A Robust Data-Driven Controller Design Methodology With Applications to Particle Accelerator Power Converters

The analysis, identification and control of periodic systems has gained increasing interest during the last few decades due to the increased use of dynamical systems that exhibit periodic motion. The vast majority of these studies focus on the analysis and control problem for a known state-space formulation of the linear time-periodic (LTP) system. On the other hand, there are also some studies that focus on data-driven identification of LTP systems with unknown state-space formulations. However, most of these methods provide numerical estimates for the harmonic transfer functions (HTFs) of an LTP system that are extremely difficult to work with during controller design. The goal of this paper is to provide a simple controller design methodology for unknown LTP systems by utilizing so-called HTFs estimates. To this end, we first build a mathematical basis of LTP controller design for known LTP systems using the Nyquist diagrams and analytically derived HTFs. We propose a new methodology to design P-, PD- and PID-type controllers for LTP systems using Nyquist diagrams and the eigenlocus of the HTFs. Having established the HTF-based controller design procedure, we extend our methodology to unknown LTP systems by presenting a new sum-of-cosine signal-based data-driven system identification method. We show that the proposed data-driven controller design method allows estimation of the HTFs and it provides simple tools for optimizing certain time-domain performance metrics. We provide numerical examples for both known and unknown LTP system cases to illustrate the performance of the proposed controller design methodology.

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A data-driven approach to model-reference control with applications to particle accelerator power converters

Control Engineering Practice ◽

10.1016/j.conengprac.2018.10.007 ◽

2019 ◽

Vol 83 ◽

pp. 11-20 ◽

Cited By ~ 7

Author(s):

Achille Nicoletti ◽

Michele Martino ◽

Alireza Karimi

Keyword(s):

Power Converters ◽

Particle Accelerator ◽

Data Driven ◽

Model Reference ◽

Model Reference Control ◽

Data Driven Approach

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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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Gain-Preserving Data-Driven Approximation of the Koopman Operator and Its Application in Robust Controller Design

Mathematics ◽

10.3390/math9090949 ◽

2021 ◽

Vol 9 (9) ◽

pp. 949

Author(s):

Keita Hara ◽

Masaki Inoue

Keyword(s):

Controller Design ◽

Internal Model Control ◽

Feedback Controller ◽

Data Driven ◽

Koopman Operator ◽

Plant System ◽

Dimensional Approximation ◽

Model Control ◽

Data Driven Modeling ◽

L2 Gain

In this paper, we address the data-driven modeling of a nonlinear dynamical system while incorporating a priori information. The nonlinear system is described using the Koopman operator, which is a linear operator defined on a lifted infinite-dimensional state-space. Assuming that the L2 gain of the system is known, the data-driven finite-dimensional approximation of the operator while preserving information about the gain, namely L2 gain-preserving data-driven modeling, is formulated. Then, its computationally efficient solution method is presented. An application of the modeling method to feedback controller design is also presented. Aiming for robust stabilization using data-driven control under a poor training dataset, we address the following two modeling problems: (1) Forward modeling: the data-driven modeling is applied to the operating data of a plant system to derive the plant model; (2) Backward modeling: L2 gain-preserving data-driven modeling is applied to the same data to derive an inverse model of the plant system. Then, a feedback controller composed of the plant and inverse models is created based on internal model control, and it robustly stabilizes the plant system. A design demonstration of the data-driven controller is provided using a numerical experiment.

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