An approach for calculating all stable PID parameters for time delay systems with uncertain parameters

There exists a large number of PID tuning rules for LTI systems. However, these rules often use time delay approximations and ignore parameter uncertainties. This work updates the classical parameter space approach to an one step PID tuning approach to guarantee robust stability for LTI time delay systems with explicit consideration of uncertainties in the plant parameters and the time delay. The basic idea is to calculate how the root boundaries changes due variation of system parameters. Bands of root boundaries are determined by this analysis. The challenging task of robust stability of time delay systems is converted to an easier minimum/maximum search to estimate the borders of the root boundary bands. The presented method satisfies robust stability with only small conservatism.