Fully-Parameterized Fixed-Order Controller Design for <i>H</i><sub>∞</sub> Loop Shaping Method Using Frequency Responses -Extension to MIMO Systems-

This paper presents a fixed-order [Formula: see text]∞ controller design based on linear matrix inequalities for multi-input–multi-output systems. The main difficulty in the development of a fixed-order controller design is that the associated solution set of the problem is defined in a non-convex cluster, and that makes the problem computationally intractable. The convex inner approximation is used to deal with this non-convexity. The proposed controller design approach is applied to some elegant numerical problems taken from various previous works. To show the effectiveness of the proposed method, the full-order [Formula: see text]∞ controller and fixed-order controllers are constructed for these models using the traditional method and popular toolboxes, respectively. Furthermore, in this paper, some strategies for choosing the central polynomial, which is the main conservatism of the proposed method, are discussed.

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Fixed-order loop shaping robust controller design for parametric models to damp inter-area oscillations

International Journal of Electrical Power & Energy Systems ◽

10.1016/j.ijepes.2016.12.013 ◽

2017 ◽

Vol 88 ◽

pp. 164-174 ◽

Cited By ~ 5

Author(s):

A.A. Abdlrahem ◽

R. Hadidi ◽

A. Karimi ◽

P. Saraf ◽

E. Makram

Keyword(s):

Controller Design ◽

Parametric Models ◽

Robust Controller ◽

Loop Shaping ◽

Fixed Order ◽

Robust Controller Design

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Design of Suboptimal Weight Using Frequency Responses Guaranteeing Performance Level of Controller for H∞ Loop Shaping Method

IEEJ Transactions on Electronics Information and Systems ◽

10.1541/ieejeiss.135.856 ◽

2015 ◽

Vol 135 (7) ◽

pp. 856-864 ◽

Cited By ~ 1

Author(s):

Takayuki Kubo ◽

Kazuhiro Yubai ◽

Daisuke Yashiro ◽

Junji Hirai

Keyword(s):

Performance Level ◽

Frequency Responses ◽

Loop Shaping

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Robust H∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions

Mathematical and Computational Applications ◽

10.3390/mca26010021 ◽

2021 ◽

Vol 26 (1) ◽

pp. 21

Author(s):

Ahmad Taher Azar ◽

Fernando E. Serrano ◽

Nashwa Ahmad Kamal

Keyword(s):

Design Methodology ◽

Closed Loop ◽

Complex Analysis ◽

Controller Design ◽

Filter Design ◽

Design Procedure ◽

Elliptic Functions ◽

Loop System ◽

Closed Loop System ◽

Loop Shaping

In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.

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