfying accuracy level specifications

Exploiting a particular system setting, this paper discusses approaches for the design of sliding mode control laws based on a sampling time dependent specified accuracy. It is well-known that this accuracy is ensured by the implementation of a control law of appropriate sliding order. However, it turns out, that in a discrete time framework this also may be achieved by a sliding mode controller of lower order enhanced by a disturbance estimation scheme. In this context the combination of a 2nd-order sliding mode control with a first-order disturbance estimator is analyzed in particular. The achieved performance is evaluated in a numerical example as well as in a practical experiment.