Progress on H (at Infinity) Optimal Sensitivity for Delay Systems. Part 1. Minimum Phase Plant with Input Delay. 1 Pole/Zero Weighting Function. Revised.
In this report we derive the solution of the minimal weighted sensitivity problem with 1 pole/1 zero sensitivity weighting functions for stable minimum phase rational plants with an input delay. We calculate the explicit feedback compensator and analyze its stability. Although we have a technique for approximating these compensators with proper compensators, the full description of this, along with an analysis of stability robustness will appear in a future report. Another report will also cover generalizations of this work to plants which are unstable, to plants which have right half plane zeros, and to the case of a more general sensitivity weighting function. Keywords include: Delay Systems, Compensators, Sensitivity Feedback System, and Weighting Functions.