A dynamic controller synthesis methodology for negative imaginary systems using the internal model control principle.

Bhowmick, Parijat; Kurawa, Suleiman; Kannan, Somasundar; Lanzon, Alexander

Abstract

This paper proposes a new controller design methodology for stable and minimum-phase Negative Imaginary (NI) systems relying on the classical Internal Model Control (IMC) principle. The closed-loop stability of the proposed scheme depends only on the DC loop gain, which is theoretically justified by the feedback stability results of the NI theory. The main objective is to design the Youla parameter of an IMC scheme, which has been cast as a Negative Imaginary (NI) controller synthesis problem. Two different methodologies have been proposed. A frequency-domain IMC design approach is first presented, which depends on solving a constrained, linear, least-square estimation problem. Then, an LMI-based methodology is developed, which can be solved by the commercially available SDP solver packages. An in-depth simulation case study on the vibration attenuation problem of a lightweight cantilever beam (a potential application of the NI theory) was carried out to demonstrate the usefulness of the NI-based IMC design methodology. Finally, the simulation results were experimentally validated on a custom-made vibration suppressor to confirm the feasibility of the proposed scheme.

Citation

BHOWMICK, P., KURAWA, S., KANNAN, S. and LANZON, A. 2024. A dynamic controller synthesis methodology for negative imaginary systems using the internal model control principle. Automatica [online], 164, article number 111621. Available from: https://doi.org/10.1016/j.automatica.2024.111621

• Journal Article Type: Article
• Acceptance Date: Feb 22, 2024
• Online Publication Date: Apr 4, 2024
• Publication Date: Jun 30, 2024
• Deposit Date: May 9, 2024
• Publicly Available Date: Apr 5, 2025
• Journal: Automatica
• Print ISSN: 0005-1098
• Electronic ISSN: 1873-2836
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 164
• Article Number: 111621
• DOI: https://doi.org/10.1016/j.automatica.2024.111621
• Keywords: Negative imaginary systems; Vibration control; DC-gain; Positive feedback; Internal model control; LMIs; Dynamic controller synthesis
• Public URL: https://rgu-repository.worktribe.com/output/2302928