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The Magnitude Optimum Criterion offers a mathematically elegant alternative: instead of empirically forcing a closed-loop damping ratio, it minimizes the error between the closed-loop frequency response and an ideal low-pass filter.

Perform a step test (open-loop) or a relay feedback test (closed-loop). Extract:

Practically, this results in a —the frequency response stays near 0 dB (unity gain) without peaking. This is analogous to the Butterworth filter design in signal processing.

Let us consider a standard feedback loop. The open-loop transfer function $L(s)$ is the product of the controller $G_c(s)$ and the process $G_p(s)$: $$L(s) = G_c(s)G_p(s)$$