4.8 Article

Synthesizing All Filtered Proportional-Integral and PID Controllers Satisfying Gain, Phase, and Sensitivity Specifications

Journal

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
Volume 70, Issue 3, Pages 2939-2947

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIE.2022.3174308

Keywords

Automatic loop shaping; feedback control design; filter design; gain margin; phase margin; proportional-derivative (PD); proportional-integral (PI); proportional-integral-derivative (PID); sensitivity

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This article presents a method for calculating all proportional-integral/proportional-derivative controllers with a given order low-pass filter that meet the requirements of gain-phase margins and sensitivity. The method is explicit and involves solving a set of polynomial and linear equations. The article also discusses extending the method to design proportional-integral-derivative or cascaded controllers with a low-pass filter when a minimum value of one of the controller components is given.
This article presents a method for calculating all the proportional-integral/proportional-derivative controllers with a low-pass filter of a given order, which satisfy gain-phase margins and sensitivity (or complementary sensitivity) specifications. The method is explicit and requires solving a set of a polynomial and two linear equations. It is shown how to extend the method to design all the proportional-integral-derivative or cascaded controllers with a low-pass filter assuming that a minimum value of one of the controller components is given.

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