Observer-based control for high order delayed systems with an unstable pole and a pole at the origin

Time delays in dynamical systems are challenging when trying to control them. One of the most common techniques consists in estimating one or more signals of interest before they are delayed, in order to use them in the control stage. In this work, an observer-based control strategy for unstable linear systems with a pole at the origin and delay is suggested. Also, the proposed observer is extended to be used in the case of a high order unstable delayed system. Likewise, the conditions to ensure the existence of the proposed observer-predictor are presented. A methodology is introduced to obtain the observer parameters. The proposed observer scheme makes use of a Proportional-Integral-Derivative control that makes it possible to ensure the tracking of step-type references and the rejection of disturbances of the same type in the closed-loop system.