Performance and aliasing analysis of multi-rate digital controllers with interlacing

This paper is concerned with multi-rate digital control with interlacing. The multi-rate controller is designed from a single fast-rate controller by implementing slow-mode components of the controller at a slow rate. The slow mode part of the controller is further decomposed to several elements to interlace: i.e., different elements are updated at different fast sampling time instances. The objective of multi-rate control with interlacing is to reduce the amount of real-time computation. This paper addresses two issues due to slow rate implementation of the slow-mode components: performance degradation and signal aliasing. The multi-rate control system is a linear periodically time-varying (LPTV) system. Using a lifting approach, the frequency response of the multi-rate system is represented by a frequency domain matrix. This matrix provides the information to quantify the aliasing and the distortion effect in the multi-rate system. Finally, as an example of multi-rate control with interlacing, track-following control for hard disk drive is considered. In particular, two different multi-rate controller structures are studied: series structure and parallel structure. Performance and aliasing analysis is presented for both the series and parallel structures.