Conditions for removing intersample ripples in multirate control

Multirate systems arise when signals of interest are sampled at different rates. Measurements from chemical processes are typically available at different sampling rates. For example, composition estimates in a distillation column are available at a much slower rate than flow, temperature and pressure measurements. Multirate systems pose a challenging problem due to several reasons such as increased complexity design, time-varying nature, etc. Systems consisting of fast-rate control moves and slow-sampled outputs are a common scenario in chemical processes and of practical interest. Traditionally, inferential techniques based on secondary measurements have been used to design the fast-rate input moves. Lifting techniques conveniently transform multirate systems to single-rate lifted systems with increased dimensionality. Controllers designed using lifting techniques require that certain causality constraints are satisfied. We show firstly, that intersample ripples can arise in the closed-loop output of a multirate system as a result of non-uniform gains of the discrete lifted system and inverse lifting. Secondly, we present conditions on the controller gains to avoid intersample ripples.