A Generalized Interpretation of Three Types of Disturbance-Based Controllers for Perturbed Integral Systems in Frequency Domain

Abstract

It is well recognized that two-degree-of-freedom controllers are more proficient than one-degree-of-freedom controllers in overcoming uncertainty and large parameter variation. Establishing the equivalence analysis criterion among different classes of two-degree-of-freedom controllers to evaluate or compare the performance of controllers can stimulate more advanced two-degree-of-freedom controllers. We establish the equivalence analysis criterion by exploring the equivalence among proportional (P) with full-order extended state observer (FESO), P with reduced-order extended state observer (RESO) and proportional-integral (PI) with reduced-order proportional-integral observer (RPIO) in the context of a class of second-order, cascade integral systems. The equivalence analysis results are also suitable for high-order cascade integral systems. Moreover, P with FESO, P with RESO and PI with RPIO can be interpreted as a class of the generalized PI controllers, which can provide parameter tuning guidelines for the traditional PI controllers. Furthermore, the parameters of PI with RPIO cascade control can be entirely applied to tune the parameters of P with FESO cascade control and P with RESO cascade control and vice versa. Lastly, simulations in high speed permanent magnetic synchronous machine starter are provided to illustrate the theoretical results in this brief.