A different look at output tracking: control of a vtol aircraft

the aim is to build a controller such that y ( t ) tracks any prescribed reference trajectory y,(t). To avoid ambiguities in the sequel, we call (1) the input-state (IS) system (i.e. without a defined output), (2) the tracking output, and (1)(2) the input-output (Io) system. When the IO system is minimum phase, the tracking problem is easily solved (at least locally) by IO linearization (see e.g., [SI). But this simple method cannot be satisfactorily applied to a nonminimum phase system: tracking by IO linearization implies integrating the internal dynamics, which is unstable in this case. I t is important to acknowledge that the obstruction to exact trajectory tracking for nonminimum phase systems is of open-loop nature: in general a state trajectory (zr(t), ur(t)), such that h(zr(t)) = y r ( t ) , is unbounded. Since the internal dynamics is not changed by feedback, exact tracking is contingent upon finding a suitable state trajectory. One approach, for slightly nonminimum phase systems, is to approximate the system by a minimum phase one [4]. Another approach, for tracking signals generated by an exosystern, can be found in 161. These methods concentrate on properties of the IO system without any attempt to investigate and use structural properties of the IS system. In this paper we propose an alternative point of view based on the following simple remark: if we had a state tracker (i.e. a controller able to track any reference state trajectory), the output tracking would reduce to the generation of a “good” state reference, which is only an open-loop problem, and hence (hopefully)