Analytical design of the PID-type controllers for linear plants based on the magnitude optimum criterion usually results in very good control quality and can be applied directly for high-order linear models with dead time, without need of any model reduction. This paper brings an analysis of properties of this tuning method in the case of the PI controller, which shows that it guarantees closed-loop stability and a large stability margin for stable linear plants without zeros, although there are limitations in the case of oscillating plants. In spite of the fact that the magnitude optimum criterion prescribes the closed-loop response only for low frequencies and the stability margin requirements are not explicitly included in the design objective, it reveals that proper open-loop behavior in the middle and high frequency ranges, decisive for the closed-loop stability and robustness, is ensured automatically for the considered class of linear systems if all damping ratios corresponding to poles of the plant transfer function without the dead-time term are sufficiently high.

The modulus optimum (MO) criterion can be used for analytical design of the PID controller for linear systems with dominant dead time. However, although the method usually gives fast and non-oscillating closed-loop responses, in the case of large dead time the stability margin gets reduced and even non-stable behavior can be observed. In this case a correction of the settings is needed to preserve the stability margin. We describe and compare two methods of design of the PID controller based on the MO criterion that for the stable first-order systems with dead time preserve the stability margin, trying to keep maximum of the performance of the original MO settings.