Finite spectrum assignment control of unstable time delay processes with relay tuning

In this paper, the finite spectrum assignment (FSA) control of open-loop unstable time delay processes consisting of a single unstable pole is considered. Astrom's relay autotuning is extended to this class of processes. The conditions for the existence of limit cycles are established using the point transformation method. From the relay-induced input-output signals, the parameters of the model are estimated based on which the FSA controller can be designed. There are only three closed-loop specification parameters necessary from the user, and these are both classical and intuitive. It is also shown that the so autotuned FSA system is practically stable in the face of perturbations in the process dynamics. Simulation examples are included for illustration.