The first step is to identify the process model. For most industrial applications, the process can be approximated by a First Order Plus Dead Time (FOPDT) model or a Second Order Plus Dead Time (SOPDT) model. $$G_p(s) = \fracK_p e^-sLTs + 1$$ Where:
For too long, industrial practitioners have defaulted to Ziegler-Nichols tuning out of familiarity, not superiority. The Magnitude Optimum criterion offers a mathematically sound, practically verified, and increasingly accessible alternative that delivers superior robustness, minimal overshoot, and excellent disturbance rejection.
Classical MO was derived for stable, self-regulating processes. New research extends the criterion to:
This article explores the theory, application, and industrial significance of the Magnitude Optimum (MO) criterion, illustrating why it has become a cornerstone of advanced control strategies.
For a perfect system, $M(s)$ should equal 1 for all frequencies. However, physical systems have inertia and delays, making this impossible. The Magnitude Optimum criterion minimizes the difference between the magnitude of $M(j\omega)$ and 1. Specifically, it approximates the magnitude squared $|M(j\omega)|^2$ as a series expansion.
Kessler's PI tuning rules for the Magnitude Optimum are: