Quantitative synthesis of uncertain non-linear feedback systems with non-minimum, phase inputs†

This research was supported in part by the Air Force Office of Scientific Research under Grant 76-2946D and the National Science Foundation under Grant ENG-7825848 at the University of Colorado.

Abstract

In a recent exact synthesis technique for feedback systems with highly uncertain non-linear plants, the non-linear plant set is replaced by an equivalent linear time invariant (lti) plant set. If it exists, the solution to the resulting Hi problem also solves the non-linear problem. However, when the system inputs are non-minimum-phase, the lti plant equivalents have both zeros and poles in the right half-plane (rhp). The feedback capabilities of such lti systems are extremely limited under the constraint of lti system stability, BO there is very little chance of a solution. Using Schauder's fixed point theorem, it is shown that here one must deliberately design for system poles in specific regions in the rhp. This defiance of conventional notions is guaranteed possible and permits a satisfactory solution for a large class of uncertain non-linear plants.

Notes

This research was supported in part by the Air Force Office of Scientific Research under Grant 76-2946D and the National Science Foundation under Grant ENG-7825848 at the University of Colorado.