A Universal Interpretation of Three Types of Resonator-Based Controllers

It is well credited that generalized active disturbance rejection controller (GADRC), proportional resonant controller (PRC) and quasi proportional resonant controller (QPRC) are proficient in suppressing fast varying sinusoidal disturbances or tracking fast varying sinusoidal signals respectively. Establishing the equivalence analysis criterion is beneficial to evaluate or compare the performance of GADRC, PRC and QPRC. Thus, we establish the equivalence analysis criterion by exploring the equivalence among GADRC, PRC and QPRC in the context of the three-phase voltage system. To be more specific, the GADRC, PRC and QPRC can be interpreted as a class of proportional integral integral-integral (PII
²
) controllers with a filter by mathematical reasoning. The equivalence analysis can provide parameter tuning of the three controllers. The differences and similarities among them can be described by
$\nu $
gap metric and Bode diagrams by MATLAB/Simulink.