Analog frequency correction

This article outlines the basic principles of analog frequency correction.

Calculating a frequency-domain control system involves working from the gain and phase curves of the open-loop transfer function (assembly: actuator – process – sensor) and striving to obtain a satisfactory shape for the closed-loop frequency response.

Based on the frequency response of a well-tuned second-order servo (damping z = 0.43, corresponding to a resonance factor Q = 2.3 dB), we aim to create a closed-loop corrector that will give a flat frequency characteristic from low frequencies onwards, with a resonance factor of around 2.3 dB, before dropping off towards high frequencies.

Using the approximate equivalences between the time and frequency properties of a servo system (see General principles of correction , in this Automatic section), we translate frequency specifications into temporal terms and vice versa.

The transition from open-loop frequency response, $T\left(\text{jω}\right)$ , to closed-loop frequency response, $F\left(\text{jω}\right)$ , uses Black's abacus (see Frequency Study of Continuous Systems). , in this section Automatic).