Nonlinear Dynamic Inversion and Block Backstepping: A Comparison

Abstract

Nonlinear dynamic inversion by time scale separation (NDI) offers a quick and sim- ple design route for (full three axis) nonlinear ight control law design that yields a low complexity control law. The resulting closed loop system can be made semiglobally stable but the stability is critically dependent on the fulfillment of the time scale separation as- sumption which in general forces the inner loop (angular rates) to be considerably faster than the outer loop (velocity components). Block backstepping (BBS) is an alternative design method that does not rely on a time scale separation requirement and directly yields semiglobal stability but that involves a somewhat more complicated design procedure and resulting control law. The two methods are closely related, however, and in this paper we make a comparison of them. In particular, we show conditions under which the extra terms in the BBS control law offer (or do not offer) significant advantages over the simple NDI control law. We show this in terms of stability region, sensitivity, and robustness.