A Cascade-Formed Accurate Quasi-PR Controller Realization by Pole-Zero Placement

Abstract

PR controller has been widely researched in various control systems for its robustness and simplicity. However, a traditional PR controller with relatively small integral gain, used for higher-order harmonics to keep stability, will cause increases in magnitudes, and decreases in phase around resonant frequency, and jeopardize stability. These all call for a more precise realization of PR controller. This paper proposes a cascade-formed PR controller realization method, which proves to realize PR controller more accurately even with a relatively small integral gain. The method is to decompose a PR controller into multiple independent PR units, and each PR unit is realized by mapping PR controller's parameters to its pole and zero positions. The distance between a pole-zero pair is found related to frequency characteristic error and is restricted accordingly to limit the error. Comprehensive comparisons of PR controllers realized by cascade form and the traditional parallel form have been conducted theoretically and experimentally, verifying that the cascade realization method is more accurate.