An approach to multirate control

Minimum phase continuous time plants of relative degree 2 or more are known to have nonminimum phase discrete time zeros under fast sampling. Remedies such as generalized sample and hold functions are known to produce poor intersample behaviour. Building on the work of Francis and Georgiou this paper proposes a multirate control scheme that requires plant compensation at a rate faster (generically by a factor of two) than the output sampling rate. The novelty of this work is the enunciation and analysis of a new class of up-samplers that alleviate poor intersample behaviour caused by previously proposed up-samplers. A major result of this paper shows that up-samplers that simply “hold” the new samples at the value of the immediate past sample value of the up-sampler input, suffice to remove the nonminimum phase problem for all plants that are minimum phase in continuous time