A Generalized Forced Oscillation Method for tuning Proportional Resonant Controllers

TL;DR

This paper introduces a generalized tuning method for proportional resonant controllers based on a modified forced oscillation approach, applicable to a wide range of plants without restrictions on their Nyquist diagram crossings.

Contribution

It extends the Ziegler-Nichols forced oscillation method to PR controllers, allowing for broader plant applicability and improved stability margin tuning.

Findings

Method successfully tuned PR controllers across various plant types.

Numerical examples demonstrate wide applicability and robustness.

Provides specific tuning formulas for stability margins.

Abstract

This paper proposes a tuning methodology for proportional resonant (PR) controllers by using the design philosophy of the Ziegler-Nichols forced oscillation method. Unlike such related methods that are usual for PID design, and those that have been recently proposed for PR controllers, the method in this paper is not restricted to plants whose Nyquist diagram crosses the negative real axis. It involves a feedback experiment with a relay of adjustable phase, which allows the identification of the most appropriate point of the frequency response for each class of plants. The validation of the proposed method, which includes the identification experiment and specific tuning formulas that provide appropriate stability margins for each class of plants, is performed by means of numerical examples in a large variety of plants, showing its wide applicability.