Nonlinear Dynamics

, Volume 93, Issue 2, pp 629–642 | Cite as

Active control of large-amplitude vibration of a membrane structure

  • Xiang Liu
  • Guoping Cai
  • Fujun Peng
  • Hua Zhang
Original Paper


This paper studies active control of large-amplitude vibration of a membrane structure with piezoelectric actuators. First, dynamic equation of large-amplitude vibration of the membrane structure is established based on the von Karman’s large deformation assumption. Next, a four-mode nonlinear model is obtained by applying Galerkin decomposition to the nonlinear dynamic equation. Then, a model reference adaptive controller is designed to suppress the large-amplitude vibration of the membrane structure, and the stability of the controller is proven by Lyapunov’s stability theory. Finally, numerical simulations are carried out to verify the validity of the studies in this paper. Simulation results indicate that the model reference adaptive controller given in this paper can suppress the large-amplitude vibration of the membrane structure effectively; this adaptive controller is robust to modeling errors, and it is also more robust than the classical velocity feedback controller in the presence of actuator disturbance and sensor disturbance.


Membrane structure Large-amplitude vibration Active vibration control Model reference adaptive control 



This work is supported by the Natural Science Foundation of China [Grant Number 11772187] and the Natural Science Foundation of Shanghai [Grant Number 16ZR1436200].


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Engineering Mechanics, State Key Laboratory of Ocean EngineeringShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China
  2. 2.Shanghai Institute of Aerospace System EngineeringShanghaiPeople’s Republic of China

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