Negative Imaginary H2 Controller Synthesis Using Nonlinear Optimization

Mohamed A. Mabrok; Ian R. Petersen

doi:10.1109/CDC.2018.8618980

Negative Imaginary H₂ Controller Synthesis Using Nonlinear Optimization

Mohamed A. Mabrok, Ian R. Petersen

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › peer-review

1 Citation (Scopus)

Abstract

Negative imaginary (NI) systems theory has attracted considerable attention in the area of robust control of highly resonant flexible structures systems. These systems, often naturally, satisfy the NI property. In this paper, we present a control synthesis methodology for NI systems based on a nonlinear optimization techniques. In the presented method, a parametrized library of strictly negative imaginary (SNI) controllers is created and used in a standard numerical nonlinear optimization setup. The SNI controller library contains generic controllers that are widely used in the control highly resonant flexible structures such as positive position feedback (PPF) and integral resonant control (IRC). Sequential quadratic programming (SQP) techniques are used in the numerical optimization problem. The synthesized controller satisfies the SNI property as well as optimizing H-{2} performance. As an application of these results, an example of controlling an Euler-Bernoulli beam with piezo-electric actuator and sensor is presented.

Original language	English
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6526-6531
Number of pages	6
ISBN (Electronic)	9781538613955
DOIs	https://doi.org/10.1109/CDC.2018.8618980
Publication status	Published - 2 Jul 2018
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2018-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	57th IEEE Conference on Decision and Control, CDC 2018
Country/Territory	United States
City	Miami
Period	17/12/18 → 19/12/18

Access to Document

10.1109/CDC.2018.8618980

Cite this

Mabrok, M. A., & Petersen, I. R. (2018). Negative Imaginary H₂ Controller Synthesis Using Nonlinear Optimization. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 6526-6531). Article 8618980 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8618980

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title = "Negative Imaginary H2 Controller Synthesis Using Nonlinear Optimization",

abstract = "Negative imaginary (NI) systems theory has attracted considerable attention in the area of robust control of highly resonant flexible structures systems. These systems, often naturally, satisfy the NI property. In this paper, we present a control synthesis methodology for NI systems based on a nonlinear optimization techniques. In the presented method, a parametrized library of strictly negative imaginary (SNI) controllers is created and used in a standard numerical nonlinear optimization setup. The SNI controller library contains generic controllers that are widely used in the control highly resonant flexible structures such as positive position feedback (PPF) and integral resonant control (IRC). Sequential quadratic programming (SQP) techniques are used in the numerical optimization problem. The synthesized controller satisfies the SNI property as well as optimizing H-\{2\} performance. As an application of these results, an example of controlling an Euler-Bernoulli beam with piezo-electric actuator and sensor is presented.",

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Mabrok, MA & Petersen, IR 2018, Negative Imaginary H₂ Controller Synthesis Using Nonlinear Optimization. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8618980, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 6526-6531, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 17/12/18. https://doi.org/10.1109/CDC.2018.8618980

Negative Imaginary H₂ Controller Synthesis Using Nonlinear Optimization. / Mabrok, Mohamed A.; Petersen, Ian R.
2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 6526-6531 8618980 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › peer-review

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