A Design Technique for Multirate Linear Systems

In this paper, a design technique for multirate linear digital control systems is described. This technique takes into account all the sampling rates involved in the system and generates a multirate system that mimics the dynamics of a desired single-rate closed-loop system. The desired closed-loop system is referred to as an ideal linear time-invariant single-rate system (ISRS) since it operates at the fastest sampling rate present in the system. The multirate system is designed to achieve state matching, at the fastest rate, with the ISRS and to exhibit a ripple-free response with zero steady-state error in response to a step reference signal. Unlike prior work in the literature, which is applicable only to static-feedback ISRS, the proposed state-space design procedure is applicable for any dynamic-feedback ISRS. The proposed design is successfully implemented on a hard-disk-drive platform for the seek control of the read-write arm. A representative sample of the experimental results are shown and discussed to highlight the proposed multirate technique.