Tradeoffs for Multi-Rate Controller Design and Exact Comparisons With Single-Rate Control

In [2] it was shown that, for many specifications of engineering interest, linear controller design is a convex optimization problem. For a simple plant, and for two robustness measures and an RMS noise merit figure, Barratt and Boyd used convex optimization in [4] to compute performance trade off curves showing the best performance achievable with any linear singlerate digital controller. In this paper show how the theory of multi-rate lifts and convex optimization can be used to calculate linear multi-rate performance tradeoff curves for the same plant considered in [4]. The performance differences that can be obtained with multi-rate sampling are exposed, and a simple exact comparison between multi-rate and single-rate sampling is possible.