Bounded tracking for non-minimum phase nonlinear systems with fast zero dynamics
In this paper, we derive tracking control laws for non-minimum phase nonlinear systems with both fast and slow, possibly unstable, zero dynamics. The fast zero dynamics arise from a perturbation of a nominal system. These fast zeros can be problematic in that they may be in the right half plane and may cause large magnitude tracking control inputs. In this paper, we combine the ideas from some recent work of Hunt, Meyer and Su with that of Devasia, Chen and Paden on an asymptotic tracking procedure for non-minimum phase nonlinear systems. We give (somewhat subtle) conditions under which the tracking control input is bounded as the magnitude of the perturbation of the nominal system becomes zero. Explicit bounds on the control inputs are calculated for both SISO and MIMO systems using some interesting non-standard singular perturbation techniques. The method is applied to a suite of examples, including the simplified planar dynamics of VTOL and CTOL aircraft.