Observer-based scheme for the control of high order systems with two unstable poles plus time delay

This paper deals with the problem of the stabilization and control of linear time invariant high order systems with two unstable real poles plus time delay. A simple observer-based controller is designed in order to achieve a stable behavior of the closed-loop system. Necessary and sufficient conditions for the existence of the proposed control structure are stated. Hence, only four proportional gains and the model of the plant are enough to obtain a stable response of the delayed system. Moreover, a robustness analysis is presented in order to compute the maximal uncertainty bound accepted for the delay term. In addition, a two degree of freedom proportional-integral control action is implemented in order to track step references and to reject step disturbances. The achieved performance of the proposed control strategy is illustrated by mean of numerical simulations.