Dynamic stabilization for a cascaded beam PDE–ODE system with boundary disturbance

We are concerned with the dynamic stabilization for a cascaded Euler–Bernoulli beam (EBB) partial differential equation (PDE)–ordinary differential equation (ODE) system subject to boundary control and matched internal uncertainty and external disturbance. State feedback stabilization of such system...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2023-06, Vol.46 (9), p.10167-10185
Main Author: Mei, Zhan‐Dong
Format: Article
Language:English
Subjects:
Boundary control
cascaded PDE–ODE system
Control theory
disturbance estimator
Euler-Bernoulli beams
Euler–Bernoulli beam equation
exponential stabilization
Feedback control
Output feedback
Partial differential equations
Stabilization
State feedback
State observers
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Summary:We are concerned with the dynamic stabilization for a cascaded Euler–Bernoulli beam (EBB) partial differential equation (PDE)–ordinary differential equation (ODE) system subject to boundary control and matched internal uncertainty and external disturbance. State feedback stabilization of such system without disturbance has been recently discussed by X.H. Wu, H. Feng (Sci China Inf Sci, 2022, 65(5): 159202). An infinite‐dimensional disturbance estimator is constructed in order to estimate the total disturbance. By compensating the total disturbance, we design a state observer to trace the state and then an estimated state and estimated total disturbance‐based output feedback control law. It is proved that the original system is exponentially stable, and other states of the closed‐loop are bounded. Some numerical simulations are presented.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9109