Control of delayed recycling systems with an unstable pole at forward path

Unstable time delay system and recycling system pose a challenge problem in their own. When unstable time delay system have recycle the control problem becomes even more difficult. A control methodology for these systems is proposed in this paper. The strategy is based on the observation that if some internal system were available, then it would be possible to decouple the backward dynamics and then a feedback controller could be designed for the forward dynamics. The key for this strategy to be carried out is the asymptotic observer-predictor proposed to estimate the required internal signals. Necessary and sufficient conditions to assure convergence of this observer are given. Then, the strategy is complemented by using a PID controller with two degree of freedom in order to track step input references. Robustness to delay uncertainty is also discussed.