Output tracking using dynamic sliding mode techniques

TLDR: A higher order generalization of the traditional first order sliding mode reachability condition is proposed which enables the designer to transfer non-minimum phase characteristics from the state responses to the artificial output (i.e., sliding function) responses if the zero dynamics has no finite escape time.

Abstract: Output tracking for a class of nonlinear SISO systems is considered whereby the output tracking error and its derivatives to some order are driven to a neighbourhood of the origin whilst the states and input remain bounded. A higher order generalization of the traditional first order sliding mode reachability condition is proposed. This enables the designer to transfer non-minimum phase characteristics from the state responses to the artificial output (i.e., sliding function) responses if the zero dynamics has no finite escape time. It is shown that this non-minimum phase artificial output behaviour may be curbed by defining a second control policy which becomes effective within a neighbourhood of the sliding surface. Possible problems with singularity are also addressed. The ball and beam system is used to illustrate the design method. © 1997 by John Wiley & Sons, Ltd.