Periodic Control of Linear Time-Invariant Systems

Abstract

A question that has intrigued many engineers (and indeed is still the subject of ongoing research) is whether one could benefit from using time-varying linear controllers, or a more tractable sub-family of periodically time-varying digital controllers on systems which are themselves time-invariant. Similar questions have been raised with regard to continuous-time linear controllers. It has been shown that periodic controllershave interesting properties including improved gain and/or phase margins relative to linear time-invariant control. Usually this is accomplished via zero placements. We have seen in Chapter 8 that non minimum phase zeros limit the gain and phase margin. Hence, if the use of periodic control results in shifting the zeros to a harmless place, the constraints on the gain/phase margins can be mitigated. Tools for achieving this will be developed in this chapter.