Observer-PID stabilization strategy for unstable first-order linear systems with large time delay

This work considers the stabilization and control of a class of unstable first-order linear systems subject to a relatively large input-output time delay. As a first step, a particular observer scheme is proposed in order to predict a specific internal signal in the process. Conditions to ensure the adequate prediction convergence of the signals are formally stated. In a second step, the internal predicted signal is used to implement classical P, PI, and PID controllers providing stability conditions for the resulting closed-loop system. The proposed control strategy allows one to address time delays as large as four times the unstable time constant of the open-loop system, in contrast with the reported related literature where the maximal bound has been stated until now as two times the unstable time constant of the open-loop system. The proposed observer-based control structure considers also the tracking of step reference signals and the rejection of input step disturbances.