Nonlinear control system design via dynamic order reduction

In this paper we present a design scheme for output tracking of nonlinear systems that are subject to regular perturbations. We show that applications of singular perturbation theory to the input-output feedback linearization technique provides a systematic method to identify the slow “dominant” states and fast “negligible” states. Similar to the backstepping design technique, a suitable state variable is converted into a “control like” variable which in the steady state is forced to approach the desired tracking control law for the reduced order system. We show that this design achieves stable approximate tracking of reasonable reference trajectories for nonlinear systems that are “dominantly” minimum phase. The order of approximation can be arbitrarily improved by addition of correction terms in the control law. The main advantage of this approach is that the design is often performed for a much simpler model which is linear in the new control variable and describes the dominant part of the original system by ignoring some of the fast states that are forced to have little effect on the steady state performance