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The model predictive control for structural vibration with local nonlinearity. (Chinese. English summary) Zbl 1438.70022

Summary: In this paper, for the problem of structural vibration control with local nonlinearity, a dynamic explicit recursive formulation in time-domain for locally nonlinear structures is derived by using the Newmark-\(\beta \) method firstly. Then, based on this formulation, a novel model predictive control algorithm for vibration of the locally nonlinear structure is proposed, which is followed by the establishment of the predictive model for this problem. It should be pointed out that the nonlinear component in the control process can be dealt with using the model linearization method. Besides, to avoid a full iteration of all dimensions for the nonlinear dynamic equations when the initial state values in each predictive period need to be computed, an explicit dimension-reduced iteration method in time-domain for locally nonlinear structures is also derived, which can greatly improve the online computation efficiency. Lastly, numerical simulations of a local nonlinear mass-spring system subjected to a harmonic excitation and an adjacent frame building with viscous dampers subjected to seismic excitation show that the proposed method is quite accurate and satisfactory in control performance.

MSC:

70Q05 Control of mechanical systems
93B18 Linearizations
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