Tuning of PID controller for unstable process

Loop-shaping H^∞ controller is designed for unstable process. It is observed that the H^∞ controller for such process can be approximated with a PID controller. Moreover, we note that the `design indicator´ is a function of the normalised delay. This fact leads us to derive the direct relation between the PID controller´s parameters and the plant constants, and the results can be regarded as a PID tuning rule for unstable process. The tuning rule has only one parameter which reflects the trade-off between performance and robustness of the closed-loop system. Simulation results show that it works for first-order delayed unstable process with the normalised delay smaller than unity