Exponential Stability and Design of Sensor Feedback Amplifiers for Fast Stabilization of Magnetizable Piezoelectric Beam Equations

• 成果类型: Article
• 署名作者: Ozer, Ahmet Ozkan; Aydn, Ahmet Kaan; Emran, Rafi
• 署名单位: Western Kentucky University; University System of Maryland; University of Maryland Baltimore County; New Jersey Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3462917
• 发表日期: 2025
• 页码: 1374-1379
• 关键词: Feedback amplifiers; STABILITY; control theory; mathematical models; oscillators; Closed loop systems; State feedback; Distributed parameter systems; feedback stabilization; intelligent materials; Lyapunov approach; maximal decay rate

摘要

The dynamic partial differential equation model governing longitudinal oscillations in magnetizable piezoelectric beams exhibits exponentially stable solutions when subjected to two boundary state feedback controllers. An analytically established exponential decay rate by the Lyapunov approach ensures the stabilization of the system to equilibrium, although the actual decay rate could potentially be improved. The decay rate of the closed-loop system is highly sensitive to the choice of material parameters and the design of the state feedback amplifiers. This article focuses on investigating the design of state feedback amplifiers to achieve a maximal exponential decay rate, which is essential for effectively suppressing oscillations in these beams. Through this design process, we explicitly determine the safe intervals of feedback amplifiers that ensure the theoretically found maximal decay rate, with the potential for even better rates. Our numerical results reaffirm the robustness of the decay rate within the chosen range of feedback amplifiers, while deviations from this range significantly impact the decay rate. To underscore the validity of our results, we present various numerical experiments.