Stabilization and control of delayed recycling high order systems with one unstable pole at the direct path

In this work the stabilization and control of delayed recycling systems is addressed. Recycling systems are characterized by possessing two main paths, named the direct (feedforward) and the recycling (feedback) paths. Such class of systems reuse the energy and/or the partially processed matter increasing the efficiency of the overall process. A control methodology is proposed for the stabilization and control of this kind of system. The particular class of systems addressed here contains one unstable pole, m stable poles, a delay term and possible p left half plane (LHP) zeros in the direct path and a delayed stable subsystem in the recycling path. The strategy is based on an asymptotic observer-predictor to estimate the required internal signals. Necessary and sufficient conditions are stated in order to guarantee the stabilization of the proposed scheme, achieving step tracking and rejection.