Pid Controller Tuning Using The Magnitude Optimum Criterion Advances In Industrial Control

While revolutionary for its time, the ZN method has a fundamental flaw: it is designed to provide a "quarter amplitude decay" ratio. This means that after a setpoint change or a disturbance, the process variable oscillates such that each peak is a quarter of the height of the previous one. In many modern applications, particularly in motion control and high-speed manufacturing, this level of oscillation is unacceptable. It results in:

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. While revolutionary for its time, the ZN method

The following chapters unpack the theory, the recipes, and the industrial case studies that have transformed a frequency‑domain ideal into a shop‑floor reality. Welcome to the quiet revolution of PID tuning—where flat magnitude meets robust performance. It results in: For a perfect system, $M(s)$

The core principle of the MO criterion is to design a controller that keeps the magnitude of the closed-loop frequency response as close to unity as possible over the widest possible frequency range. By making physical systems have inertia and delays