Stabilisation of first-order plus dead-time unstable processes using PID controllers

The problem of stabilising first-order plus dead-time unstable processes using PID controllers is considered. The D-partition technique is applied to characterise the stability domain in the space of system and controller parameters. Moreover, analytical expressions are derived for describing the stability domain boundaries. These analytical expressions can be used to construct the complete set of stabilising PID controller parameters for open-loop unstable time-delay processes. They can also be used to investigate the effect of time delay on the stabilisability of the process.